Apparatus and method for controlling a resonator

Abstract

To provide a method and apparatus for controlling a resonator.SOLUTION: There are provided a method and apparatus for modifying or controlling a resonator connected to a signal loop having an input, an output, and a closed loop frequency response. The signal loop has a primary resonator having a primary frequency response. There is provided at least one adjustable resonator having an adjustable frequency and a secondary Q-factor. An adjustable scaling block applies a gain factor. A controller is connected to the at least one adjustable resonator and the adjustable scaling block. The controller has instructions to adjust the closed loop frequency response toward a desired closed loop frequency response by controlling the adjustable frequency of the at least one adjustable resonator and the gain factor of the adjustable scaling block.SELECTED DRAWING: Figure 1

Description

[Technical field]

[0001] The present disclosure relates to coupling of resonant structures (a primary resonator of interest and a secondary variable resonator) to modify the closed-loop characteristics of the primary resonator by tuning an element in the signal loop that also includes the primary resonator. [Background technology]

[0002] Resonant structures are common elements in many electronic circuits. These resonant structures may have fixed performance characteristics or may be tunable based on a control signal applied to the resonant structure or a physical change to the resonant structure. Resonators are deployed in all kinds of communications circuits, one example being radio frequency (RF) filters.

[0003] RF filters with moderate to high Qs, on the order of 100 or more, may also be found in communications circuits. Mechanical resonator filters such as MEMs are also finding a place in modern technology circuits.

[0004] Antennas as Resonators: Some resonator applications are found in antennas, where the antenna circuit is designed to tune the antenna to a specific frequency band and provide impedance matching, typically to a common reference impedance of 50 Ω. Antenna impedance matching is typically achieved using lumped impedance matching components that provide a fixed antenna impedance, especially for Electrically Small Antennas (ESAs) for RF applications. These ESA antennas are typically half-wave dipole or quarter-wave monopole antennas and must be designed for a specific application frequency or frequency range.

[0005] SAW / BAW Resonators: Other high performance resonator applications are in the area of ​​Surface Acoustic Wave (SAW) filters and the related Bulk Acoustic Wave (BAW) filters. SAW and BAW RF filters provide very narrow bandwidth (high Q) filtering for communications applications below approximately 6 GHz carrier frequencies. Because of the technology deployed, these SAW / BAW devices are subject to thermal fluctuations and aging effects that greatly reduce the effectiveness of their filtering. The manufacturing process uses various technology overlays to mitigate or eliminate this thermal effect. Summary of the Invention

[0006] According to aspects of the present description, various circuit designs are provided that can modify the frequency response of the primary resonator. In one example, a filter used as a resonator element coupled to an external resonator in conjunction with a high performance tunable active RF filter can modify and enhance the performance of the external resonator. System level enhancements can be done with, for example, a) a high performance tunable RF active filter coupled to an electrically small RF antenna, and b) a SAW / BAW RF filter. The primary resonator can be different types of resonators, such as electric resonators, electromagnetic resonators, electromechanical resonators, piezoelectric resonators, and optical resonators.

[0007] Examples of suitable tunable resonators that may be used are presented in detail in PCT Publication No. WO2017 / 089803, entitled "Variable Filter" (herein "Nielsen"), the contents of which are incorporated herein in their entirety.

[0008] According to certain aspects, the resonator to be controlled or modified may be an external (i.e., off-chip) resonator, preferably a higher Q resonator than the tunable resonator. However, this need not be the case. The controlled resonator may be on-chip and / or may have a lower Q (i.e., closer to the Q of the tunable resonator). In some embodiments, the resonator may also be an antenna.

[0009] References to "high and low Q" as used herein are general terms, and the meaning of high Q and low Q may vary depending on the context in which they are used, as would be understood by one of ordinary skill in the art. In some cases, the Q of the primary resonator may be considered to be higher than the tunable resonator, and the high Q resonator may be considered to be 10 times higher, or even 100 times higher, than the tunable resonator. According to a particular embodiment, an apparatus and method are provided for actively coupling two separate resonators in a signal loop, where one resonator is typically, but not limited to, an external resonator, a high-performance fixed resonator with near-high Q, while the other resonator is a variable low Q resonator. The purpose of the coupling is to control the performance metric of the external resonator by controlling the low Q variable resonator through controlling the s-plane poles of the external resonator after coupling. Two detailed examples are provided where the external resonator is first an antenna and then a BAW / SAW RF filter. Careful attention is given to the problems and solutions to the problems in incorporating this concept into a chip.

[0010] In certain aspects, the concepts of "on-chip" and "off-chip" are used and described. In a general context, and in the context of this document, these terms refer to integrated circuits with bulky components reduced to a relatively small size. The term "Small" can be used and is a comparative term that depends on the context in which it is used, since physical size is determined by a large set of variables. Furthermore, the substrate technology generally determines the choice of chip implementation. This means that the implementation of a complex technology may result in multiple chips that need to be interconnected at a given level. Therefore, this description considers the case where part of the circuit is implemented on one type of substrate and one or more other components of the circuit are implemented on a different substrate. These other components are "off-chip" relative to the chip that holds the majority of the components. Very high Q off-chip resonators in the range of thousands, such as SAW and / or BAW, can be used as frequency tuning elements in communication circuits. For example, such high-Q resonator SAW / BAW filters are typically of fixed frequency and bandwidth, but are subject to performance variations due to the manufacturing process as well as performance variations due to operating temperature.

[0011] According to one aspect, there is provided a resonant circuit comprising a signal loop having an input, an output, and a closed loop frequency response, the signal loop comprising a primary resonator having a primary frequency response and a primary Q-factor, at least one tunable resonator having a tunable frequency and a secondary Q-factor, the primary Q-factor being about 10 times greater than the secondary Q-factor, and a tunable scaling block that applies a gain factor. A controller coupled to the at least one tunable resonator and the tunable scaling block, the controller having instructions to tune the closed loop frequency response to a desired closed loop frequency response by controlling the tunable frequency of the at least one tunable resonator and the gain factor of the tunable scaling block.

[0012] According to other aspects, the resonant circuit may include one or more of the following elements, alone or in combination: the primary Q factor may be about 100 times or more greater than the secondary Q factor; the primary frequency response of the primary resonator may be within a predetermined error factor of a desired frequency response, and the controller controls the closed loop frequency response to within the predetermined error factor of the primary resonator; the primary resonator may be a fixed resonator or a frequency tunable resonator; the primary resonator may be an antenna, and the antenna may comprise an input of the signal loop; the signal loop further comprises a phase shifter that applies an adjustable delay factor, and the controller is connected to control the phase shifter; the resonant circuit. may further comprise a plurality of tunable resonators connected in series or in parallel; the primary resonator may be an electrical resonator, an electromagnetic resonator, a mechanical resonator, or a resonator based on material properties; the resonant circuit may further comprise a plurality of primary resonators connected in parallel or in series in a signal loop; the signal loop may comprise a first component comprising a primary resonator and a second component comprising at least one tunable resonator, where the first component is fabricated from a first material and the second component is fabricated from a second material different from the first material, and further, the first component and the second component may be fabricated as separate and distinct components.

[0013] According to one aspect, there is provided a method of modifying a closed loop frequency response of a resonant circuit, the resonant circuit comprising a signal loop having an input, an output, a primary resonator having a primary frequency response, at least one tunable resonator having a tunable frequency, and a tunable scaling block having a gain factor, the method including controlling a frequency of the at least one tunable resonator and a gain factor of the tunable scaling block to tune the closed loop frequency response of the resonant circuit to a desired closed loop frequency response, wherein the Q factor of the primary resonator is about 10 times greater than the Q factor of the at least one tunable resonator.

[0014] According to other aspects, the method may include one or more of the following aspects, alone or in combination: the Q factor of the primary resonator may be greater than the Q factor of the at least one tunable resonator by a factor of about 100 or more; the method may further include tuning a primary frequency response of the primary resonator; the primary resonator may be an antenna, and the antenna may comprise an input of a signal loop; the signal loop may further comprise a phase shifter, and tuning the closed loop frequency response may further include tuning a phase of the phase shifter; the multiple tunable resonators may be connected in series. the primary resonator may be an electrical resonator, an electromagnetic resonator, a mechanical resonator, or a resonator based on material properties; the multiple primary resonators may be connected in parallel or in series within the signal loop; the signal loop may comprise a first component comprising the primary resonator and a second component comprising at least one tunable resonator, where the first component is fabricated from a first material and the second component is fabricated from a second material different from the first material, and further, the first component and the second component are fabricated as separate and distinct components.

[0015] According to one aspect, a resonant circuit is provided, the resonant circuit comprising a signal loop having an input, an output, and a closed loop frequency response, the signal loop comprising a first component comprising a primary resonator, the primary resonator having a primary frequency response, and a second component comprising at least one tunable resonator, the at least one tunable resonator having a tunable frequency. The tunable scaling block applies a gain factor. The first component is fabricated from a first material, and the second component is fabricated from a second material different from the first material. A controller is coupled to the at least one tunable resonator and the tunable scaling block, the controller comprising instructions for tuning the closed loop frequency response to a desired closed loop frequency response by controlling the tunable frequency of the at least one tunable resonator and the gain factor of the tunable scaling block.

[0016] According to other aspects, the resonant circuit may include one or more of the following aspects, alone or in combination: the first component and the second component are fabricated as separate and distinct components; the primary resonator may have a primary Q factor that is about 10 times or more greater than a Q factor of the at least one tunable resonator; a primary frequency response of the primary resonator may be within a predetermined error factor of a desired frequency response, and the controller controls the closed loop frequency response to within the predetermined error factor of the primary resonator; the primary resonator may be a fixed resonator or a tunable resonator. the primary resonator may be an antenna, the antenna comprising an input of the signal loop; the signal loop may further comprise a phase shifter that applies an adjustable delay factor, the controller being connected to control the phase shifter; the resonant circuit may further comprise a plurality of adjustable resonators connected in series or in parallel; the primary resonator may be an electric resonator, an electromagnetic resonator, a mechanical resonator, or a resonator based on material properties; the resonant circuit may further comprise a plurality of primary resonators connected in parallel or in series within the signal loop.

[0017] According to one aspect, a method of modifying a closed loop frequency response of a resonant circuit is provided, the method including the steps of providing a resonant circuit comprising a signal loop, the signal loop comprising an input, an output, a first component comprising a primary resonator, the primary resonator having a primary frequency response, a second component comprising at least one tunable resonator, the at least one tunable resonator having a tunable frequency, and an adjustable scaling block that applies a gain factor, the first component being fabricated from a first material and the second component being fabricated from a second material different from the first material; and controlling a frequency of the at least one tunable resonator and a gain factor of the adjustable scaling block to adjust the closed loop frequency response of the resonant circuit to a desired closed loop frequency response.

[0018] According to other aspects, the method may include one or more of the following aspects, alone or in combination: the primary resonator has a primary Q factor that is about 10 times or more greater than a Q factor of the at least one tunable resonator, or about 100 times or more greater; the method may further include adjusting a resonant operating frequency of the primary resonator; the primary resonator may be an antenna, and the antenna may comprise an input of the signal loop; a phase shifter may be provided, and adjusting the closed-loop frequency response further includes adjusting a phase of the phase shifter; the multiple tunable resonators may be connected in series or in parallel; the primary resonator may be an electrical resonator, an electromagnetic resonator, a mechanical resonator, or a resonator based on material properties; the multiple primary resonators may be connected in parallel or in series in the signal loop.

[0019] According to one aspect, a communications circuit is provided, the communications circuit comprising: a signal loop comprising an antenna block for receiving a desired electromagnetic signal, an input port, an output port, and a signal conditioning block between the input port and the output port, where the antenna block is in bidirectional communication with the input port of the signal loop, and where the signal conditioning block applies a phase shift and a gain factor to the desired signal; and a controller block configured to adjust the phase shift and gain factor of the signal conditioning block to improve a signal quality factor of the desired signal from the antenna block.

[0020] According to other aspects, the communications circuit may include one or more of the following aspects, alone or in combination: the signal conditioning block may comprise one or more variable frequency resonators and a gain block that applies a gain factor; the controller block may adjust the phase shift by adjusting the one or more variable frequency resonators; the controller block may control the signal conditioning block to match an impedance of an antenna of the antenna block; the signal quality factor may include at least one of a measure of available antenna power delivered to the output port and a signal-to-noise ratio of the desired signal, and the controller may adjust the gain factor to improve the signal-to-noise ratio or modify a bandwidth of the desired signal; the communications circuit may further comprise a receiver block that receives the desired signal from the signal conditioning block and processes the desired signal, the desired signal being a carrier wave. and the receiver block comprises a demodulator; the bidirectional coupling element can be connected to the antenna block and the signal conditioning block; the signal conditioning block can adjust the impedance of the communication circuit to enhance the available energy transferred from the antenna of the antenna block to the receiver block; the signal loop can comprise an encoder that encodes a data stream on a return path from the signal loop to the antenna block and transmits it by the antenna block; the data stream that is encoded on the return path is provided by a sensor; the signal conditioning block can comprise a negative impedance element and a phase shifter element; the signal conditioning block can comprise a phase shifter that applies a phase shift and a gain block that applies a gain factor; the controller can be configured to improve the signal quality factor by varying the gain factor between positive and negative values.

[0021] According to one aspect, a method is provided for encoding and reflecting an electromagnetic signal received at an antenna, the method including the steps of coupling the electromagnetic signal received at the antenna into a signal loop, applying a phase shift and a gain factor to the received electromagnetic signal in the signal loop, encoding a data stream onto the received electromagnetic signal using an encoder in the signal loop, and coupling the encoded electromagnetic signal from the signal loop to an antenna for transmission by the antenna.

[0022] According to other aspects, the method can include one or more of the following aspects, alone or in combination: adjusting the phase shift can include adjusting one or more variable frequency resonators; the antenna can be in bidirectional communication with the signal loop; the antenna can be connected within the signal loop.

[0023] According to one aspect, a communication circuit is provided, the communication circuit comprising: a signal loop with a signal conditioning block, an antenna connected to receive an electromagnetic signal and transmit the electromagnetic signal to the signal loop, where the signal conditioning block applies a phase shift and a gain factor to the desired signal in the signal loop, and an encoder for encoding a data stream with the electromagnetic signal in the signal loop, the antenna being connected to the signal loop such that the encoded electromagnetic signal is transmitted by the antenna.

[0024] The antenna block can be in bidirectional communication with the input port of the signal loop or can be connected in series to the signal conditioning block. The data stream can be provided by the sensor. [Brief description of the drawings]

[0025] These and other features will become more apparent from the following description in which reference is made to the accompanying drawings, which are for illustrative purposes only and are not intended to be limiting in any way. [Figure 1]FIG. 2 is a block diagram of a tunable filter including a tunable resonator and a tunable scaling block in the signal loop. [Diagram 2] 1 is a graph showing band pass characteristics of a tunable filter. [Diagram 3] A visual definition of a fundamental resonator with S-plane poles. [Figure 4] FIG. 2 is a block diagram of a first-order variable filter ATL-1. [Diagram 5] 5 is a root locus of the first-order variable filter in FIG. [Figure 6] 5 is a Bode plot of the tunable filter of FIG. 4. [Figure 7] FIG. 1 is a block diagram of a Q spoiler based on a resonant block in parallel with a FET variable resistor. [Figure 8] FIG. 2 is a block diagram of a second-order variable filter ATL-2. [Figure 9] 9 is a root locus of the second-order variable filter of FIG. 8. [Figure 10] FIG. 1 is a block diagram of a third-order variable filter ATL-3. [Figure 11] 11 is a Bode plot of the third-order tunable filter of FIG. 10. [Figure 12] 11 is a root locus of the third-order variable filter of FIG. 10 with different values ​​for Q. [Figure 13] 11 is a root locus of the third-order variable filter of FIG. 10 with different values ​​for Q. [Figure 14] FIG. 2 is a simplified block diagram of an example of a first-order variable filter. [Figure 15] 15 is a root locus of the adaptive filter shown in FIG. 14 after Q enhancement. [Figure 16] 15 is a root locus of the adaptive filter shown in FIG. 14 after Q-spoiler is performed. [Figure 17] 15 is a plot of the passband of the adaptive filter shown in FIG. 14 comparing Q-boosting and Q-spoiler. [Figure 18] 15 is a plot illustrating the effect on the passband of the adaptive filter of FIG. 14 by varying the resonant frequency. [Figure 19]FIG. 1 is a block diagram of three first-order variable filters connected in series. [Figure 20] FIG. 1 is a block diagram of three first-order variable filters connected in series with an additional feedback path. [Figure 21] 1 shows a conceptual graph illustrating the effect of additional feedback paths on filter pole movement. [Figure 22] This is the root locus of three cascaded first-order variable filters. [Figure 23] 20 is a frequency response of the adaptive filter shown in FIG. 19 for different G values. [Figure 24] 21 is a frequency response of the adaptive filter shown in FIG. 20 with intermediate level 2 feedback. [Diagram 25] 21A-21C are root locus diagrams for negative (left) and positive (right) level-2 feedback of the adaptive filter shown in FIG. 20. [Figure 26] 21 is a plot of the frequency response of the adaptive filter shown in FIG. 20 with positive, intermediate, and negative Level 2 feedback. [Figure 27] 21 is a Bode plot of the adaptive filter shown in FIG. 20 with alternating resonator frequencies. [Figure 28] 21 is a root locus for the adaptive filter shown in FIG. 20 with alternating resonator frequencies. [Figure 29] 1 is an exemplary ATL1 frequency response after tuning. [Diagram 30] 1 is an example ATL3 frequency response after tuning. [Diagram 31] FIG. 1 is an example ATL3 root locus diagram. [Diagram 32] FIG. 13 is a block diagram of the ATL1 core module calibration and stabilization. [Diagram 33] 11 is a series of graphs illustrating Q control alternating between higher and lower levels during closed loop calibration. [Diagram 34] 1 shows a special case ATL3 circuit for potential phase control applications. [Diagram 35]1 shows the frequency and phase response of a classical passive Butterworth filter of order 3. [Diagram 36] Graph showing detail of a classic Butterworth close to the center frequency: frequency response (left) and phase (right). [Figure 37] A pole-zero map of a classic third-order Butterworth filter, showing three pole pairs and three zeros. [Figure 38] This is the topology of ATL3 (ATL3 T-2). [Figure 39] Phase shift control voltages: allowable phase shifter functions across the conceptual ATL1 passband for two values ​​of p1 and p2. [Diagram 40] 1 is an idealized model of ATL1 with two embodiments. [Diagram 41] A typical Nyquist stability criterion plot showing the phasor of the inverse frequency response. [Diagram 42] 1 is a Nyquist plot of the open loop transfer function after a phase shift. [Diagram 43] FIG. 13 is a diagram of a possible all-bandpass active circuit used as the ATL1 phase shifter with two embodiments. [Diagram 44] This is a pole-zero plot of an all-pass filter, showing a phase shifter (ωp=1, Dp=0.2). [Diagram 45] Normalized frequency response for an all-pass filter. [Figure 46] FIG. 13 is a schematic diagram showing a selectable variable gain of the polarization output. [Figure 47] 13 is a Nyquist plot of ATL1 using a phase-selectable gain block and an all-pass phase shifter. [Figure 48] FIG. 1 is a block diagram of an ATL3 configured to perform phase shifting using gain polarization switching. [Figure 49]FIG. 13 is a block diagram showing an ATL3 reconfigured as a triple resonator to perform phase shift processing. [Figure 50] Nyquist plot after ATL3 correction for 1.5 radians of parasitic delay using gain polarization switching. [Figure 51] 57 is an estimated root locus plot for the Nyquist realization shown in FIG. 56. [Figure 52] 1 is a plot showing the effect of gain polarization switching on frequency response bandwidth. [Figure 53] FIG. 1 illustrates coupling a dipole antenna to an external EM radiation source. [Figure 54] Graph showing the input impedance (left) and conductance (right) of a dipole wire antenna. [Figure 55] 1 is a graph showing the input impedance of an electrically small dipole wire antenna having a nominal dimension of 0.1 wavelengths. [Figure 56] 1 is a graph showing the input impedance of an electrically small dipole wire antenna having an antenna Q of approximately 10 to 20 over a relative bandwidth of 20%. [Figure 57] 1 is a graph showing a series shunt capacitance Smith chart for loop antenna impedance matching. [Figure 58] FIG. 1 is a diagram of the structure of a dielectric resonator antenna. [Figure 59] FIG. 2 is a block diagram showing a conceptual implementation of the ATLF. [Figure 60] 1 is a graph illustrating the performance of a complex high-order bandpass filter matching circuit according to the prior art. [Figure 61] 1 is a graph showing a prior art example of a reconfigurable filter; [Figure 62] FIG. 2 is a block diagram showing an antenna subsystem coupled to an ATLF resonator. [Figure 63] 11 is a series of graphs showing plots specific to the ATL1 resonator at given values. [Figure 64]FIG. 1 is a block diagram showing ATL1 comprising a directional coupler and an output splitter. [Figure 65] This is a pole-zero diagram for an antenna with low radiation resistance. [Figure 66] This is a pole-zero diagram for a perfectly matched antenna. [Figure 67] FIG. 1 is a series of block diagrams of a transceiver without network matching functionality. [Figure 68] FIG. 2 is a block diagram showing a feedback loop comprising a retrodirectional coupler, a gain stage, a phase shifter, and a resonator. [Figure 69] 1 is a series of plots showing the closed-loop poles and zeros of the ATLF. [Figure 70] 1 is a series of plots illustrating distorted root locus due to mismatched phase shifters. [Figure 71] 13 is a plot of the root locus after applying phase correction. [Figure 72] 1 is a Nyquist plot for the case of mismatched phase shifters. [Figure 73] Nyquist plots of the ATL1 loop with no delay, finite delay, and infinite delay. [Figure 74] FIG. 1 shows an antenna test setup. [Figure 75] FIG. 2 shows an equivalent circuit of a coupled test antenna and a Thevenin equivalent circuit. [Figure 76] FIG. 1 shows an approximation circuit of a coupled test antenna. [Figure 77] FIG. 2 is a block diagram showing impedance matching of an antenna to a receiver load with an L matching circuit. [Figure 78] 1 is a plot of a complex antenna error surface. [Figure 79] FIG. 2 is a block diagram showing ATLF impedance matching based on reflection coefficient. [Figure 80] FIG. 1 is a block diagram showing an ATLF Category 1 consisting of a circulator, a scaling block, and a phase shifter. [Figure 81] FIG. 2 is a block diagram illustrating an antenna with an inductive reactance attached to an RF voltage source. [Figure 82] FIG. 13 is a diagram showing inductance elimination by a capacitor. [Figure 83] 1 is a plot showing the real part of the impedance inside port 1 of the circulator. The plot on the left is a contour plot of Re(Zr) and the plot on the right is the characteristic contour for Re(Zr) near 1. [Figure 84] 1 is a plot showing the power coupling coefficient from the antenna to the receiver for three values ​​of equivalent antenna impedance. [Figure 85] 1 is a plot showing the current output of the antenna for Z=R. [Figure 86] FIG. 2 is a block diagram showing equivalent reflections caused by an inductor of an antenna. [Figure 87] Receiver "a node" plot showing that the power wave signal increases steadily with G. [Figure 88] 1 is a Nyquist plot of the ATLF stability region. [Figure 89] FIG. 1 is a block diagram of an objective signal-to-noise (SNR) optimization. [Figure 90] FIG. 1 is a high-level block diagram of a wireless data receiver using ATLF for antenna impedance matching and system interface. [Figure 91] 1 is a series of plots conceptually illustrating an equalizer that mitigates filter shaping distortion. [Figure 92] 1 is a plot showing that points on either side of the Nyquist curve behave the same as a given class. [Figure 93] FIG. 1 is a diagram of an ideal antenna with a radiation resistance of R connected to a receiver with impedance Rr. [Figure 94] FIG. 1 shows an ATLF consisting of an antenna and a negative resistance. [Figure 95] FIG. 2 shows a loop antenna having an inverted gain stage. [Figure 96] It is a plot showing the antenna reflection coefficient regarding the frequency range 0.75 < w < 1.25. [Figure 97] It is a graph showing the root locus of an ideal ATLF. [Figure 98] It is a graph showing the amplitude of the transfer function of ATLF regarding various values of the varactor diode capacitance normalized with respect to Cv = 1. [Figure 99] A diagram of a loop antenna having a parallel varactor capacitor instead of a series (upper) one, and a plot of the antenna deflection coefficient regarding the frequency range 0.75 < w < 1.25. [Figure 100] It is a diagram of the varactor utilization tuning of a short dipole antenna. [Figure 101] It is a plot of the reflection coefficient of a short dipole antenna. [Figure 102] It is a block diagram of a circuit configuration for performing inductive tuning of a dipole antenna and a varactor diode. [Figure 103] It is a block diagram of a feedback loop having a directional coupler, a gain stage, a phase shifter, and antenna reflection. [Figure 104] It is a series of plots showing the poles and roots of the antenna reflection and phase shifter plotted on the left and in the center, and all root loci are plotted on the right. [Figure 105] It is a plot showing that the achievable Q enhancement is limited by the unstable closed-loop poles on the real axis (a plot generated for 0 < G < 1). [Fig. 106] It is a block diagram showing a lead circuit for adding stability to the loop. [Figure 107] It is a plot of the root locus, showing the enhancement of the stability of the dominant pole. [Figure 108] It is a series of plots of the antenna reflection and the poles and roots of the ATL1 resonator plotted on the left plot and the center plot, and all root loci plotted on the right. [Fig. 109]As before, this is a plot of the root locus of an ATL filter with delay, a phase compensator and a resonator acting as an antenna reflection. [Figure 110] FIG. 1 is a block diagram showing a circuit in the form of an ATLXR filter tenner category 2 based on ATL1 (top) and ATL3 (bottom). [Figure 111] 1 is a plot showing the root locus of ATLF using ATL2. [Figure 112] 1 is a diagram and plot showing root locus and Nyquist plots for an ATLF circuit equivalent to a fixed frequency negative resistance; [Figure 113] FIG. 1 is a block diagram showing the configurations of ATLF categories 2 and 3. The upper part shows the configuration of ATLF category 2 consisting of directional couplers, phase shifters, and scaling blocks, and the lower part shows the configuration of ATLF category 3 consisting of directional hybrid couplers attached to ports 2 and 3 and bidirectional phase shifters realized with varactor diodes. [Fig. 114] FIG. 1 is a block diagram showing an ATL1 configuration with a splitter and a directional coupler. [Fig. 115] FIG. 13 is a diagram of a bidirectional phase shifter alternative. [Fig. 116] FIG. 1 shows an ATLF (upper part) equivalent to a negative resistance circuit, and a Thevenin equivalent circuit of the ATLF (lower part). [Fig. 117] A plot showing the operation of the ATLF in the Z-plane (top) and an impedance phasor diagram showing the resonance of the ATLF current (bottom). [Fig. 118] FIG. 2 shows the Norton and Thevenin equivalent circuits of the ATLF. [Figure 119] FIG. 13 is a diagram showing the equivalent impedance of a negative resistance port. [Figure 120] 1A-1C are diagrams of various approaches to implementing an ATL filter tenner circuit. [Figure 121] 13 is an open-loop Nyquist plot of an ATLF combined with three cascaded ATL1s. [Figure 122]122 is a Nyquist plot of the circuit of FIG. 121 with transmission delay. [Figure 123] This is the Nyquist locus after correction of Figure 122 by tuning of the resonators to ωr = 1.037. [Figure 124] The Nyquist locus after correction of Figure 122 by tuning of the resonators to ωr = 0.919 [Fig. 125] 1 is a plot of the Nyquist locus for a transmission delay of 3 radians. [Fig. 126] 13 is a plot of the Nyquist locus of the ATLF with the resonator detuned. [Figure 127] 1 is an initial Nyquist plot varying with two possible resonant frequencies. [Figure 128] A plot of stable and unstable regions, clearly showing what could have gone wrong. [Figure 129] 13 is a plot showing that an inward pointing Nyquist loop is possible but cannot destabilize the ATLF. [Fig. 130] 13 is a plot showing a portion of a Nyquist plot for an ATLF after calibration with the Nyquist locus changing due to changes in antenna impedance. [Fig. 131] FIG. 131 is a plot showing the change in the passband characteristics of the ATLF due to the change in antenna impedance for FIG. 130. [Fig. 132] 1 is a plot showing the Nyquist locus when the ATLF is unstable. [Fig. 133] FIG. 2 is a block diagram showing a low power oscillation and frequency detection circuit. [Fig. 134] FIG. 1 is a block diagram of an ATLF-based transceiver. [Fig. 135]FIG. 13 shows a timeline for active ATLF calibration based on data packet reception time. [Fig. 136] 1 is a Nyquist plot of a resonant model of an antenna with pure delay. [Fig. 137] 1 is a Nyquist plot of the combined antenna and ATL3 resonator. [Figure 138] FIG. 2 illustrates scattering sources that affect an antenna. [Fig. 139] 1 is a series of plots showing potential Nyquist plots for an antenna in various environments. [Fig. 140] A detailed Nyquist plot with an interferer. [Fig. 141] 11 is a plot showing the effect of phase shifter control moving the Nyquist loop up and down to produce passband frequency jumps. [Fig. 142] 1 is a plot showing tangled Nyquist loops of a single antenna reflection coefficient when moving over a ground plane in the presence of scatterers. [Fig. 143] 143 is a plot showing the frequency response corresponding to the 1 / G operating point of FIG. 142. [Fig. 144] FIG. 1 is a block diagram showing an ATL3 incorporated in an antenna resonator loop. [Fig. 145] 13 is a plot showing the ATL3Q enhanced effective frequency response when scattered by a near field object. [Fig. 146] FIG. 1 is a block diagram of an integrated wireless sensor transceiver system consisting of a minimum of four components. [Fig. 147] FIG. 13 is a block diagram showing a receiver mode 1 with ATL1a used as an RF filter. [Fig. 148] FIG. 13 is a block diagram showing mode 2 when ATL1a and ATL1b are cascaded. [Figure 149] FIG. 13 is a block diagram showing mode 2 with the attenuator switched. [Fig. 150]FIG. 13 is a block diagram showing how transmitting mode 3 works in conjunction with mode 1. [Fig. 151] FIG. 13 is a block diagram showing calibration mode 4. [Fig. 152] FIG. 13 is a block diagram showing calibration mode 5. [Fig. 153] FIG. 13 is a block diagram in which ATLa and ATLb are the same ATL1, with a resonator in the through path and a scaling block and a phase shifter in the feedback path. [Fig. 154] 1 is a pole-zero plot of an all-pass filter representing a phase shifter. [Fig. 155] 1 is a plot showing the frequency dependence of an all-pass filter. [Fig. 156] 1 is a frequency plot of the resonator with open loop Q=10 (ωr=1 and Dr=0.05). [Fig. 157] A pole-zero plot of the resonator of FIG. [Fig. 158] FIG. 157 is a plot of the zero degree root locus for the resonator of FIG. 156. [Fig. 159] 1 is a phase plot of the phase shifter after achieving a 50 degree misalignment. [Fig. 160] FIG. 159 is a plot of the zero degree root locus of ATL1 for the mismatched phase case. [Fig. 161] 159 is a plot of the loop gain required to reach the oscillation state as a function of the phase shifter mismatch of FIG. 159. [Fig. 162] FIG. 13 is a block diagram of a configuration for passband calibration of an ATLa. [Fig. 163] FIG. 1 is a block diagram of an ATLF configuration for full-duplex communication without a transmitter. [Fig. 164] FIG. 1 is a block diagram showing a network of multiple readers (R) and multiple sensors (S). [Fig. 165] FIG. 1 illustrates an AV approaching an RF lane marker (RFLM). [Fig. 166] FIG. 1 illustrates a multi-lane road representing each RFLM with a unique ID. [Fig. 167]FIG. 1 is a block diagram of a simple envelope analysis process. [Fig. 168] FIG. 1 shows a 2D road surface where the simulation is simplified. [Fig. 169] A plot of the position of the RFLM (circle) and the trajectory of the vehicle AVPI (bold line). [Fig. 170] 13 is a plot of the signal at the RFLM due to the signal from the AVPI passing through. [Fig. 171] 171 is a plot showing coherent demodulation and envelope processing of the overlapped RFLMs of FIG. 170. [Fig. 172] 1 is a plot showing the envelope when the AVPI is in the center of the lane. [Fig. 173] 1 is a plot showing two parallel trajectories corresponding to two AVPIs located to the right and left of a single AV along a road. [Fig. 174] 174 is a plot showing the envelopes of two position query response signals from the AVPI of FIG. 173. [Fig. 175] This figure shows two AVs arranged side by side with AVPI spaced approximately the same distance from RFLMs arranged in row 2. [Fig. 176] FIG. 1 is a block diagram of an overall vehicle navigation system. [Fig. 177] FIG. 1 is a block diagram of a possible implementation of a durable RFLM. [Fig. 178] FIG. 1 is a block diagram illustrating a train sensor network application. [Fig. 179] FIG. 1 is a block diagram showing a basic ATLXR circuit. [Fig. 180] FIG. 1 is a block diagram showing a basic ATLXR open loop circuit. [Fig. 181] FIG. 180 is an open loop pole-zero plot of ATLXR. [Fig. 182] 1 is a plot showing an equivalent polynomial representation of a Pade approximation of loop delay. [Fig. 183] 1 is a plot showing the closed-loop locus of high-order Q poles of F. [Fig. 184]1 is a plot showing an ATLXR with a nearly single-pole primary resonator F and three tunable secondary R. [Fig. 185] 1 is a plot showing a representative Q enhancement of a first-order cavity F. [Fig. 186] 1 is a plot showing the frequency shift of the poles of a Q-enhanced primary cavity F. [Fig. 187] 1 is a plot showing the root locus for a 90 degree phase shift caused by parasitic delays. [Fig. 188] FIG. 2 is a block diagram showing a preferred embodiment of the ATLXR. [Fig. 189] FIG. 1 is a block diagram illustrating one embodiment of an ATLXR, in which both slow coarse frequency control and fast control of the closed loop poles are provided by the ATLXR feedback loop via {f,p,g} control. [Fig. 190] FIG. 1 is a block diagram illustrating multiple ATLXR circuits that result in a multi-pole bandpass filter. [Fig. 191] FIG. 1 is a block diagram showing a practical implementation including a multi-resonator BAW chip with a single-port resonator. [Fig. 192] FIG. 2 is a block diagram showing a generic ATLXR chip with a switch matrix and blocks of selectable ATLXR circuitry. [Fig. 193] FIG. 1 shows a moderately high-Q resonator made with via connections in a PCB. [Fig. 194] FIG. 1 shows an ATLXR Q-enhanced resonator printed on a circuit board. [Fig. 195] FIG. 13 shows ATLXR's Q-enhanced stripline resonator printed on a layer of a circuit board to save space used for chip antennas. [Fig. 196] FIG. 1 is a diagram of a SAW resonator device. [Figure 197] FIG. 1 is a diagram of a BAW resonator device. [Figure 198] FIG. 1 is a diagram of an external BAW with three parallel resonators resonating at different frequencies f1, f2, and f3 associated with a Q of approximately 100 for each resonance. [Figure 199]FIG. 13 is a block diagram of an ATLXR configuration comprising a high-Q primary triple resonator coupled to a negative feedback path with three low-Q secondary tunable ATL resonators. [Figure 200] 199 is a series of root locus plots of the ATLXR feedback example of FIG. 199 as the combined resonant ATL frequency of R is varied. [Figure 201] FIG. 1 is a diagram of a coupled-line bandpass filter (circuit board), which can be thought of as a universal resonator. [Fig. 202] 13 is a plot of the filter response of a third order Butterworth filter with first order ATLXR resonators. [Fig. 203] 13 is a plot of the root locus of a coupled outer Butterworth filter showing the center pole Q enhancement. [Fig. 204] FIG. 1 is a diagram of a waveguide filter that can be used as the primary resonator of the ATLXR. [Fig. 205] FIG. 1 is a block diagram showing an active amplifier enabling unidirectional ATLXR Category 1 combining. [Fig. 206] FIG. 1 is a block diagram showing a bidirectional configuration of an ATLXR Category 2 with a circulator. [Fig. 207] FIG. 13 is a block diagram showing a Category 2 ATLXR configuration with swapped signal flows. [Fig. 208] FIG. 1 is a block diagram showing a Category 3 ATLXR configuration. [Fig. 209] FIG. 1 is a block diagram showing the configuration of ATLXR Category 4. [Fig. 210] FIG. 1 is a block diagram of an ATLXR configuration with a high-Q first-order resonator in series. [Fig. 211] FIG. 1 is a block diagram illustrating the current flow and the resulting magnetic field generation complicated by the current flow into the ground plane. [Fig. 212] FIG. 13 shows the root locus of the ATL filter based on ATL3. [Fig. 213] FIG. 13 shows the root locus of the ATL Filter / ATL3 when the varactors are appropriately set. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0026] We first discuss examples of tunable resonators that can be used to control a primary resonator. We then discuss examples where these tunable resonators can be used, such as antennas and filters, such as SAW / BAW filters.

[0027] In addition to tunable resonators and scaling blocks, modification of the primary resonator can also be achieved using tunable phase shifters, examples of which are also described below.

[0028] Overview of ATL Active Analog Variable Bandpass Filters

[0029] In this discussion, a variable resonator is a variable frequency resonator element that can preferably be tuned. The bandwidth of a non-tunable resonator filter can be controlled by feedback across the resonator element. The bandwidth of the resonator is preferably narrow enough to avoid spurious passband responses, but can be tuned over a wide range of frequencies. There is also a gain element, possibly referred to herein as a scaling block, that is tunable to provide positive gain, negative gain, or zero gain. As described in more detail below, this allows the scaling block to selectively operate as a Q-enhancer and a Q-spoiler, as the situation requires.

[0030] As used herein, the term "resonator" may be used to describe a simple resonator element such as an LC tank circuit. The term may also refer in some cases to a resonator in combination with a scaling block. In the following description, a resonator in combination with a scaling block connected in a signal loop is denoted as ATL1 and described in more detail below. Other more complex resonant circuits are described below, such as circuits including multiple resonator elements, multiple scaling blocks, multiple loops, etc. An example of a suitable variable resonator that may be used may be referred to herein as an ATL filter, which is described in detail by Nielsen. Although other variable resonators may be used, a detailed description of the ATL is provided below, as it has been found that such circuits may be used to realize workable circuits.

[0031] In particular, the ATL can be thought of as a variable analog filter, which includes a signal loop including a signal path and a feedback path connected between a signal input and a signal output. Multiple resonators and other loop control elements, such as adjustable scaling gain blocks, may be coupled to the signal loop.

[0032] A controller is connected to tune the frequency-tunable resonators and adjust the gain coefficients of each tunable scaling block to the desired frequency response.

[0033] ATLs can be of different orders, such as first, second, or third order filters. The order of the ATL depends on the filter order of the resonators. ATLs can be designed with higher orders beyond third order, at the expense of increased complexity in controlling higher order circuits. Some general comments on filter orders include the following code:

[0034] The first order ATL (ATL1) will contain one resonator with a single resonant dominant pole pair.

[0035] A second order ATL (ATL2) would contain two such resonators with two dominant pole pairs, an example being two coupled LC tank resonators in a cascaded fashion.

[0036] A third-order ATL (ATL3) would contain three such resonators with three dominant pole pairs.

[0037] Higher order ATLs, fourth or higher, are possible, but these ATLs introduce spurious bands when scaling block feedback is performed and generally result in bandpass filters (BPFs) with more difficult tuning characteristics.

[0038] Figure 29 shows the frequency response of the tuning example ATL1, and Figure 30 shows the frequency response of the tuning example ATL3. Figure 31 is a root locus plot of the ATL3 example shown in Figure 30.

[0039] A block diagram of an ATL 1 in its simplest form is shown in Figure 1, with a single variable resonator 502 and a variable scaling block 504 in the signal loop. Figure 1 also shows the input / output buffer 102 and resonator coupling 104 on the main path 508, with the scaling block 504 placed in the feedback path 510. ATLs are intended to be used to transmit, receive and process communication signals for a variety of purposes. Generally, a communication signal is a modulated signal used to transmit information or data. Typically this involves an analog carrier frequency encoded with the information signal using known methods such as frequency modulation, amplitude modulation or phase modulation.

[0040] The basic operating principle of the ATL, which provides control over bandpass characteristics, is shown in Figure 2, where the wide dashed trace 602 is the resonator frequency response at initial setup. The narrow dashed trace 604 is the sharp frequency response of the closed loop filter set to narrow band (high Q) at the initial frequency setting. Assume the resonator is tuned up in frequency as indicated by the black arrow 610 to the wide solid trace 606. The narrow solid trace 608 is the resulting closed loop response at the new resonator response frequency.

[0041] The examples described herein relate primarily to first (ATL1), second (ATL2) and third order (ATL3) ATLs, although it will be understood that the teachings herein may also be applied to higher order filters as appropriate.

[0042] In the various examples presented herein, the circuit is shown for convenience in the style of FIG. 1, which typically shows an arrangement with a main path 508 and a feedback path 510, with the gain block 504 (which may also be called a scaling block) having both positive and negative values ​​on the feedback path 510. This is done for consistency and to make the circuits easier to compare. However, the circuit is more appropriately thought of as a loop with appropriate input and output coupling, where a loop is formed from what would otherwise be the main path 508 and the feedback path 510, with the elements of the loop being directly connected within the loop. As a loop, the order of the components within the loop may be altered while still providing the desired resonant characteristics.

[0043] Elements of ATL

[0044] Before looking at the structure of ATL, let's look at the following ATL elements: Tunable Resonator Bandwidth or Q Control Scaling Blocks Phase Shifter

[0045] Tunable ATL Resonator(R)

[0046] Referring to FIG. 3, a visual definition of an elemental resonator with s-plane poles is shown. Resonator block 1301 is shown in FIG. 3. Resonator 1301 is represented with two poles in the S-plane, as also shown in the right diagram of FIG. 3. The two poles are represented by 'x'. Resonator 1301 incorporates a feedback loop across resonator element 1401 as shown in FIG. 4, allowing for Q control. FIG. 4 is a block diagram showing a first order tunable filter ATL-1, having an input 410, resonator element 1301 with output 412, combiner 1404, resonator 1401, and gain or scaling block 802. As shown in FIG. 3, resonator block 1401 is a basic ATL resonator element 1301 with two control inputs 1302 and 1304, connected to a signal loop with gain or scaling block 802 as shown in FIG. 4, and with two control inputs 1302 and 1304: one to change the frequency (1302), and the other to change the Q (1304).

[0047] Depending on the circuit implemented, the resonators may be implemented as resonator elements, such as LC tank circuits, or as second order section (SOS) filter elements. SOS implementations are described in more detail below. Referring to FIG. 8, a block diagram of a second order tunable filter ATL-2 is shown, having an input 810, a combiner 1404, a resonator 1301, a gain buffer 102, a gain block 812, and an output 814. FIG. 9 shows the root loci for the second order tunable filter of FIG. 8, with the open loop root indicated by an 'x', two poles located at 1902, and two conjugate poles at 1904 for this dual SOS resonator configuration. The dominant root loci 1906b and 1908b are in the jω axis as the closed loop gain G increases, while the other loci 1906a and 1908a are in the jω axis.

[0048] As will be appreciated from the discussion herein, there are numerous possible combinations of resonators and scaling blocks, and signal paths that can be used to design an ATL. The specific design will depend on the desired circuit performance, as described elsewhere. In general, an ATL includes a feedback loop that includes a desired number of resonators and scaling blocks. Each ATL may be connected in parallel or in series with other ATL elements, or other circuit elements, and may have additional Level 2 feedback loops that include multiple ATLs. Additionally, there may be nested loops within an ATL element, including loops for each resonator, or a subset of resonators. As used herein, the term "Level 2 feedback" is intended to refer to feedback or circuit loops that provide feedback paths around multiple orthogonal ATLn elements. This includes what may be referred to as Level 3 or Level 4 feedback.

[0049] The resonant frequency of R1401 can be varied with some components included in the resonant circuit. Typically, this can be achieved using a rotor diode, or a variable dielectric capacitor can be used for the variable capacitance, in which case the "f control" in Figure 3 would be an analog bias voltage. Other variants of varying the resonant frequency are well known, such as a discrete capacitance in or out of the circuit, and the "f control" could be a digital signal. Another variant is that a MEMS variable capacitor or MEMS variable inductor could be used. The variable capacitance or inductance could also be achieved by mechanical tuning of a component. For example, R1401 could be a microwave resonant cavity where one or more dimensions of the cavity are mechanically adjustable by some mechanism providing the "f control".

[0050] The two poles of R 1401 are a conjugate pair and cannot be controlled individually. Therefore, for simplicity of explanation, we consider only the positive frequency pole. Therefore, we consider the elemental resonator to have a single pole in the region of s (the region of s with a positive imaginary component). The element 1301 in Figure 4 is a two port device with a transfer function given in the Laplace domain, H, shown as a standard second order bandpass transfer function as above. R (s):

number

[0051] Q-Control Scaling Block

[0052] "Q control" 1304 in FIG. 3 above may comprise a control device associated with the capacitance or inductance or resonator that controls the component Q of the resonant cavity. When the Q control increases the component Q, this is referred to herein as Q-enhancement. When the Q control decreases the component Q of the resonant cavity, this is referred to herein as Q-spoiler. Q-enhancement is equivalent to decreasing D, thus moving the resonant pole of R closer to the jω-axis of the S-plane. Q-spoiler is equivalent to increasing D, thus moving the resonant pole of R further away from the jω-axis, thus increasing D. Q-enhancement and Q-spoiler can be selectively used to move the resonant pole towards or away from the jω-axis to synthesize any multi-pole filter function (multiple Rs).

[0053] The scaling blocks 802 shown in FIG. 4 are provided to allow better control over the feedback response. The gain coefficients of each scaling block 802 are variable, including gains that include both positive and negative gain values. For example, if the gain of the scaling block 802 is greater than zero, Q enhancement is performed. If the gain of the scaling block 802 is less than zero, Q spoiling is performed.

[0054] Q-corruption may alternatively be implemented within the resonator element itself by inserting a FET circuit across the resonator element which increases the loss of the resonator.

[0055] In general, each loop or secondary loop of an ATLn element will have additional scaling blocks as described below. As an example, for an ATL3 circuit element (see Figure 20 for reference), in which a series of three ATL1 core modules are connected in a loop and may be controlled separately, there may be four scaling blocks surrounding each resonator element 1401 in loop 110, and one level 2 feedback scaling block in loop 110a, as described below.

[0056] In general, each scaling block enables a Q-enhancement resonator, and the Q-corruption resonators are independent. Alternatively, the resonator may be a Q-enhanced resonator that uses an amplifier that allows only Q-enhancement. As mentioned before, the Q-enhancement resonator is nested within the feedback loop of the ATLn element that contains the scaling block, overriding the Q-enhancement and providing the required Q-dropper performance when required. This, of course, makes clear from the fact that the resonator can be any type of frequency-untunable resonator, including but not limited to, rotor diodes, switched disk capacitors, variable dielectric capacitors, variable capacitors, MEMS variable capacitors, fixed inductors, variable inductors, MEMS variable inductors, or mechanically tunable resonators.

[0057] ATL Phase Shifter

[0058] We have seen that the closed loop passband of an ATL1 core module consists of the range of frequencies where the open loop phase shift of the center frequency is a multiple of 360 degrees. Therefore, the number n of serially connected ATL1 core modules requires phase control via the serial connection. For example, if n = 3 and three ATL1 core modules are connected in series creating the ATL3 shown above, phase control must be provided so that the end-to-end phase shift is a multiple of 360 degrees.

[0059] We will show later that there are various ways to achieve this phase control.

[0060] ATL1 Core Module Topology

[0061] We now describe a first order ATL circuit called ATL1 which contains a single resonator component 1401, a unitary gain or scaling block 802, and a combiner 1404 to close the feedback loop as shown in Figure 4. ATL1 is the core module of the ATL variable filter in that all variants of the ATL variable filter use different combinations of this ATL1 core module.

[0062] If the center frequency control of the ATL1 core module is omitted, the ATL1 core module can be described in a simplified way. This allows an intuitive understanding of the ATLn variants based on this ATL1 core module. In one example, the resonator 1301 may be a second-order bandpass filter with the following transfer function:

[0063]

number

[0064] Ω with coefficients evaluated based on D and O. The gain G802 is variable and controls the closed loop Q. At resonance the phase shift through the resonator 1401 is ideally 0 degrees. In a physical implementation the phase shift is generally not zero due to parasitic and transport effects, but they may be neglected for this evaluation: the implemented circuit may require a phase shift element associated with G802. The effects of parasitic and transport phases will be explained later. To vary the frequency it is necessary to change Ω O It is ignored for the ATL1 resonator.

[0065] Note that, according to the notation used herein, a first order ATL1 core module has a first order resonator. What is referred to by "order" is the number of second order sections (SOS) used that make up the overall resonator. The SOS transfer function refers to the Laplace function of the frequency variable, which is second order in the denominator. In the present context, as stated above, the SOS is always

number

[0066] Where? O is the resonant frequency in radians per second. D is the damping factor and a is a real constant. The mapping of Figure 3 to f is f n = ω n / 2π

[0067] The mapping onto Q is given by the conventional definition.

number

[0068] In this explanation, {F N ,Q} can be used interchangeably with the operation {ωn,D}

[0069] An essential analysis of the operation of ATL1 is possible using the root locus method. Root locus is a standard method for determining the poles of a closed loop system given a variable loop gain. The result of a root locus calculation in this situation is the locus of these closed loop poles as they vary with the change in loop gain G, for example as shown in Figure 5. Figure 5 is the root locus of the first order variable filter shown in Figure 4. The poles are shown at 1502 and 1504, while the root locus of the poles is shown by lines 1504 and 1508. This allows one to understand any spurious passbands and any tuning limits of ATL1. As a first example, let us consider the case of Ω O With A = 1 and D = 0.5, the ATL1 SOS resonator has a very low Q for this example. A Bode plot of the resonator's transfer function is shown in Figure 6, which is a Bode plot for the first order variable filter shown in Figure 4. Figure 6 shows a plot of magnitude 612 and phase 614 versus frequency. Note that due to the high damping factor (low Q) assumed in this example, the phase change with frequency is rather gradual around the resonance.

[0070] Now consider the effect of the feedback gain G on the closed loop poles. This is calculated by a 0 degree root locus calculation and is shown in Figure 5, where the poles of the ATL1 Core Module SOS resonator are represented by x (1502 or 1504). Line 1506 is the closed loop root orbit as the closed loop gain G increases from 0 to 1.2. This is the orbit of the pole denoted by number 1502. The root locus of the conjugate closed loop root orbit 1504 is line 1508. These movements are plotted along the jωS plane axes (root locus in the domain of complex frequency variables) s = σ + jΩ) exhibits progressively higher Q as the closed-loop gain G increases. When the closed-loop gain decreases as the Q dropper does, the root locus for poles 1506 and 1508 moves along the jω axis (not shown in Figure 5). In Figure 5, when the root locus crosses the right-hand plane, the closed-loop roots are unstable.

[0071] In this unstable region of operation, ATL1 cannot be used and the root orbit becomes meaningless. Therefore, we simply plot the range of G for which the closed loop poles remain in the left hand side plane (LHP). Note that for values ​​of G where the closed loop poles coincide with the jω axis, ATL1 oscillates at its resonant frequency. ω 0 In this example, it is normalized. ω 0 = 1. The radial dotted lines on the root graph indicate the damping values ​​of D. Q can be related to D based on the relationship, as shown above. Also, in this example, the gain G value where the root trajectory intersects the jω axis and ATL1 becomes unstable is G=1.

[0072] As the Q of the open loop SOS ATL1 resonator decreases, filtering in the initial forward pass is limited by a 20 dB change per decade of frequency. The problem with this is that out-of-band signals and broadband noise are not significantly attenuated by the signal's initial forward pass. As the ATL1 Q increases, these out-of-band signals are only rejected at the output if they are subtracted out in the summing block 1404 of the ATL1 circuit in Figure 4. This means that the signal flowing through the gain block 802 becomes larger and larger. To reduce this, we have the option of 1) increasing the Q of the SOS feedback resonator or 2) adding additional SOS feedback resonators.

[0073] Adding an SOS feedback resonator results in ATL2. Adding a third SOS feedback resonator creates ATL3.

[0074] Another way to implement a variable Q for an SOS resonator is a "Q spoiler" implemented via a variable resistance element in the SOS, such as a variable FET circuit or a PIN diode, that can increase the losses of the SOS, thus reducing the Q. This affects the damping coefficient of the SOS, which is designed to have a higher Q than is normally desired. The variable resistance reduces (spoils) the Q so that the poles of the SOS are farther apart, as JΩ axis the LHP as described above. This is a degree of freedom (DOF) that allows for higher outlier damping than if an SOS with a fixed lower Q were implemented. One embodiment of a Q-spoiler circuit is shown in Figure 7 based on a parallel resonant SOS 1701. In this case, the Q spoiler is implemented using a FET 1702 operating in the triode region in parallel with the resonator 1701, controlled by the Q spoiler control voltage 1704, providing an equivalent variable resistance function. In another implementation, the FET 1702 can be implemented with a PIN diode. It will be appreciated that these design options may be incorporated into any of the adaptive filter circuits described herein.

[0075] ATL1 Detailed Example

[0076] Referring to FIG. 14, the single resonator 2702 is a fixed resonant circuit with feedback gain 2704. For clarity, the alternative of modifying the Q of this circuit and using a bipolar gain element G in the gain block 2704 is ignored, where G can be negative for a Q dropper or positive for Q enhancement. Although the gain block 2704 is shown as a two-port gain block, it is understood that it may be arranged as a one-port gain block with negative or positive resistance. A negative resistance results in a G that is equally greater than zero, providing Q enhancement. A positive resistance, on the other hand, corresponds to a negative G, which gives a Q.

[0077] The root locus of the positive frequency closed loop poles for a positive G1510 is shown in Figure 15. This means that the closed loop poles are on the jω axis. Similarly, the root locus of the negative G1610 is shown in Figure 16. This means that the closed loop poles are on the jω axis.

[0078] FIG. 17 shows an example of a passband response with neutral Q (G=0) 1710, Q enhancement. (G = 0.15) 1712 and Q spoiling (G = - 0.5) 1714. Notice how the bandwidth is modulated by small changes in the feedback gain G.

[0079] Consider the case where resonator R provides a means to vary the resonant frequency of ATL1. The frequency response examples show normalized frequency values ​​for resonances of R of 0.9 (line 1810), 1 (line 1812) and 1.1 (line 1814) with G=0.15. The time required to tune from one frequency to the next is approximately equal to the inverse of the bandwidth of ATL1.

[0080] ATL3 Topology

[0081] The topology of the third order tunable filter ATL3 is shown in Figure 10 and includes three cascaded ATL1 SOS resonators, each with a feedback loop 1010, a method to change the center frequency of the resonator, and a method to change the Q of the resonator. As with ATL2, a unit gain buffer 102 is placed between all the resonators 1301 for isolation, and a cabiner 1404 closes the feedback loop. Figure 10 also shows the input 1012, output 1014, and gain block 1016. It is important to note the fundamental ability to control both the center frequency and gain of each individual resonator in this ATLn configuration. Initially, we will set the center frequency of each resonator the same, and later we will discuss ATL3 with different center frequencies.

[0082] The Bode plots for the triple resonators are shown in Figure 11 where each has the same center frequency and it can be seen that the out of band open loop attenuation for the triple resonator is 60 dB per decade since it is based on a low Q resonator. Figure 11 shows the magnitude 1110 and phase 1112 plots. The zero degree root locus is shown in Figure 12 versus D = 0.5 or Q = 1. The root locus is interesting in that there are three root orbitals 2306a / b / c emanating from each triple of open loop poles 2302 and 2304 and the scaling of the image makes the three individual roots indistinguishable. Note that one of the root orbitals 2306a / 2308a follows exactly the same contour as before while the other root 2306b / 2308b goes further into the left hand side plane (LHP) and has no effect on the circuit. However the third pole orbit 2306c / 2308c is aligned along the JΩ axis. This can result in spurious modes at frequencies much lower than the intended passband. However, for gains G where the dominant pole is close enough to the jΩ axis to achieve the desired high Q closed loop pole, this potentially troublesome pole is still far from the jΩ axis and causes negligible spurious responses in practical implementations. Serendipity shows that as the Q of the ATL3 SOS resonator is increased such that D decreases, this potentially troublesome root progresses further into the LHP, with a locus from poles 2402 and 2444 to 2406c, as shown in the zero degree root locus example in Figure 13, calculated for D=0.1, or resonator Q=5. As with all ATLn implementations, stability is obtained when the root locus remains within the LHP. This is discussed in more detail below.

[0083] There are three possible topologies for ATL3.

[0084] ATL3 Topology 1 (ATL3 T-1) can be seen in Figure 19, which consists of three individual ATL1 modules, each with an individually tunable center frequency and Q, and each incorporating a feedback loop with adjustable gain. This configuration provides the six degrees of tuning required to uniquely release the third order filter. Figure 19 shows the resonator 1301, the feedback loop 110, and the buffer 102. The movement of the poles of this ATL3 T-1 in the S-plane is shown on the left side of Figure 21.

[0085] ATL3 Topology 2 (ATL3 T-2) shown in FIG. 38 considers adding a single feedback loop 3810 around three consecutive ATL1 core modules, connecting the output of the last ATL1 to the input of the first ATL1. As shown, FIG. 38 has an input 3812, a combiner 3814, a resonator 3816, an output 3818, and a gain block 3820. However, ATL3 T-2 does not have a feedback loop within the individual ATL1 modules. As pointed out, this topology leads to substandard design situations, meaning that the performance of this topology may not meet strict design performance criteria. However, there are advantages in some cases that are always driven by design tradeoffs.

[0086] The ATL3 topology 3 (ATL3 T-3) can be seen in FIG. 20, wrapping the level 2 feedback path 110a around three ATL1 core modules, each with individual Q and center frequency control. In addition to the level 2 feedback path 110a, FIG. 20 shows the resonator 1301, the buffer 102, and the feedback loop 110. With the additional ATL3 level 2 feedback loop 110a, the pole movement in the S-plane is as shown on the right side of FIG. 21. The arrow 3602 in FIG. 21 is for negative feedback (Q spoiling) and the arrow 3604 is for positive feedback (Q enhancement). The pole movement of this ATL3 T-3 in the S-plane is shown on the right side of FIG. 21. Note that only the dominant pole is moving towards or away from the jω axis.

[0087] Due to this pole control, the ATL3 T-3 is the preferred embodiment and all future references to the ATL3 will refer to this topology.

[0088] The tunable analog ATL3 pole control allows control of the passband of the variable bandwidth filter, allowing for a variety of complex filter responses. The nature of the dominant pole that occurs in this ATL3 topology leads one to consider it a single-pole filter implementation, a fact that will be amplified later.

[0089] We will also show later that the phase control required for the ATL variable filter may be implemented by slight detuning of the ATL1 core module that constitutes the ATL3.In this way, no separate phase control element is required, simplifying design and manufacturing.

[0090] Butterworth bandpass filter response replication example

[0091] First, as an example, consider the classical third-order passive Butterworth filter as a bandpass filter centered at normalized frequency Ω = 1. Butterworth filters are particularly used when linear passband phase is desired.

[0092] The total transfer function of this classical passive Butterworth filter is written as:

number

[0093] This is a sixth order filter with 6 poles and 3 zeros at DC (0,0). The frequency (3510) and phase (3512) responses are shown in Figure 35.

[0094] The frequency (3610) and phase (3612) response around this Butterworth center frequency is shown in detail in FIG. 36, where it can be seen that the phase shift is fairly linear, but not exactly so.

[0095] The pole-zero map of this Butterworth is shown in Figure 37. One will notice for this classic passive Butterworth filter:

[0096] The phase shift is 0 degrees at the center frequency.

[0097] We see 6 poles and 3 zeros. We talk about a third order filter, considering only the positive frequency poles and therefore understanding that each pole has a conjugate pole.

[0098] Note that the two flank poles are approximately half the distance to the j Ω axis as the central pole, which means that these passive Butterworth poles have twice the Q of the central pole.

[0099] ATL3 Preferred Topology Results for Butterworth and Chebyshev Filter Performance Replication

[0100] In the preferred ATL3 topology, the arrangement of three ATL1 core modules allows the realization of three resonant poles as described. As well as the classical passive Butterworth filter described above, this can also be used to provide similar results as a classical passive third order Chebyshev type bandpass filter.

[0101] 19, an equivalent Chebyshev scheme is shown using three ATL1 core modules, where resonators 1401 each have a feedback path 110 (not shown) with a scaling block, and are separated by buffers 102. In this example, the poles of the three ATL1 core modules are generated as above and scaled along the jω axis.

[0102] If arbitrary placement of poles is desired to achieve a particular filter response, Q enhancement / spoiler can be provided for each individual ATL1 core module in Figure 19. However, the controls become more complex as six controls are required. Also, there is redundancy in the controls since the order of the resonators is generally irrelevant. This introduces confusion into the pole placement stability tracking algorithm described later.

[0103] Level 2 Feedback for Simplified Bandwidth Control

[0104] A simpler band control is the band control implementing a level 2 feedback loop 110a as shown in Figure 20. In this case, the feedback around each ATL1 core module is driven by a common control source (not shown) and each ATL1 core module feedback loop has a gain block (not shown) as explained above. Thus, as shown diagrammatically on the left side of Figure 21, the first level control of the ATL1 core module moves the three poles in unison towards or away from the jω axis.

[0105] The outer Level 2 control loop 110a around the three individual ATL1 core modules also has gain blocks (not shown). The addition of Level 2 control in the preferred ATL3 embodiment allows the outer adjacent poles to be spread out and the central dominant pole to be moved towards or away from the jw-axis, as shown diagrammatically on the right side of FIG. 21. It is important to note that the three poles can be moved in opposite directions. This important result allows the bandwidth of the filter to be relatively easily controlled while maintaining a similar frequency response.

[0106] In this ATL3 implementation evaluation, three ATL1 core module resonators with the following attributes are considered:

number

[0107] This places the poles at:

number

[0108] Now suppose that each of these three ATL1 core module resonators has a feedback loop, resulting in three cascaded individual ATL1 core modules. The root locus is shown in Figure 22.

[0109] Referring to Figure 22, 'x' 3702a / b / c specifies the location of the pole with feedback gain 0. The gain is positive towards the right excursion 3704a / b / c jω axis of excursion (Q-enhancement) and negative towards the left 3706a / b / c (Q-dropper). From the point of view of negative resistance amplification (Q-enhancement), this means that the resistance is zero at the 'x' position, with positive resistance towards the left excursion of the root orbit (Q-spoiler) and negative resistance towards the right excursion. Note how the control goes along the contour of a constant natural resonant frequency. The feedback gain for each root orbit ranges from -1 to G <0.9.

[0110] Figure 23 shows the normalized frequency response of three ATL1 core modules for feedback gains of 0 (line 2310), -1.0 (line 2312) and 0.9 (line 2314), illustrating the effect of Q-enhancement (positive G) and Q-spoiler (negative G) compared to neutral gain (G=0). In this plot, peak amplitudes have been normalized to 1 to make the plot clearer.

[0111] Next, we consider a modified preferred ATL3 topology with three resonators, where the three resonators are Q-dropped ATL1 core modules with a gain of G = - 0.9. Figure 24 shows the frequency response 2410 for the preferred ATL3 topology when the level 2 feedback gain is G = 0.

[0112] Now let's look at how we can make this look like a third order passive Chebyshev bandpass filter response by modifying the preferred ATL3 topology level 2 feedback.

[0113] Referring to Figure 25, the left plot is for a negative favorable ATL3 topology Level 2 feedback and the right plot is for a positive favorable ATL3 topology Level 2 feedback. Note how this can be used to adjust the position of the flanking poles relative to the central pole, as explained above. Figure 26 shows how the preferred ATL3 topology level 2 feedback is used to control the bandwidth of the filter. Positive level 2 feedback narrows the filter bandwidth and negative level 2 feedback widens it. Only a small amount of ATL3 topology level 2 feedback is needed for this control. In Figure 26, the level 2 feedback was 0 (line 2610), -0.002 (line 2612), and +0.002 (line 2614), as shown.

[0114] As can be seen, the preferred ATL3 topology Level 2 feedback control of FIG. 20 allows for an effective means of bandwidth control that can be practically implemented.

[0115] Preferred ATL3 topology center frequency

[0116] Now consider a modification to the preferred ATL3 topology shown in Figure 20, where the SOS resonator 1401 pole locations are shifted in frequency and therefore not covolved. The S-plane, as considered earlier. This may allow for greater flexibility in controlling the closed loop frequency response of the preferred ATL3 topology. The benefit of this increased flexibility is that different frequency responses may be achieved. This additional flexibility may be important in some applications beyond the scope of this disclosure. As an example of staggered frequency resonators, consider the case of normalized SOS resonators with ω = 0.9 rad / sec, 1.0 rad / sec, and 1.1 rad / sec, with D fixed at 0.15 (Q = 3.33) for all three resonators. The Bode plot of these three SOS resonators cascaded is shown in Figure 27 showing the potential for a flatter passband, with magnitude shown at 2710 and phase shown at 2712.

[0117] FIG. 28 shows the zero degree root locus of this configuration, which is very similar to that shown in FIG. 12, where each of the three SOS resonators has the same center frequency.

[0118] ATL Topology Overview

[0119] In summary, the ATL1 core module may provide excellent bandpass filtering performance for many applications. The ATL1 core module provides the basic frequency tuning and Q adjustment of the ATL concept.

[0120] However, the ATL2 and ATL3 filters allow flexibility in tuning to the application, with ATL3 providing the best rejection of out-of-band signals for typically found closed-loop Q values.

[0121] With the decoupling of pole root orbits, the Level 2 feedback implementation provides an unparalleled ability to set the root orbits of the closed-loop ATL n poles for n ≥ 2. This pole decoupling, shown in Figure 28 and Figure 21, is a key attribute of ATL3.

[0122] Phase shift control of ATLn

[0123] General Phase Shift Control Considerations

[0124] As mentioned above, adjustable phase shifters can be used to provide some circuit control. Some examples of adjustable phase shifters that can be used in the context of ATL-based circuits are described below. Other types of phase shift elements that provide an appropriate level of performance can also be used.

[0125] Since the ATL3 is composed of three ATL1 core modules, it is important to examine the phase control of this ATL1 core module. The closed loop passband of the ATL1 core module was found to be formed around a range of frequencies where the open loop phase shift is a multiple of 360 degrees. As it is desired to have only a single passband, the resonator passband may be positioned to coincide with the frequencies of multiples of the 360 ​​degree phase shift. If the resonator peak frequency is misaligned, the closed loop response peak will still coincide with the frequency where a multiple of 360 degrees is achieved, but the passband may become distorted.

[0126] The phase control can in principle be any circuit that is capable of varying the signal phase shift at the resonant frequency.

[0127] The phase shift provided should be relatively smooth throughout the entire closed-loop Q-dependent bandwidth of ATL1.

[0128] The phase shift across the band depends on the control voltage (p). This is shown in Figure 39, where p1 (line 3910) and p2 (line 3912) represent two different values ​​of the control voltage p, and the curves show a typical phase response with frequency. Figure 39 also shows the ATL1 band 3914.

[0129] The magnitude of the transfer function through the phase shifter must not significantly change the Q-dependent bandwidth of ATL1.

[0130] A variable phase shift may be introduced by starting with a variable delay line consisting of a series of diodes along a transmission line. By varying the diode voltage, the group delay can be changed, and by varying the group delay, the phase can be shifted.

[0131] An array of victors has a non-uniform amplitude response in terms of frequency because of its finite length and spacing. In this context, a single victor behaves similarly to a low-Q resonator with variable capacitance, and three victors behave similarly to three coupled resonators as in the ATL3. Thus, a variable delay line can be approximated by using a small number of victor diodes to create a structure with a variable group delay that has a reasonably uniform magnitude response for the desired frequency range. Similarly, the 90-degree hybrid couplers used in quadrature modulator chips are essentially Hilbert transformers operating over a modest frequency range. In other words, the variable phase shifters, resonators, delay lines and quadrature modulators may be considered as circuits arranged and optimized to provide variable delay over a range of frequencies.

[0132] By generalizing the variable resonator and variable phase shifter, and recognizing that they are functionally similar in the context of their application to ATLn, we can use multiple sub-circuits in a loop, with each sub-circuit controlled to give the desired delay and amplitude response that can be controlled by multiple control voltages.

[0133] Phase shift control of ATL1

[0134] The ATL1 core module is a single variable resonator subcircuit. With careful design, the phase shift may be a multiple of 360 degrees at any desired frequency within the passband of the resonator. Shifting the resonant frequency will shift the phase equally. The ATL1 response peak occurs when the loop phase shift is a multiple of 360 degrees. The limitation of the ATL1 having only a variable resonator is that the resonator phase shift adjustment is limited. Therefore, if there is a large phase error in the loop, a single resonator does not have enough range and it is necessary to add a variable and a fixed phase shifter. However, based on the discussion of general phase shift control considerations above, this is equivalent to stringing together many delay-controllable subcircuits in series.

[0135] Now let us replace another resonator with a variable phase shifter. A phase shifter has a flat frequency response in terms of size, so it can be used over a wider frequency range, but this comes at the cost of adding more components, some of which are difficult to integrate on the chip. If three resonators are added, this corresponds to a special case architecture of ATL3. This shows three variable resonators 502 at the input, which can be the input 3410, the output 3412, the ATL1 elements, the feedback path 110, the coupler 104, and the gain element 112.

[0136] It is also recognized that there may be more than two resonator sections, with the important consequence that more delay tuning is possible when more controllable resonators are present, which means tuning of a wider frequency range without the need for additional fixed or variable phase shift elements.

[0137] Furthermore, as mentioned above, it has been found that the detuned resonator adds a controllable phase shift. This important fact can be used to add a modest, controllable phase shift without resorting to a separate phase shift control element.

[0138] As mentioned before, the phase shifter is necessary to make up for the excess phase that inevitably accumulates in the ATL1 closed loop design. The objective is to bring the phase to a multiple of 360 degrees at the desired resonant frequency. Thus, the phase shifter control is a parameter that does not improve the performance of ATL1 further than the idealized model shown in Figure 40, but is necessary for practical implementations. Figure 40 shows an idealized model of ATL1 with two implementations, having the resonator 4010 and scaling block 4012 in different locations.

[0139] Regardless of the implementation, the phase shift function has the denominator in the following transfer function:

number

[0140] where XR is the open loop transfer function and G is the loop gain. A typical Nyquist stability plot is shown in Figure 41 where the points on the locus crossing the positive portion of the real axis coincide with the open loop phases that are multiples of 360 degrees.

[0141] The frequency response may be determined (with respect to the closed loop denominator) as the inverse of the facet shown between the real axis points of 1 / G and the open loop transfer function F(jw). So, it generally has a set of resonance and anti-resonance points as shown in Figure 41. As G is increased, 1 / G will eventually intercept the outermost resonance points and move towards the left. Note that this is the same as the root locus where the poles cross the Jw axis.

[0142] A pure phase shifter is

number

[0143] α rotates the Nyquist plot clockwise by radians. However, as circuits become infinitely more complex, a pure phase shift is not achievable; it can only be implemented over a narrow frequency range. Consider Figure 42, which shows the Nyquist plot of a resonator over a small frequency range as curve 4210. Then α is applied. As the length of the phaser increases from 1 / G to the resonance point, the resonant response decreases. As G becomes larger, ATL1 peaks at point A rather than at resonance. Also note that as G becomes larger, the peak closed-loop response of ATL1 shifts in frequency, which is undesirable. Therefore, we want to add a phase shift - α - to correct the Nyquist curve 4212 to curve 4210.

[0144] We can see that the peak response of a finite Q is not necessarily at a frequency that coincides with an open loop phase shift that is a multiple of 360 degrees. However, as Q is increased to large values, the loop phase approaches a multiple of 360 degrees. We can set the phase shift correctly by rotating the open loop transfer function so that its peak moves along the real axis. In this case, the frequency does not change as Q is enhanced or ruined. So to set the phase correctly, we can look at how the peak passband frequency changes with increasing G, such that the minimum value of G is obtained at the desired Q.

[0145] It is also clear from this discussion that the desired phase shifter function is not a constant, but a smooth function over the range of the ATL1's closed-loop narrowband response. Think of the simplest phase shifter circuit as an RC circuit with a phase shift.

number

[0146] The problem with this phase shifter is that as the capacitance C of the basactor increases, so does the loss in the circuit. Also, the range of the phase shift is not sufficient. To solve this multiple RC segments may be used. This solves both problems but requires more complexity.

[0147] The desired on-chip phase shifter is a type of resonant delay circuit that provides a smoothly varying delay over a relatively small bandwidth. Such a phase shifter is the all-pass circuit shown in Figure 43, having resistor 4310, capacitor 4312, inductor 4314, and differential amplifier 4316.

[0148] The transfer function of this all-pass circuit is

number

[0149] can be placed in the form

number

[0150] From Ω P And D P In the circuit of Figure 43, R can be implemented with a combination of FETs and capacitors implemented as actuator diodes that allow control of the location of the poles and zeros. Increasing R moves the poles along the JΩ axis, and the phase shift becomes steeper as a function of frequency. Similarly, by changing the actuator capacitance, the poles can be moved vertically. The pole-zero diagram for this all-pass network with normalized frequency is shown in Figure 44.

[0151] The normalized frequency response of this all-pass circuit is shown in Figure 45. The signal magnitude response is:

[0152] It is optionally flat and allows quadrature control of frequency and phase separately from the control of the actuator control voltage g. And

[0153] The phase changes smoothly over the passband of ATL1, exhibiting a decreasing slope with frequency.

[0154] Change the all-pass frequency Ω P shifts the phase curve left or right to provide phase control for a particular passband. The constant amplitude response of Figure 45 has the advantage that the phase can be changed without any change in loop gain. Also, note that this phase shifter has a range approaching 360 degrees.

[0155] ATLn Phase Shift Control Considerations

[0156] ATLn is a bandpass filter made up of "n" consecutive ATL1 core modules, each in one of three possible topologies as explained above. Each ATL1 module in the group is individual in performance and can be tuned both in terms of the center frequency and Q of the resonator, and an amplifier can be included in the feedback loop around the resonator. Each ATL1 is isolated from the other ATL1 modules, ideally using a circuit-coupling buffer that introduces a zero-point phase shift.

[0157] Ideally, the open loop phase shift of the ATL1 resonator should be zero degrees at the passband center frequency and highly linear throughout the passband. This can be achieved with an ideal resonator that has no parasitic elements. As is known in the art, the phase of a signal can be affected by many different factors as it passes through a circuit, a certain portion of which includes stray capacitances and inductances that can be denoted as "parasitics." There are parasitic elements associated with the ATL1 resonator (or resonators as in ATLn), which results in a phase shift associated with the buffer amplifier. In ATLn for n≧2, the excess phase shift can exceed 360 degrees. Certainly, the excess phase needs to be considered.

[0158] In general, if the ATLn circuit is mounted on a chip where parasitics are largely minimized, well modeled and understood, and the ATLn circuit is intended to be used over a reasonable frequency tuning range, a fixed phase shifter may be sufficient. In other circumstances, such as when the ATLn is implemented as a discrete component or with surface mount technology, it may be necessary to incorporate a variable phase shifter to correct the phase of the signal passing through the circuit.

[0159] The phase shifter used will depend on the actual implementation of the circuit. Various types of phase shifters are known in the art, and a skilled artisan can incorporate appropriate phase shifters into the ATLn as required. In the discussion of the ATLn topologies above, it was shown that there is no need to implement a separate phase shifter element, since the net loop phase error can be easily controlled by small frequency adjustments to the ATL1 core modules that make up the ATLn. This important result applies to all ATLn variants of ATL variable filters, n > 1.

[0160] Gain Polarization Switching and ATL1 Phase Shift Control

[0161] To achieve full 360 degree parasitic phase shift control, an alternative is to add polarization selection to the output of a variable gain block that operates with an all-pass phase shifter. The gain block is realized with a differential amplifier and FETs to control the source current and therefore the gain of the differential amplifier. One of the two outputs of the differential amplifier can be selected with a switch. A simplified circuit diagram of a variable gain with polarization selectable output 4610 is shown in Figure 46, with an input 4612 for the gain control 4614 and current adjustment.

[0162] This gain polarization switching circuit is a simple integration of a differential amplifier with control of gain based on adjusting the current through a differential FET pair via the bottom FET shown. Selection of the output from the two differential outputs provides polarity selection. Alternatively, a full Gilbert cell integration could be used. Gilbert cells are more elaborate than required for an ATL3 implementation. However, there may be other considerations not considered here that make a Gilbert cell a better choice.

[0163] The circuit is set at the desired frequency of ATL1, in this case Ω = 1. A full-phase phase shifter with polarization control in the second order corrects for the parasitic phase shift. The closed loop center frequency will be at the correct frequency when the phase shift at that frequency is a multiple of 360 degrees.

[0164] A typical Nyquist plot based on this ATL1 phase-shift control implementation is shown in Figure 47. In this case, the parasitic delay caused a phase shift of 0.6 radians. The allpass circuit compensates for this by resonating at 1.02, and the Ω = 0 point coincides with the intercept point on the real axis.

[0165] The use of this technique can be extended to ATLn implementations.

[0166] Gain Polarization Switching and ATLn-Based Phase Shift Control

[0167] Because the all-pass network is based on a resonator, we have been led to investigate the implementation of the ATLn circuit for phase shifting, including gain switching, as described above, as an alternative to the all-pass network circuit for phase control, which is preferred to the ATL1 phase control. The elimination of the additional parts of the active all-pass network is a reasonable objective. Furthermore, the all-pass phase shifter provides a constant magnitude that is not required for phase shifting.

[0168] The tunability can be improved slightly by adding additional resonators, such as ATL3, which has three resonators. The motivation is to make the resonators less detunable to accommodate any parasitic phase shifts. This makes the Nyquist locus of the real axis more perpendicular to the real axis, resulting in less tilted bandpass and more independent control of the center frequency and bandwidth of the closed loop passband. Figure 48 shows a block diagram of ATL3 with three cascaded resonators 4810, variable gain block 4812, gain polarity selection buffer 4814, sum 4816, and output 4818.

[0169] As with the ATL2, the isolated resonator 4910 is not necessary and the three required resonators can be grouped into a composite bandpass filter with three poles as shown in Figure 49. Shown in Figure 49 are the gain block 4912, sum 4914, isolation buffer 4916, input at 4918, and output at 4920. We feed this ATL3 with a parasitic phase error of 1.5 radians. The resonators must be detuned by approximately 5% each to accommodate this worst case parasitic phase shift. Also, as previously discussed, if the parasitic phase shift increases beyond 1.5 radians, the other polarization output of the variable gain block is used. Figure 50 shows the Nyquist plot of a detuned ATL3 resonator with gain switching to complement the 1.5 radian parasitic phase error. When the phase error is near ±π / 2, the Nyquist plot is nearly symmetrical about the imaginary axis. This means that either polarization of G gives the same performance due to Q enhancement.

[0170] It is interesting to consider the root locus plot of ATL3 in this case. Unfortunately, parasitic delays cannot be directly represented in a root locus plot. However, we may get a reasonable idea of ​​the behavior by ignoring the parasitic delays in this instance. The root locus is plotted in Figure 51 for the case of three resonant poles. Ω = 1 for the damping factor D = 0.1, which corresponds to Q 5.

[0171] What is interesting about the Figure 51 plot is how the closed-loop poles are divided for the two polarizations of loop gain G.

[0172] The 180 degree root locus plot on the left has two dominant poles on the JΩ axis, so there is Q enhancement for both of these poles.

[0173] In the 0 degree root locus plot on the right, only the poles are Q-enhanced.

[0174] The result is a simple bandwidth control, shown in the frequency plot of Figure 52, with line 5210 showing G=0, line 5212 showing G10, and line 5214 showing G>0. By varying the G control with a polarization switch, one can switch between two controllable bandwidths.

[0175] ATLn self-calibration

[0176] Here we will explain how to use ATLn as a subsystem in a specific application. In this example, you can set the control voltage to tune the performance of ATLn for your target application based on the following principles:

[0177] The resonator block may be based on a control voltage on a photodiode for center frequency selection.

[0178] The gain block may require a control voltage to scale the signal or to control the feedback gain and overall bandwidth (Q) of the ATLn.

[0179] Signal phase shifters implemented with actuator diodes may require additional control voltages.

[0180] Signal phase shifts arise from component and interconnect delays and phase shifts due to implementation either a) at the bulk component level; b) at the component surface mount level; or c) at the integrated chip level. These phase changes in the feedback loop must be compensated for with a phase shifter that can properly restore the overall phase shift of the loop.

[0181] In summary, there are three control voltages to set: F: Center frequency control voltage G: Loop gain and bandwidth control voltage P: Phase adjustment control voltage

[0182] These control voltages, as determined, are placed into a look-up table (LUT) that provides a mapping between the application or user parameters of bandwidth (denoted by B) and center frequency (denoted by F) and outputs {f,g,p}. The LUT actually consists of three separate tables with input variables including {B, F} and a separate table consisting of the individual settings of f, g, and p.

[0183] The set of LUT manifold functions is fairly smooth, so accurate interpolation from a small set of calibration points in {B,F} space is sufficient.

[0184] In this example, the basic ATL1 calibration data resides in a LUT. For ATLn there are 3n calibration LUTs, each of which is Phase Entries Loop Gain and Bandwidth Control Entries An entry to set the frequency of each of the n resonators.

[0185] Thus, for ATL1 there may be three such LUs, while for ATL3 there may be nine.

[0186] The following describes various considerations that may or may not be relevant for a particular implementation.

[0187] ATL1 Calibration and Stability Control

[0188] We will start with an example of calibration and stabilization of a single ATL1 core module. Figure 32 presents a circuit with built-in processing for the purpose of calibrating and stabilizing the response of the ATL1 block 7502. Figure 32 shows the ATL-1 7502, power detector 7512, ADC 7514, frequency down converter 7510, frequency counter 7509, temperature sensor 7508, μP 7504, LUT 7516, control PWM(f,Q) 7506, frequency synthesizer 7507, and crystal reference 7505.

[0189] With reference to FIG. 32, a microprocessor 7504, which is generally a system asset, regulates the frequency and Q control of ATL1 7502 via a digital-to-analog converter (DAC) implemented as a pulse-width modulation (PWM) circuit 7506, and a temperature sensor 7508. The microprocessor drives ATL1 7502 until the onset of self-oscillation. The frequency of this self-oscillation is down-converted in block 7510 by a crystal reference 7505, also set by the microprocessor 7504, and a frequency synthesizer signal generated by a frequency synthesizer 7507. A frequency counter 7509 or other measuring means determines the frequency of the down-converted signal. In this way the resonant frequency of the ATL1 core module may be determined. There is also a power detector 7512 and an analog-to-digital converter (ADC) block 7514 that can estimate the rate of increase of the self-oscillation signal at the output of ATL1 7502. The microprocessor 7504 estimates this exponential rise in power and this determines where the closed loop pole of the ATL1 7502 is. Currently, it will be just to the right of the Jw axis. If the Q enhancement is reduced slightly, the self-oscillation will continue with high accuracy at the same frequency, but will begin to decay exponentially. Now the pole is to the left of the Jw axis. Again, based on the power detector 7512, this exponential decay may be measured and the operating point may be measured. By repeatedly bringing the ATL1 7502 into self-oscillation and reducing the Q enhancement by a controlled amount, the mapping to the ATL1 7502 and the f and Q control signals may be completed. This calibration may be based on on-chip circuits that require no additional off-chip components other than a crystal reference source. During operation, a calibration break may be made so that the LUT 7516 is continuously updated. In the case of a wireless sensor, the transmitter and receiver functions are separated by epochs of inactivity during which the calibration process takes place.

[0190] ATL1 Q Control

[0191] Figure 33 shows an example of the Q control of ATL1 alternating between high and low levels which places the closed loop poles of ATL1 in alternating right and left hand planes. The resulting exponential rise and decay is easily measured by a power detector with numerical analysis performed on a microprocessor. Thus, the applied Q control voltage can be mapped to a specific pole location. This is stored in the LUT so that when a pole location is required for the filtering operation of ATL1, the LUT can be interpolated and the {f,Q} control voltage can be set.

[0192] The actual part of the closed extremum is easily measured. Suppose the pole lies in the right-hand plane such that it is of the form x = Aexp(Bt), where a and b are unknown constants. Then, if the envelope voltage is measured at two different times T 1 And T 2 As a result, X 1 And X 2 Respectively, the desired parameter b is

number

[0193] At any time T 1 And T 2 You can set the voltage x 1 and x 2 A fixed threshold, measured or otherwise, can be set to x 1 and x 2 , and the time difference T 2 -T 1 You can measure it. Either approach is easy.

[0194] In an application that includes an ATLn implementation, the above calibration procedure is repeated for each ATL1 core module within the ATLn.

[0195] It can be seen from the above that the ATLn could be designed to widen its bandwidth relatively easily. As shown above, the level 2 feedback gain G around 3R in ATL3 is a simple and robust way to change the passband from one that represents a single-pole passband response to a broadened response similar to a third-order Chebyshev filter.

[0196] ATL3 Control Examples

[0197] The application of this control concept lies in wireless sensors and has the potential to offer the following aspects:

[0198] First, the ATL3 can be configured on the fly to be a power spectral density sensor for cognitive radio.

[0199] The ATL3 then acts as both a transmit and a receiver filter for this passband, using a transmit / receive (T / R) switch to change the filter direction for transmit / receive functions.

[0200] In receive mode, the ATL3 can be coupled to an adaptive loop that uses the SNR of the digitally sampled output to optimize the filter parameters. Because the {f,Q} controls are orthogonal, this SNR optimization is robustly achieved with a simple dithering algorithm.

[0201] Finally, when configuring the ATL3, it is necessary to know where the poles are as a function of the control. This can be achieved by using the auxiliary ATL1 on the chip for calibration purposes. By alternating pole positions in the left and right planes (unstable and stable, respectively), the envelope of the self-oscillation of the ATL1 may be used as a probe signal to estimate the real part of the pole position. The imaginary component depends on the frequency of the self-oscillation. Self-oscillation may be measured based on a comparison with a crystal-locked synthesizer frequency. Instead of the ATL1, the three resonators (R) of the ATL3 could also be used directly. However, the implementation of the ATL1 allows the calibration to be done continuously and in parallel with the operation of the ATL3 dedicated to the actual signal processing. The measurements of the ATL1 pole positions as a function of the control voltage and possibly the chip temperature are stored in a LUT. The values ​​of the LUT are interpolated when configuring the ATL3.

[0202] It should be noted that the exponential decay time of this procedure is very fast and may require a fast DAC. Also, there is an assumption that the pole frequency does not change when crossing from an unstable RHP to a stable LHP, which is a reasonable assumption. Therefore, this approach to calibrating and stabilizing a single ATL1 core module is suitable for general purposes. However, for the highest calibration accuracy, a second approach to calibration and stabilization is now presented.

[0203] High-precision ATL1 calibration and stability processing objectives

[0204] Although the ATL1 calibration is stable over time, it does vary based primarily on ambient temperature, and may not be sufficient for precision filtering operation in applications requiring high-Q narrowband operation with the poles very close to the JΩ axis. In addition to normal aging effects of components, there is some sensitivity in the ATL due to temperature drift of components which can cause bandpass shifts on the order of several MHz. Additionally, the ATL passband is affected by load matching at the input and output terminals.

[0205] If you want the highest accuracy, all you need is:

[0206] Ability to set 1 MHz bandwidth for ATL1 core module

[0207] The ATL1 core module's center frequency resolution of approximately 100 kHz requires a relative frequency accuracy of 100 ppm.

[0208] This relative frequency accuracy is typically provided by a crystal reference available in every communications device. For applications where the highest accuracy is not required or an external crystal reference is not available, high performance is still achievable.

[0209] Factory calibration may not be sufficient for this level of highest accuracy, requiring initialization and / or run-time calibration. Furthermore, for narrow bandwidth operation, the Q enhancement factor may be large, requiring the loop gain to be set very accurately. If the loop gain changes by only 100 ppm in a high-precision application where a narrowband linear filtering mode is desired, the ATLn will move the closed loop poles of the Jw axis into the right-hand plane (RHP), resulting in either a) self-oscillation; or b) transition into injection lock. Thus, precise calibration of the loop gain is also required. To address these calibration issues, two calibration modes are envisaged, which are detailed below.

[0210] ATL1 initialization self-calibration mode

[0211] The ATL1 self-calibration in any system implementation (at the individual component level, at the surface mount level or as an integrated chip) is based on the measurement of the ATL1 passband as a function of the {f,g,p} control voltages. The ATL1 can enter this self-calibration mode whenever requested by a) the LUT or b) a higher application layer where weighting of previous and current measurements can be done. These ATL1 measurements are done with input and output loads of the circuit so that deviations due to port impedance mismatch are taken into account. If not available at the system level, a temperature sensor is also provided in the ATL1 circuit so that sensitivity due to temperature changes is calculated. Note that this is done by multiple calibration runs and analysis of the drift during the run. This on-situ calibration also accounts for voltage regulation errors and offsets of the DAC voltages of the {f,g,p} controls.

[0212] Initialization is only required when the initial parameters of operating frequency and bandwidth (Q) are set. If multiple operating frequencies are required, such as in a frequency hopping application, initialization is required at each operating frequency. Initialization is not performed routinely because the ATL1 operation, and by extension ATLn, have proven to be stable over time. The only parameter that affects the operating calibration is the ambient temperature of operation, which is subject to run-time calibration.

[0213] When implementing ATLn, each ATL1 core module is often initialized separately to establish its own LUT.

[0214] ATL1 Runtime Calibration Mode

[0215] Run-time calibration is application specific. Wireless applications of ATL1 have an inherent baseband data demodulation process from which a signal can be extracted as a metric indicative of the quality of the ATL1 filtering. The {f,g,p} control parameters can be set by dithering or other optimization strategies to maximize the quality of the ATL1 filtering. Modifications to the LUT can be noted as deviations from this optimization process. Thus, the LUT is continuously optimized. The algorithm for long-term annealing of the LUT can be customized to the specific application.

[0216] The frequency passband response is measured relative to a crystal-based reference oscillator or other frequency reference source.

[0217] Overview of the ATL1 high-precision calibration process

[0218] In this section, we propose a high-precision calibration structure that facilitates the two calibration modes from the previous section: ATL1 Initialized Self-Calibration and ATL1 Runtime Calibration. This structure depends on the physical implementation of the ATL1 core module, which can be at the individual component level, surface mount level, or integrated chip implementation. Any application can be considered (e.g. ATL3 or ATLF), but to initially focus only on the concepts of self-calibration and stability control, the ATL1 core module is implemented within an overall wireless sensor transceiver system consisting of a minimal set of four components: the antenna 14610, the switch array 14612, the ATLa 14614, the ATLb 14616, the down / up conversion and ADC / DAC sampling 14618, the ATL control 14620, the baseband processing 14622, the LO / ADC clock synthesizer 14624, the power conditioning 14626, the transceiver chip 14628, the clock crystal 14630, and the power supply 14632. This example shows a pair of standard ATL1 core modules, labeled ATL1a and ATL1b. These are chip implementations of ATL1 and are considered identical and uncalibrated. However, the calibration process that follows would be the same for the discrete component level and surface mount implementations in Figure 146. However, the chip level implementation is likely to provide the highest level of accuracy.

[0219] Referring to the entire wireless sensor transceiver system for this example, as shown in Figure 146, the antenna is in calibration mode, transmit mode, and receive mode. Obviously, the switch has some insertion loss and contributes to the receiver noise figure (NF). We will consider this issue later. Baseband processing is used to generate observable objects that can control ATL1a and ATL1b. The controls are shown as red lines that also affect the switch arrangement.

[0220] The overall goal is to develop a practical means of self-calibration of ATL1a and ATL1b that is done solely within the transceiver module outlined in Figure 146. That is, a transceiver module is fabricated as shown in Figure 146 and inserted into an initially uncalibrated transceiver system. Upon application of power, the transceiver module enters a self-calibration mode and generates a look-up table (LUT) of the ATL1a and ATL1b control voltages required to support a particular center frequency and Q. Calibration continues during operation in various modes. In this way the transceiver chip self-learns during operation.

[0221] To enable this calibration, a clock crystal sets the reference frequency to be used. However, cheap clock crystals are only accurate to within about 100 ppm, so in various scenarios, as mentioned above, an input reference signal can be used to determine the frequency offset of the clock crystal, and this can also be stored in the LUT.

[0222] It is important to realize that ATL1 may operate as a stable oscillator with a non-tunable frequency, and this output may be fed to another ATL1 to determine its frequency characteristics. Following this method, ATL1a becomes a voltage controlled oscillator (VCO) that feeds ATL1b, which in turn uses ATL1b as a VCO to determine the bandpass characteristics of ATL1b. Since ATL1a and ATL1b are built on the same chip die, operate at the same temperature, apply the same voltages in the same way, and age in the same way, they are very closely matched in terms of operating characteristics. This helps with calibration, which we will discuss in more detail later. The key innovation is that the chip is a transceiver, and therefore has baseband processing that is clocked based on a frequency-corrected clock. Thus, the stability of the clock crystal is effectively mapped to ATL1a and ATL1b. In other words, ATL1a is used as a VCO that is set to operate at a specific frequency based on the control settings. Then, based on the down conversion (based on the LO synthesizer derived from the clock crystal) and ADC sampling (clock also based on the clock crystal), the frequency of the ATL1a relative to the corrected clock crystal frequency can be determined. When the closed loop resonant pole of the ATL1a retreats away from the jw axis and no longer oscillates, it acts as a high Q filter. Just as the ATL1a goes from oscillation mode to filter mode, the frequency of oscillation is exactly the center frequency of the ATL1a high Q filter.

[0223] For non-chip implementations, the same considerations apply at the system level, although the accuracy of the calibration can impact the quality of the implementation.

[0224] As used herein, references to high and low Q will be understood based on the context in which they are used, as would be understood by one of ordinary skill in the art. In some cases, the Q of a primary resonator is considered to be high relative to a tunable resonator, with a high Q resonator being a factor of 10 or even 100 times greater than a tunable resonator.

[0225] Operational Mode

[0226] There are many different modes in which the switch arrangement can be implemented.

[0227] In the basic receive mode (mode 1 shown in Figure 147), the ATL1a forms an RF filter. Figure 147 shows the antenna 14710, the ATLa 14712, and the down-conversion ADC sampling 14714. In this mode, the ATL1a has a relatively high Q and therefore a high gain.

[0228] ATL1a and ATL1b are cascaded (mode 2 shown in Figure 148) with ATL1a having a lower Q and wider bandwidth and ATL1b having a narrower bandwidth and higher Q. Figure 148 shows the antenna 14810, ATLa 14812, ATLb 14814, and the downconversion ADC sampling 14816. The idea is that ATL1a has better intermodulation performance because it suppresses some of the out of band tones and is a lower Q. ATL1b has a higher Q and narrower bandwidth.

[0229] An interim switched-in attenuator is inserted between ATL1a and ATL1b as shown below. Figure 149 may be necessary to keep the gain within a reasonable upper limit on stability, as described below. Figure 149 shows the antenna 14910, ATLa 14912, attenuator 14914, ATLb 14916, and the downconversion ADC sampling. If the gain is too high, it is difficult to ensure that the transceiver chip remains stable. Note that this attenuator is a relatively trivial circuit that can be added at the output of ATL1a.

[0230] Currently, we are limited to a time division duplex (TDD) protocol where the transceiver transmits in one time interval and receives in another, but other protocols can be used. Selection of the appropriate protocol is beyond the current discussion, as long as the mode can handle this. Mode 3 is the basic transmit mode that operates in conjunction with Mode 1 for receive mode, as shown in Figure 150. Figure 150 shows the antenna 15010, the ATLb 1501, and the up-conversion DAC sampling 15014. The switch array facilitates switching between Mode 1 and Mode 3 for TDD functionality.

[0231] High Precision Calibration Mode

[0232] Now consider a set of switchable modes for calibration. In mode 4, the closed loop resonant pole essentially operates as a VCO, as shown in Figure 151. Jw axis. Figure 151 shows ATLb 15110, attenuator 15112, ALTa 15114, and downconversion ADC sampling 15116. This ATL1b VCO signal is attenuated to a low level by a simple attenuator associated with the ATL1b output that can be switched in. The attenuated nostril wave signal goes into ATL1a, where it is downconverted and sampled. Subsequent processing measures the level and frequency of the signal output of ATL1a. In this way the bandwidth and center frequency of ATL1a may be adjusted.

[0233] Mode 5, shown in Figure 152, is the inverse of Mode 4 in that ATL1a is used as a VCO and feeds ATL1b which acts as a filter. Figure 152 shows ATL1 15210, attenuator 15212, ATLb 15214, and downconversion ADC sampling 15216.

[0234] High-precision ATLn self-calibration

[0235] Here we teach that by adding a single ATL1 core module to any ATLn circuit, precision calibration may be achieved. The circuit in Figure 146 starts out operational, but with no calibration data whatsoever. When the circuit in Figure 146 first powers up, it erases the contents of the LUT and goes into a basic calibration mode starting with an empty LUT.

[0236] Now assume the system starts in mode 5 of Figure 152. We will simply assume that ATL1a and ATL1b have resonators in the through path, with scaling blocks and phase shifters as shown in Figure 153. Figure 153 shows coupler 15310, resonator 15312, scaling block 15314, and phase shifter 15316. As always, we assume three control voltages {f,g,p}: one for the resonator frequency, one for the scaling block setting, and a third to control the phase shifter.

[0237] For illustration purposes, we will assume that ATL1b can be configured with a resonator with an open-loop Q of approximately 10. If the scaling block is set to G = 0, there is no feedback, only an open-loop Q. Therefore, the output of ATL1a passing through ATL1b should be observable in the baseband processing to the extent that its frequency can be accurately determined relative to a clock crystal.

[0238] We also assume that the fabrication of ATL1b is sufficiently controlled that the resonator of ATL1b can be set to be in the middle of the tunable band. This means that we assume reasonable fabrication control of the actuator diodes used in the resonator. Also, the resonator of ATL1a is initially set to be in the middle of the tunable band.

[0239] This increases the gain. Note that the ATL1a resonator oscillation condition is met when the loop phase around ATL1a is a multiple of 360 degrees and the loop gain is slightly less than unity. Next, adjust the ATL1a phase voltage control to achieve this resonance condition. Then adjust the ATL1a phase scaling block to minimum feedback gain to maintain oscillation. The limited bandwidth of the baseband processing makes it difficult to observe the oscillation. Therefore, an initial search for the resonator voltage and phase is required for ATL1a.

[0240] As shown above, the phase shifter is modeled as an all-pass filter of the form

number

[0241] Now the pole-zero plot is given in FIG.

[0242] The frequency response is shown in Figure 155. Note that the magnitude response is flat and the phase has a decreasing slope with frequency representing a nearly constant delay over an approximate frequency range of ±20%, as required for an ideal phase shifter. Changing the Allpass Center Frequency P , the phase curve can be shifted left or right providing phase control.

[0243] Next, looking at the frequency plot of the open loop resonator inside the ATL1 core module,

number

[0244] The response for ωr = 1 and Dr = 0.05, corresponding to an open-loop Q of 10, is Figure 156. The pole-zero plot of the resonator is shown in Figure 157.

[0245] The open loop transfer function is

number

[0246] where G is the gain of the scaling block and the subscript “ap” refers to allpass. The zero degree root locus of the resonator is shown in Figure 158, which further shows both the poles and zeros of the phase shifter.

[0247] This pole behavior starts at the open loop pole position of the resonator (for G = 0) and increases in axis as JwG increases. The locus is the axis for JwG = 1.

[0248] We now introduce a phase shifter that provides an excess of 50° in the loop, which is implemented by selecting ω Ap = 0.9. The new phase plot of the phase shifter now shows a 50° lag, as can be seen in Figure 159.

[0249] The modified root locus is given in Figure 160 for the same range of G (0 to G<1) as before. Notice that for G = 1, the oscillation condition is not reached. Therefore, the loop gain must be increased in the event of phase mismatch in order to reach the unstable condition. Also, as G is increased beyond G=1, the oscillation frequency decreases. This makes sense since the resonator needs to be at a lower frequency so that it has a positive phase shift to offset the negative shift of the allpass phase shifter circuit.

[0250] In the case of ω Ap= 0.9, G = 1.26 or a 26% higher G is required to reach the oscillation condition. If the phase shifter is mismatched in another way so that it provides a positive phase shift, the oscillation frequency increases, resulting in a negative phase shift in the resonator to offset the positive phase shift of all the pass networks. Figure 161 shows a plot of the loop gain required to reach the oscillation condition as a function of phase shifter mismatch. Map this to the equivalent phase shift shown in Figure 156.

[0251] It can be seen that the resonant frequency and phase shifter values ​​of the ATL1 core module can be set by increasing G to point out the point where the ATL1 core module begins to oscillate. The following steps are one possible sequence:

[0252] Configure the switch array to give mode 4 shown in Figure 151.

[0253] Set ATL1a to zero feedback gain so a broadband response is obtained.

[0254] Adjust the resonator frequency control voltage to set the desired upper limit for the ATL1b resonant frequency.

[0255] Make sure the local oscillator (LO) in Figure 146 is set to approximately the same frequency resulting from step 4.

[0256] Increase the feedback gain of ATL1b until it reaches the oscillation threshold.

[0257] The phase shifter is dithered so that the feedback gain can be backed off to find the minimum gain value for the oscillation threshold.

[0258] Finding this point, we put the frequency of oscillation, the feedback gain control voltage and the phase shifter control voltage into the LUT - this represents the calibration point for the ATL1b that will precisely set the pole location of the ATL1b on the Jw axis for the particular oscillation frequency for which the phase shifter is correctly set.

[0259] Once the upper half of the resonator control has been completed in this incremental manner, proceed to the lower half. Returning to the ATL1b resonator starting voltage, the resonator voltage is gradually lowered following the procedure above until the full resonator range has been calibrated and the LUT completed. Once this initial point is found, the remainder of the procedure is relatively fast and efficient.

[0260] Once ATL1b's oscillation condition is complete, mode 5, shown in Figure 152, is switched and the functions of ATL1a and ATL1b are reversed; that is, ATL1b is configured for wider bandwidth since there is no feedback. Since ATL1a and ATL1b are essentially identical, differing only in manufacturing tolerances, the LUT entries of ATL1b can be used as an initial point for ATL1a calibration. If ATL1a and ATL1b are located on the same chip and operated under the same conditions (temperature, supply voltage, etc.), the LUT entries of ATL1a should be very close.

[0261] ATL1a is then configured as an oscillator and the calibration table for ATL1a is filled following the steps above.

[0262] The LUT is then used to find the closed loop resonant poles for both the ATL1a and ATL1b axes. The final step is to interpolate these values ​​to a uniform frequency sampling.

[0263] Mode 4 (Figure 151) can now be used again, but now with the ATL1b as a VCO that can be tuned fairly precisely. The exact frequency of the ATL1b is ultimately determined by LO down-conversion and Digital Signal Processing (DSP) baseband processing. This determined frequency is "exact" in the context of a clock crystal.

[0264] Next, determine the closed-loop Q of ATL1a as a function of the applied loop gain. Suppose you want ATL1a to have a passband centered at frequency ω. A From the previous calibration we know that the feedback gain and phase shifter settings will lead to oscillation. Now we need to know how much to reduce this feedback gain setting from this oscillation condition. This is achieved as shown in Figure 162, which shows the down conversion ADC processing for ATL1b 16210, ATL1a 16212, and Amplitude 16214.

[0265] ATL1b oscillates as a VCO. A The signal is passed to ATL1a. The phase shifter control and open loop resonator control voltages of ATL1a are synchronously dithered based on the LUT entries. This dithers the passband of ATL1a in terms of its center frequency. The downconversion, ADC and subsequent processing determine the amplitude variation of the frequency component at ω. A This variation is used to determine the bandwidth of ATL1a with a particular feedback gain. This observation becomes an entry into the LUT of ATL1a. The feedback gain of ATL1a is then incremented and the process is repeated.

[0266] Once many such bandwidth observations are made as a function of the ATL1a feedback control voltage, one can choose to either a) interpolate these values ​​into a piecewise curve fit or b) fit a quadratic or cubic polynomial to the data. The latter, while fitting a quadratic or cubic polynomial to the LUT data, is felt to be the more accurate approach.

[0267] Once ATL1a has been calibrated in this manner, we can return to Mode 5 (Figure 152) and use ATL1a as a VCO to measure the bandwidth of ATL1b for various feedback gain settings.

[0268] It should be pointed out that adding a single ATL1 core module for calibration purposes only helps to enable high-precision calibration of any ATLn implementation. The initialization steps above are repeated for each ATL1 core module that makes up an ATLn.

[0269] Resonant circuit control

[0270] As discussed above, it is desirable to be able to tune the characteristics of the now pre-determined primary resonant structures by coupling these pre-determined primary resonant structures to secondary variable resonant structures. This allows the net circuitry to automatically mitigate ambient temperature changes, component aging, and drift of such pre-determined primary resonant structures, thus improving overall system performance.

[0271] The coupling of this resonant structure requires the addition of a tunable resonator with a primary resonator. In one example, if the tunable resonator is an ATL-based circuit that controls an external resonator (XR), the circuit design may be referred to as ATLXR. The following discussion will be in terms of an ATL-based circuit used with an external resonator, and the term ATLXR is used as a shorthand reference to the primary resonator being modified by the tunable resonator. However, it will be understood that the principles discussed may be extended to other circuit designs in which other types of resonators are controlled using the ATL-based circuit described herein. Types of tunable resonators.

[0272] The primary resonator can be a fixed resonator or a frequency tunable resonator, however, for practical reasons it is preferred that the primary resonator is stable over the cycle time of the secondary variable resonator control and response loop so that the pre-determined external primary resonant structure appears "quasi-fixed" for system performance.

[0273] This approach can be used to make small post-production adjustments that may increase the production yield of high-Q and medium-Q filters. The yield improvement may be the amount of adjusting the Q and / or center frequency of a fixed resonant structure. For example, the frequency response of a primary resonator may be designed to operate within a given error factor, such as may be specified by a manufacturing specification. A tunable resonator is used to control the primary resonator within this given error factor, such that the closed loop frequency response approaches the ideal frequency response of the primary resonator.

[0274] In one example, consider an external resonator, denoted XR, having a predetermined frequency response characteristic, with a medium to high Q. The XR resonator is connected in a signal loop with an active signal amplification gain block g and an additional second variable resonator, as shown in FIG. 179. The variable R resonator 17910 is controllable in terms of resonant frequency by control f 17916 and may have a low Q relative to the external resonator F 17912. Gain block G 17914 is controllable by g 17918.

[0275] The ATLXR provides fine tuning of the primary resonator by employing a non-tunable secondary low-Q circuit in the signal loop containing the primary resonator. The given resonance characteristics of the primary resonator may be effectively altered by the action of:

[0276] Change in resonant frequency of low-Q resonator R by controlling f;

[0277] and / or variation of the closed-loop Q of resonator R by gain block G via control g.

[0278] ATLXR operating principle: Control of the poles of the primary resonator

[0279] As noted above, while the term ATLXR is used herein, the controlled primary resonator may be a resonator other than an "exenal resonator" and the tunable resonator may be a resonator other than an ATL-based circuit. However, for these examples, the following ATLXR acronym table is provided for reference so that the context of this example is shown.

number

[0280] For purposes of illustrating the principles of operation, one example of an embodiment of the ATLXR and its operation may be described using a pole-zero diagram of the open loop response of the ATLXR. The operation will be described based on the primary resonator being a two port resonator. However, the principles of operation for a one port resonator are essentially the same.

[0281] Consider the open loop circuit shown in Figure 180. For this example, assume that the F 18010, R 18012, and P 18014 components are linear and time invariant. R is controlled by f 18016 and P is controlled by p 18018. However, the discussion extends to minor deviations of the nonlinear and time varying components as above. In the preferred embodiment, the resonator is typically modeled as a high Q resonant pole and R may be represented by a low Q pole with Q=10-20 or so based on the following considerations:

[0282] Requiring a fundamental resonator R with a higher Q than about 10–20 makes chip integration more difficult.

[0283] Conversely, requiring a fundamental resonator R with too low a Q can result in excessive Q expansion that can contribute to circuit linearity problems.

[0284] In addition, you must represent the loop delay, which includes the following module delays:

[0285] Delay of phase shifter P;

[0286] The delay of the connection wire between F and

[0287] Additional delay for the buffer used in the tunable secondary resonator R.

[0288] As discussed previously, there are a variety of tunable ATLn resonator configurations that can be adjusted to compensate for phase changes in the circuit, eliminating the need for a separate phase shifter component.

[0289] A pole-zero plot of the open loop ATLXR response is shown in Figure 181. The s-plane is shown with the vertical axis as the jw axis and the horizontal axis as the real axis. Also shown are the poles of the Pade delay model 18110.

[0290] The collection of poles 18110 and zeros 18112 illustrated in Figure 181 as "Pade model of the open loop delay" is a polynomial approximation of the phase exponential term of exp(-sTD), where TD is the total cumulative delay of the signal loop not including the delay of the primary resonator or the tunable resonators. Thus, the Pade poles and zeros are equivalent and not physical. These poles and zeros form an all pass filter structure that only affects the phase and not the amplitude.

[0291] Regarding the Pade poles and zeros in Figure 181, the essential consideration is that these equivalent poles are farther inside the left plane than a) the R tunable poles and b) the higher order Q poles of the first order resonator. Also, in the closed loop case, the movement of the poles with increased loop gain of the Pade poles can be neglected.

[0292] Figure 182 shows the poles and zeros of the Pade representation for a normalized loop delay of two periods of the ATLXR band center frequency. The effect of increasing the loop delay further is to affect the phase tilt more as the poles move closer to the jw axis. However, a higher order Pade model would be required. Alternatively, the Pade poles and zeros can be more clearly represented as a bandpass response. However, this is not really necessary when the delay is small.

[0293] However, the Pade delay model accurately represents the effect of any delays occurring within the signal loop. As shown above, the poles of the ATLXR variable resonators R are shown in the same location, but may be slightly offset from each other. The details of the poles of these variable resonators R are derivative, but the main attribute is that these poles are controllable with f to move up and down in frequency (parallel to the jw axis). This is made easy by the varactor diode control (f control) of each variable resonator R. These resonators also have a zero at S=0.

[0294] Next, the operation of the ATLXR is explained based on Fig. 183. In the closed loop case, as the ATLXR loop gain g increases, the high-order Q dominant pole of the first-order resonator closest to the jω axis follows one of the loci, as shown by the small arrow. The locus follows depends on the position of the pole of R (controlled by f) and the phase setting of P.

[0295] In this way, the secondary variable resonator R adjusts the s-plane operating point of the primary or external resonator XR.

[0296] For clarity, the locus of the delay and other poles of R are not shown because these poles are not overly related to the high-order Q pole as it only needs to move a short distance, requiring only the small closed-loop gain explained above. Thus, the poles of the secondary variable resonator R and the delay model do not change significantly. In this way, the dominant pole of the primary or external resonator XR can be placed at the desired location by adjusting the settings of the variable resonator R and the phase control P.

[0297] ATLXR Overview

[0298] The ideas developed herein are applicable to embodiments in which the ATLXR places a controllable variable resonator (R) with a variable gain block inside a signal loop that includes a near-high Q external resonator (XR) to moderately "manipulate" the closed-loop frequency response of the ATLXR incorporating the primary resonator or external resonator XR. This manipulation of the primary external resonator is in fact the manipulation of a closed-loop ATLXR circuit that includes the primary resonator and the tunable resonator. The dynamic modification of the closed-loop ATLXR is sufficient to obtain the desired passband response and compensate for moderate temperature changes, initial manufacturing tolerances, and device aging of the primary resonator or external resonator XR. The closed-loop resonance that affects the signal path transfer function from the input to the output port is a modified version of the resonance dominant pole of the stand-alone primary resonator.

[0299] The transfer function from the input to the output port of the ATLXR gives a narrow bandpass frequency response that is approximately equal to that of a single high-order Q dominant pole that can be manipulated with the controls {f,g,p} acting on a second-order variable resonator R.

[0300] The pole of the primary resonator may not be explicitly controlled, but may be controlled by the action of an implicitly coupled signal loop to move the pole to a desired location in the s-plane, including but not limited to:

[0301] Enhance the Q of the primary resonator.

[0302] Compensate for initial manufacturing variations of the primary resonator.

[0303] It compensates for the frequency shift of the primary resonator due to temperature fluctuations.

[0304] Compensates for frequency shifts in the primary resonator due to component aging.

[0305] ATLXRs can be cascaded with other ATLXRs to achieve specific arrangements of the poles of the primary resonator in the S-plane, such that certain multi-pole filters can be realized, such as Chebyshev or Butterworth bandpass filters incorporating external resonators, XRs.

[0306] The ATLXR facilitates the bandpass equalization function that is part of the adaptive filter.

[0307] The overall SAW provides a 20 MHz bandpass, while the ATLXR emphasizes specific sub-bands of 1 MHz bandwidth, following a frequency hopping sub-band like Bluetooth® which follows a frequency hopping scheme.

[0308] The detailed analysis presented above relates to a particular embodiment of the circuit used to control the primary resonator and is provided to aid in gaining a deeper understanding of the principles involved in the approach being proposed. However, it should also be understood that the above discussion may not be fully applicable in all circumstances, since once the design principles are understood, other applications and other design examples may be used that deviate from the analysis as shown above. As such, the above discussion should be viewed as informative and not taken as a requirement for all types of circuits.

[0309] ATLXR Resonator Features

[0310] Primary external resonator XR: XR is used to represent the transfer function of an external resonator that is considered external to the ATLXR chip. Note that the XR resonator may be an electrical, electromagnetic or electronic resonator such as:

[0311] The electrical resonator may be a circuit made up of inductors or capacitors.

[0312] The electromagnetic resonators can be distributed as microstrip or stripline or waveguide bipolar resonators.

[0313] The mechanical resonators may be SAW or BAW devices as well as MEMS resonators.

[0314] Resonators based on material properties such as ferrite material YIG (yttrium iron garnet) based resonators with slow magnetic field based frequency control

[0315] Second-order variable resonator R: As explained above, the ATLXR variable resonator R is generally a low Q resonator that can be differentiated on the chip and can be controllable in terms of frequency response, both in terms of resonant frequency and bandwidth. Examples of suitable resonators R in the ATLXR described above are described extensively above.

[0316] R(s) is the transfer function of the second order resonator of the ATL signal loop, with control of f. The control f would usually act on some form of actuator diode (possibly a MEMS device) to vary the capacitance of R. P is the discrete switching phase. 5 has several phase states selectable by control of p. The gain block G has a variable gain controllable by g. Finally, there are couplers at the input and output of the ATLXR circuit.

[0317] Variable R resonators are ideally integrated on-chip in the preferred embodiment. R typically consists of fixed-value integrated capacitors and spiral inductors in addition to variable-value actuator diodes controllable by f. R may also be implemented based on distributed transmission line components integrated on the chip die. Another option for R resonators is that they are implemented based on integrated MEMS devices resulting in variable inductors or variable capacitors. Examples of suitable R resonators may include those described in detail in Nielsen.

[0318] Variations and options

[0319] As can be seen, different alternatives and variations on the ATLXR circuit exist. Possible variations include:

[0320] The primary resonator may be a single port rather than a two port device. Thus, for example, applications of multi-pole BAW chip devices can be envisaged, as shown in Fig. 191. Here, the resonators are on a common BAW chip with ground and one port connection from each resonator to the ATLXR chip. What is proposed in this embodiment is an external resonator chip consisting of multiple BAW resonators, each with one port connection to a matching ATLXR chip constituting a multi-pole filter. An internal tunable resonator block R closes the signal loop if required.

[0321] Other implementations of the ATLXR signal loop may include a negative resistance amplifier.

[0322] The primary resonator may be part of an antenna or radiating system, which may include any antenna that has some resonant properties as a chip antenna or a printed circuit antenna.

[0323] The ATLXR may be arranged as shown in FIG. 192, which has multiple general ATLXR blocks and a switch matrix connecting various antennas and various resonators. It has general ports to attach to BAW resonators, printed resonators, chip antennas, resonators, etc. On the other side, the switch matrix connects to the ATLXR circuitry, or if no expansion is required, the ATLXR is not connected. FIG. 192 shows the BAW / SAW resonators 19210, PCB printed resonators 19212, chip antennas 19214, switch matrix 19216, blocks of ATLXR circuitry 19218, and a general ATLXR chip 19220.

[0324] The switch and multiple ATLXR circuits may be integrated into a general-purpose transceiver chip, and then a general external resonator may be attached to a general pin of the ATLXR, which may be an antenna, a printed circuit board resonator, a SAW / BAW resonator, etc.

[0325] Preferred Embodiments

[0326] A preferred embodiment in the context of an ATL-based circuit is illustrated in FIG. 188. FIG. 188 shows components F18810 controlled by f18814, R18812, P18816 controlled by p18818, coupler 18820, signal output 18822, gain block G18824 controlled by g18826, signal input 18828, and chip integrated circuit 18830. The signal loop can have a single variable resonator or multiple variable resonators. Furthermore, one or more primary resonators may be connected in series or in series-parallel in a loop with one or more variable resonators.

[0327] As mentioned above, XR(s) is used to define the transfer function of the first resonator. The first resonator is typically, but not necessarily, an external resonator external to the ATLXR chip. R(s) is the transfer function of the internal or tunable resonator of the ATL signal loop, with control f. Control f can act on a varactor diode of a given form, or perhaps a MEMS device, to vary the capacitance of R. P is a discrete switching phase, which can have several phase states selectable by controlling p. Gain block G has a variable gain controllable by g. Finally, couplers are provided at the input and output of the ATLXR circuit.

[0328] In one example, the tunable resonator may be integrated on the chip. In some examples, the tunable resonator may consist of a fixed value integrated capacitor and a spiral inductor in addition to a variable value photodiode controllable by f. R may also be implemented based on distributed transmission line components integrated on the chip die. Another option for the resonator of R is implemented based on an integrated MEMS device, resulting in a variable inductor or variable capacitor. Other suitable resonators will also be recognized by those skilled in the art.

[0329] In summary, the ATLXR signal loop has a tunable resonator R coupled with a primary or external resonator that can be of various types. This allows for a composite closed-loop resonator response combined with a single dominant pole that can be manipulated with control {f,g,p} in the tunable secondary resonator.

[0330] In one example, the poles of the external cavity can be moved modestly to a desired s-plane location by: A set of low-Q resonators: It can be controlled by frequency, Preferably using a selectable phase shift, Variable gain.

[0331] A low-Q resonator and variable gain are deployed in the signal loop to move the external resonator pole to the desired location.

[0332] The basic ATLXR of FIG. 209 assumes that the primary resonator is controllable in FIG. 188, however the primary resonator F may be controllable or tunable between different operating frequencies as in the example of FIG. 189, with components F 18810, f 18814 with R 18812, controlled by P 18816, gain block G 18824, controlled by coupler 18820, signal out 18822, g 18826, signal out 18828, and chip integrated circuit 18830, and additionally with coarse frequency control of F 18910. For example, the primary resonator may be a ferrite-based resonator with the addition of a magnetic field for slow control. Or it may be a MEMS-type resonator with a relatively slow coarse frequency control. These can be incorporated into the ATLXR signal loop as shown to provide fast electronic control of the closed loop poles.

[0333] ATLXR can be directly extended to implement multi-pole filters. An example is shown in Figure 190 for a two-pole ATLXR filter. Figure 190 shows components F 18810 controlled by f 18814, R 18812, P 18816 controlled by p 18818, coupler 18820, signal out 18822, gain blocks G 18824, g 18826, signal out 18828, and chip integrated circuit 18830. 19010 is controlled by v 19012. Additional control of v over the variable attenuator V is provided so that the overall throughput gain of the multi-ATLXR circuit does not result in uncontrolled self-oscillation. Clearly the cascaded configuration of Figure 190 is extendable to any order bandpass filter where each ATLXR circuit implements one SOS (second order section or biquad) of the overall transfer function of the bandpass filter.

[0334] Yes, it is possible. As with the discussion above, these variations are described and depicted in terms, but these variations are applicable to other circuit designs based on other types of resonators. An external resonator chip consisting of multiple BAW resonators, each with one port connection to a matching ATLXR chip that constitutes a multi-pole filter. An internal resonator block R forms the required additional feedback port.

[0335] Implementation of ATLXR

[0336] The complexity of the integrated chip is generally considered secondary as small signal transistors may be integrated at negligible cost. Inductors and capacitors occupy larger die area and may therefore be more costly. Thus, cost-effective integration of variable R resonators will only achieve low Q values, typically around 10. To achieve a highly selective bandpass filter response, it is necessary for the filter poles to have high Q values ​​(e.g., much higher than 10) and therefore significant Q enhancement may be required. Arbitrary high Q enhancement is possible with ATLn, but at the expense of reduced linearity. The advantage of off-chip external resonators is that the initial Q can be quite high, so only modest further enhancement of Q is required.

[0337] In some instances, the primary resonator may have a Q of about 10 times greater than that of the adjustable resonator, and may be 100 times greater than the Q of the tunable resonator. In the context of the present discussion, references to values ​​of 10 or 100 are not intended to be definite limits, but should be considered general ranges that are close in nature, but include factors that may be slightly outside.

[0338] In some examples, the primary resonator may be an external resonator. The term "external" is used generally herein to refer to a primary resonator, as this is expected to be the most likely scenario in which the teachings may be used. However, it will be understood that the present teachings may also be applied to resonators other than external resonators. A resonator may be considered external if it is made of a different material or with a different technique than the tunable resonant circuit. A resonator may also be considered external if it is on a different substrate than that of the tunable resonant circuit, which substrates may then be bonded or otherwise attached to one another in various ways known in the art, which in turn will depend on the final form of the primary resonator and the tunable resonator. For example, the primary resonator may be a first component, formed of a first material, and the tunable resonator may be a second component made of a second material different from the first material. An example of this is shown, for example, in FIG. 188 where the resonator is "off-chip" relative to the tunable resonator, and in FIG. 191 where a BAW filter on a different substrate is shown. Other designs will be apparent to those skilled in the art and will not be discussed further.

[0339] Printed resonator variants do not generally achieve the high Q of SAW or BAW, but have a much higher Q than chip resonator implementations. Useful printed resonators may include a waveguide-like cavity constructed on a PC board with a number of connections including the field. This is shown in Figure 193, which is a top-down view of the resonator showing the feed structure and via hole connections stitching around the perimeter of the waveguide cavity. The feed through connection in the PCB is shown at 19310 and the feed is shown at 19312. Metallization on the top and bottom sides of the printed circuit board is not shown for clarity. A single port resonator is shown, but this could be made two port by adding another feed probe.

[0340] This type of resonator has the advantage that it provides a higher Q since the losses are dielectric in nature and not conductive. Multiple resonators 19412 may be implemented as shown in FIG. 194, each connected to an ATLXR chip 19410.

[0341] The multi-level board offers the possibility to stack the printed resonators as shown in the figure. Figure 195 has an ATLXR chip 19510 and a chip antenna 19512. Generally, at least 10 layers are used in a smartphone, so the number of stripline resonators in 19514 may be stacked as shown in the figure to occupy less space. If the ATLXR chip uses a ball grid connector, the resonators are stacked under the chip for compactness. This allows for very cost-effective implementation of external resonator XR with initial Q in the order of 100 for microwave frequency applications. At higher frequencies, printed resonators become more attractive as they are smaller, but may require low-loss dielectric substrates to maintain the Q of the external resonator XR at around 100.

[0342] ATLXR Coupling Configuration

[0343] Two characteristics of ATLXR are described below:

[0344] The first feature is a set of coupled resonators, including: A primary resonator, such as an external resonator XR, typically with a high Q; and Tunable resonators (usually low Q) that are adjustable in terms of resonant frequency and bandwidth

[0345] The second characteristic is an active signal loop incorporating a set of resonators. This generally involves a coupling architecture that couples signals to and from the resonators to achieve the desired effect. Coupling mechanisms may consist of circulators, directional couplers, multi-port devices, etc. There may be one resonator or multiple resonators in the loop. Furthermore, "resonator" means a system of resonators, unless specifically referred to as a single resonator.

[0346] Of interest is to consider a first order resonant structure in combination with the ATL adaptive filter resonant structure described above. There are a variety of architectures that can be used, four of which are presented below and are generally differentiated by the coupling configuration. Other implementations may be possible as will be recognized by those skilled in the art.

[0347] ATLXR Implementation Category 1: Unidirectional signal flow

[0348] Category 1 is the first ATLXR implementation category and has two main characteristics. First, all signals are unidirectional. Second, the input signals are separated from the feedback signals via directional sum blocks. However, this assumes that the sum blocks are non-reciprocal.

[0349] There are two ways to implement such a sum block. The first is to use a circulator as shown in Figure 80. Circulators are bulky, expensive, and non-reciprocal devices that are indistinguishable on a chip. They create a unidirectional flow and the output 5 is tapped off the buffer output for feedback processing as shown below. Figure 80 shows the source 8020, input 8010, circulator 8012, gain scaling block 8014, phase shifter 8016, loop 8022, and output 8018.

[0350] A better way to implement ATLXR Category 1 is to use an active differential amplifier 20502 as a non-reciprocal summing block that forces unidirectional signal flow in the loop (as shown at the top of Figure 205, with the top circuit having a resonator 20504) a phase shifter 20506 and a gain block 20508, and the bottom circuit has the ATL circuit 1301 and an external resonator 20510. The output may be taken anywhere and the order of the components in the loop is arbitrary. It will be understood that although the resonators are labelled 1301 in the various drawings depicting the ATL circuits, they may be higher or lower order ATL circuits or may be basic resonators such as resonator 1401 previously described.

[0351] This active feedback approach is ideal because the differential amplifier circuit is easy to implement on a chip and does not require inductors or other components that are difficult to implement at the chip level.

[0352] An ATLXR Category 1 implementation using the ATL3 implementation shown at the bottom of Figure 205. As mentioned before, the ATL3 implementation allows for loop phase shift control in the low Q secondary cavity and a phase shifter. 5 It is as easy as switching between two phase polarizations.

[0353] ATLXR Implementation Category 2: Bidirectional signal exchange with an external resonator

[0354] Category 2 implementations of ATLXR use a directional coupler or circulator as the combining element between the primary resonator (XR) and the tunable resonant circuit, as shown in Figure 110 and Figure 206, and are shown using implementations ATL1 or ATL3 as the tunable resonator circuit. Other ATL implementations are also possible.

[0355] In this category, the circulator or directional coupler is turned backwards to intentionally reflect the feedback signal by the external resonator when the input component is now part of the loop. The role of the circulator or directional coupler is to separate the bidirectional flow in the external resonator into separate flows in the loop. As described below, in the case of the ATLF, for example, when a 10 dB reverse directional coupler 20704 is used, it feeds the signal to be bounced back by the antenna 20702 shown in the top of FIG. 207, or feeds the signal to the input of an external resonator such as a BAW or printed circuit antenna when the light is recirculated in a one-port external resonator as shown in the bottom of FIG. 207, the circuit further includes a resonator 20706 and a gain / phase block 20708.

[0356] The conditions under which an external resonator is an antenna are detailed below as an ATLF, but we recognize that antenna matching is poor and as a result we intentionally include an antenna in the feedback loop, thus constructing a reflection of the antenna for active impedance matching.

[0357] ATLXR Implementation Category 3: ATL as a Negative Resistance Amplifier

[0358] The Category 3 implementation of ATLXR uses a hybrid coupler, as shown below at the bottom. Figure 113, where the ATL is implemented as a negative resistance amplifier. In this implementation category, there is no requirement for a directional coupler.

[0359] The hybrid coupler is part of an in-line bidirectional phase shifter. This is an example of a phase shifter implementation and has nothing to do with the ATLF feedback loop, i.e. a phase shifter may be developed in a different way without the hybrid coupler.

[0360] As can be seen, the ATLXR Category 3 is similar to Category 2, except that the entire circuit consists of a bidirectional signal flow rather than just a path between the external resonator and the secondary resonator loop. This results in a negative resistance gain block, unlike the two-port gain blocks typically used. Referring to Figure 208, the ATLXR configuration of Category 3 is illustrated.

[0361] ATLXR Implementation Category 4: Use of an external two-port resonator

[0362] ATLXR category 4 consists of an external resonator as a two port resonator. This two port resonator can be a printed antenna, a printed resonator, or a two port BAW / SAW. Category 4 is shown in Figure 209, with an antenna 20902, a resonator 20904, and a gain / phase block 20906. Thus, for example, applications of multi-pole BAW chip devices can be envisaged, as shown in Figure 191. Figure 191 shows components F 18810, R 18812 controlled by f 18814, p 18818 controlled by P 18816, coupler 18820, signal out 18822, gain block G 18824 controlled by g 18826, signal out 18828, ATLXR chip 19110, BAW chip 19112, and attenuator 19114 controlled by 19116. Here the resonators are on a common BAW chip with ground and one port connection from each resonator to the ATLXR chip. Proposed in this embodiment is an external resonator chip consisting of multiple BAW resonators, each with one port connection to a matching ATLXR chip forming a multi-pole filter. The internal resonator block R forms the required additional feedback port.

[0363] ATLXR Implementation Using a Switch Matrix

[0364] An ATLXR may be arranged as shown in Figure 192 with several common ATLXR blocks and a switch matrix connecting various antennas and various resonators. It has ports common to 5 BAW resonators, printed resonators, chip antennas, no resonators mounted at all, etc. On the other side, the switch matrix connects to the ATLXR circuitry, or if no expansion is required, the ATLXR is not connected.

[0365] The switch and multiple ATLXR circuits can be integrated into a general-purpose transceiver chip and common external resonators may be attached to the common pins of the ATLXR. These may be antennas, printed circuit board resonators, SAW / BAW resonators, etc.

[0366] After exploring the ATLXR concept for improving the performance of the primary resonator, we consider two specific communication system use cases:

[0367] The primary resonator is any Electrically Small Antenna (ESA) subsystem; and

[0368] The primary resonator is an external BAW or SAW RF resonator filter.

[0369] Optimizing system performance of arbitrary electrically small antennas using coupled resonators.

[0370] Wireless transceivers have become highly integrated and optimized over the past decades until advanced WiFi transceivers operating at 2.45 GHz or 5 GHz consist of just a few components enabled by a central high level of integration. The transceiver chip fits onto a few square centimeters of circuit board. This has empowered applications such as IoT and wireless smart sensors. However, the availability of inexpensive wireless transceivers is driving further cost reduction, performance improvement and antenna size reduction.

[0371] Impedance Matching Considerations for Electrically Small Antennas

[0372] Electrically Small Antennas (ESAs) are structures with dimensions significantly smaller than the operating wavelength and therefore are generally difficult to impedance match over a frequency band using existing methods. Suffice it to say that proper impedance matching between the antenna and receiver is essential for efficient energy transfer. To proceed, some brief background material on antennas must be considered to give insight into what constitutes an antenna: a) how ATLn resonators couple in the context of the ATLXR discussed above;

[0373] The essence of an antenna is easiest to understand when it is operated in a transmitting mode: it is a device that alternately accelerates and decelerates a current flow of electric charge such that the radiated electromagnetic (EM) field has an amplitude that depends inversely on the distance from this radiating device, typically 10 wavelengths from the radiating source.

[0374] When an antenna is used in receive mode, the integral of the Lorentz response predicts that the performance of the receive antenna will mutually affect the performance of the transmit mode antenna, and the current distribution in the antenna and the antenna impedance will be the same for both transmit and receive functions. Therefore, the calculated impedance characteristics can be used to analyze the antenna in transmit mode and to verify the operation of the antenna in receive mode.

[0375] The integral of the Lorentz reaction is the core of this core characteristic of antenna mutual coupling effects. Consider another EM generator at a given distance from the antenna that generates E and B fields in the vicinity of the wire dipole as shown in Figure 53. We introduce J as a current and M as an equivalent field current, which, although fictitious, works well in antenna analysis. Figure 53 shows a remote source 5310, a radiating wave 5312, and a wire dipole 5314.

[0376] Lorentz reaction integral

[0377] The Lorentz reaction integral, which measures how an antenna structure couples to an incoming external field, is

number

[0378] The current distribution in an electrically small wire antenna can be determined from the same Lorentz reaction integral by determining the current distribution: the specific opening voltage; and Zero tangential electric field on a wire structure.

[0379] Once the antenna current distribution is known, the input impedance is easily extracted.

[0380] The Lorentz reaction integral provides a way to calculate the general coupling between two antenna structures. The Lorentz reaction integral shows that the coupling is reciprocal: the coupling does not depend on which antenna is radiating and which is receiving. As a result, the antenna impedance is the same for both transmitting and receiving. This principle of reciprocity allows us to analyze antennas as transmitting structures, usually simply, and use the results directly to tell the reciprocal how the antenna receives the signal. In the transmitting mode, accelerating electrons moving along a wire conductor generate an EM field that has a 1 / r component, where r is the distance from the observation point to the antenna center.

[0381] Characteristics of dipole and loop antennas

[0382] Dipole Antennas: For a wire dipole antenna with no magnetic coupling, the Lorentz reaction integral is

number

[0383] The input impedance and conductivity of a dipole antenna of variable electrical length is shown in Figure 54, where the electrical length is the total length of the physical dipole antenna in terms of wavelengths. The real component is shown at 5410 and the imaginary component is shown at 5412. For lengths shorter than resonance, the antenna behaves as a capacitor, and longer than resonance, it behaves as an inductor. Note that at resonance, the slope of the real component is not overly steep, so the series LRC dipole impedance model is a reasonable approximation.

[0384] The dipole antenna impedance is connected to a series LRC model.

number

[0385] This model is a reasonable fit for a larger frequency range, but at resonance the radiation resistance R is Ω. Another possibility is the admittance model of a parallel GLC.

number

[0386] This is accurate over a narrow frequency range around the resonance; i.e., looking at the right-hand plot of Figure 54, the conductivity passes a stationary point at the resonance and should be considered constant to the first order. The susceptibility varies approximately linearly as does the quantity (ΩC - 1 / ΩL). Away from resonance, both the acceptance and susceptibility increase monotonically with frequency, showing that neither the series nor the parallel model are accurate.

[0387] It is interesting to note that neither the series nor the parallel LRC models can be a true fractional constant since the radiation resistance is a function of electrical length and therefore frequency. Therefore, the LRC model for a dipole antenna is likely to be accurate only over a relatively narrow bandwidth for higher Q dipole antennas.

[0388] All of this creates challenges in modeling the impedance matching of dipole antennas.

[0389] To complicate matters, in the 2.4 GHz and 5 GHz operating bands, a half-wavelength dipole, or a quarter-wavelength monopole, is physically too large for small wireless sensor applications, and a more compact antenna is needed. In Figure 55, consider the input impedance of a small antenna with nominal dimensions of 0.1 wavelengths. A series LRC model of such a short dipole shows that the radiation resistance is 2 ohms while the series capacitive reactance is 2000 ohms. Therefore, a resonant circuit with a very large Q and component accuracy is needed to efficiently compensate for this large capacitive reactance: a nontrivial impedance matching circuit that transforms the 2 ohms to 50 ohms.

[0390] Note that this dipole antenna itself has a Q of over 1000, so reducing the antenna Q may help achieve a wider bandwidth. However, this comes at the cost of imposing losses that add directly to the receiver noise figure (NF). If we make the dipole antenna just a little longer than the resonant frequency length, we can achieve a reasonable antenna Q and easily couple this to the ATL1. Figure 56 shows the impedance of an electrically small dipole wire antenna with an antenna Q on the order of 10 to 20 with a relative bandwidth of over 20%.

[0391] Loop Antenna: This antenna structure produces a magnetic field primarily perpendicular to the loop plane and corresponds to a (fictitious) magnetic current dipole that is also perpendicular to the loop plane. The equivalent expression for this antenna is the magnetic current M flowing perpendicular to the plane of the loop. Note that M is different and fictitious than J, which is real. The Lorentz coupling integral for a loop antenna is,

number

[0392] Showing that loop antennas are sensitive to magnetic components of far-field external sources rather than electrical components

[0393] An electrically small current loop antenna has an input impedance that can be represented by a series resistor inductor model.

number

[0394] Impedance matching is as a rule achieved by a series capacitor - jX(Ω) resonant with the antenna inductance and R(Ω) which is generally in the order of several Ohms: a resistance too small for compatibility with low-power integrated electronics.

[0395] The result is matching with either series or shunt capacitors. Segment 5710 of the Smith chart curve shown in Figure 57 (normalized to 50 ohms) is the series capacitor, and 5712 is the shunt capacitance. This only matches the antenna at one frequency. If it is desired to be well matched over a wider range of frequencies, a more complex impedance matching circuit is required.

[0396] Ground Plane Effect: Dipole and loop antennas are balanced in a symmetrical manner about their terminals. However, in the construction of small radio circuits, the ground plane is useful because it forms a potential reference point that is distributed throughout the circuit. Unfortunately, as frequency increases, the ground: No longer equals the desired potential surface Very difficult to model It is the cause of many EMI (electromagnetic interference) problems.

[0397] Regarding the antenna, the ground plane must be considered as part of the antenna, which significantly complicates the analysis and modeling of antenna impedance matching.

[0398] The physical limit to making a loop or dipole antenna and still radiate is theoretically zero size, but in practice there is a limit as the radiation resistance drops rapidly to zero as the dimensions shrink. Impedance matching allows large currents to flow through the radiation resistance. Consider a 2+j200 series model that can represent a small loop antenna 5810, as shown in Figure 58. One can still match to 50 ohms, but the components are harder in the sense that they require a series capacitance of -j1 series impedance and a shunt capacitance of -j7 ohms. The -j1 series capacitance is not practical and is omitted, so a small impedance mismatch is lost.

[0399] Printed Antennas: For many wireless applications, printed antennas such as the inverted-F antenna (PIFA) are cheap and efficient. The PIFA antenna is an example of an unbalanced antenna with a ground plane. It is commonly used as a printed antenna for small radio transceivers. Figure 211 illustrates the current flow and resulting field generation represented by arrows 21102, complicated by current flow in the ground plane. However, for many applications a size of about a quarter wavelength may still prove prohibitive.

[0400] Aperture Antennas: Wire dipoles and wire loops are two basic types of radiating structures: all wire antennas are a combination of these two antenna types. Aperture antennas that couple to waveguide structures are different, but that is not important for this discussion other than to say that some kind of wire antenna is still needed to couple from field modes to conduction modes.

[0401] It is important to note that the electrically small antennas listed above are all resonant structures, which is why they are captured in chip antennas.

[0402] Characteristics of dielectric resonator antennas: Chip antennas

[0403] Electrically small wire antennas can be further reduced in size by wrapping the antenna wire around a small dielectric block with a high dielectric constant (typically 5-55), and the dielectric resonator antenna has become known as a "chip antenna". With dimensions in the millimeter range, these chip antennas are significantly smaller than the typical wavelengths used for 2.45 GHz antennas, where the free space wavelength is in the range of 10 cm. Various possibilities for folded line and coil structures can be constructed with ceramics grown around the conductor. These tiny versions of dielectric resonator antennas are also called chip antennas.

[0404] Chip antennas are typically mounted such that the ground plane is the significant circuit element, with the ground plane essentially forming the other half of the antenna.

[0405] A typical implementation of a chip antenna with conventional matching components is not only complicated, as shown at the top of Figure 59, but is generally only approximately such that the antenna is not exactly matched to the transceiver. Figure 59 shows an antenna 5910, a filter network 5912, and a transceiver 5914. The circuit ground plane essentially forms the other half of the antenna, adding more impedance matching complexity. Additionally, the transceiver must (typically) provide a match to typically 50 ohms, which implies internal buffering that impacts overall efficiency. Additionally, matching components not only add cost, but also require board space; additional manufacturing steps; and are losses. Referring to the bottom of Figure 59, a transceiver chip with ATLn 5916, a chip antenna 5918, and a ground plate 5920 are shown.

[0406] If the Q of the chip antenna 5918 is too high, a wide tuning range cannot be achieved. To aid in this, a diode may be placed as a shunt component from the chip antenna terminal to ground. As with the ATL1 resonator, this allows smooth tuning over a wide frequency range.

[0407] Moreover, when integrating a chip antenna, the input impedance changes significantly with layout and the model needs to match the network analyzer (NWA) measurements. Again, impedance matching modeling is not trivial.

[0408] In one example, when integrating the ATLn with an electrically small antenna, the ATLn directional coupler is realized using a spiral transformer and an inductor. For a desired tuning bandwidth of more than 10%, the coupling ratio |c| is 0.1. As a result, we usually use the sigma-based coupling ratio |c| of 0.1. 11 (±jΩ 0)·)>> 1. The ATL1 is therefore sensitive to impedance mismatches at its input port. This would seem to prohibit connecting an antenna directly to the ATL1, since the VSWR would usually be too large and the whole system would self-oscillate at uncontrolled frequencies. As a solution, a low noise amplifier (LNA) could be included between the antenna and the ATL1. However, this would require additional components to match the antenna and the LNA, or a significant part of the available power would be reflected back to the antenna and re-radiated.

[0409] In contrast, tuning of the circuit, called ATLF (ATL-based filter circuit), described below, can be accomplished by allowing automatic conjugate impedance matching between the antenna and the receiver. In this way, the ATLF can be used to achieve a high degree of energy transfer between the antenna and the transmitter / receiver, but in a specific band of interest within the larger frequency envelope of the modulated signal carrier.

[0410] To understand resonance modeling and impedance correction, we need to take a closer look at the ESA antenna. Figure 54 shows a plot of the input impedance and conductivity of a variable electrical length dipole antenna, where the electrical length is the physical length in terms of wavelengths. For lengths shorter than resonance, the antenna behaves as a capacitor, and longer than resonance, it behaves as an inductor. It is interesting to note that neither the series LRC nor the parallel LRC antenna models are true fractional constants, since the antenna radiation resistance is a function of electrical length.

[0411] The reason why a resonant dipole is practical is that in the parallel LRC model, the conductivity peak is obtained at the same electrical length where the susceptibility simultaneously becomes zero. Such an antenna will therefore have an impedance matched to a fixed value of about 72 ohms.

[0412] Specifically, for example, in the common 2.4 GHz and 5 GHz type frequency bands, half-wave dipoles or quarter-wave monopoles are physically too large and many applications require more compact antennas.

[0413] Such small ESAs have highly reactive components and low radiation resistance. In Figure 55 consider the input impedance of a much shorter antenna, nominally 0.1 wavelengths. A lineal RC model of such a short dipole shows that the radiation resistance is almost 2 ohms and the series capacitive reactance is 2,000 ohms. To efficiently compensate for this large capacitive reactance requires a resonant circuit with enormous Q and component accuracy. A matching circuit to convert 2 ohms to 50 ohms is not trivial and would represent significant losses if real lumped matching components were used.

[0414] If you make the dipole antenna a bit longer you can achieve a reasonable antenna Q. Figure 56 shows the impedance of a dipole of nominal 0.35 wavelengths in length. The radiation resistance is increased to 30 ohms and the series capacitive reactance is more manageable. 375 ohms.

[0415] Matching an ESA over a wide frequency tuning range without significant mismatch losses typically requires complex matching circuits with high quality components. Therefore, the requirement for ESA antenna design becomes the objective of achieving a compact design in terms of physical size while achieving an input port impedance that is not difficult to match for applications such as wireless sensors and mobile phones with reasonable components.

[0416] This fixed impedance antenna is then connected to a matching fixed impedance transceiver subsystem. While this approach simplifies the radio design, it has two major drawbacks:

[0417] Signal Loss in Combined Antenna / Transceiver Systems: The antenna impedance matching of the antenna is a fixed, relatively constant average impedance over the operating band of the transceiver, across the operating range of the transceiver. This results in approximately a 2-3 dB loss in signal strength on both the transmit and receive sides. This loss in signal strength reduces the range of the transceiver.

[0418] In addition to signal loss, battery power can also be lost in the lumped impedance matching elements of the antenna and transceiver.

[0419] As disclosed by Nielsen, a conjugate matching antenna circuit can be used to maximize or at least increase the amount of energy transferred between the ESA antenna and the transceiver across the entire bandwidth of the transmission. This circuit is called the Arotec ATL Filter Tena, or simply ATLF. The ATLF can be applied to both transmit and receive functions.

[0420] Of particular importance is that the ATLF conjugate-matched antenna circuit is functional in conditions where the antenna impedance is not static. The control of the circuit used for complex conjugate matching of an antenna in situations or applications where the reflection coefficient of the target antenna is caused by the local environment of the target antenna to achieve conjugate coupling with the antenna is not static. Changes in the reflection coefficient may be caused by 1) local environment factors, or 2) coupling of the target antenna with nearby objects, or 3) application-specific changes in the antenna impedance. Antenna optimization techniques for communication systems and other applications in such dynamic environments may lose sight of the true reflection coefficient of the target antenna, resulting in failure to optimize the antenna or in the antenna being effectively isolated from the transceiver system.

[0421] Consideration of impedance matching methods for antennas that are not electrically small antennas

[0422] Impedance matching of high power transmitting antennas is widely implemented based on a metric called Voltage Standing Wave Ratio (VSWR). Although such antennas are not electrically small, we review this method for completeness.

[0423] These methods are used to automatically match the impedance between the transmitter and the antenna, but they are generally based on minimizing the voltage standing wave ratio (VSWR) of the transmission line, usually between the antenna and the transmitter, but the same can be done for the transmission line between the antenna and the receiver.

[0424] This method looks at the VSWR present in the signal transmission line to the antenna as a measure of the impedance mismatch between the transmitter and the antenna, and then adjusts variable inductor and capacitor circuit elements to minimize the VSWR. Variable line length elements are another way to minimize VSWR. Special equipment is required on the antenna tower to measure VSWR.

[0425] In this method, the center frequency of transmission is tuned so that the VSWR is adjusted to minimize the impedance mismatch of the antenna over the entire bandwidth of the transmission. This is in contrast to the approach described below, which optimizes the matching between the antenna and the receiver / transmitter.

[0426] Antenna impedance matching using resonant structure coupling

[0427] Rather than working to improve the impedance matching circuitry within the antenna, the performance of the antenna itself can be optimized, such as the ATL mentioned above, by pairing it with an external resonant structure with the right characteristics, such as a chip, dipole, or loop antenna. The antenna subsystem linked to this resonator is called an ATL Filtertena (ATLF). However, other resonant structures that can do certain things by having certain characteristics similar to an ATL may also be used to modify the performance of the antenna towards a desired result.

[0428] The term "filtenna" is sometimes used to refer to a circuit with an antenna, typically a one port antenna element, and a two port filter network. An example is shown at the top of Figure 59. Typically the filters in a filtenna are bandpass structures that are essentially matched circuits. A filtenna need only be considered as a group of antennas and matched networks, usually with bandpass characteristics. A filtenna bandpass matching circuit can be high order and complex, such as the conventional example in Figure 60, which produces a high order Chebyshev-like bandpass response from an otherwise narrowband antenna.

[0429] The term "reconfigurable antenna" can be used to refer to a given type of control applied to an antenna to change the frequency response or radiation pattern of said antenna. This may be accomplished by means of diode control or PIN switches coupling at different parts of the antenna. One prior art example of a transducer-based tunable antenna that falls under the definition of a reconfigurable antenna has a response as shown in Figure 61. Many other examples of reconfigurable antennas exist in the literature, one category being the use of active secondary radiators to achieve the reconfigurable antenna characteristic.

[0430] What will be presented is a circuit topology and method that achieves dynamic antenna matching without the use of an antenna impedance matching circuit. The discussion herein will be in terms of ATL-based circuits and therefore will be referred to using the term ATLF. However, it will be appreciated that similar strategies and design principles may be used with other circuit elements, as will be appreciated.

[0431] The ATLF coupled resonant structure antenna subsystem reduces or eliminates the need for impedance matching when connecting to a circuit as an antenna feed. This form of antenna impedance matching with the ATLF is effective in both transmit and receive modes. Additionally, an antenna subsystem linked to an ATLF resonator can also be used to transfer received antenna energy to a connected transceiver.

[0432] Roughly speaking, the ATLF achieves impedance matching by synthesizing the unknown reflection coefficient of the antenna, which causes the ATLF to form an equivalent conjugate impedance match with the receiver, which is the condition for maximum energy transfer from the antenna to the receiver. The actual reflection coefficient of the antenna is dynamic and specific to the antenna structure at the exact operating frequency, but is not known a priori by the ATLF.

[0433] This synthesis of the unknown reflection coefficient of the antenna is performed by analyzing the SNR feedback derived from the receiver demodulation available from the receiver chain, and dithering both the amplitude and phase within the ATLF to achieve the required conjugate impedance match. Once this is done, the ATLF effectively narrows the signal bandwidth by further increasing the absolute value of the effective reflection coefficient, thereby increasing the Q of the received signal. The narrowing of the bandwidth is limited by the self-calibration and stability control of the ATLF described below, which ensures stability by preventing the feedback loop from destabilizing the ATLF by crossing the jω axis into the RHP.

[0434] In transmit mode, the lookup table parameters can be used for optimization rather than the demodulated SNR feedback from the receiver. However, the transmitter matching is based on the feedback from the receiver as the SNR estimate sets the appropriate values ​​stored in the LUT that can be used for transmit mode, based on the principle of reciprocity.

[0435] The ATLF resonator link antenna subsystem is shown as two coupled resonators in Figure 62 in receive mode, so that it can be distributed with typical antenna matching components and the transceiver device can be directly connected to the ATLF resonator link antenna subsystem. Figure 62 shows an impedance unmatched antenna 6210, the antenna and recirculation loop at the ATL port 6212, the ATL resonator 6214, the ATL gain block 6216, and the receive signal output 6218. This is because the electrically small low loss antenna is a resonant circuit element that is absorbed into the ATLn as a resonator subcircuit.

[0436] The ATLF can be used as follows:

[0437] a filter, the filter comprising an antenna that is filtered and impedance matched to the transceiver; and / or

[0438] A reconfigurable antenna, optionally with frequency control, is applied to an antenna, usually in the form of a varactor diode.

[0439] However, traditional antenna impedance matching is eliminated within the ATLF, as the antenna is directly coupled to the ATLn as an embedded resonator. This is achieved by the self-calibration of the ATLn, described below, which optimizes operation regardless of the attached antenna. This not only reduces part count by eliminating the need for matching components, but also significantly eliminates the losses associated with lumped element impedance matching, improving antenna subsystem performance.

[0440] The incremental chip die size to accommodate the ATLF is a minor cost driver. Inductors are often a size issue, and Qs of 15 or greater are considered cost-effective. Thus, an ATLn resonator Q of about 10 is a reasonable starting point. Successful ATLn enhancement factors (ratio of closed-loop Q to open-loop Q) can be on the order of 100, comparable to surface acoustic wave (SAW) filters for the same filtering performance.

[0441] Electrically small antennas as resonators.

[0442] As an example, let us assume a shortened dipole with a Q in the order of 10. This antenna is still too long for practical sensor implementation, but there are ways to realize a more compact antenna with a similar impedance, which will be considered later. The impedance of such a device is given in Figure 56.

[0443] Consider a series LRC model of a target antenna that is accurate over a relatively narrow bandwidth. For simplicity of notation, assume that the antenna port impedance is normalized to 1 ohm. z A is specified as follows:

number

[0444] The reflection coefficient (looking into the antenna port) is given by:

number

[0445] This can be expressed as follows:

number

[0446] Consider the case where the normalized radiation resistance is negligibly small, such as R ≈ 0. In this case, the pole-zero plot is as shown in Figure 65.

[0447] Next, consider an antenna that is perfectly matched at the resonant frequency of the antenna, such that R = 1. It can be seen that the pole-zero plot for this case is shown in Figure 66. Other possibilities for a resonant but mismatched antenna can be considered, but the range from R = 0 to R = 1 will limit the problem.

[0448] In contrast, the ATLF block diagram shown in the lower portion of FIG. 67 can dispense with the matching components and directly connects the transceiver device to the chip antenna. Since the chip antenna effectively becomes part of the resonator in the ATLn, it is to be shown that the ATLF can be operated such that the circuit does not require impedance matching. The ATLn self-calibrates and optimizes the performance of this antenna subsystem regardless of whether an antenna is attached or not, as described below. FIG. 67 shows two block diagrams of a transceiver without matching network functionality. The top diagram shows the antenna 6710, L,C matching 6712, transceiver chip 6714, SAW RF filter 6716, battery 6718, and clock crystal 6720. The bottom diagram shows the metal electrodes 6722, transceiver chip 6714, ATLn 6724, battery 6718, and clock crystal 6720.

[0449] ATL1 Resonant Variable Analog Filter

[0450] As previously mentioned, the ATLF is described below in terms of an ATL based circuit. However, circuits offering similar benefits may be provided using other components that perform functions more or less similar to those performed by the ATL based circuit. In its basic form, the circuit connected to the antenna includes a signal conditioning block including an adjustable phase shift element and an adjustable scaling block connected in a signal loop with the antenna, where the adjustable phase shift element and the adjustable scaling block are controlled to condition the signal to modify the signal received by the antenna toward a desired signal. Preferably, the signal conditioning block also includes an adjustable resonator. It will also be appreciated that the signal conditioning block may be split into separate components and distributed throughout the signal loop to provide the desired signal conditioning.

[0451] The following analysis is given in the context of a specific example of an ATL-based circuit and is included with the intent of improving understanding of the principles involved. However, it will be appreciated that the analysis may not be applicable to all implementations and that design variations may be offered while still achieving beneficial results.

[0452] In the context of ATL-based circuits, we will perform a brief review of the ATL1 presented in some detail above to understand the concatenation of the two resonant structures of the ATLF: the mismatched target antenna and the tunable analog ATLn filter. Here, we start with the simplest idealized model of the ATL1, as shown in Figure 40, consisting of a resonator and a scaling block in a feedback configuration, as detailed above. As shown below, two implementations are possible, each with both advantages and disadvantages. The first is the loop, which is important because the actual physical location of the input and output ports of the ATL adaptive filter is secondary.

[0453] As detailed elsewhere, the ATL1 resonator transfer function is given by the standard second-order model

number

[0454] A plot of the resonator characteristic at normalized frequency is shown in Figure 63. ω r =1 and D r =0.05 D r =0.05,'If the open loop Q is 10, or the relative bandwidth 10%.

[0455] Note that in this second-order model, the through gain of the resonator at resonance, s = jΩR, is HR(jΩR) = 1. As explained elsewhere:

[0456] The ATL1 resonant frequency Ω can be adjusted by the actuator diode control voltage. And

[0457] The ATL1 scaling block provides a gain of G that is controlled by the control voltage g.

[0458] The closed-loop ATL1 transfer function at resonance is [Number]

[0459] At resonance, the closed-loop through gain is [Number]

[0460] The bandwidth in radians per second is [Number]

[0461] Q is defined as follows. [Number]

[0462] Finally, the Q enhancement factor for any resonator, the change in Q from the open-loop resonator to the closed-loop, is R Q represented by and given as the following equation [Number] This equation emphasizes that the Q enhancement is simply the change in Q from the open-loop resonator to the closed-loop resonator and does not depend on the initial characteristics of the resonator.

[0463] From this expression, the two ratios of the open-loop to the closed-loop Q, ·R Q > 1, when the values of 0 < G < 1 correspond to the Q enhancement, ·RQ Note that for values ​​of G<1, G<0 corresponding to Q-spoil- ing, we obtain

[0464] Note that R becomes indeterminate for values ​​of QG = 1. This corresponds to a pole crossing the RHP of the S-plane, which is an unstable condition.

[0465] For chip implementation, the DR is fixed based on what can be easily integrated into the chip. DR = 0.05 is reasonable for an easily designed integrated LC chip resonator resulting in a resonator Q of 10. The key point here is that such a low Q means that the resonator components can be physically small when integrated.

[0466] Zooming out to account for the component size issue, the resonant frequency is given by:

number

[0467] As shown in FIG. 64, we include a directional coupler 6410 and an output splitter 6412 in ATL1. Here, we have a resonator 6414 in a feedback loop 6416, and a scaling block 6418 appears to be a buffer before the output splitter 6412. The directional coupler 6410 returns the resonator output to the loop, minimizing the connection to the input port 6420. The directional coupler 6410 is valuable in this context because the recirculated signal is much larger in amplitude than the input signal by a ratio of 1 / (1-G) (at resonance), where G denotes the overall open-loop gain at resonance controlled by the control voltage g. This signal ratio results in a large return gain at the input port 6420 of the ATL. For ATL1, a small amount of return gain is necessary, but too much may overwhelm the resonance of the target antenna, making calibration difficult. Therefore, a moderate amount of directivity in the directional coupler is desirable. The splitter in FIG. 64 may be easily implemented with a simple reversible resistor circuit.

[0468] Adding a phase shifter to the ATLF

[0469] The implementation of the phase shifter in ATL1 is described above. Now consider combining a phase shifter into the feedback loop of the ATLF, shown in Figure 68 and consisting of a resonator 6810, a gain element 6812, a phase shifter 6814, a directional coupler 6816, an input 6818, and an output 6820. As shown herein, there are various implementations of circuits available to provide the directional coupler function.

[0470] The overall transfer function is

number

[0471] The numerator of this transfer function can vary depending on where the output and input are given. For now, let us assume that the input is a current impressed on the antenna and we get the output from the output of a gain block. Now we can take into account the coupled poles and zeros and plot the closed loop poles as a function of G as shown in Figure 69.

[0472] As the resonator poles increase in JwG, they eventually cross the line at a maximum input into the right-hand plane, which is the open-loop zero of the phase-shifter all-pass network. The open-loop poles of the all-pass filter conveniently fall deep into the left-hand plane, becoming the secondary closed-loop poles.

[0473] In Figure 69 we show the case of aligned phase shifter and resonator. If the phase shifter is misaligned, a distorted root orbit results as shown in Figure 70. Note that the resonator ΩR needs to be adjusted to compensate for the phase error of the phase shifter to obtain the same ATL1 center frequency.

[0474] It is useful to look at the Nyquist plot for this misaligned phase shifter case shown in FIG. If -1 / G comes in from the left as G increases, you will see that as G gets larger and the -1 / G point gets very close to the outer contour, the frequency response has two soft resonant peaks that merge into one peak (F(j)Ω) on the Nyquist plot.

[0475] For completeness, another all path network is added to represent any phase error due to propagation delay around the loop, and a phase shifter all path network is added to compensate. Parasitic poles and unwanted excess delay zeros cause some complications in the root locus, but it also shows that phase compensation works. An example root locus is shown in Figure 71.

[0476] As explained in the Self-Calibration section, the rules for optimizing the three control voltages {f,p,g} still hold and can be generalized as follows: Given a particular output {signal level, Q enhancement, bandwidth} constraint, if {f,p,g}g is set to be minimized, f = center frequency control voltage g = ATL1 loop gain voltage control p = ATL1 phase adjustment voltage control

[0477] This optimization appears to be convex in a moderate neighborhood of the optimum of {f,p,g} when the open loop poles of the resonators have a higher Q than the Q of the resonators used in the all-pass phase shift network. Additional complications due to internal loop reflections can make this optimization frustrating and create local optimum minima.

[0478] A Nyquist plot can be used to show the effect of adding additional delay to the loop so that multiple increments of 360 degrees associated with the round trip delay are accumulated. As excess delay is increased in the ATL1 loop, the passband narrows as the off-resonance point moves significantly due to the phase shift of the delay. This is shown in Figure 73, which shows a Nyquist plot of XR(s) as the delay is increased from no delay (line 7310) to a finite delay (line 7312) and then to infinite delay (line 7314).

[0479] Antenna coupling and impedance in ATLF

[0480] We may now consider the problem of antenna coupling and impedances so that these can be calculated for resonant coupling to the ATLF. Consider Figure 74, which has a test transmitting antenna 7410 in the far field of a receiving antenna 7412 terminated in a Z load 7414.

[0481] Based on the Lorentz reaction integral, we can determine the self-impedance of the test antenna (Z11), the mutual coupling impedance (Z12) and the self-impedance (Z22) of the receiving antenna. Using these impedances, we can derive the equivalent coupling circuit shown in the top of Figure 75 and the Thevenin equivalent circuit shown in the bottom of Figure 75. Fin VG is the generator voltage of the test antenna with a source impedance of ZG. Figure 75 shows a resistor 7510, a source 7512, and a load 7514 terminating at Z.

[0482] Since the antennas are far apart, it is reasonable to assume that the current flow in the receiving antenna does not affect the transmitting antenna. ·)Z12 ·) ≪ ·)Z11 ·) ·)Z12 ·) ≪ ·)Z22 ·)

[0483] Based on this, the circuit of Figure 75 may be approximated as the circuit shown in Figure 76, consisting of a source 7610, resistor 7612, and a load 7614 terminated at Z. The significance of this circuit is that the equivalent source impedance of the generator is now Z*Z22 so that the best power transfer is achieved by conjugate load impedance matching of Z22.

[0484] In the ATLF analysis we use both the impedance and the reflection coefficient of the antenna. The advantage of the reflection coefficient is that this can be directly related to the transfer function and combined in the ATL1 transfer function. By incorporating the antenna as a resonator into the ATL1 it is more direct to deal with the impedance.

[0485] Antenna inductance matching in ATLF

[0486] To put some substance into the impedance matching discussion, let us first consider a typical narrowband matching example with an ATLF. The tuning band over which the ATLF operates may be wide, but the instantaneous band is considered small enough for an L match. As a first example, consider matching a radiation resistance of R = 20 ohms to a receiver. RR = 50 ohms. This is done at a resonant frequency of 1 GHz. The L match is FIG. 77 illustrates a source 7710 , an inductor 7712 , a resistor 7714 , a receiver 7716 , a capacitor 7718 , an SNR measurement 7720 , and an SNR optimizer 7722 connected to the inductor 7712 and the capacitor 7718 .

[0487] With the proper values ​​of physical L and C, the impedance looking from the antenna to the matching network and receiver is exactly 20 ohms. And because only lossless inductors and capacitors are used in the matching, the full power available from the antenna is dissipated in the receiver resistance RR.

[0488] Next, consider the reflection coefficient for the antenna resistance R.

number

[0489] We plot out |Γ r | 2 As a function of L and C, we obtain the contour plot in Figure 78. This is a favorable convex error surface that is easy to optimize when L and C use a simple gradient search optimizer. That is, if we can measure the SNR, which is a monotonic function of the noise figure (NF), then NF is a monotonic function of |Γ. r | 2 Then, by maximizing the SNR, |Γ r|. In this example, |Γ r | is a simple nearly convex function of the matching parameters. Putting all this together, a simple gradient search in the SNR will find the global minimum. | r (L,C)| The only caveat is that ISI and narrowband interference spectral peaks are not considered here.

[0490] Matching L is simple and good for narrow bandwidths. The final bandwidth depends on how different R is from the next value RR. If R = RR then L = C = 0 and the bandwidth is infinite. However, if R = RR, then the bandwidth of the match is very small. If the resulting bandwidth is too small to accommodate the desired antenna signal, then a more complex physical matching network is required, with more physical Ls and Cs.

[0491] The challenge of chip integration of L match can be significant where the range of L and C required to accommodate the range of the antenna is critical. Tunable inductors can be implemented with MEMS devices. However, MEMS do not integrate well with standard RFCs or MMCs due to the required mechanical structure and high control voltages, so when circuit cost becomes an issue, a MEMS solution is usually not feasible. Of course, it is possible to integrate an inductor for C, but a variable physical L would require an active GIC type circuit which is difficult at microwave frequencies with added noise. MEMS or GIC circuits are difficult, expensive and have a limited range of component values.

[0492] The ATLF antenna match point is in most cases where only two parameters are changed. However, severe matching problems (large antenna reactance, or R = R r It has been observed that for some applications (such as

[0493] Reactive Antenna Component Matching for ATLF Using Adaptive Resistance ATL Implementation

[0494] The ATLF implementation of a negative resistance device, shown in block diagram form at the top of Figure 94, operates only at the resonant frequency of the antenna itself. This resonant frequency occurs when the antenna has zero reactance. In a practical implementation, the negative resistance device will have some reactance associated with it that pushes it toward resonance. We first consider an ATLF circuit with a fixed frequency negative resistance device and then extend that treatment to a variable negative resistance implementation, providing instability.

[0495] The method of attaching a negative resistance device to an antenna may be approximated by the circuit shown in the upper part of Figure 112. The circuit of Figure 112 shows an antenna model 11210 having resistor 11212, capacitor 11214, and inductor 11216, along with a coupling cap 11218, and the negative resistance provided by resistor 11220 and inductor 11222. The root locus and Nyquist plot for this circuit are shown in the lower part of Figure 112. Applying a large magnitude of negative resistance pushes the magnitude of the ATLF reflection coefficient up by more than one, resulting in an enhancement of the Q. Note how the poles wrap around and cross the axis at a significantly different frequency than the resonance of the Jw antenna. Also, a second resonance occurs at a much lower frequency. This is also evident in the Nyquist plot.

[0496] It is clear that the antenna has a soft resonance, but as the gain is increased the Q enhancement can completely change the band center and appear unpredictable, this is where the ATLF provides more predictable control of the Q enhanced passband.

[0497] Now consider a phase shifter consisting of a directional coupler and a vector diode. The S-parameters of the four-port coupler are:

number

[0498] where

number

[0499] Operationally, the signal loop looks like this:

[0500] The signal from the antenna enters port 1 and exits ports 2 and 3.

[0501] In a matched gain block, the signal from port 3 is lost.

[0502] The signal from port 2 passes through a phase shifter and a gain block.

[0503] The signal is split after the gain block, with one part sent as output and the balance routed to port 3 and back to the antenna port.

[0504] The antenna reflects this and the signal loops back to port 1, forming a resonant loop structure.

[0505] Directional couplers may provide coupling ratios of 3 dB or higher and may be implemented as 90 degree or 180 degree couplers.

[0506] One possible implementation is as shown in Figure 114, which includes a 3 dB hybrid 90 degree coupler in the gain block with a 0 degree output port 2, followed by a 3 dB splitter as the ATL1 output coupler. The return signal from the output coupler is coupled into the 90 degree hybrid coupler port 4, with the feedback signal passing through a phase shifter and resonator. Figure 114 shows the input 11410, 90 degree hybrid coupler 11412, gain block 11414, 3 db splitter 11416, phase shifter 11418, and resonator 11420, with Z and resonator term 11422.

[0507] If the phase is set correctly in this embodiment, the 90 degree coupler is lossless and no signal is sent to port 3, so no termination resistor is consumed. Therefore, at resonance, the entire signal is sent to the inside of the feedback loop through port 4. Furthermore, due to the ideal components at resonance with the phase shifter set correctly, no circuit losses occur and all of the generated power is available at the input port of the 3 dB output power splitter. As a result, the noise figure (NF) of ATL1 is minimized when the phase matching is done correctly and ideally no loop losses occur. Therefore, this arrangement achieves the best NF and the highest frequency selectivity.

[0508] Negative resistance amplifiers include, but are not limited to, tunnel diodes, Gunn diodes, or Impatt diodes. Of course, any type of appropriately biased FET may be used to provide the negative resistance. Such implementations are believed to be known to those skilled in the art. It is important to note that the phase shifter is scanned in both directions.

[0509] It must be realized that phase shifters impose some losses. Also, couplers cannot be differentiated at the chip level. There are many ways to implement a varactor controlled bidirectional phase shifter. Two of these are shown in Figure 115. Scheme 11510 at the top of Figure 115 uses a variable RC time constant. The bottom scheme 11512 uses several stages of inductors and capacitors. Both schemes 11510 and 11512 show a resistor 11514, an inductor 11516, and a capacitor 11518.

[0510] When designing an ATLF, the required phase delay correction can be minimized by integration. In addition, the phase shift through the components can be known reasonably accurately. Therefore, a fixed phase correction may be included, and the phase shifter need only be adjusted for phase errors or phase shifts that cannot be corrected with a fixed network, such as a variable phase shift in delay over a wide frequency range. If the required phase adjustment is small, a simple variable phase shifter can be used that combines the ATL negative resistance implementation with the phase shifter described above.

[0511] Active antenna reflection coefficient synthesis at ATLF.

[0512] The purpose of the ATLF is to synthesize an inductance-matching example of a physical capacitor. This is achieved by matching the reflection coefficient. If the reflection coefficient of the ATLF looks like the reflection coefficient of a capacitor, the circuit will react as if the physical capacitor actually produced a reflection coefficient. In this case, the reactive inductance of the antenna is cancelled.

[0513] Consider this basic concept of matching based on reflection coefficients, as shown in Figure 79. Here we have an arbitrary antenna impedance.

number

[0514] The reflection coefficient for any characteristic impedance is ΓA for the antenna and ΓR for the receiver. If we have the condition ΓR=ΓA*, then the antenna is matched to the receiver and the available power of the antenna signal is fully utilized. This condition also entails the caveat of SnrO as mentioned above. Nevertheless, maximizing SnrO is the best thing we can do to recover the antenna signal.

[0515] Now let us consider how to realize the black box receiver shown in Figure 79, having a black box receiver circuit 7910 and a source 7912. A possible realization is a Category 1 ATLF implementation using a circulator. Here the signal is input to the circulator, coupled to a gain stage and a phase shifter, and then back to the circulator and back to the antenna. Unfortunately, the circulator is not inseparable due to the required ferrite and magnetic field source, but it is implementable in a non-chip configuration. Based on this active scheme, we can certainly generate any reflection coefficient. ΓR|> 1 as needed. Thus, we can satisfy the conjugate matching condition ΓR=ΓA*, which means that we have fully utilized the signal power available from the antenna.

[0516] Regarding NF, it appears that the noise associated with the gain stages adds linearly at the input of the circulator, making the generator ΓA otherwise noise-free. In other words, conjugate matching is done, but the penalty could be an additional noise term due to the insertion loss of the gain block and circulator.

[0517] This theory of matching based on the reflection coefficient shows that it may be useful to inject a signal towards the antenna and essentially transport available power to the receiver. This apparent oddity is explained by considering an antenna with a reactance of inductance L connected to a controlled RF voltage source, VR(t), as shown in Figure 81. Figure 81 shows a source 8110, a resistor 8112, an inductor 8114, and an RF voltage source 8116. The current flowing out of the antenna, i(t), is reduced due to the inductive impedance. If no inductance was present,

number

[0518] This corresponds to the case when an inductor couples to a matched resistive load, R, without an inductor obstructing the flow. This current flows in the antenna as a voltage across the inductor.

number

[0519] As a result, the composite RF voltage applied to the antenna port (at the inductor end) is

number

[0520] Consider the resultant RF voltage as coming from a capacitor in series with a resistor, R, as shown in Figure 82. Figure 82 shows a source 8210, resistor 8212, inductor 8214, and capacitor 8416. Then the voltage across the capacitor is given by:

number

[0521] As a result, we must have

number

[0522] This is to be expected since the series L and C resonate at a frequency.

number

[0523] Next consider the active reflection coefficient generator of Figure 80 and find the equivalent impedance produced by the reflection coefficient, G, which controls the gain, G, and phase, φ. The voltage signal from the antenna to circulator port 1 is given as V in. Thus the return signal to the antenna, VF, is designated as:

number

[0524] It enters the circulator at port 3. This results in an equal reflection coefficient.

number

[0525] For now, we will assume that the input impedance of the circulator port and the subsequent gain block has an impedance R. We will later develop this general information by adding a small component to Γ. Based on the impedance of the antenna, R, this reflection coefficient can again be written in terms of an equivalent impedance, denoted as RZ. Given R

number

[0526] Now we can plot the real part of ZR, as shown in Figure 83. For a gain of G,

number

[0527] Next, we reveal the power loss factor of the antenna source. To do this, we subtract the inductive component of the antenna impedance, ZR, and then recalculate the reflection coefficient, which we call Γ. a . Next, calculate the coefficients of .

number

[0528] Note that as the antenna reactance increases, the region where antenna coupling is reasonable decreases, requiring higher gain. This is expected because the active feedback must match the larger amplitude reflection coefficient of the antenna. With a larger reflection coefficient, the resonance becomes stronger and the region shrinks.

[0529] Also, the optimum point, G, is such that the PF is about G = 1: if G is increased further the PF begins to decrease, because the equivalent resistance of the receiver feedback becomes less than R, and eventually becomes negative as G is increased beyond 1.

[0530] Next, it is interesting to plot the current flowing from the antenna. To calculate this, we first calculate the power wave into the receiver (circulator) A and the reflection from the circulator B. The reflection coefficient can be expressed as:

number

[0531] Then the voltage at port 1 of the circulator is given by:

number

[0532] The current flowing from the antenna to the circulator port is

number

[0533] We also

number

[0534] This gives the equation for the circulator port voltages in terms of known values

number

number

[0535] Once V r We can decide

number

number

[0536] Our first example is Z = R, as shown in Figure 85, such that the optimal solution is for G=0. Note that with R = 1 and V = 1, the current is 0.5, so I = V / 2R = 0.5. But notice that for Φ=π, the current increases as G increases. Also, for G = 1 and Φ=π the current increases to 1 as the equivalent impedance of the receiver becomes zero: we are drawing more current from the antenna, but the power coupling factor is zero, so the power available at the receiver is not being used.

[0537] However, the interesting point here is that the forward power wave emanating from the antenna goes into the active load of the circulator and is then reflected back to the antenna by combining b. Therefore, the information of a is utilized at the receiver. As a result, we actually need to look at the voltage of a, not the voltage at port 1 of the circulator.

[0538] However, a=0.5, regardless of the reflection coefficient generated by the receiver. Thus, the whole active feedback scheme does not seem to be quite realized - this is because the antenna is starting to match. Once an inductor is added to the antenna, the antenna signal is partially reflected back to the input of the inductor, becoming the "b" signal from the inductor, which then becomes "a" inside the antenna. This is illustrated in Figure 86 with the inductor 2-port S-parameters 8610 and the recover section 8612.

[0539] Now consider the node receiver plots, which are shown in Figure 87 for all of the receiver G and Φ states. Note that as G increases, the amplitude of the input power wave continues to increase monotonically. Note that this is the signal that is input to the receiver gain block. It may seem like we have created a "super antenna", but unfortunately we have not. The problem is that the a signal is sending contributions from the active receiver along the path b → a 2 →S 22 →b 2 →a, what you are seeing is a combination of the power wave from the antenna and a recirculated signal going from the receiver back to the inductor port (antenna port), the recirculated signal is coherent with the antenna power wave but with added receiver noise, which complicates the analysis.

[0540] Feedback provides gain so that the apparent power wave from the antenna can grow, but as it passes through the receiver it adds noise that degrades the overall NF. You cannot have an NF less than 1, so the apparent signal boost in Figure 87 is a misconception.

[0541] In summary, it is clear that sampling the signal output of a receiver as the signal passes through a resonance is not a clear indicator of the optimum operating point. The true measurement is again the SNR.

[0542] The signal graph in Figure 87 provides another way of interpreting what is going on. A power wave emanating from the antenna hits the inductor 2 port, where it is reflected and partially transmitted. Without active feedback and termination R at the output of the inductor, the power wave would be reduced by |S21| less than 1 for the inductor. However, this reduction does not necessarily degrade the SNR, since the inductor does not add noise. Now we have a feedback signal b → a2 → S22 → b2 → a that would be added to the antenna power wave restoring its amplitude if the reflection coefficient of the active receiver were to be serially scaled with R to emulate a resonant capacitor. However, the process of doing this adds noise from the active gain block in the receiver. The higher the inductance, the larger the magnitude of the reflection coefficient the receiver would have to generate to compensate for the loss. |S21| increases with inductance (|S21|= R / (|R + jwL|). The larger the contribution from the receiver, the more receiver noise is added to the mix. It is also clear from Figure 87 that G can increase beyond the level needed for compensation. |S21| provides additional gain to the antenna power wave. However, the SNR does not improve any further and in fact the SNR starts to go down.

[0543] SNR as a measure of ATLF antenna impedance matching quality

[0544] An indirect measurement of the matching conditions in the receive mode may be facilitated by measuring the SNR of the demodulated output with the simple objective of adjusting the matching components so that the SNR is maximized. There are several points to note in this regard.

[0545] If the only sources of noise are the thermal noise of the antenna based on the effective temperature of the environment it is exposed to, and the intrinsic noise of the receiver RF amplifier, then maximizing the SNR of the demodulated received signal output is equivalent to minimizing NF or FOM as discussed previously. NF has the following penalty terms:

number

[0546] There are other sources of noise such as non-thermal interference that antennas pick up from channels adjacent to the signal of interest. Antennas are matched to have a narrow bandwidth around the frequency channel of the desired signal, because SNR measurements cannot distinguish between thermal noise and interference noise.

[0547] If the noise at the receiver is negligible compared to the thermal and interference noise from the antenna, matching becomes irrelevant since in-band noise and signals are treated similarly, so there is no advantage to maximizing the antenna power reaching the receiver.

[0548] Additionally, if the signal filtering does not have the correct shape to match the signal modulation, ISI noise (Inter-Symbol Interference, discussed elsewhere) will be generated at the receiver. In general, for antenna matching, ISI noise will increase if the antenna match bandwidth becomes too narrow. This is a factor to consider when the ATLF received signal bandwidth is too narrow to be of any use in the first place, as discussed next.

[0549] Note that in matching based on SNR maximization, two processes are taking place. First, the antennas are matched to transfer maximum signal power to the receiver. Second, as explained below, the matching process limits the bandwidth due to resonances in the matching network. Thus, noise and interference from outside the resonance peaks are suppressed relative to the desired antenna signal.

[0550] Next, Fig. 89 is a block diagram of the process that is being attempted, showing an antenna 8910 receiving a signal and matching it to a receiver, whereupon the signal is demodulated to extract data symbol values ​​that are used to optimize the information content contained in both the SNR and ISI metrics. Fig. 89 shows the antenna 8910, impedance matching 8912, receiver RF / IF 8914, data demodulation process 8916, SNR estimation 8918, and SNR optimization algorithm 8920. The result of this process is also an estimate of the SNR of the demodulated data symbol samples. These are used in the SNR optimization, which includes an optimization algorithm that sets parameters related to the antenna matching.

[0551] ATLF SNR measurement

[0552] As mentioned above, the ATLF can be pre-calibrated with factory measurements and calibrations, with values ​​stored in the LUT. However, the real benefit of the ATLF is in adapting to changes in antenna characteristics. Also, Q enhancement within the ATL requires feedback to be precisely determined and implemented. Then ultimately, it is the noise in the demodulated signal that matters, not the amplitude or bandwidth of the demodulated signal itself. The ATLF needs to respond to the filtering functions performed in the demodulation process, such as by the equalizers used to minimize ISI and in-band interference. It is necessary for the ATLF to dynamically adapt to work in conjunction with these other systems and not impair them. It is therefore important to pay attention to the entire processing feedback loop.

[0553] As described above, we use the LUT values ​​as an initial setup, and also dynamically update the LUT for instances such as frequency hopping protocols required for fast adaptation of the ATLF. We then rely on the current SNR measurement to guide further tuning of the ATLF.

[0554] Figure 90 shows a high level block diagram of a wireless data receiver that can use the ATLF for antenna matching and interfacing. Figure 90 shows the antenna 9010, ALTF 9012, receiver RF / IF / BB 9014, baseband equalizer 9016, data demodulation processing 9018, inner fast loop 9020, outer slow loop 9022, and SNR optimization algorithm 9024. It is worth running through Figure 90 to highlight how timing issues are driving the architecture.

[0555] The antenna output is coupled to an ATLF, which matches the antenna to a receiver with some combination of RF, IF, and baseband (BB) downconversion, as well as additional filtering.

[0556] The BB output (which can also be close to the IF) is digitized and fed into a baseband equalizer, which shapes the baseband filters to minimize ISI (inter-symbol interference) noise as well as in-band noise. The equalizer operates in a relatively fast feedback loop as shown, since it needs to keep up with channel variations due to multipath effects. Variations of the equalizer are the Rake receivers used in spread spectrum receivers and OFDM receivers, where the channel state is continuously tracked and estimated. Regardless of the details, the objective is to mitigate the effects of channel frequency selectivity, as done by modifying the multipath.

[0557] Data is extracted from the demodulated baseband signal. Additionally, some indication of SNR is obtained from the demodulation process, which then drives the ATLF optimization.

[0558] The ATLF is not subject to multipath and does not need to absorb radio channel variations. However, the ATLF does need to absorb antenna impedance variations, which occur when electromagnetic scattering or absorbing objects are placed in the near field of the antenna that affect the antenna impedance. The variations in the antenna near field are expected to be much slower and much less frequent than the variations in the multipath communication channel. Therefore, it is desirable to have the ATLF as the slower outer loop.

[0559] An example of where antenna impedance change is important is a smart bandage where the patient changes position affecting the antenna's near field and therefore changing the impedance position that the ATLF must accommodate. However, this change occurs slowly and relatively infrequently compared to changes in the room multipath channel.

[0560] An equalizer can undo some of the filter shaping distortion imposed by the ATLF. Thus, the ATLF focuses on matching and produces a soft-shouldered filter response, which can be restored to some extent by an equalizer, as shown conceptually in Figure 91. Thus, there is no need to have a complex ATLF with multiple poles. However, there is a moderately enhanced NF such that the outer frequency components of the RF signal band are not well matched.

[0561] Implementation of ATL Filtena (ATLF)

[0562] The complication of this discussion is that, as shown above, there are a variety of antenna circuit models that approximate the impedance behavior of an antenna over a relatively narrow bandwidth. Therefore, rather than attempting a unified approach, we will step through a series of examples that cover a range of simple idealized circuits to more practical embodiments. Other examples are possible.

[0563] Radiation resistance component of antenna impedance

[0564] Let us start with an imaginary antenna whose impedance consists only of its radiation resistance. Real antennas always include a reactive component, which we will shortly add. Figure 93 shows the equivalent circuit of this idealized antenna connected to a resistive receiver RR, an AC voltage source 9310 and a resistor 9312. We will assume that the striking voltage source from the distant radiation source is a sine wave with an RMS (root-mean-square) amplitude of . V. Thus the power available from this antenna is

number

[0565] The antenna is connected to a resistor receiver RR. The power transferred from the antenna to the receiver is

number

[0566] We define the reflection coefficient of an antenna as:

number

number

number

[0567] Then, R R load represents the impedance of the receiver and the receiver has a noise figure (NF) of NF R. The overall noise figure for the antenna and receiver is then,

number

[0568] It is based on the assumption that the equivalent noise temperature of the antenna is 293.0K. It clearly shows the inflation of antenna-receiver NF due to antenna-receiver mismatch. The Antenna-Receiver Figure of Merit (FOM) may be defined as this NF. This makes sense since the antenna-receiver gain is arbitrary and the FOM should only focus on the receiver's ability to utilize the available power that the antenna provides. If the receiver's NF is NFR= 1 it will not generate intrinsic noise and there will be no consequence of mismatch. That is, mismatch only reduces the overall signal gain of the receiver but does not contribute to the NF. This also means that in-band noise and signals from the antenna source are treated exactly the same, so mismatch affects both equally. Antenna matching is only necessary if the receiver generates additional noise. Similarly, it can be stated that if the interfering noise at the antenna input is much greater than the receiver's intrinsic noise, there will be little effect on antenna mismatch.

[0569] A few observations are pertinent at this point.

[0570] If the antenna has no substantial reactive component to radiation resistance (such as the simple resistor model currently considered), the NF mismatch and inflation losses are usually modest. Consider an example with R = 20 and R = 50. Then

number

[0571] When antenna reactance is taken into account, losses due to antenna mismatch become more significant. In such situations, the tuning parameters of the matching circuit must be adjusted. Antennas with small dimensions relative to the wavelength usually have highly reactive components.

[0572] If the SNR of the signal received at the output of the antenna is very high, then the mismatch of the antenna is not of concern. However, if the same antenna is used for transmission, the mismatch will be the same for the transmit and receive channels, since they will affect each other under the assumption that the carrier frequencies are close together. Mismatch losses in transmit mode mean that the transmitter operates inefficiently, which can have a significant impact on battery usage and / or range.

[0573] In receiver mode, the desired signal output of the antenna is typically buried in thermal background noise and interference. Furthermore, due to multipath, the exact received signal strength varies widely. Therefore, it is not practical to infer the condition of the antenna match from observations of the RF signal. The desired signal must be downconverted, filtered, and processed before structural features of the signal can be reliably measured on which to assess the condition of the antenna match.

[0574] In transmit mode, the reflection coefficient of an antenna can be measured directly based on a VSWR (Voltage Standing Wave Ratio) measurement, which is usually easy to implement. Suppose we have antennas used for transmitting and receiving at approximately the same carrier frequency. We might then, in principle, match antennas based on VSWR or other measurements in transmit mode and apply the same match to receive mode by correlation. This method is sufficient if the antennas are spread out enough that the frequency separation between transmit and receive channels is small compared to the antenna bandwidth. However, this is not an assumption we are making here, and we aim to tune the antenna matching based only on the typically weak received signal in order to transfer optimal energy transfer from the antenna to the receiver.

[0575] Coupling reactive antenna impedance components to a resonant ATL using a reverse coupler

[0576] In summary, the ATLF consists of an antenna resonator coupled to a resonant ATL that self-configures as a negative resistance as shown in the upper part of Figure 94. The antenna resonator is represented by a series LRC model, where R represents the radiation resistance. The negative resistance ATL exhibits a direct dependence on G, which is set by the control g, Γ G = G(g), which is the reflection coefficient given by the series RLC representing the antenna, and the capacitance C V This shows a varactor diode with Γ Α FIG. 94 shows an antenna (series LRC) 9410, a negative resistance 9412, a resistor 9414, an inductor 9416, and a capacitor 9418.

[0577] Unlike other embodiments of the ATLn that include a directional coupler, what is important about the ATLF is that the directional coupler is reversed from that shown in the small loop antenna example of Figure 95. Figure 95 shows a small loop antenna 9510, a capacitor 9512, a directional coupler 9514, and a gain block 9516. This allows for the coupling of the antenna resonator with the ATLn resonator which is central to proper performance of the ATLF. If the coupler were not reversed, the negative resistance reflection by the ATL would be fed back into the ATL itself, rather than towards the antenna.

[0578] We start with a small loop antenna as the initial configuration, as shown in Figure 95. Here we have a series actuator diode that sets a capacitance to cancel the inductive reactance of the loop antenna. The gain is placed as a scaling block and a backward coupler. The operation is that a signal comes into the loop antenna as a voltage source. This is amplified by the gain section which acts as a one port reflector which is reflected by the mismatched antenna. The backward coupler serves to block the reflection from the gain stage which is controlled by g.

[0579] Combining this into an idealized loop, the overall transfer function is given as:

number

[0580] Consider a series LRC model of an antenna whose port impedance is denoted as z. Given A

number

[0581] The reflection coefficient (at the antenna port) is

number

[0582] Here we use impedance normalization such that the characteristic impedance is 1. This reflection coefficient can be expressed as ΓA

number

[0583] This reflection coefficient is plotted as line 9610 in FIG. 96 for the normalized frequency range 0.75 < w - 1.25. As expected, the CV capacitance cancels the antenna reactance and the reflection coefficient at resonance is a negative real value.

[0584] Antennas where the radiation resistance and conductor losses are not functions of frequency are interesting to consider in this context. ΓA is a constant amplitude function with a pole-zero pattern similar to all pass filters. As shown in FIG. 97, the root locus in this case.

[0585] The root locus shows a typical Q enhancement for R = 0.1. For R > 1, negative G needs to be used. Note the following points.

[0586] Negative G and |G| > 1 occur for negative resistance in the range of -1. G0

[0587] Positive G and |G| > 1 occur for negative resistance in the range of -∞. G - 1

[0588] Note that all impedances are normalized to the characteristic impedance.

[0589] Here, it is assumed that the output is obtained from the scaling block output. Also, the input interaction with the antenna may be represented by a series voltage source. Plugging in some normalized values of C = 1, L = 1, R = 0.1, the root locus shown on the left side of 97 for G is obtained for G < 0. It is clear that G must be negative.

Number

[0590] This root locus shows that the typical ATLn behavior of pole motion is present and that the closed loop poles can be controlled to cross the JwR1 axis, i.e., provided that the radiation impedance is less than the characteristic impedance. For R>1, there is a limit to the Q enhancement potential of this circuit, as shown in the right-hand root locus plot of Figure 97. Note that for R>1, the open loop poles are actually on the negative real axis and there is no resonance. However, providing feedback will produce a Q enhancement from 0 to a finite value limited by R.

[0591] Now consider the transfer function for the value of G. Ga = 1 / min(Act(T)) + .01

[0592] This gives a closed loop Q of about 100. The frequency response is plotted at the top of Figure 98, line 9810.

[0593] Like CVATL1, which changes the capacitance of the varactor, it can be tuned over a wide frequency range. The normalized curves are shown at the bottom of Figure 98, where line 9812 shows C. V= 0.8, line 9814 shows C. V= 1.0, line 9816 shows C. V= 1.2, and line 9818 shows C. V= 1.4.

[0594] Suppose we put the inverter diode in parallel with the loop antenna instead of in series, as in the circuit of Figure 99 with the small loop antenna 9910, capacitor 9912, directional coupler 9914, and gain block 9916. The only change is that now Γ A is the negative value of the previous case which results in the Smith chart plot of line 9918 below in Figure 99.

[0595] Obviously, all of the bandpass response and Q enhancement considerations remain the same as before. The only change is that G is now positive instead of negative. We can also consider a short dipole antenna tuned as in Figure 100. Here the dipole is best modelled as a series capacitor and shunt conduction, taking into account radiation resistance as well as orthogonal losses. An inductor 10020 is placed in parallel with this to provide the tuning range for the inductor. Figure 100 shows the capacitor 10010, antenna 10012, inductor 10014, directional coupler 10016 and gain block 10018.

[0596] In this configuration, the input impedance to the antenna as seen by the reverse coupler is

number

[0597] The bottom part of Figure 98 shows the transfer function of the ATLF for various values ​​of normalized photodiode capacitance. This is calculated by first determining the reflection coefficient of the antenna with matched L and Cv. The ideal ATL1 is then assigned the reflection coefficient of the smallest real part of the antenna reflection over the frequency range of interest and added with 0.01. This gives a Q in the range of about 100.

[0598] The reflection coefficients are plotted as shown in Figure 10110 and show similar behavior as before, but ΓA is a bit larger and is not symmetric about the actual axis.

[0599] It is interesting to note that the circuit shown in Figure 102, in which the diode 10210 is more logically placed after the inductor 10212, unfortunately has a very small tuning range. If the diode is in series with the inductor, the tuning range is restored. Figure 102 shows the antenna 10214, the capacitor 10216, the directional coupler 10216, and the gain block 10218.

[0600] Now consider the combination of a phase shifter in a feedback loop as shown in Figure 103. Figure 103 shows an antenna reflection 10310, a directional coupler 10312, a phase shifter 10314, and a gain stage 10316. The overall transfer function is

number

[0601] The numerator of this transfer function may vary depending on where the output and input are placed. For now, let us assume that the input is a current impressed on the antenna and we get the output from the output of the gain block. Now we can take into account the coupled poles and zeros and plot the closed loop poles as a function of G as shown in Figure 104.

[0602] This now reveals some complexity regarding the coupled resonance of the antenna reflections and the phase shifters. Note that the important result is that the closed loop dominant pole is determined by the phase shifters and not the antenna reflections. The poles of Γα(s) unfortunately travel towards the real axis and then one of the poles travels along the real axis inside the right hand plane, ultimately destabilizing the process. In this example, an unstable pole appears on the real axis before the Q enhancement is complete, as shown in Figure 105.

[0603] Fortunately, this circuit can be stabilized with a simple lead circuit that slows down the pole movement. All that needs to be done is to add an RC lead circuit as shown in Figure 106. Figure 106 shows a capacitor 10610 and a resistor 10612. This restoration circuit can be placed anywhere in the loop of Figure 103 to increase stability. By adding this circuit, the root locus changes to that of Figure 107, showing the increased stability of the dominant pole.

[0604] Next, we replace the phase shifter with a resonator and obtain the root locus plots shown in Figure 108 and Figure 109. Notice that using a resonator has a simpler response, in that only the dominant pole crosses the Jw axis. The secondary antenna pole becomes the root locus on the left. The main advantage of this replacement is that the loop is stable without the need for additional corrections.

[0605] Note that we now essentially have an ATL1 which has an unwanted loop delay which can be compensated for by de-energizing the resonator as shown above. Figure 110. The only deviation in ATL1 is that the directional coupler is set up differently and reversed to send a feedback signal that reflects off the antenna instead of back into the ATL1 loop. Figure 110 shows the antenna reconfiguration 11010, the reverse directional coupler 11012, the gain stage 11014, and the resonator 11016.

[0606] This can be extended to the ATL2 circuit, as also shown at the bottom of Figure 110. The root locus of an ATLF based on ATL2 is shown in Figure 111. Note that the two resonator poles lead to a good dominant pole moving towards the Jw axis as well as spurious poles at higher frequencies. However, for high Q extensions this becomes much less sensitive. The pole to the left of the resonator is the antenna pole and finally the far left is the all path circuit pole simulating the loop delay.

[0607] Finally, to complete the root locus of the ATLF based on ATL3, it is given in Figure 212. Again, there is no problem with the dominant pole moving in a nice way towards the Jw axis. However, there is again the possibility of annoying spurious passband modes at higher frequencies. Again, with high Q enhancement this will not be an issue.

[0608] For calibration purposes, one can specify the desired frequency and vary the capacitances of the antenna's victors and the individual resonators of ATL3. If tuned correctly, the root locus will appear as shown in Figure 213. It is important to note that a rather surprising and non-trivial result is that if all is set correctly, the dominant pole for the ATL3 filter tenner moves straight towards the jw axis, with no spurious passbands. This is a minimum G solution that can be used for calibration as shown above. Thus the previous calibration rule remains as the four victors are set to {f1,f2,f3,fAnt} such that G is minimized for any constrained Q expansion or bandwidth.

[0609] ATLn as a negative resistance element

[0610] As shown above, the key element of the ALTF is that the directional coupler is reversed from the normal ATLn configuration and the antenna is coupled inside the resonant structure of the ATLn with a controllable bandwidth. When the normal directional coupler is reversed, this causes the ATLn to act as a negative resistance to provide return gain for the input power. If the ATLF is implemented in this way, there is no need for a directional coupler. This can be highly desirable since a suitable directional coupler is difficult to realize on a chip with physically small L and C. Therefore, in this section, we take a different approach to the ATLF and dispense with a directional coupler, and then implement a reflective phase shifter with gain over a limited bandwidth. This can be interpreted as a combination of a resonator, an antenna, and a phase shifter. Since our goal here is to explain the circuit topology and not the detailed design, we will return to the ATLF with ATL1 and explain the ATLF.

[0611] Consider the feedback gain circuit to the right of the ATLF circuit in Figure 95. The reflection coefficient for the directional coupler is G. The equivalent impedance is therefore,

number

[0612] Where Z0 is the reference or characteristic impedance and ZG is the equivalent input impedance. This gives

number

[0613] In this idealized example, G is realistic and positive. Thus, for G > 1, we see that ZG is a negative resistance 0. Next, Figure 116 shows an AC voltage source 11610, resistor 11612, and inductor 11614, which is augmented in Figure 116 with a transducer, inductor and negative resistance ZG. The diagram at the bottom of Figure 116 is the Thévenin equivalent circuit of the one shown above. VA is a voltage source derivable from the input EM signal based on the reaction integral. Of importance from the perspective of generating the bandpass response of the ATLF is the use of Z in ZG as a function of frequency. The current constraint I is specified as follows:

number

[0614] next,

number

number

number

[0615] ATLF Runtime Tuning

[0616] As with ATLn, The ATLF's {g,p,f} controls can be set based on look-up table (LUT) entries for specific inputs {Q, required center passband frequency}. The LUT can be collected based on standardized measurements in an anechoic chamber. However, this initial calibration at the factory is only useful when the antenna is at steady state. If the antenna is changed for a different antenna, or if the antenna impedance changes due to near-field interactions, the LUT entries will be in error. To be useful, the ATLF needs to have a run-time calibration method.

[0617] Maximizing the SNR of the demodulated signal from the receiver is one approach: {g,p,f} are dithered such that the SNR of the processed output is maximized. Consider a constant power data modulated signal coupled to an ATLF antenna. Assume that the position and orientation of the ATLF antenna remain fixed. The output of the ATLF is demodulated and the SNR of the data samples is calculated continuously in time. Assume that the processing receiver demodulator has its own clock and carrier synchronization scheme, which is done as an internal process of the data demodulation. For the nominal SNR, this demodulation function with carrier and clock optimization is relatively independent of the ATLF optimization. Then, dither the {g,p,f} controls with a time constant slower than the receiver clock and carrier tracking loop. As a result, an optimal point may be found and the LUT updated. Those skilled in the art will select the appropriate numerical optimization algorithm to use. In this way, the LUT for the operating point (carrier frequency and bandwidth) of the data signal can be optimized to optimize the SNR. The input to the LUT is the parameters of the data signal, not the desired center frequency and bandwidth used to self-calibrate the ATLn.

[0618] The bandwidth is set appropriately, taking into account that if the bandwidth is too wide, there will be too much adjacent channel noise to get into the receiver, if the bandwidth is too narrow, ISI (Inter-Symbol Interference) will occur.

[0619] Now assume that the ATLF is still stationary with a stationary antenna and no change in the vicinity, but the data signal is frequency hopping. However, since the hopping sequence is known, we set the ATLF with the LUT entries for the upcoming data burst, but with {f,g,p} slightly dithered to new values ​​to indicate whether the SNR obtained after the burst is demodulated has increased or decreased. We can then use a gradient algorithm to optimize the specific parameters related to the data burst. That is, if the measured SNR based on the current dither is better than before, we slightly nudge the LUT entries towards the current ATLF parameter set. In this way, we can slowly optimize the LUT entries for the current data modulation. Since the ATLF chip is used in a specific wireless application and is not expected to handle multiple modulation types, it is generally sufficient to optimize it for the specific data modulation. However, if the intended use is multiple modulation types, a LUT may be generated and used for each signal type. Since the SNR measurements are random, the {f,g,p} optimization based on dithering is essentially a stochastic gradient search algorithm.

[0620] Secondly, allowing the antenna to move means the multipath environment changes. However, this does not mean that the antenna impedance changes. Only if the antenna is changed should the ATLF LUT parameters be changed if the SNR remains maximum. Multipath causes a fade in the dynamics and the SNR changes from burst to the next burst at the same hopping frequency as the modulated data signal. Therefore, the change in SNR is more due to the change in multipath as opposed to the change in {f,g,p}. Fortunately, a stochastic search can be used to find the optimal {f,g,p}. Adjustments to the ATLF parameters should be made in very small increments only to avoid instability.

[0621] Another complication is changes in the near environment of the antenna. An example would be a smart bandage where the patient changes position affecting the near field of the antenna or rolls over periodically. In such cases, the impedance of the antenna changes and the entries in the LUT need to be changed. It is therefore a compromise between tracking the changes with a reasonable response time and determining the optimal {f,g,p}. There are solutions to this kind of problem and they are covered in extensive publications in the public domain. A classic application is the cable modem equalizer.

[0622] Dithering algorithms are the simplest run-time calibration and are generally robust. However, there are pathological cases where the dithering algorithm fails. New machine learning algorithms may be applicable. Algorithms vary widely depending on the specific application.

[0623] ATLF Bandwidth

[0624] The signal bandwidth of the ATLF can be visualized by looking at the reflection coefficient back into the antenna. We consider the antenna to be resonant with a series LRC model as before. The reflection coefficient looking into the antenna, Γ, A is specified as follows:

number

[0625] It is based on the characteristic impedance being R. Therefore, the pole-zero pattern has two zeros on the jw-axis and poles on the LHP. The smaller the ratio of R / L, the closer the poles are to the jw-axis. Now, the ATLF transfer function has the form:

number

[0626] Although many details have been ignored, the increase in G shows that the poles move towards the jω axis, narrowing the bandwidth corresponding to the phase value.

[0627] Regardless of the details of the root locus, as R / L decreases, the starting point of the root locus gets closer to the jω axis and the bandwidth becomes smaller. It should be noted that this applies to the case of effective Q spoiling: with the ATLF active feedback gain, the poles can be further pushed into the interior of the LHP away from the jω axis, reducing the bandwidth.

[0628] Figure 88 shows the Nyquist plot and the possibility of determining the bandwidth and stability region showing the Nyquist contour 8810 and the G = 2 circle 8812. Note that the 3dB bandwidth also depends on the numerator of the transfer function, and the transfer function is not considered part of Nyquist. As G increases, the circle of e -jφ / G becomes smaller, indicating an increase in the region of S, an increase in the unstable region, and a narrower bandwidth. Thus, for 0 < G < 1, the circle radius is larger than 1, so there is no instability.

[0629] Diagram of the merits of ATLF

[0630] The figure of merit (FOM) of ATLF, also called the figure of merit, shows how well the entire antenna responds to the incoming electromagnetic (EM) signal in the receiving mode. This FOM is flexible in that it can vary depending on the specific design scenario as different antennas may be accommodated by ATLF. Therefore, the FOM needs to separate the performance of the antenna element itself from the performance of ATLF, i.e., the ability of ATLF to accommodate a specific antenna.

[0631] An antenna intercepts signals contained in an input EM field and converts them into conducted power. The effectiveness of an antenna in performing this task is quantified by its radiation resistance, denoted herein as R. The power available from an antenna depends of course on the signal amplitude as voltage or current. The complexities of determining the signal amplitude may be ignored for this FOM calculation, since it is merely a property of the antenna and not the ATLF. Thus, one may assume that there is available power at the antenna terminal output, PAv, specified as follows:

number

[0632] Where IA is the RMS level of the current leaving the antenna terminal. Otherwise, you can consider VA as the RMS voltage at the antenna terminal, and the available power is

number

[0633] The actual power delivered to the receiver depends on the input impedance of the ATLF and the signal gain associated with the ATLF. However, this ATLF gain should not be part of the FOM. What is important instead is how much power the ATLF uses available and how much noise is contributed by the ATLF. Let RF denote the input resonant impedance of the ATLF. Next, the Norton and Thevenin equivalent circuit of the ATLF is shown in Figure 118, showing resistor 11810 and source 11812.

[0634] The objective of the ATLF is to make the most of the available power: RF=RA. If this condition is not met, some power will be reflected from the ATLF based on the reflection coefficient specified as:

number

[0635] subject

number

number

[0636] This is the intended form of showing power loss due to impedance mismatch.

[0637] Next, assume that the receiver has a load resistance, RR represents the receiver impedance, and the receiver has a noise figure (NF) of NF. Then the overall noise figure for the antenna and receiver is,

number

[0638] It is based on the assumption that the equivalent noise temperature of the antenna is 2930K. This relationship shows the inflation of NF due to antenna and receiver mismatch. The antenna receiver figure of merit (FOM) may be defined as this NF. This makes sense since the antenna receiver gain is arbitrary and the FOM should only focus on the receiver's ability to utilize the available power that the antenna provides. For NF, R does not introduce any intrinsic noise into the receiver and there is no consequence of antenna mismatch. That is, mismatch only reduces the overall signal gain of the receiver but does not contribute to NF. This also means that in-band noise and signals from antenna sources are treated exactly the same, so mismatch affects both equally. Antenna matching is only necessary if the receiver generates additional noise. Similarly, it can be stated that if the interfering noise at the antenna input is much greater than the receiver's intrinsic noise, there is little effect on antenna mismatch.

[0639] As explained above, the ATLF as a negative resistor generates additional independent thermal noise represented by an equivalent noise source at the input to the ATLF negative resistor block, characterized by the Noise Figure (NF) of the ATLF, denoted as NfAtlF. The overall NF of the ATLF is:

number

[0640] Where Snr in is the SNR associated with the usable power output of the antenna. Snr O is the SNR at the output of the ATLF, assuming you are evaluating this at the resonant frequency.

[0641] If the antenna is subjected to blackbody thermal radiation at room temperature and has a conducted noise spectral density at the antenna terminals of ΗA. Similarly, the ATLF negative resistor has the same input noise density of ΗF. Then we have

number

[0642] When the NF of the ATLF negative resistor is written as follows:

number

[0643] In summary, the overall NF of the ATLF is F, which is the product of the NF of the negative resistor used in the ATLF (FF) and the penalty term

number

[0644] The use of Nf in the FOM is reasonable as it captures how well the ATLF absorbs and transfers the antenna signal to the gain stage. This can be compared to a traditional arrangement where the matching circuit represents component losses and mismatches over the desired frequency range. Nf also shows equivalent noise inflation due to ATLF mismatches, especially between the antenna radiation resistance and the active electronics used as a negative resistance. Determining this impedance is a delicate matter: ΓF)>1 due to negative resistance.

[0645] Consider a negative element equivalent circuit as shown in Figure 119 where the input signal from an antenna is coupled into a four-port directional coupler. Figure 119 shows a four-port directional coupler 11910, a gain 11912, a resistor 11914, a ground 1196, and a phase shifter 11918. The output of this coupler is amplified, phase shifted and sent back to the coupler. Assume a high ratio coupler so that the pair of ports {1,2} and the pair {3,4} are strongly coupled. Assume that the gain G is high enough so that the path from port 1 to gain G and the path from port 3 to port 1 can have gain. Then, at port 1, the phase shifter is equivalent to a negative resistance if it is set correctly to offset the 90 degree shift of the hybrid coupler. It is clear that at the resonant frequency, signal reflection will occur at port 1 due to the mismatch of R, regardless of the frequency dependence. A characteristic impedance of the circuit in Figure 119 leads to signal loss related to that factor.

number

[0646] For negative resistance transistor devices, we can consider a similar equivalent circuit operating over a narrow band. Hence the term

number

[0647] Excess loss factor

number

number

[0648] ATLF Configuration

[0649] Therefore, the main implementation problem of the ATLF is that of resonator coupling. For this, there are various circuit configurations that may be developed, some of which are divided into categories and shown in the block diagram of Figure 120:

[0650] A shows a direct connection from antenna 12010 to ATLn 12012, which provides frequency decoupling and Q adjustment, but does not provide coupling to antenna 12010.

[0651] B shows LNA 12014 acting as an active isolator to decouple the antenna subcircuit from the ATLn filters. If the antenna 12010 does not match the characteristic impedance on the target band, it will not effectively couple to ATL1 12012. Therefore, B includes a matching network 12016 and LNA 12014.

[0652] C shows a small antenna 12010 which can be modelled as an LRC circuit, where the actuator 12018 changes the effective antenna capacitance, which changes the resonance of the antenna, partially matching the antenna over the operating band with the ATL1 resonator 12020.

[0653] D is the same as C, but with a cascade of ATL1 12020 and ATLn 12012. The first ATL1 interacts with antenna 12010 and is a low Q circuit with actuator 12018. The reason for this circuit is to do a partial boost of Q creating a dominant pole pair that is further boosted by the second ATLn. This approach makes it easier to accommodate a wider range of antennas.

[0654] E shows the controllable negative resistance solution provided by the configured ATLn, later shown in the ATLF implementation. E shows the antenna 12010, the resonator 12022, the phase shifter 12024, and the negative impedance 12026.

[0655] FIG. 120 shows an ATLF implementation based on an off-chip directional coupler. FIG. 120 shows the antenna 12010, the coupler 12028, and the scaling, resonator, and topology block 12030.

[0656] G is similar to F, but shows that if the phase shifter can be removed and replaced with three resonators 12022, which, with minor adjustments as described above, provide a suitable range of phase correction. G shows antenna 12010, coupler 12028, and scaling block 12032.

[0657] H shows an ATLF consisting of a special antenna 12010 consisting of a radiating element 12034 and an integrated directional coupler 12036, providing a two port antenna that can be connected to versions F and G. Thus, the scaling, phase and resonators as shown in one block 12030.

[0658] Other implementations are possible, provided the implementation of choice is driven by system-level parameters and performance goals.

[0659] ATLF Calibration

[0660] As we will explain how to set the control voltages to adapt the performance of ATLn for the target application, it can be set based on the following principle: In this example, for ATL1, there can be 3 such LUTs, for ATL3 there can be 9 LUs.

[0661] The following describes various considerations that may or may not be relevant for a particular implementation.

[0662] Next, we discuss an example of the calibration and stabilization of a single ATL1 core module. Figure 32 presents a circuit with built-in processing for the purpose of calibrating and stabilizing the response of the ATL1 block 7502.

[0663] The microprocessor 7504 is generally a system asset and adjusts the frequency and Q control of the ATL1 7502 via a DAC implemented as a pulse width modulation (PWM) circuit 7506, based on readings from a temperature sensor 7508. The microprocessor drives the ATL1 7502 until the onset of self-oscillation. The frequency of this self-oscillation is down-converted in block 7510 by a crystal reference 7505, also set by the microprocessor 7504, and a frequency synthesizer signal generated by a frequency synthesizer 7507. A frequency counter 7509 or other measurement means determines the frequency of the down-converted signal. In this way the resonant frequency of the ATL1 core module may be determined. There is also a power detector 7512 and an ADC block 7514 that can estimate the rate of increase of the self-oscillating signal at the output of the ATL1 7502. The microprocessor 7504 estimates this exponential rise in power and thus determines where the closed loop poles of the ATL1 7502 are located. Currently, it will be just right on the Jw axis. If the Q enhancement is reduced slightly, the self-oscillation will continue with high accuracy at the same frequency, but will begin to decay exponentially. Now, Paul points out that while the ATL1 calibration is stable over time, changing mainly based on ambient temperature, the calibration of the ATLF depends on transitioning to deliberately oscillating conditions. We rely on the fact that crossing the outer circle of the Nyquist locus results in instability. Complex variable theory offers two perspectives on stability that are relevant in the present context.

[0664] Stability of open-loop transfer functions from complex variable theory.

[0665] The first result, which comes from complex variable theory, is that the open loop transfer function is itself stable and has no poles inside the right hand plane. This is true as long as the components are unconditionally stable. In the architecture we have, we assume that the resonators and the gain blocks are stable, which is certainly true for the resonators since they are passive auxiliary circuits with no active gain. The gain blocks can be assumed to be unconditionally stable, and therefore can be considered correct. However, a situation can arise when the gain blocks are based on transistor configurations that are not unconditionally stable, and as the impedance of other loop components changes slightly, we can see the poles gradually move closer to the right hand plane and change the Nyquist stability criteria. This is a design problem that can be avoided or minimized. However, the implementation of the negative resistance of the ATLF is slightly more difficult in that the gain blocks are not indeed unconditionally stable. Reflections by the resonators or phase shifters and reflections by the negative resistance can easily lead to situations where the poles are pushed inside the right hand plane outside the normal operating band. This can be at frequencies much lower or higher than the bandwidth of the resonator, and the reflection coefficient approaches 1. This needs to be avoided by careful design to ensure that 1) no open loop poles lie in the right-hand plane, and 2) any potential poles are designed out.

[0666] Analytic continuity from the theory of complex variables

[0667] Another consequence of the complex variable theory we rely on is analytical continuity. This shows that any point inside the outer circle is unstable. This is why when we determine the point of (f,g) that gives us marginal stability (the boundary point), we get a portion of the Nyquist locus. Thus, we can overshoot the boundary by any amount in terms of g-control and still be in an unstable region. On the flip side, outside this boundary we have strictly stable behavior.

[0668] What's more is that any operating point at a short distance from the Nyquist locus has a predictable natural mode that is exponentially decaying in the stable region and exponentially growing in the unstable region. The useful part is that the coefficient of this growth or decay is proportional to the slope distance to the Nyquist contour. It's almost as if we were flying in an airplane and distorting it. The Jw axis conforms to the outer Nyquist contour. This allows us to accurately predict how changes in g and f will affect Q. This is shown in Figure 92. It is this continuity property that makes calibration and tracking smooth and possible. Figure 92 shows the stable region 9210, the unstable region 9212, the locus of points with the same exponential decay 9214, the locus of points with the same exponential growth 9216, and the outer Nyquist contour 9218.

[0669] An interesting property is that the Nyquist locus is more likely to have small loops visible due to antenna reflections for antennas near the field. These loops will always be inside the unstable region as shown in Figure 128. The reason for this is that the feathers of the Nyquist locus (for any realizable stable open loop response) are always in a clockwise direction as frequency increases. Also, reflections from scattering points are much faster for clockwise rotating feathers. If we sketch this out, we can see that only inward facing loops are possible. This means that near field scattering will result in gaps in frequencies that can be tuned. However, this helps with stability as the loops cannot grow outwards and thus the loops will not suddenly destabilize the ATLF. This is shown in Figure 129.

[0670] Calibration of ATLF

[0671] Single Frequency ATLF Calibration Procedure

[0672] Single Frequency ATLF Calibration Procedure An example procedure for ATLF calibration under single frequency operation, assuming no pre-calibration, is given below. Other procedures may be possible.

[0673] Setting f = 1 places the resonator in the center of the tuning band.

[0674] Increase g until the RF detector indicates an oscillation mode, just beyond this point.

[0675] Vary f until the baseband detector also lights up. Now we are at the correct frequency.

[0676] Reduce g until the baseband detector extinguishes. If the RF detector extinguishes at the same point, the ATLF is correctly tuned in frequency. If the RF detector still shows an oscillating mode, the frequency has shifted due to a gain block coming out of saturation. To fix this, shift f so that the baseband detector lights up again. Correct tuning is when the RF and baseband detectors light up and extinguish at the same time.

[0677] Assume that the shape of G(g) is known exactly, but G(g) is not known. However, G(g) = 1 is determined at the point when both the RF detector and the baseband detector move from the active state to the extinction state simultaneously.

number

number

[0678] Express Q in terms of changes in g that we know we need

number

number

[0679] To be able to solve the necessary changes in g

number

[0680] Once configured and the receiver is functioning properly, the LUT can be used to set the Nyquist locus boundaries for the desired frequencies and g that gives the desired Q.

[0681] During operation, you might want to use the SNR to track changes in the g and f values. For both static antennas and fixed multipath, this is easy since you only need a gradient along the variable direction of g and f. Find the gradient numerically by dithering g and f by small amounts.

[0682] This is more difficult with variable multipath and / or variable antenna impedance, as the SNR varies randomly. If the multipath and antenna impedance are slowly changing, we can assume they are quasi-static and complete an iteration of the SNR steepest ascent routine before the characteristics change. In this way we are constantly tracking the values ​​of g(t) and f(t) required for the optimum point. If the variations are slow relative to the time required to measure the SNR, multiple iterations of the steepest descent are possible to converge or track closely.

[0683] Multi-frequency ATLF calibration procedure

[0684] If a frequency hopping scheme is used by the communication channel, each set of frequencies is preferably calibrated by the ATLF. Doing so may give a vector of settings of f and g as a function of hopping frequency. One calibration procedure could calibrate each hopping frequency as if it were a single frequency. However, another, more efficient procedure could also be used.

[0685] An obvious improvement would be to calibrate the frequencies in turn and realize that the change from a lower hopping frequency of f and g to the next higher hopping frequency is very small, so the result of the previous frequency calibration is just an initial guess for the next higher frequency.

[0686] It is clear that the parametric curves of g(frequency) and f(frequency) are then fairly smooth. Spline interpolation may be used to combine the calibration data. This may be used more in tracking. In tracking, the SNR is used again. The problem is that the SNR available in the ATLF transceiver may be highly frequency dependent in areas of multipath. Dithering therefore only makes sense when comparing specific frequencies. This means that the dithering calculation of the numerical gradient has to wait until a specific frequency appears. If the multipath varies in time more than the convergence time of the SNR optimization, it is necessary to open up the bandwidth of the ATLF so that more SNR data is present. This is a compromise, since the ATLF only gives the best match for segments of the tuning range, not for individual frequencies. The innovation followed here is the choice of this matching for what size frequency segments and how many segments to actively track.

[0687] This grouping does not work well when the multipath frequency changes rapidly. In conclusion, the grouping of hopping frequencies relative to the coherence bandwidth of the multipath channel is preferably done in terms of sharing SNR data samples, and the steepest descent algorithm preferably converges within the coherence time of the channel. While this may seem rather limiting, the optimization algorithm only has to keep up with the antenna impedance changes and the slow changes in the ATLF based on temperature, supply voltage, and aging. Therefore, changes to the final LUT can be made very slowly. That said, there are cases where the ATLF cannot be properly calibrated and adjusted, such as when the sensor antenna is constantly changing and the nearby field scattering changes significantly.

[0688] Initial ATLF calibration, acquisition and tracking phase

[0689] In one embodiment of the ATLF, it may be useful to think of three states as follows:

[0690] Initial calibration phase: The ATLF is first powered up after mounting the antennas and installing it in its housing with all antenna covers etc. The LUT is populated with only configuration data, such as:

[0691] Is this a single frequency or frequency hopping application?

[0692] When I wake up

[0693] When to start calibration

[0694] When to obtain it, etc.

[0695] For single frequency applications, the calibration is developed only for that single frequency. It uses self-oscillation mode to determine the Nyquist boundary point. It can record temperature several times simultaneously to start estimating temperature related parameters. It then goes to sleep and wakes up when it is time to start the acquisition phase.

[0696] For multi-frequency sensors, calibration is done in the same way, but for each hopping frequency mentioned above. We assume that commissioning provides a procedure to handle the calibration in an efficient way, such as using a spline fit, rather than doing it for each frequency individually.

[0697] Acquisition phase: The sensor wakes up and starts acquisition mode. The time information may not be accurate as it waits for a packet to arrive at a specific frequency based on the LUT. If necessary, it can do a self-calibration step to fine-tune the antenna center frequency and bandwidth position. Since the ATLF may not have accurate time information, it opens the receiver and waits for a data packet on a specific frequency. When a packet arrives, it will give information to accurately set the clock for the next packet and the next carrier frequency in the hopping sequence. Between the end of the first packet and the start of the next packet, it can optionally Self-calibrate if necessary. If necessary, it may self-calibrate multiple times until the LUT is accurate. The acquisition phase may consume a disproportionate amount of energy if not optimally configured. Either way, it will exit in acquisition mode once the LUT entries are accurate and receive performance is optimal.

[0698] Tracking phase: At the completion of acquisition, self-calibration based on self-oscillation is no longer necessary and you may enter track mode. This means that only the SNR is used to fine-tune the ATLF during reception. SNR tuning is very low power, but requires a series of data packets, since a stochastic gradient method is used. Such stochastic gradient determination requires dithering, which results in a slight degradation of the ATLF tuning. As explained, if the coherence bandwidth or coherence time is too short, the SNR gradient estimation becomes unreliable and noisy, and track mode does not work. In this case, you must return to acquisition mode and rely on self-oscillation to control the ATLF and prepare for the next packet. The penalty is that acquisition consumes more power than track mode.

[0699] Suboptimal Track Mode

[0700] If track mode fails because the coherence bandwidth or coherence time is too short and the energy taken to acquire is too high, there is an option to control the bandwidth to give acceptable average results for a segment of the hopping frequency band. That is, instead of retuning the ATLF for every specific frequency hopping packet, the frequency hopping band can be grouped into two or three segments. The ATLF will use a wider bandwidth. Now there is a lot more data available, since packets for a group of hopping frequencies occur more frequently than individual frequencies. Thus, the compromised version of track mode works again.

[0701] As part of the overall commissioning of the sensor, the rules and thresholds for transitioning between these four modes are built into the LUT configuration.

[0702] The above phases and modes are given as examples, and they may be modified, substituted or combined with other phases and modes by those skilled in the art once the design principles discussed herein are properly understood.

[0703] Runtime calibration of ATLn and ATLF

[0704] Next, consider run-time calibration. There are a variety of ways to achieve this. In the example wireless sensor application above, the telemetry link is used intermittently, so there is a significant percentage of the time that the ATLn and ATLF self-calibrate. This self-calibration can be tailored to the specifics of the application.

[0705] For example, consider a smart bandage application where the transceiver chip wakes up every second, transmits a data packet on a specific frequency, and goes back to sleep. If ATL1b is used in mode 3 (Fig. 150) to transmit, mode 4 (Fig. 151) may be run a few milliseconds before the transmission to precisely set the control voltage of ATL1b based on using ATL1a as the VCO set to the transmit frequency. Then, just before the transmission is made, the ATLF is reconfigured for mode 3 (Fig. 150) with ATL1b precisely tuned in frequency. Generally a receive mode is also required so that the bandage sensor can be controlled a) what to transmit, b) when to transmit, and c) on what frequency channel. Typically, to save power, the receiver wakes up at a predetermined time based on the radio telemetry protocol used. Before the receive mode epoch mode 4 (Fig. 151) is set, ATL1b is the VCO set at the expected receive frequency. The control of ATL1a is dithered so that the passband is correctly centered and has the correct frequency. The frequency error of ATL1b may be corrected at the same time.

[0706] This intermittent run-time calibration does not need to be done continuously, but it should be done periodically. The problem is that the calibration requires additional battery energy, which is also minimized. For every calibration measurement, the LUT may be annealed with new information. So, the ATLn and ATLF are self-calibrated and kept up to date.

[0707] Another mode of calibration is that ATL1a and / or ATL1b are continuously adapted to optimize receiver performance, and is done only at the receiver MOD. Depending on the baseband processing, there is generally some utility for measuring signal quality. This could possibly be the result of some clocking phase tracking loop for optimal demodulation of the communication signal. The control voltage can be dithered to optimize this demodulation process.

[0708] Overview of ATLF self-calibration

[0709] As discussed, self-calibration of the ATLF can occur when power is first applied after the circuit is built. This may be part of a factory calibration, or the final user may do this as an initialization step. At run time, calibration of the ATLn can continue as needed.

[0710] Replace the calibration coefficients in a look-up table (LUT), or

[0711] It dynamically changes the coefficients in response to changes in the antenna environment, changes in circuit temperature, or other effects such as aging.

[0712] Therefore, the ATLF adapts to the embedded environment, which is important in the case of wireless sensor bandages, changes in antenna proximity as the patient moves, and the patient's skin impedance.

[0713] This resonant matching, which is the output of the ATLF self-calibration process, accomplishes several goals simultaneously. As explained above, matching components are removed, which not only reduces the part count where matching components are not required, but also eliminates the losses associated with more typical impedance matching. In simple terms, the resonances of the antenna structure are absorbed by the ATLn, which undergoes a self-calibration process to optimize the performance of the antenna subsystem. Minimize losses between: the antenna radiated power and the transmit power supplied to the antenna, Available power of the received electromagnetic (EM) signal and reception of the received signal for receiver processing. It provides optimization for a given bandwidth and center frequency that can be dynamically changed, i.e. the resonance match between the ATLN and ATLF is optimized over the entire tuning bandwidth of the ATLn.

[0714] This ATLF optimization is not a compromise of the best match that can be achieved with a small number of discontinuous matching components. This becomes important as tuning bandwidth increases and instantaneous channel bandwidth decreases. For example, if tuning is over 10% bandwidth and the wireless communication channel is over 0.1% bandwidth, instead of compromising tuning beyond the 10% bandwidth, the ATLF automatically optimizes to the best match for every 0.1% bandwidth increment across the entire 10% tuning range.

[0715] ATLF Control

[0716] A discussion of the control of the ATLF is provided below in the context of an ATL-based circuit. This discussion may be translated to other embodiments, depending on the final configuration.

[0717] To understand the control aspects of the ATLF, we will walk through a technical overview of the ATLF, which includes:

[0718] Variable analog bandpass filters with simultaneously and independently adjustable frequency and adjustable bandwidth (ATL).

[0719] A conjugate antenna impedance matching network (ATLF) based on the vertical integration of the ATL.

[0720] Control and optimization of the ATLF circuitry ensures that the antenna impedance remains reasonably static over a period of several minutes, changing from the initial impedance value to the new impedance value.

[0721] From this understanding, an ATLF circuit control circuit and control method for applications where the antenna impedance is rapidly changing will be described.

[0722] The control of the ATLn has been discussed above. The main difference between the ATLF and the ATLn in terms of control is that the input port impedance of the ATLn is assumed to be a real value, designed so that the control does not have to contend with an unknown time-varying impedance. The ATLF on the other hand has an unknown port impedance at the point of the antenna. Furthermore, the antenna impedance can vary significantly with time as scattering objects in the near field change.

[0723] For ATLn, it is possible to consider a calibration look-up table (LUT) for coarse control and use the SNR measurement for fine control as described above. The LUT is fundamentally dimensioned in terms of the control voltage with the possibility of compensation for temperature variations, supply voltage measurements, component aging, etc.

[0724] Unmodeled parameters such as tolerance for slow component drift over time may be handled by SNR optimization. Essentially, the more information that can be stored in the LUT, the less fine tuning that needs to be done in run-time control. The LUT can be built as an initial calibration step or developed at run-time priors. Regardless of the step, as the calibration matures, the emphasis on run-time control becomes less important as the LUT becomes more accurate. Calibration may be thought of as a form of supervised learning where the labeled data used for training is the output of a communication process. At run-time, after a coarse set by the LUT, the objective of maximizing SNR drives the control. Feedback from this process on fine adjustments to the LUT control is used for subsequent annealing adjustments of the LUT over time.

[0725] ATLF follows a similar ATLn strategy where a LUT is used for coarse tuning and SNR optimization is used for run-time fine tuning. However, ATLF must contend with unknown time-varying antenna port impedances. Near field scattering objects affect the antenna impedance, resulting in three very different cases for the control of ATLF. These static, quasi-static and dynamic antenna impedance cases have been discussed.

[0726] Static Antenna Impedance: Consider a sensor mounted on some equipment in a climate-controlled environment, where there is no possibility of scattering objects entering the antenna's near field. In this case, the antenna environment is static, and the antenna impedance is static. This is the same scenario from the control point of view of the ATLn control with static input and output port impedances. In this case, the ATLF LUT can be pre-calibrated or accumulated over time. Ultimately, it is only the unmodeled components of the LUT that need to be tracked based on the SNR optimization procedure. For example, if the LUT has no provision for temperature variations, the ATLF control will track the slow variations. Note that the frequency selectivity of multipath may occur between a static sensor and a reader, but does not affect the antenna impedance, since the effect of a moving reader is small from the point of view of a moving scattering object.

[0727] Quasi-static antenna impedance: Consider a sensor mounted on some equipment outdoors where there are large variations in temperature and humidity that affect the antenna impedance. One method of control is to build a high-dimensional LUT that takes these environmental effects into account. Assuming a sufficiently elaborate LUT, there is no difference compared to the static case. However, if it is not practical to calibrate a high-dimensional LUT, then run-time control tracking is required. In any case, the LUT needs to be built and refined over time.

[0728] Dynamic Antenna Impedance: In this scenario, the antenna impedance can change significantly (10% or more) over short time intervals (fractions of seconds), which means the control system must keep up with that rate. While a LUT can be used for an initial coarse setting, tracking the antenna impedance is critical to achieving a higher Q (reduced bandwidth). As an example, a smart bandage on a moving patient can result in significant changes in the antenna impedance. When the signal to be demodulated is largely unknown, only the SNR can be used for optimization. When the signal structure is known, a more powerful optimization process can be implemented to make the optimization faster and more robust. However, this more elaborate processing requires energy. Thus, there is a point where the energy saved by a more optimal tuning of the ATLF is more than offset by the additional increment of energy required for the processing.

[0729] For the ATLF to be successful in these cases, the following mechanisms are required: First we build the LUT so that ATLF can work. Makes runtime adjustments to the LUT as it grows over time. Rapid runtime tuning of ATLF.

[0730] A key feature of the ATLF in the static antenna impedance case is that once attached to an antenna, sensor etc. it is likely to be fully self-calibrating. For example, a pipeline sensor installation can be made as simple as the sensor being placed on the pipe from the package and then starting the self-calibration algorithm which builds the route. If the LUT is satisfactory it can be put into service. A mechanism to detect the need for recalibration (if the run-time SNR optimization is not sufficient for tracking or the optimization is not on track) is part of the control algorithm so that the sensor can always return to the initial self-calibration mode.

[0731] Obviously, it is not possible to describe the installation, commissioning and use of all possible sensors in the required algorithms. Instead, we will focus on the calibration tools that need to be incorporated. This is similar to a transceiver chip in a mobile phone. It mainly consists of hardware processing blocks that perform different functions with associated software drivers. The smartphone designer then needs to generate a "main program" that calls all the subroutines that call the hardware processing blocks with the goal of the final application target. This integration is not a trivial task and is where power consumption minimization comes in. There are application-specific questions that the system designer needs to address: Setting the First ATLF Calibration Duration Parameter Specify the required precision for the LUT before releasing it at runtime How much runtime calibration feedback data is allowed to affect the LUT values If this change continues over time If the ATLF needs to go into periodic recalibration to make it more robust

[0732] The aim is therefore to develop and describe the basic building blocks.

[0733] Effect of variable antenna impedance

[0734] The Nyquist trajectory is central to visualizing the ATLF mechanism. As explained above, if s=jω is the complex frequency, then H OL (s) is the open loop response of the resonator, the antenna reflection coefficient Γ a , and any loop parasitics such as the propagation delay and phase shift of the gain blocks. What is extracted from the open loop is a pure real-valued gain G, which is a nonlinear monotonic function of the gain control parameter, denoted g, and the polarity control, denoted p. Also, G is frequency independent. Hence, H 0LSuppose we factorize (s) as follows:

number

[0735] Additionally, we have a frequency control, f, that affects the varactor diode of the resonator in the loop. In general, the resonant frequency is nonlinear, but the monotonically increasing function of fH(s|g,p,f), where the function H(s) is tuned in terms of parameters g, p, and f, is the function that the open-loop response continues to be once the pure real-valued gain of G(g,p) is fully factored. Note that the notation for G(g,p) explicitly indicates that this real gain is neither a function of frequency s nor of the frequency control, f. Furthermore, assume that the polarity control takes one of two Boolean values, 0 and 1, such that

number

[0736] Of course, this factorization is incomplete, but note that if H(s|g,p,f) includes dependencies on g and p, then G(g,p) can be extracted as the real gain that is frequency independent. Then, the following approximation is required:

number

[0737] This approximate factorization can absorb the frequency variations in the gain blocks, but it cannot absorb the degree to which the frequency variations change with p or g. The approximation is valid to a first order approximation, but the implications need to be understood.

[0738] The motivation for factorization is that factorization results in a clear Nyquist plot from which the fundamental behavior can be extracted. Consider the initial introductory figure 130 where the left contour represents the Nyquist locus as the system is calibrated, and the black dots indicate frequency points on the Nyquist locus for the desired center frequency of the ATLF passband. Figure 130 shows the Nyquist locus at calibration 13010, the operating point 13012, the desired center frequency 13014, the operating center frequency after antenna impedance change 13016, and the Nyquist locus at actual operation 13018. The green dot essentially represents the operating point of 1 / G and is based on the settings of g and p. As stated above, the operating point is based on a criterion. It needs to be outside the outer circle of the Nyquist locus for stability. The closer to the Nyquist plot, the higher the Q enhancement. In the negative real axis segment, as g gets larger, the operating point moves closer to the right, closer to the origin. Similarly, for an operating point on the positive real axis segment, as g becomes larger, the operating point moves to the left, closer to the origin. Eventually g becomes so large that the operating point crosses the Nyquist locus, which is a point of infinite-Q augmentation and also a point of instability.

[0739] Now consider a small change in antenna impedance (or other effect) which results in a gradual shift of the Nyquist locus to the right contour of Figure 130. There is also a shift in the desired operating frequency. This shift in the Nyquist locus results in a change in the passband characteristics which can be sketched as shown in Figure 131, with much lower Q enhancement and a misaligned passband. Figure 131 shows the desired center frequency 13110, the frequency response centered at the desired frequency 13112, and the mismatch frequency response 13114.

[0740] The worse scenario is that the ATLF becomes unstable with the change in antenna impedance as shown in Figure 132. Figure 132 shows the Nyquist locus at actual operation 13210, the Nyquist locus at initial calibration 13212, the initial operating point 13214, the initial operating point 13214, and the new operating point at operation 13216. As shown in the figure, the left contour of Figure 132 shifts to the left such that the Nyquist contour surrounds the operating point. Now the ATLF becomes unstable and therefore starts to oscillate at a frequency that is generally independent of the desired signal. With sufficient Q enhancement, the operating point is relatively close to the Nyquist locus and there is always a possibility of oscillation with a small perturbation in the antenna impedance. From this Nyquist plot visualization, the objective of the ATLF control algorithm can be clearly stated.

[0741] The objective of the ATLF control algorithm: to maintain the operating point at a constant distance from the Nyquist contour and to maintain the desired frequency point on the Nyquist locus such that that frequency point coincides with the intercept point on the real axis.

[0742] An idealized ATLF consisting of non-reactive antennas and loops with controllable delays.

[0743] First, we assume that the antenna is a real entity with no reactance: the ATLF is a pure delay that can be controlled to provide the appropriate phase shift. Then we have

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[0744] where the delay T decreases monotonically as f increases. The Nyquist locus is G(g)r, which is the radius. Hence there is a redundant specification with respect to the radius. We know that oscillations occur when G(g)r ≥ 1 at some frequency. The truth is that G(g)r cannot exceed unity because the oscillation amplitude will become large and the gain block will begin to saturate. For control purposes, we assume that we know exactly the level of g that causes G(g)r = 1. We also know the shape of the function G(g) accurately enough, not the scaling offset. The shape may be known to within a few percent from the chip design, which is accurate enough. However, there is a small difference between a highly Q-enhanced stable state and an unstable oscillation, so we need to know the scaling very accurately. Thus this scaling is only known by calibration. To simplify control, we arbitrarily assume that r is exactly unity and the difference is absorbed by G. We can now meaningfully scale G via calibration, so that G(g) = 1 for values ​​of g that just start the oscillation condition. Then, if you know the shape of G(g), you have a good enough characterization of the loop gain.

[0745] Next, we need to characterize T(f). Like G(g), T(f) is known to within a few percent, but the scaling is not precise enough. However, we know that once oscillations occur, the frequency can in principle be measured accurately relative to the clock crystal time. Thus, the frequency of oscillatio...

Claims

1. 1. A resonant RF filter circuit, comprising:

1. A signal loop having a signal input connected to receive an input signal, a signal output connected to output a filtered signal, and a closed loop frequency response characterizing the filtered signal at the signal output relative to the input signal, a first component comprising a primary resonator, the primary resonator having a primary frequency response; a second component comprising at least one tunable resonator, the at least one tunable resonator having a tunable resonant frequency; and an adjustable scaling block that applies a gain factor; a signal loop, the first component being constructed from a first material and the second component being constructed from a second material different from the first material; a controller coupled to the at least one tunable resonator and the tunable scaling block, the controller having instructions to tune the closed loop frequency response to a desired closed loop frequency response by controlling the tunable frequency of the at least one tunable resonator and the gain factor of the tunable scaling block.

2. 2. The resonant circuit of claim 1, wherein the first component and the second component are separate and distinct components.

3. 2. The resonant circuit of claim 1, wherein the primary resonator has a primary Q factor that is at least 10 times greater than the Q factor of the at least one tunable resonator.

4. 2. The resonant circuit of claim 1, wherein the primary resonator has a primary Q factor that is 100 times greater than the Q factor of the at least one tunable resonator.

5. 2. The resonant circuit of claim 1, wherein the primary frequency response of the primary resonator is within a predetermined error factor of the desired closed loop frequency response, and the controller controls the closed loop frequency response to within the predetermined error factor of the primary resonator.

6. The resonant circuit of claim 1 , wherein the primary resonator is a fixed resonator or a tunable resonator.

7. The resonant circuit of claim 1 , wherein the primary resonator is an antenna, the antenna comprising the signal input of the signal loop.

8. The resonant circuit of claim 1 , wherein the signal loop further comprises a phase shifter that applies an adjustable delay factor, and the controller is connected to control the phase shifter.

9. 10. The resonant circuit of claim 1, further comprising a plurality of tunable resonators connected in series or parallel.

10. The resonant circuit of claim 1 , wherein the primary resonator is an electrical resonator, an electromagnetic resonator, a mechanical resonator, or a material property based resonator.

11. The resonant circuit of claim 1 , further comprising a plurality of primary resonators connected in parallel or series within the signal loop.

12. 1. A method for modifying a closed loop frequency response of a resonant RF filter circuit, comprising: providing the resonant RF filter circuit with a signal loop, the signal loop comprising: A signal input; A signal output; a first component comprising a primary resonator, the primary resonator having a primary frequency response; a second component comprising at least one tunable resonator, the at least one tunable resonator having a tunable resonant frequency; and an adjustable scaling block which applies a gain factor to the signal loop; the first component being composed of a first material and the second component being composed of a second material different from the first material; and controlling the resonant frequency of at least one tunable resonator and the gain factor of the tunable scaling block to tune the closed loop frequency response of the resonant RF filter circuit to a desired closed loop frequency response.

13. The method of claim 12 , wherein the primary resonator has a primary Q factor that is at least 10 times greater than the Q factor of the at least one tunable resonator.

14. The method of claim 12 , wherein the primary resonator has a primary Q factor that is at least 100 times greater than the Q factor of the at least one tunable resonator.

15. The method of claim 12 further comprising the step of adjusting a resonant operating frequency of the primary resonator.

16. The method of claim 12 , wherein the primary resonator is an antenna, the antenna comprising the signal input of the signal loop.

17. The method of claim 12 , wherein the signal loop further comprises a phase shifter, and adjusting the closed loop frequency response further comprises adjusting a phase of the phase shifter.

18. The method of claim 12 , further comprising a plurality of tunable resonators connected in series or parallel.

19. The method of claim 12 , wherein the primary resonator is an electrical resonator, an electromagnetic resonator, a mechanical resonator, or a resonator based on material properties.

20. The method of claim 12 , further comprising a plurality of primary resonators connected in parallel or series within the signal loop.

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