Apparatus and method for controlling resonator

Abstract

To provide apparatuses and methods which perform coupling of resonant structures (a primary resonator of interest, and a secondary variable resonator) in a manner such that the closed loop characteristics of the primary resonator is modified by adjusting elements in a signal loop that also includes the primary resonator.SOLUTION: There is provided an 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 includes a primary resonator having a primary frequency response, at least one adjustable resonator having an adjustable frequency and a secondary Q-factor, and an adjustable scaling block applying 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 adjusting elements of 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 found in all manner 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 ohms. Antenna impedance matching is typically achieved using lumped impedance matching components that provide a fixed antenna impedance, especially for electrically small antennas (ESAs) in 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. Due to the technology employed, these SAW / BAW devices are subject to thermal fluctuations and aging effects that significantly reduce their filtering effectiveness. 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 achieved, for example, with a) an electrically miniaturized RF antenna, and b) a high-performance tunable RF active filter coupled to a SAW / BAW RF filter. The primary resonator can be a different type of resonator, such as an electric resonator, an electromagnetic resonator, an electromechanical resonator, a piezoelectric resonator, or an optical resonator.

[0007] Examples of suitable tunable resonators that can 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 resonator with a higher Q 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 will be understood by those skilled in the art. In some cases, the Q of the primary resonator may be considered higher than that of a tunable resonator, and a high Q resonator may be considered 10 times higher, or even 100 times higher, than a tunable resonator. According to certain aspects, 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 a substantially high Q, while the other resonator is a low-Q variable resonator. The purpose of the coupling is to control the performance index of the external resonator by controlling the low-Q variable resonator through controlling the s-plane poles of the coupled external resonator. Two detailed examples are provided, where the external resonator is first an antenna and then a BAW / SAW RF filter. Careful attention is paid to the problems and solutions to these 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 in which bulky components have been 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, as physical size is determined by a large set of variables. Furthermore, substrate technology generally determines the choice of chip packaging. This means that packaging of 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 a circuit is packaged on one type of substrate and one or more other components of the circuit are packaged 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 thousands range, such as SAW and / or BAW, can be used as frequency tuning elements in communications circuits. For example, such high-Q resonator SAW / BAW filters are generally of fixed frequency and bandwidth, but are subject to performance variations due to the manufacturing process as well as 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 greater than or equal to about 10 times the secondary Q-factor; and an adjustable scaling block that applies a gain factor. A controller coupled to the at least one tunable resonator and the adjustable scaling block, the controller having instructions to adjust 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 adjustable scaling block.

[0012] According to other aspects, the resonant circuit may include one or more of the following elements, singly 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 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 a signal loop; the signal loop may comprise a first component comprising the primary resonator and a second component comprising at least one tunable resonator, wherein 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 wherein 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 for 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 an adjustable scaling block having a gain factor, the method including controlling the frequency of the at least one tunable resonator and the 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, 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 adjusting 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 adjusting the closed-loop frequency response may further include adjusting a phase of the phase shifter; the multiple tunable resonators may be connected in series. the primary resonator can be an electric resonator, an electromagnetic resonator, a mechanical resonator, or a resonator based on material properties; multiple primary resonators can be connected in parallel or in series within a signal loop; the signal loop can include a first component comprising the primary resonator and a second component comprising at least one tunable resonator, wherein 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 wherein 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. An adjustable 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 adjustable scaling block, the controller having instructions for adjusting 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 adjustable 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, or 100 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 for modifying a closed-loop frequency response of a resonant circuit is provided, the method including: providing a resonant circuit having 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, wherein 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 controlling the frequency of the at least one tunable resonator and the 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, or about 100 times or more greater than, a Q factor of the at least one tunable resonator; 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 electric 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.

[0019] According to one aspect, a communications circuit is provided, the communications circuit comprising: a signal loop including an antenna block that receives a desired electromagnetic signal; an input port; an output port; and a signal conditioning block between the input port and the output port, wherein the antenna block is in bidirectional communication with the input port of the signal loop, and 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 include 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 include 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 to be 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, there is provided a method for encoding and reflecting an electromagnetic signal received by an antenna, the method including: coupling the electromagnetic signal received by 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; and the antenna can be connected within the signal loop.

[0023] According to one aspect, a communications circuit is provided, the communications circuit comprising: a signal loop including a signal conditioning block; an antenna connected to receive an electromagnetic signal and transmit the electromagnetic signal to the signal loop, the signal conditioning block applying a phase shift and a gain factor to the desired signal within the signal loop; and an encoder for encoding a data stream with the electromagnetic signal within the signal loop, the antenna 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 explanation 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. 1 is a block diagram of a tunable filter including a tunable resonator and a tunable scaling block in the signal loop. [Figure 2] 10 is a graph showing the bandpass characteristics of a tunable filter. [Figure 3] A visual definition of a fundamental resonator with S-plane poles. [Figure 4] FIG. 1 is a block diagram of a first-order variable filter ATL-1. [Figure 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. 1 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 variable 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. 1 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 with Q enhancement. [Figure 16] 15 is a root locus of the adaptive filter shown in FIG. 14 after Q-spoiler. [Figure 17] 15 is a plot of the passband of the adaptive filter shown in FIG. 14 comparing Q-enhancing and Q-spoiler. [Figure 18] 15 is a plot illustrating the effect on the passband of the adaptive filter of FIG. 14 of varying 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] The root locus of three cascaded first-order variable filters is [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. [Figure 25] 21A and 21B are root loci 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, neutral, 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 of the adaptive filter shown in FIG. 20 with alternating resonator frequencies. [Figure 29] 1 is an exemplary ATL1 frequency response after tuning. [Figure 30] 1 is an example ATL3 frequency response after tuning. [Figure 31] FIG. 1 is an exemplary ATL3 root locus diagram. [Figure 32] FIG. 10 is a block diagram of the ATL1 core module calibration and stabilization. [Figure 33] 10 is a series of graphs illustrating Q control alternating between higher and lower levels during closed loop calibration. [Figure 34] 1 shows a special case ATL3 circuit with potential phase control applications. [Figure 35]1 shows the frequency and phase responses of a classical passive Butterworth filter of order 3. [Figure 36] Graph showing details 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] The allowable phase shifter functions across the notional ATL1 passband for two values ​​of phase shift control voltages: p1 and p2. [Figure 40] 1 is an idealized model of ATL1 with two embodiments. [Figure 41] A typical Nyquist stability criterion plot showing the phasors of the inverse frequency response. [Figure 42] 1 is a Nyquist plot of the open-loop transfer function after a phase shift. [Figure 43] 1A and 1B are diagrams of possible all-bandpass active circuits used as ATL1 phase shifters with two embodiments. [Figure 44] Pole-zero plot of an all-pass filter showing a phase shifter (ωp=1, Dp=0.2). [Figure 45] Normalized frequency response for an all-pass filter. [Figure 46] FIG. 10 is a schematic diagram illustrating a selectable polarization output for variable gain. [Figure 47] 10 is a Nyquist plot of ATL1 using a phase-selectable gain block and an all-bandpass 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. 10 is a block diagram showing 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] 10 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 20% relative bandwidth. [Figure 57] 1 is a graph showing a series shunt capacitance Smith chart for loop antenna impedance matching. [Figure 58] 1 is a diagram of the structure of a dielectric resonator antenna. [Figure 59] FIG. 1 is a block diagram illustrating a conceptual implementation of an 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 illustrating a prior art example of a reconfigurable filter; [Figure 62] FIG. 1 is a block diagram illustrating an antenna subsystem coupled to an ATLF resonator. [Figure 63] 10 is a series of graphs showing plots specific to the ATL1 resonator at given values. [Figure 64]FIG. 1 is a block diagram illustrating ATL1 with 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] 1 is a series of block diagrams of a transceiver without network matching functionality. [Figure 68] FIG. 2 is a block diagram illustrating 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] 10 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 illustrates an antenna test setup. [Figure 75] 1 shows an equivalent circuit of a coupled test antenna and a Thevenin equivalent circuit. [Figure 76] FIG. 1 shows an approximate circuit of a coupled test antenna. [Figure 77] FIG. 1 is a block diagram showing impedance matching of an antenna to a receiver load using an L-matching circuit. [Figure 78] 1 is a plot of the complex antenna error surface. [Figure 79] FIG. 1 is a block diagram illustrating ATLF impedance matching based on reflection coefficients. [Figure 80] FIG. 1 is a block diagram illustrating an ATLF Category 1 consisting of a circulator, a scaling block, and a phase shifter. [Figure 81] FIG. 1 is a block diagram illustrating an antenna with an inductive reactance attached to an RF voltage source. [Figure 82] FIG. 10 is a diagram illustrating 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 the 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 the equivalent reflection caused by the inductor of the antenna. [Figure 87] Receiver "a node" plot showing the power wave signal steadily increasing 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] This plot shows that points on either side of the Nyquist curve behave the same as a given class. [Figure 93] 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 is a diagram showing an ATLF consisting of an antenna and a negative resistance. [Figure 95] FIG. 1 shows a loop antenna with an inverting gain stage. [Figure 96] It is a plot showing the antenna reflection coefficient with respect to the frequency range 0.75 < w < 1.25. [Figure 97] It is a graph showing the ideal root locus of the ATLF. [Figure 98] It is a graph showing the amplitude of the transfer function of the ATLF with respect to various values of the varactor diode capacitance normalized with respect to Cv = 1. [Figure 99] It is 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 with respect to 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 center, and all the 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). [Figure 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 the root loci plotted on the right. [Figure 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 the circuitry of an ATLXR filtener category 2 implementation based on ATL1 (top) and ATL3 (bottom). [Figure 111] 10 is a plot showing the root locus of ATLF using ATL2. [Figure 112] 10A and 10B are diagrams and plots showing root locus and Nyquist plots for an ATLF circuit equivalent to a fixed frequency negative resistance. [Figure 113] This is a block diagram showing the configurations of ATLF categories 2 and 3. The upper part shows the configuration of ATLF category 2, which consists of a directional coupler, a phase shifter, and a scaling block. The lower part shows the configuration of ATLF category 3, which consists of a directional hybrid coupler attached to ports 2 and 3 and a bidirectional phase shifter realized with varactor diodes. [Figure 114] FIG. 1 is a block diagram illustrating an ATL1 configuration with a splitter and a directional coupler. [Figure 115] FIG. 10 is a diagram of a bidirectional phase shifter alternative. [Figure 116] FIG. 1 shows an ATLF (top) equivalent to a negative resistance circuit, and a Thevenin equivalent circuit of the ATLF (bottom). [Figure 117] Plot showing the operation of the ATLF in the Z-plane (top) and impedance phasor diagram showing the resonance of the ATLF current (bottom). [Figure 118] FIG. 1 shows the Norton and Thevenin equivalent circuits of the ATLF. [Figure 119] FIG. 10 is a diagram illustrating 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] 10 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] The corrected Nyquist locus of Figure 122 by tuning the resonators to ωr = 1.037. [Figure 124] The corrected Nyquist locus of Figure 122 by tuning the resonators to ωr = 0.919 [Figure 125] 1 is a plot of the Nyquist locus for a transmission delay of 3 radians. [Figure 126] 10 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, highlighting what could have gone wrong. [Figure 129] 10 is a plot showing that an inward-pointing Nyquist loop is possible but cannot destabilize the ATLF. [Figure 130] 10 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. [Figure 131] 130 is a plot showing the change in passband characteristics of the ATLF due to changes in antenna impedance. [Figure 132] 1 is a plot showing the Nyquist locus when the ATLF is unstable. [Figure 133] FIG. 2 is a block diagram illustrating a low-power oscillation and frequency detection circuit. [Figure 134] FIG. 1 is a block diagram of an ATLF-based transceiver. [Figure 135]FIG. 10 shows a timeline for active ATLF calibration relative to data packet reception time. [Figure 136] 1 is a Nyquist plot of a resonant model of an antenna with pure delay. [Figure 137] 10 is a Nyquist plot of the combined antenna and ATL3 resonator. [Figure 138] FIG. 1 illustrates scattering sources affecting an antenna. [Figure 139] 1 is a series of plots showing potential Nyquist plots for an antenna in various environments. [Figure 140] A detailed Nyquist plot with an interferer. [Figure 141] 10 is a plot showing the effect of phase shifter control by moving the Nyquist loop up and down to create passband frequency jumps. [Figure 142] 1 is a plot showing the intertwined Nyquist loops of a single antenna reflection coefficient when moving over a ground plane in the presence of scatterers. [Figure 143] 143 is a plot showing the frequency response corresponding to the 1 / G operating point of FIG. 142. [Figure 144] FIG. 10 is a block diagram illustrating an ATL3 incorporated in an antenna resonator loop. [Figure 145] 10 is a plot showing the ATL3Q enhanced effective frequency response when scattered by a near-field object. [Figure 146] FIG. 1 is a block diagram of a comprehensive wireless sensor transceiver system consisting of a minimum of four components. [Figure 147] FIG. 10 is a block diagram showing receiver mode 1 with ATL1a used as an RF filter. [Figure 148] FIG. 10 is a block diagram showing mode 2 when ATL1a and ATL1b are cascade-connected. [Figure 149] FIG. 10 is a block diagram illustrating Mode 2 with the attenuator switched. [Figure 150]FIG. 10 is a block diagram showing how transmitting mode 3 works in conjunction with mode 1. [Figure 151] FIG. 10 is a block diagram showing calibration mode 4. [Figure 152] FIG. 10 is a block diagram showing calibration mode 5. [Figure 153] FIG. 10 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. [Figure 155] 1 is a plot showing the frequency dependence of an all-bandpass filter. [Figure 156] 10 is a frequency plot of the resonator for open loop Q=10 (ωr=1 and Dr=0.05). [Figure 157] 157 is a pole-zero plot of the resonator of FIG. 156. [Figure 158] FIG. 157 is a plot of the zero-degree root locus for the resonator of FIG. [Figure 159] 10 is a phase plot of the phase shifter after achieving a 50 degree mismatch. [Figure 160] FIG. 159 is a plot of the zero-degree root locus of ATL1 for the mismatched phase case. [Figure 161] 159 is a plot of the loop gain required to reach oscillation conditions as a function of the phase shifter mismatch of FIG. 159. [Figure 162] FIG. 1 is a block diagram of the configuration for passband calibration of ATLa. [Figure 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). [Figure 165] FIG. 1 illustrates an AV approaching an RF lane marker (RFLM). [Figure 166] FIG. 1 illustrates a multi-lane road representing each RFLM with a unique ID. [Figure 167]FIG. 1 is a block diagram of a simple envelope analysis process. [Figure 168] FIG. 1 shows a 2D road surface where the simulation is simplified. [Figure 169] Plot of the position of RFLM (circle) and the trajectory of the vehicle AVPI (bold line). [Figure 170] 10 is a plot of the signal at the RFLM due to the signal from the AVPI passing through. [Figure 171] 171 is a plot showing coherent demodulation and envelope processing of the overlapped RFLMs of FIG. 170. [Fig. 172] 10 is a plot showing the envelope when the AVPI is in the center of the lane. [Figure 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. [Figure 175] This figure shows two AVs arranged side by side, with AVPI spaced approximately the same distance from RFLMs arranged in column 2. [Figure 176] FIG. 1 is a block diagram of an entire vehicle navigation system. [Figure 177] FIG. 1 is a block diagram of a possible implementation of a durable RFLM. [Figure 178] FIG. 1 is a block diagram illustrating a train sensor network application. [Figure 179] FIG. 1 is a block diagram showing a basic ATLXR circuit. [Figure 180] FIG. 1 is a block diagram illustrating a basic ATLXR open loop circuit. [Figure 181] FIG. 180 is an open loop pole-zero plot of the ATLXR. [Figure 182] 1 is a plot showing an equivalent polynomial representation of a Pade approximation of loop delay. [Figure 183] 10 is a plot showing the closed-loop locus of high-order Q poles of F. [Figure 184]10 is a plot showing an ATLXR with a nearly single-pole primary resonator F and three tunable secondary R. [Figure 185] 1 is a plot showing a typical Q enhancement of a first-order cavity F. [Figure 186] 10 is a plot showing the frequency shift of the poles of a Q-enhanced first-order cavity F. [Figure 187] 10 is a plot showing the root locus for a 90 degree phase shift caused by parasitic delays. [Figure 188] FIG. 1 is a block diagram illustrating a preferred embodiment of the ATLXR. [Figure 189] FIG. 1 is a block diagram illustrating one embodiment of an ATLXR, where both slow coarse frequency control and fast control of the closed-loop poles are achieved by the ATLXR feedback loop via {f,p,g} control. [Figure 190] FIG. 1 is a block diagram illustrating multiple ATLXR circuits that result in a multi-pole bandpass filter. [Figure 191] FIG. 1 is a block diagram showing a practical implementation including a multi-resonator BAW chip with a single-port resonator. [Figure 192] FIG. 1 is a block diagram illustrating a generic ATLXR chip with a switch matrix and blocks of selectable ATLXR circuitry. [Figure 193] FIG. 1 shows a moderately high-Q resonator made with via connections in a PCB. [Figure 194] FIG. 1 shows the Q-enhanced resonator of ATLXR printed on a circuit board. [Figure 195] FIG. 10 shows ATLXR's Q-enhanced stripline resonator printed on a layer of a circuit board to save space used for chip antennas. [Figure 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] 1 is a diagram of an external BAW in which three parallel resonators resonate at different frequencies f1, f2, and f3 associated with a Q of approximately 100 per resonance. [Figure 199]FIG. 12 is a block diagram of an ATLXR configuration comprising a high-Q first-order triple resonator coupled to a negative feedback path with three low-Q second-order variable 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) that can be thought of as a generalized resonator. [Figure 202] 10 is a plot of the filter response of a third-order Butterworth filter with first-order ATLXR resonators. [Figure 203] 10 is a plot of the root locus of a coupled outer Butterworth filter showing the Q enhancement of the center pole. [Figure 204] FIG. 1 is a diagram of a waveguide filter that can be used as the primary resonator of an ATLXR. [Figure 205] FIG. 1 is a block diagram illustrating an active amplifier that enables unidirectional ATLXR Category 1 coupling. [Figure 206] FIG. 1 is a block diagram illustrating a bidirectional configuration of an ATLXR Category 2 with a circulator. [Figure 207] FIG. 10 is a block diagram illustrating a Category 2 ATLXR configuration with interchanged signal flow. [Figure 208] FIG. 1 is a block diagram showing a Category 3 ATLXR configuration. [Figure 209] FIG. 1 is a block diagram showing the configuration of ATLXR Category 4. [Figure 210] FIG. 1 is a block diagram of an ATLXR configuration with a high-Q first-order resonator in series. [Figure 211] FIG. 1 is a block diagram illustrating the resulting magnetic field generation complicated by current flow and current flow into the ground plane. [Figure 212] FIG. 10 shows the root locus of the ATL filter based on ATL3. [Figure 213] FIG. 10 shows the root locus of the ATL filter / ATL3 when the varactors are properly set. DETAILED DESCRIPTION OF THE INVENTION

[0026] First, we will discuss examples of variable resonators that can be used to control a primary resonator. Then we will discuss examples where these variable 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 preferably a variable-frequency resonator element that can be tuned. The bandwidth of a non-tunable resonator filter can be controlled by feedback across the resonator element. The resonator bandwidth is preferably narrow enough to avoid spurious passband responses, but tunable over a wide range of frequencies. There is also a gain element, potentially referred to herein as a scaling block, that can be tuned 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 needed in certain circumstances.

[0030] As used herein, the term "resonator" can be used to describe a simple resonator element, such as an LC tank circuit. This term can 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 will be referred to as ATL1 and will be described in more detail below. Other, more complex resonant circuits, such as circuits including multiple resonator elements, multiple scaling blocks, multiple loops, etc., will be described below. An example of a suitable variable resonator that can be used will be referred to herein as an ATL filter, which is described in detail by Nielsen. While other variable resonators can be used, a detailed description of an ATL is provided below, as it has been found that such circuits can be used to realize workable circuits.

[0031] In particular, the ATL can be thought of as a variable analog filter, containing a signal loop with 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 match 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. A general comment on filter order is 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 include two such resonators with two dominant pole pairs, an example being two coupled LC tank resonators in cascade fashion.

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

[0037] Higher order ATLs, 4th order or higher, are possible, but these ATLs introduce spurious bands when scaling block feedback is implemented 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 diagram for the ATL3 example shown in Figure 30.

[0039] A block diagram of an ATL in its simplest form is shown in Figure 1, with a single variable resonator 502 and 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 located in the feedback path 510. ATLs are intended for use in transmitting, receiving, and processing communication signals for a variety of purposes. Communication signals are typically modulated signals used to transmit information or data. They typically include an analog carrier frequency encoded with an 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 the initial setting. 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 typically illustrated in the style of FIG. 1, showing an arrangement with a main path 508 and a feedback path 510, with the gain block 504 (also referred to as a scaling block) and the feedback path 510 having both positive and negative values. This is done for consistency and ease of comparing circuits. However, the circuit is more appropriately thought of as a loop with appropriate input / output coupling, where a loop is formed from what would otherwise be the main path 508 and the feedback path 510, with its elements 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] ATL Elements

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

[0045] Tunable ATL Resonator(R)

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

[0047] Depending on the circuit implementation, the resonators may be implemented as resonator elements such as LC tank circuits or as second-order section (SOS) filter elements. SOS implementations are discussed in more detail below. Referring to Figure 8, a block diagram of the second-order tunable filter ATL-2 is shown, with an input 810, a combiner 1404, a resonator 1301, a gain buffer 102, a gain block 812, and an output 814. Figure 9 shows the root loci for the second-order tunable filter of Figure 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 along the jω axis as the closed-loop gain G increases, while the other loci 1906a and 1908a are along the jω axis.

[0048] As will be appreciated from the discussion herein, there are numerous possible combinations of resonators, scaling blocks, and signal paths that can be used in the design of an ATL. The specific design depends on the desired circuit performance, as discussed elsewhere. Generally, an ATL includes a feedback loop containing the desired number of resonators and scaling blocks. Each ATL can be connected in parallel or in series with other ATL elements or other circuit elements, and there may be additional Level 2 feedback loops containing multiple ATLs. Additionally, there may be nested loops within an ATL element, each containing a loop 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 ATL elements. This includes what might be referred to as Level 3 or Level 4 feedback.

[0049] The resonant frequency of R1401 can be varied by adjusting several components 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 variations for varying the resonant frequency are well known, such as adding discrete capacitance to or from the circuit, and the "f control" could be a digital signal. Another variation is the use of a MEMS variable capacitor or MEMS variable inductor. Variable capacitance or inductance can also be achieved by mechanically tuning a component. For example, R1401 could be a microwave resonant cavity in which one or more dimensions of the cavity are mechanically adjustable by some mechanism, providing "f control."

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

number

[0051] Q-Control Scaling Block

[0052] "Q control" 1304 in Figure 3 above can comprise a control device associated with the capacitance or inductance or resonator that controls the component Q of the resonant cavity. When Q control increases the component Q, this is referred to herein as Q-enhancement. When 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, and therefore moves the resonant pole of R closer to the jω-axis of the S-plane. Q-spoiler is equivalent to increasing D, and therefore moves the resonant pole of R further away from the jω-axis, thereby increasing D. Q-enhancement and Q-spoiler can be selectively used to move the resonant pole toward 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 for 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 a scaling block 802 is greater than zero, Q enhancement occurs. If the gain of a scaling block 802 is less than zero, Q spoiling occurs.

[0054] Q-corruption can 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), where 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, while the Q-corruption resonator is independent. Alternatively, the resonator may be a Q-enhanced resonator using an amplifier that only enables Q-enhancement. As previously mentioned, the Q-enhancement resonator is nested within the feedback loop of the ATLn element containing the scaling block, overriding the Q-enhancement and providing the desired Q-dropper performance when needed. This, of course, makes clear that the resonator can be any type of frequency-tunable resonator, including, but not limited to, an inductor diode, a switched disk capacitor, a variable dielectric capacitor, a variable capacitor, a MEMS variable capacitor, a fixed inductor, a variable inductor, a MEMS variable inductor, or a mechanically tunable resonator.

[0057] ATL Phase Shifter

[0058] We saw 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 to create 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 the first order of ATL circuits, called ATL1, which contains a single resonator component 1401, a unity 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 for an intuitive understanding of the ATLn variants based on this ATL1 core module. In one example, resonator 1301 may be a second-order bandpass filter with the following transfer function:

[0063]

number

[0064] ΩO, using coefficients evaluated based on D and . The gain G 802 is variable and controls the closed-loop Q. At resonance, the phase shift through resonator 1401 is ideally 0 degrees. In physical implementations, the phase shift is generally non-zero due to parasitic and transport effects, but these may be ignored in this evaluation: the implemented circuit may require a phase-shift element related to G 802. The effects of parasitic and transport phases, discussed later, must be changed to vary the frequency. ΩO is ignored for resonators in OATL1.

[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 Ω is the resonant frequency in radians per second, D is the damping coefficient, and a is a real constant. The mapping to f in Figure 3 is f = ω / 2π

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

number

[0068] In this description, {FN,Q} can be used interchangeably with the operation {ωn,D}

[0069] A fundamental analysis of the ATL1's operation is possible using the root locus technique. Root locus is a standard method for determining the poles of a closed-loop system when a variable loop gain is present. The result of a root locus calculation in this situation is the locus of these closed-loop poles as they vary with the loop gain G, as shown in Figure 5. Figure 5 is the root locus for 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 at 1504 and 1508. This allows us to understand any spurious passbands and any tuning limitations of the ATL1. As a first example, with Ω = 1 and D = 0.5, the ATL1 SOS resonator has a very low Q in this example. A Bode plot of the resonator's transfer function is shown in Figure 6, which is the Bode plot for the first-order variable filter shown in Figure 4. Figure 6 also plots the magnitude 612 and phase 614 versus frequency. Note that due to the high damping factor (low Q) assumed in this example, the phase variation with frequency is rather gradual around resonance.

[0070] Next, 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. Here, the poles of the ATL1 Core Module SOS resonator are represented by x (1502 or 1504). Line 1506 is the closed-loop root locus as the closed-loop gain G increases from 0 to 1.2. This is the trajectory of the pole denoted by number 1502. The root locus of the conjugate closed-loop root locus 1504 is line 1508. These movements are plotted along the axes of the jωS plane (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 in the Q dropper, 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 operating region, ATL1 is unusable, 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 plane (LHP). Note that for values ​​of G where the closed-loop poles coincide with the jω axis, ATL1 oscillates at its resonant frequency, ω0, normalized in this example, ω0 = 1. The dotted radial lines on the root graph indicate the damping value of D. Q can be related to D based on the relationship shown above. Also, in this example, the gain G value where the root orbit 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 in summing block 1404 in the ATL1 circuit of Figure 4. This means that the signal flowing through gain block 802 becomes larger and larger. To reduce this, you 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 in an SOS resonator is through a "Q spoiler" implemented via a variable resistance element within the SOS, such as a variable FET circuit or PIN diode, which can increase the losses of the SOS and therefore reduce its Q. This affects the damping coefficient of an SOS designed to have a higher Q than typically desired. The variable resistance reduces (spoils) the Q by moving the poles of the SOS farther apart. The JΩ axis is attached to the LHP as described above. This is a degree of freedom (DOF) that allows for higher outlier attenuation 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 an alternative 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, single resonator 2702 is a fixed resonant circuit with feedback gain 2704. For clarity, another way to change the Q of this circuit is to use a bipolar gain element G in gain block 2704; G can be negative for Q dropper or positive for Q enhancement, but this is ignored. While 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 G being equivalently greater than zero, providing Q enhancement. A positive resistance, on the other hand, corresponds to a negative G, which provides a higher Q.

[0077] The root locus of the positive frequency closed loop poles for positive G1510 is shown in Figure 15, where the closed loop poles are on the jω axis. Similarly, the root locus of the negative G1610 is shown in Figure 16, where 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. Example frequency responses are shown, normalized to frequency values ​​for R resonances 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 for varying the resonator's center frequency, and a method for varying the Q of the resonators. As with ATL2, unit-gain buffers 1012 are placed between all resonators 1301 for isolation, and a capacitor 1404 closes the feedback loop. Figure 10 also shows the input 1012, output 1014, and gain block 1016. It is important to note that in this ATLn configuration, the fundamental ability to independently control both the center frequency and gain of each resonator is important. Initially, we will set the center frequency of each resonator to the same; 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 the out-of-band open-loop attenuation of the triple resonator is seen to be 60 dB per decade since it is based on a low-Q resonator. Figure 11 also shows the magnitude 1110 and phase 1112 plots. The zero-degree root locus is shown in Figure 12 for D = 0.5 or Q = 1. The root locus is interesting in that there are three root orbits 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 orbits 2306a / 2308a follows the exact same contour as before, while the other root 2306b / 2308b goes further into the left-hand plane (LHP) and has no effect on the circuit. However, the third pole orbit 2306c / 2308c is aligned with the JΩ axis. This can result in spurious modes at frequencies far below the intended passband. However, if the dominant pole is close enough to the jΩ axis at gain G 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 increases as D decreases, this potentially troublesome root advances further into the LHP, with a locus from poles 2402 and 2404 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 achieved 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), seen in Figure 19, consists of three individual ATL1 modules, each with an independently tunable center frequency and Q, and each incorporating a feedback loop with adjustable gain. This configuration achieves the six degrees of tuning required to uniquely release the third-order filter. Figure 19 shows resonator 1301, feedback loop 110, and 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, contemplates 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 includes 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 noted, this topology introduces suboptimal design situations, meaning that the performance of this topology may not meet strict design performance criteria. However, there are advantages, as always driven by design tradeoffs, in some cases.

[0086] The ATL3 Topology 3 (ATL3 T-3) can be seen in FIG. 20, where the Level 2 feedback path 110a wraps 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, buffer 102, and feedback loop 110. The additional ATL3 Level 2 feedback loop 110a results in pole movement in the S-plane as shown on the right side of FIG. 21. Arrow 3602 in FIG. 21 is for negative feedback (Q spoiling), and 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 toward 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 for 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 has led some 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 makes up the ATL3. In this way, a separate phase control element is not required, simplifying design and manufacturing.

[0090] Butterworth bandpass filter response replication example

[0091] First, as an example, consider the classic 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 classic 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 detailed in Figure 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 only consider the positive frequency poles and therefore speak of a third order filter, understanding that each pole has a conjugate pole.

[0098] Note that the two flank poles are approximately half the distance to the Ω axis as the center pole, which means that these passive Butterworth poles have twice the Q of the center 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 three resonant poles to be achieved as described. As well as the classic passive Butterworth filter described above, this can also be used to provide similar results as a classic passive third-order Chebyshev bandpass filter.

[0101] Referring to Figure 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 are aligned along the jω axis.

[0102] If arbitrary pole placement 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, the order of the resonators is generally irrelevant, so there is redundancy in the controls. This can confuse the pole placement stability tracking algorithm described later.

[0103] Level 2 feedback for simplified bandwidth control

[0104] A simpler bandwidth control is one that implements 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 described above. Thus, as shown schematically on the left side of Figure 21, the first level control of the ATL1 core modules moves the three poles in unison toward 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 apart and the central dominant pole to be moved toward or away from the jw-axis, as shown schematically 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 for relatively easy control of the filter bandwidth 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 a feedback gain of 0. The gain is positive toward the right excursion 3704a / b / c (Q-enhancement) and negative toward the left excursion 3706a / b / c (Q-dropper). From the perspective of negative resistance amplification (Q-enhancement), this means that resistance is zero at the 'x' position, with positive resistance toward the left excursion (Q-spoiler) and negative resistance toward the right excursion of the root trajectory. Note how the control follows the contour of a constant natural resonant frequency. The feedback gain for each root trajectory 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 see 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 the negative favorable ATL3 topology Level 2 feedback and the right plot is for the positive favorable ATL3 topology Level 2 feedback. Note how this can be used to adjust the position of the flanking poles relative to the center pole, as explained above. Figure 26 shows how the preferred ATL3 topology Level 2 feedback is used to control the filter bandwidth. Positive Level 2 feedback narrows the filter bandwidth, while negative Level 2 feedback widens it. Only a small amount of ATL3 topology Level 2 feedback is required 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 previously considered, potentially allows 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 / s, 1.0 rad / s, and 1.1 rad / s, with D fixed at 0.15 (Q = 3.33) for all three resonators. The Bode plot of these three cascaded SOS resonators, showing the potential for a flatter passband, is shown in Figure 27, with magnitude indicated at 2710 and phase indicated at 2712.

[0117] FIG. 28 shows the zero-degree root locus for 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 the ATL3 providing the best rejection of out-of-band signals for typically found closed-loop Q values.

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

[0122] ATLn phase shift control

[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] Because the ATL3 is composed of three ATL1 core modules, it is important to examine the phase control of these ATL1 core modules. We found that the closed-loop passband of the ATL1 core modules is centered around a range of frequencies where the open-loop phase shift is a multiple of 360 degrees. While it is desirable to have only a single passband, the resonator passband can be positioned to coincide with the frequency of a multiple of 360 degrees. Even if the resonator peak frequency is shifted, the closed-loop response peak will still coincide with the frequency where the multiple of 360 degrees is achieved, but the passband may be distorted.

[0126] The phase control can in principle be any circuit that is able to vary 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 can be introduced by starting with a variable delay line consisting of a series of diodes along the 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] Because arrays of vibrators have finite length and spacing, they have non-uniform amplitude responses with respect to frequency. In this context, a single vibrator behaves similarly to a low-Q resonator with variable capacitance, while three vibrators behave similarly to three coupled resonators, as in the ATL3. Therefore, a variable delay line can be approximated by using a small number of vibrator diodes to create a structure with a variable group delay that has a reasonably uniform magnitude response over 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 variable resonators and variable phase shifters 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 a desired delay and amplitude response that can be controlled by multiple control voltages.

[0133] ATL1 phase shift control

[0134] The ATL1 core module is a single variable resonator subcircuit. With careful design, the phase shift can be a multiple of 360 degrees at any desired frequency within the resonator's passband. Shifting the resonant frequency results in an equal phase shift. The ATL1 response peak occurs when the loop phase shift is a multiple of 360 degrees. A limitation of the ATL1, which only has a variable resonator, is that the resonator's phase shift adjustment is limited. Therefore, if the loop has a large phase error, a single resonator does not have enough range and variable and fixed phase shifters must be added. However, based on the discussion of general phase shift control considerations above, this is equivalent to stringing many delay-controllable subcircuits in series.

[0135] Next, we consider replacing another resonator with a variable phase shifter. Phase shifters have a flat frequency response from a magnitude standpoint, so they 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 onto the chip. If three resonators are added, this corresponds to a special case architecture of ATL3. This shows three variable resonators 502, which can be the input 3410, output 3412, ATL1 elements, feedback path 110, coupler 104, and gain element 112.

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

[0137] Furthermore, as mentioned above, it has been found that detuned resonators add a controllable phase shift, and 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 previously, the phase shifter is necessary to compensate 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. Therefore, the phase shifter control is a parameter that does not improve the performance of the ATL1 further than the idealized model shown in Figure 40, but is necessary for practical implementations. Figure 40 shows an idealized model of the ATL1 with two implementations, each with 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 points on the locus crossing the positive portion of the real axis coincide with open-loop phases that are multiples of 360 degrees.

[0141] The frequency response can be determined (with respect to the closed-loop denominator) as the reciprocal of the facet shown between the real axis points of 1 / G and the open-loop transfer function F(jw). As such, it generally has a set of resonance and anti-resonance points as shown in Figure 41. As G increases, 1 / G eventually intercepts the outermost resonance points and moves towards the left. Note that this is the same as the root locus where the poles intersect 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, where the Nyquist plot of a resonator over a small frequency range is shown as curve 4210. Next, α is applied. As the phase length of the resonator increases from 1 / G to resonance, the resonant response decreases. As G increases, ATL1 peaks at point A rather than at resonance. Also, note that as G increases, the peak closed-loop response of ATL1 shifts 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 correctly set the phase shift 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 degraded. Therefore, to correctly set the phase, we can look at how the peak passband frequency changes with increasing G, so that the minimum value of G is obtained at the desired Q.

[0145] Also clear from this discussion is 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 phase shifter increases, the loss in the circuit also increases. Also, the range of the phase shift is not sufficient. Multiple RC segments may be used to solve this problem. This solves both problems, but requires more complexity.

[0147] The desired chip-mounted 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, which has 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 of

number

[0150] From Ω, P and DP can be extracted. In the circuit of Figure 43, R can be implemented with a combination of a FET and a capacitor implemented as a piezoelectric diode, which allows control of the pole and zero locations. Increasing R moves the pole along the JΩ axis, and the phase shift becomes steeper as a function of frequency. Similarly, by changing the piezoelectric capacitance, the pole 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 allows for quadrature control of frequency and voltage g, which can be flat if required, and is separate from the control of the inverter control voltage g.

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

[0154] Changing the all-pass frequency, the ΩP, shifts the phase curve left or right, providing phase control for a particular passband. The constant amplitude response of Figure 45 has the advantage of allowing phase to be changed without changing the loop gain. Also, note that this phase shifter has a range approaching 360 degrees.

[0155] ATLn Phase Shift Control Considerations

[0156] An ATLn is a bandpass filter consisting of "n" consecutive ATL1 core modules, each in one of three possible topologies, as described above. Each ATL1 module in the group is individual in performance, tunable in terms of both 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 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 is completely free of parasitics. As is known in the art, the phase of a signal can be affected by many different factors as the signal passes through a circuit, a certain portion of which includes stray capacitance and inductance, which can be referred to as "parasitics." There are parasitics associated with the ATL1 resonator (or resonators such as in ATLn), which introduces a phase shift associated with the buffer amplifier. In ATLn for n≧2, excess phase shift can exceed 360 degrees. Certainly, excess phase must be considered.

[0158] In general, when 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 environments, 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 needed. In the discussion of the ATLn topology above, it was shown that net loop phase error can be easily controlled by small frequency adjustments to the ATL1 core modules that make up the ATLn, eliminating the need to implement separate phase shifter elements. This important result applies to all ATLn variants of ATL variable filters with n > 1.

[0160] Gain Polarization Switching and ATL1 Phase Shift Control

[0161] To achieve full 360-degree parasitic phase shift control, an alternative approach is to add polarization selection to the output of a variable gain block operating with an all-pass phase shifter. The gain block is implemented with a differential amplifier and FET 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 input 4612 and current adjustment for gain control 4614.

[0162] This gain polarization switching circuit is a simple integration of a differential amplifier with gain control based on adjusting the current through the differential FET pair via the bottom FET shown. Output selection from two differential outputs provides polarity selection. Alternatively, a full Gilbert cell integration could be used. Gilbert cells are more sophisticated 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. The full-phase phase shifter with polarization control in the second order corrects for the parasitic phase shift. The closed-loop center frequency will be the correct frequency if 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 all-pass networks are based on resonators, we began investigating the implementation of ATLn circuits for phase shifting, including gain switching, as an alternative to the phase-control all-pass network circuits preferred over ATL1 phase control. Eliminating the additional components of an active all-pass network is a reasonable objective. Furthermore, all-pass phase shifters provide a constant magnitude that is not required for phase shifting.

[0168] Adding additional resonators, such as the ATL3 with three resonators, can improve tunability slightly. The motivation is to reduce the resonator detuning to accommodate any parasitic phase shift. This makes the Nyquist locus of the real axis more perpendicular to the real axis, resulting in less bandpass slope and more independent control of the center frequency and bandwidth of the closed-loop passband. Figure 48 shows a block diagram of the ATL3 with three cascaded resonators 4810, a variable gain block 4812, a gain polarity selection buffer 4814, a sum 4816, and an output 4818.

[0169] As with the ATL2, the isolated resonator 4910 is not required; instead, 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 buffers 4916 and 4918, inputs, and output 4920. We feed this ATL3 with a parasitic phase error of 1.5 radians. The resonators must each be detuned by approximately 5% 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 for a detuned ATL3 resonator with gain switching to compensate for 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 will give the same performance due to Q enhancement.

[0170] In this case, it is interesting to consider the root locus plot of the ATL3. Unfortunately, parasitic delays cannot be directly represented in a root locus plot. However, we may get a reasonable idea of ​​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 shows 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 simple bandwidth control, shown in the frequency plot of Figure 52, with line 5210 indicating G = 0, line 5212 indicating G 10, and line 5214 indicating G > 0. By varying the G control with a polarization switch, one can switch between two controllable bandwidths.

[0175] ATLn self-calibration

[0176] Now we will look at how to use ATLn as a subsystem in a specific application. In this example, you can set the control voltage to adjust the performance of ATLn for the 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 at either a) the bulk component level; b) the component surface mount level; or c) 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 independent tables for 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 Entry Loop gain and bandwidth control entries An entry to set the frequency of each n resonator.

[0185] So for ATL1 there may be three such LUTs, but for ATL3 there may be nine.

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

[0187] ATL1 Calibration and Stability Control

[0188] We will start with an example of calibrating and stabilizing 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 downconverter 7510, frequency counter 7509, temperature sensor 7508, μP 7504, LUT 7516, control PWM(f,Q) 7506, frequency synthesizer 7507, and crystal reference 7505.

[0189] Referring to FIG. 32, a microprocessor 7504, typically a system asset, adjusts 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 self-oscillation begins. The frequency of this self-oscillation is downconverted in block 7510 by a frequency synthesizer signal generated by a crystal reference 7505 and frequency synthesizer 7507, also set by the microprocessor 7504. A frequency counter 7509 or other measurement means determines the frequency of the downconverted signal. In this way, the resonant frequency of the ATL1 core module may be determined. Additionally, a power detector 7512 and an analog-to-digital converter (ADC) block 7514 are provided, which can estimate the rate of increase of the self-oscillation signal at the output of ATL1 7502. The microprocessor 7504 estimates this exponential power rise and determines where the ATL1 7502's closed-loop pole is located. Currently, it is just to the right of the Jw axis. If the Q enhancement is slightly reduced, self-oscillation continues at the same frequency with high precision, but begins to exponentially decay. The pole is now just to the left of the Jw axis. Again, this exponential decay can be measured using the power detector 7512 to determine the operating point. 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 can be performed based on on-chip circuitry, requiring no additional off-chip components other than a crystal reference source. During operation, calibration breaks may be implemented to continuously update the LUT 7516. In the case of wireless sensors, the transmitter and receiver functions are separated by periods of inactivity during which the calibration process takes place.

[0190] ATL1 Q Control

[0191] Figure 33 shows an example of ATL1's Q control alternating between high and low levels, placing ATL1's closed-loop poles 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 ATL1's filtering operation, 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, T1 and T2, resulting in X1 and X2, respectively, the desired parameter b is

number

[0193] Either the times T1 and T2 can be set to the voltage x1 and x2 are measured, or else a fixed threshold can be set to x1 and x2, and the time difference T2-T1 may be measured. Either approach is simple.

[0194] In applications that include 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 ATLn can be designed to widen its bandwidth relatively easily. As shown above, ATL3's level 2 feedback gain G around 3R 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 the transmit / receive (T / R) switch to change the direction of the filter for the transmit / receive function.

[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 located as a function of the control. This can be achieved by using the on-chip auxiliary ATL1 for calibration purposes. By alternating pole locations in the left and right planes (unstable and stable, respectively), the envelope of the ATL1's self-oscillation may be used as a probe signal to estimate the actual portion of the pole location. The imaginary component depends on the frequency of the self-oscillation. Self-oscillation may be measured based on comparison with a crystal-locked synthesizer frequency. The three resonators (R) of the ATL3 could also be used directly instead of the ATL1. However, the ATL1 implementation allows calibration to be performed continuously, parallel to the operation of the ATL3, which is dedicated to actual signal processing. Measurements of the ATL1 pole locations as a function of control voltage and possibly chip temperature are stored in a LUT. The LUT values ​​are interpolated during ATL3 configuration.

[0202] It should be noted that the exponential decay time of this procedure is very fast and may require a high-speed 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, to obtain 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 varies primarily based on ambient temperature, and may be insufficient for precision filtering in applications requiring high-Q narrowband operation with poles very close to the JΩ axis. In addition to normal component aging effects, there is some sensitivity to ATL due to component temperature drift, 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] For 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 all communications devices. For applications where the highest accuracy is not required or where 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 can be large, requiring very precise loop gain settings. If the loop gain changes by only 100 ppm in high-precision applications 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) injection locking. Therefore, precise calibration of the loop gain is also required. To address these calibration issues, two calibration modes are envisioned, detailed below.

[0210] ATL1 initialization self-calibration mode

[0211] ATL1 self-calibration in any system implementation (at the discrete component level, surface mount level, or integrated chip) is based on measurements 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, which can weight previous and current measurements. These ATL1 measurements are taken using the circuit's input and output loads to account for deviations due to port impedance mismatches. If not available at the system level, a temperature sensor is also included in the ATL1 circuit so that sensitivity due to temperature changes can be calculated. Note that this is done through multiple calibration runs and analysis of runtime drift. This in-situ calibration also accounts for voltage regulation errors and offsets in the {f,g,p} control DAC voltages.

[0212] Initialization is required only when the initial parameters for operating frequency and bandwidth (Q) are set. If multiple operating frequencies are required, such as in frequency hopping applications, initialization is required at each operating frequency. Initialization is not performed routinely because ATL1 operation, and by extension ATLn, has proven stable over time. The only parameter that affects operational calibration is the ambient temperature of operation, which is the subject of 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] Runtime calibration is application-specific. ATL1 wireless applications have a unique baseband data demodulation process that can extract signals as a metric for the quality of the ATL1 filtering. The {f,g,p} control parameters can be set through dithering or other optimization strategies to maximize the quality of the ATL1 filtering. LUT modifications 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 for specific applications.

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

[0217] ATL1 high-precision calibration process overview

[0218] This section proposes a high-precision calibration structure that facilitates the two calibration modes from the previous section: ATL1 initialization self-calibration and ATL1 runtime calibration. This structure depends on the physical implementation of the ATL1 core module, which can be at the discrete component level, surface-mount level, or integrated chip implementation. While any application (e.g., ATL3 or ATLF) can be considered, 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: antenna 14610, switch array 14612, ATL1 14614, ATLb 14616, down / up conversion and ADC / DAC sampling 14618, ATL control 14620, baseband processing 14622, LO / ADC clock synthesizer 14624, power conditioning 14626, transceiver chip 14628, clock crystal 14630, and power supply 14632. This example shows a pair of standard ATL1 core modules, labeled ATL1a and ATL1b. These are chip implementations of the ATL1 and are considered identical and uncalibrated. However, the calibration process below would be the same for discrete component-level and surface-mount implementations of Figure 146. However, chip-level implementations are 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 explore 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 occurs 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, the 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, the input reference signal can be used to determine the frequency offset of the clock crystal, which can also be stored in the LUT.

[0222] It's important to note that ATL1 can operate as a stable oscillator with a non-tunable frequency, with its output fed to another ATL1 to determine its frequency characteristics. Following this approach, ATL1a becomes a voltage-controlled oscillator (VCO) that feeds ATL1b, which in turn uses ATL1b as a VCO to determine ATL1b's bandpass characteristics. Because 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 aids in calibration, which will be discussed in more detail later. A key innovation is that, because the chip is a transceiver, it has baseband processing 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 configured to operate at a specific frequency based on its control settings. Then, based on down-conversion (based on a clock crystal-derived LO synthesizer) and ADC sampling (a 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 moves back away from the jw axis and no longer oscillates, it operates as a high-Q filter. Just as the ATL1a exits oscillation mode and enters filter mode, the frequency of oscillation is precisely 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 affect 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, and a high Q resonator is considered to be a factor of 10 or even 100 times greater than the tunable resonator.

[0225] Operational Mode

[0226] There are 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 the RF filter. Figure 147 shows the antenna 14710, the ATL1a 14712, and the downconversion ADC sampling 14714. In this mode, the ATL1a has a relatively high Q and also has 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, ATL1a 14812, ATLb 14814, and downconversion ADC sampling 14816. The idea is that ATL1a has better intermodulation performance because it suppresses some of the out-of-band tones and has 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 for stability, as discussed below. Figure 149 shows the antenna 14910, ATL1a 14912, attenuator 14914, ATLb 14916, and downconversion ADC sampling. If the gain is too high, it will be 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 the time division duplexing (TDD) protocol, in which the transceiver transmits in one time interval and receives in another, but other protocols can be used. Selecting the appropriate protocol is beyond the scope of this discussion, as long as the mode can handle it. 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, ATLb 1501, and upconversion DAC sampling 15014. A switch array facilitates switching between Mode 1 and Mode 3 for TDD functionality.

[0231] High Precision Calibration Mode

[0232] Next, consider the set of switchable modes for calibration. In Mode 4, the closed-loop resonant pole essentially operates as a VCO, as shown in Figure 151. The Jw axis. Figure 151 shows ATL1b 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, which can be switched in. The attenuated nostril wave signal enters 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 reverse of Mode 4 in that ATL1a is used as a VCO and feeds ATL1b, which acts as a filter. Figure 152 shows ATL1a 15210, attenuator 15212, ATLb 15214, and down-conversion ADC sampling 15216.

[0234] High-precision ATLn self-calibration

[0235] This demonstrates that adding a single ATL1 core module to any ATLn circuit can achieve precision calibration. The circuit in Figure 146 starts out operational, but with no calibration data. When the circuit in Figure 146 first powers up, it erases the LUT contents and enters 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 usual, we assume three control voltages {f,g,p}: one for the resonator frequency, one for the scaling block setting, and a third for the phase shifter control.

[0237] For purposes of illustration, 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 the clock crystal.

[0238] We also assume that the fabrication of ATL1b is sufficiently controlled so that the resonator of ATL1b can be set to be in the middle of the tunable band. This implies reasonable fabrication control of the electrode 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 set the minimum feedback gain to maintain oscillation. The limited bandwidth of baseband processing makes it difficult to observe 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] The pole-zero plot here is given in FIG.

[0242] The frequency response is shown in Figure 155. Note that, as required for an ideal phase shifter, 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%. By changing the all-pass center frequency ΩP, 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 all-pass.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 mismatch the phase shifter providing a 50° excess in the loop, which is implemented by choosing ωAp = 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, to reach the unstable condition, the loop gain must be increased when a phase mismatch occurs. Also, as G increases beyond G=1, the oscillation frequency decreases. This makes sense because the resonator needs to be at a lower frequency so that it has a positive phase shift to offset the negative shift of the all-pass phase shifter circuit.

[0250] For 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 other ways 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 of the ATL1 core module and the phase shifter value can be set by increasing G and pointing out the point at which the ATL1 core module begins to vibrate. 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 to get a broadband response.

[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, which 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, we move on to the lower half. Returning to the starting voltage for the ATL1b resonator, we gradually decrease the resonator voltage following the steps above until the full resonator range has been calibrated and the LUT is complete. Once this initial point is found, the remainder of the procedure is relatively fast and efficient.

[0260] Once ATL1b is ready to oscillate, Mode 5 (Figure 152) is switched on, reversing the functions of ATL1a and ATL1b. This means that ATL1b is configured for wider bandwidth because it has no feedback. Because ATL1a and ATL1b are essentially identical, differing only in manufacturing tolerances, the LUT entries for 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 for 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 determines whether the closed loop resonant poles are on 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 the ATL1b can be used as a VCO that can be tuned fairly precisely. The exact frequency of the ATL1b is ultimately determined by LO downconversion 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 characteristic 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, you know that the feedback gain and phase shifter settings will lead to oscillation. Next, you need to know how much to reduce this feedback gain setting from this oscillation condition. This is accomplished 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. The A signal is passed to ATL1a. ATL1a's phase shifter control and open-loop resonator control voltages are synchronously dithered based on the LUT entry. This dithers the passband of ATL1a about its center frequency. 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 ATL1a's LUT. ATL1a's feedback gain is then incremented, and the process repeats.

[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 is felt to be a more accurate approach than fitting a quadratic or cubic polynomial to the LUT data.

[0267] Once ATL1a has been calibrated in this way, 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 solely for calibration purposes helps enable high-precision calibration of any ATLn implementation. The initialization procedure described above is repeated for each ATL1 core module that makes up an ATLn.

[0269] Resonant circuit control

[0270] As mentioned above, it is desirable to be able to adjust the characteristics of the currently predetermined primary resonant structures by coupling these predetermined primary resonant structures to secondary variable resonant structures. This allows the network circuit to automatically mitigate ambient temperature changes, component aging, and drift of such predetermined primary resonant structures, thereby 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 controlling an external resonator (XR), the circuit design may be referred to as an 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 be stable over the cycle time of the secondary variable resonator control and response loop so that the predetermined 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 can be the amount of adjusting the Q and / or center frequency of a fixed resonator structure. For example, the frequency response of a primary resonator may be designed to operate within a predetermined error factor, such as may be specified by manufacturing specifications. A tunable resonator is used to control the primary resonator within this predetermined error factor, so that the closed-loop frequency response approaches the ideal frequency response of the primary resonator.

[0274] In one example, consider an external resonator, designated XR, that has 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 Figure 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 predetermined resonance characteristics of the primary resonator can be effectively altered by the effects of:

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

[0277] and / or variation of the closed-loop Q of the resonator R by the gain block G via the 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 embodiment of the ATLXR and its operation may be described using a pole-zero diagram of the ATLXR's open-loop response. 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, we 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 nonlinear and time-varying components as described above. In preferred embodiments, the resonator is typically modeled as a high-Q resonant pole, while R may be represented by a low-Q pole with a Q of 10-20 or so based on the following considerations:

[0282] Requiring a basic 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] Additionally, you must represent the loop delay, which includes the following module delays:

[0285] Delay of phase shifter P;

[0286] the delay of the connection line between F and

[0287] Additional delay of 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 shown in Figure 181 as the "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 or tunable resonators. Thus, the Pade poles and zeros are equivalent and not physical. These poles and zeros form an all-pass filter structure that affects only the phase, not the amplitude.

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

[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 further increasing the loop delay is to affect the phase tilt more greatly 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 actually 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 facilitated 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 will be explained based on Figure 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 two loci, as indicated by the small arrows. 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 resonator or external resonator XR.

[0296] For clarity, the loci of the other poles of delay and R are not shown because these poles are not overly related to the high-order Q pole when it only needs to move a short distance, requiring only the small closed-loop gain described above. Therefore, the poles of the second-order variable resonator R and the delay model do not change significantly. In this way, the dominant pole of the first-order 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 an ATLXR places a controllably variable resonator (R) with a variable gain block inside a signal loop that includes a substantially 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 effect, manipulation of a closed-loop ATLXR circuit that includes the primary resonator and a tunable resonator. Dynamic modification of the closed-loop ATLXR is sufficient to obtain a desired passband response and compensate for moderate temperature variations, 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 a stand-alone primary resonator.

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

[0300] The poles of the first-order 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 in the primary resonator.

[0303] Compensates for frequency shifts in 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 placement of the poles of the primary resonators in the S-plane, so that specific multi-pole filters can be realized, such as Chebyshev or Butterworth bandpass filters incorporating external resonator XRs.

[0306] 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 with 1 MHz bandwidth, following a frequency hopping sub-band similar to Bluetooth®, which follows a frequency hopping scheme.

[0308] The detailed analysis presented above relates to a specific embodiment of a circuit used to control the primary resonator and is provided to help gain a deeper understanding of the principles involved in the proposed approach. However, once the design principles are understood, it should also be understood that the above discussion may not be fully applicable in all situations, as other applications and other design examples may be used that deviate from the analysis, as indicated above. Therefore, the above discussion should be viewed as informative and not 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 electric, electromagnetic or electrical resonator such as:

[0311] The electrical resonator may be a circuit made up of an inductor or a capacitor.

[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 described above, the ATLXR variable resonator R is generally a low-Q resonator that can be differentiated on-chip and controlled 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 in the ATL signal loop, with control of f. Control f would typically act on a photodiode (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 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 preferred embodiments. R typically consists of fixed-value integrated capacitors and spiral inductors, along with variable-value inverter 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 to implement them based on integrated MEMS devices that provide variable inductors or capacitors. Examples of suitable R resonators include those described in detail in Nielsen.

[0318] Variations and Options

[0319] As can be seen, different alternatives and variations to 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, a multi-pole BAW chip device application can be envisioned, as shown in Figure 191. Here, the resonators are on a common BAW chip with a ground and one port connection from each resonator to the ATLXR chip. This embodiment proposes an external resonator chip consisting of multiple BAW resonators, each with a single port connection to a matching ATLXR chip, forming a multi-pole filter. An internal tunable resonator block R closes the signal loop as needed.

[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 antennas with some resonant properties as chip antennas or printed circuit antennas.

[0323] The ATLXR may be arranged as shown in Figure 192, which has multiple general ATLXR blocks and a switch matrix connecting various antennas and various resonators. This has general ports for attaching 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. Figure 192 shows 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 shown in FIG. 188. FIG. 188 shows components F 18810 controlled by f 18814, R 18812, P 18816 controlled by p 18818, coupler 18820, signal output 18822, gain block G 18824 controlled by g 18826, 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-order resonator. Although not required, the first-order resonator is typically 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, and has a control f. The control f can act on a varactor diode of a given configuration, 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. The 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 a chip. In some examples, the tunable resonator may consist of a fixed-value integrated capacitor and spiral inductor, along with a variable-value inverter diode controlled by f. R may also be implemented based on distributed transmission line components integrated on the chip die. Another option for the R resonator is to implement it 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, which 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 controls {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 position 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] While the basic ATLXR of Figure 209 assumes that the primary resonator is controllable as in Figure 188, the primary resonator F may be controllable or tunable between different operating frequencies, as in the example of Figure 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, and signal 18828, and chip integrated circuit 18830, and additional coarse frequency control of F 18910. For example, the primary resonator may be a ferrite-based resonator with an added magnetic field for slow control. Or, it may be a MEMS-based resonator with 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] ATLXRs 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, and 18828, and chip integrated circuit 18830. 19010 is controlled by v 19012. Additional control of v relative to the variable attenuator V is provided to ensure the overall throughput gain of the multi-ATLXR circuit does not result in uncontrolled self-oscillation. Clearly, the cascade configuration of Figure 190 can be extended to any order bandpass filter, with each ATLXR circuit implementing one SOS (second-order section or biquad) of the bandpass filter's overall transfer function.

[0334] Yes, it is. 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 a single port connection to a matching ATLXR chip, forms a multi-pole filter. An internal resonator block R forms the required additional feedback port.

[0335] ATLXR implementation

[0336] The complexity of the integrated chip is generally considered secondary, as small signal transistors can be integrated at negligible cost. Inductors and capacitors occupy a larger die area and therefore may be more costly. Therefore, cost-effective integration of variable R resonators generally only achieves low Q values ​​of around 10. To achieve a highly selective bandpass filter response, the filter poles must have high Q values ​​(e.g., much higher than 10) and therefore may require significant Q enhancement. Arbitrarily 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 tunable resonator, and may be 100 times greater than that of the tunable resonator. In the context of the present discussion, reference to values ​​of 10 or 100 is not intended to be a definite limit, but should be considered a general range that is close in nature but includes factors that may be slightly outside.

[0338] In some examples, the primary resonator may be an external resonator. Because this is expected to be the most likely scenario in which the teachings can be used, the term “external” is generally used herein to refer to a primary resonator. However, it will be understood that the present teachings can 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 the substrate of the tunable resonant circuit, which substrates may then be bonded or otherwise attached to each other by various methods known in the art, which in turn will depend on the final configuration 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 is on a different substrate. Other designs will be apparent to those skilled in the art and will not be discussed further.

[0339] Printed resonator variants generally do not achieve the high Q of SAW or BAW, but have a much higher Q than chip resonator implementations. Useful printed resonators may include waveguide-like cavities 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 via connections within the PCB are shown at 19310, and the feed is shown at 19312. Metallization on the top and bottom surfaces 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 of providing 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 shows an ATLXR chip 19510 and a chip antenna 19512. Because smartphones typically use at least 10 layers, the stripline resonators in 19514 may be stacked as shown to occupy less space. If the ATLXR chip uses a ball-grid connector, the resonators are stacked underneath the chip for compactness. This allows for a very cost-effective implementation of external resonator XRs with initial Q values ​​on the order of 100 for microwave frequency applications. At higher frequencies, printed resonators become more attractive due to their smaller size, but may require a low-loss dielectric substrate to maintain the Q of the external resonator XR at around 100.

[0342] ATLXR Coupling Configuration

[0343] Two characteristics of ATLXR are discussed 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 (typically 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 typically 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, multiport devices, etc. There may be one resonator or multiple resonators in the loop. Furthermore, "resonator" refers to a system of resonators unless specifically referring to a single resonator.

[0346] Of interest is considering 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 shown 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, input signals are separated from 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 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 to force unidirectional signal flow within the loop (as shown at the top of Figure 205). The top circuit has a phase shifter 20506 and a gain block 20508, while the bottom circuit has an ATL circuit 1301 and an external resonator 20510. The output may be taken anywhere, and the order of the components within the loop is arbitrary. While the resonator is labeled 1301 in the various drawings depicting ATL circuits, it will be understood that it could be a high- or low-order ATL circuit, or even a basic resonator like resonator 1401 described previously.

[0351] This active feedback technique 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 previously, the ATL3 implementation allows for loop phase shift control within a low-Q second-order cavity and phase shifters. May 2. Switching between phase polarizations is as easy as

[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 back through the external resonator while 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 explained below, in the case of an ATLF, for example, if a 10 dB reverse directional coupler 20704 is used, this feeds the signal to be bounced back by the antenna 20702 shown at the top of Figure 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 at the bottom of Figure 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 the antenna is poorly matched. As a result, we intentionally include the 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 shows the ATL 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. That is, phase shifters 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 simply 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 envisioned, 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 output 18822, gain block G 18824 controlled by g 18826, signal output 18828, ATLXR chip 19110, BAW chip 19112, and attenuator 19114 controlled by 19116. Here, the resonators are on a common BAW chip with one port connection to ground and each resonator to the ATLXR chip. This embodiment proposes 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 multiple generic ATLXR blocks and a switch matrix connecting various antennas and resonators. This has a generic port. May be a BAW resonator, a printed resonator, a chip antenna, or no resonator at all. On the other side, the switch matrix connects to the ATLXR circuit. Or, if no expansion is required, no ATLXR is connected.

[0365] The switch and multiple ATLXR circuits can be integrated into general-purpose transceiver chips and common external resonators, such as antennas, printed circuit board resonators, and SAW / BAW resonators, may be attached to common pins on the ATLXR.

[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 few 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 can fit onto a circuit board measuring just a few square centimeters. This has empowered applications such as IoT and wireless smart sensors. However, the availability of inexpensive wireless transceivers is driving further cost reductions, performance improvements, and antenna size reductions.

[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 operating in transmit mode: a device that alternately accelerates and decelerates the flow of electrical 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 that the current distribution within 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 verify the operation of the antenna in receive mode.

[0375] The integral of the Lorentz reaction is at 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 magnetic fields in the vicinity of the wire dipole, as shown in Figure 53. We introduce J as a current and M as an equivalent magnetic field current, which, although fictitious, works well in antenna analysis. Figure 53 shows a remote source 5310, a radiated 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 antenna 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 reciprocally tell us how the antenna receives a signal. In the transmitting mode, accelerated electrons traveling along a wire conductor generate an EM field with 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 Antenna: 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 by 5410 and the imaginary component by 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 parallel GLC admittance model.

number

[0386] This is accurate over a narrow frequency range around resonance. That is, looking at the right plot of Figure 54, the conductivity passes a stationary point at 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 conductivity and susceptibility increase monotonically with frequency, indicating that neither the series nor the parallel model is accurate.

[0387] It is interesting to note that neither the series nor the parallel LRC model can be a true fractional constant, since radiation resistance is a function of electrical length and therefore frequency. Therefore, the LRC model for a dipole antenna may only be accurate 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 even a quarter-wavelength monopole, is physically too large for small wireless sensor applications, necessitating the need for a more compact antenna. In Figure 5, 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, to efficiently compensate for this large capacitive reactance, a resonant circuit with very high Q and component accuracy is required: a nontrivial impedance-matching circuit that transforms 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's noise figure (NF). Making the dipole antenna just a little longer than the resonant frequency length achieves a reasonable antenna Q, which can be easily coupled to ATL1. Figure 56 shows the impedance of an electrically small dipole wire antenna with an antenna Q on the order of 10 to 20, exceeding 20% ​​of the relative bandwidth.

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

number

[0392] This shows that the loop antenna is sensitive to the magnetic components of far-field external sources rather than to the electrical components.

[0393] Electrically small current loop antennas have an input impedance that can be represented by a series resistor-inductor model.

number

[0394] Impedance matching is in principle achieved by a series capacitor - jX(Ω) resonating 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 a series or shunt capacitor. 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 matches the antenna only at one frequency. If a good match over a wider range of frequencies is desired, 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 distributed throughout the circuit. Unfortunately, as frequency increases, the ground: No longer equals the desired potential surface It is quite 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 creating a loop or dipole antenna that can still radiate is theoretically zero size, but there is a practical limit because radiation resistance rapidly drops to zero as 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 more difficult in the sense that they require a series capacitance of -j1 ohms and a shunt capacitance of -j7 ohms. The -j1 series capacitance is impractical and is omitted, resulting in a slight loss of impedance mismatch.

[0399] Printed Antennas: For many wireless applications, printed antennas such as the inverted-F antenna (PIFA) are inexpensive 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 shows 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 approximately one-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 this 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's wire around a small dielectric block with a high dielectric constant (typically 5-55), resulting in dielectric resonator antennas becoming known as "chip antennas." With dimensions measured in millimeters, these chip antennas are significantly smaller than the typical wavelengths used for 2.45 GHz antennas, where the free-space wavelength is in the 10 cm range. Various possibilities for folded line and coil structures can be constructed with ceramic grown around the conductor. These small versions of dielectric resonator antennas are also called chip antennas.

[0404] Chip antennas are typically mounted such that the ground plane is the critical 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, as shown in the top of Figure 59, is not only complex, but also generally results in an approximate, rather than exact, match of the antenna 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 50 ohms, which implies internal buffering, which impacts overall efficiency. Furthermore, matching components not only add cost, but also require board space, additional manufacturing steps, and losses. Referring to the bottom of Figure 59, a transceiver chip with an 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 assist with this, a photodiode may be placed as a shunt component from the chip antenna terminal to ground. Similar to the ATL1 resonator, this allows smooth tuning over a wide frequency range.

[0407] Furthermore, when integrating a chip antenna, the input impedance changes significantly with layout, and the model must 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 inductor. For a desired tuning bandwidth greater than 10%, the coupling ratio |c| is 0.1. As a result, we typically achieve a 1. Therefore, the ATLn is sensitive to impedance mismatches at its input port. This seems prohibitive to directly connect an antenna to the ATLn, since the VSWR is usually too large, causing the entire system to self-oscillate at uncontrolled frequencies. A solution would be to include a low-noise amplifier (LNA) between the antenna and the ATLn. However, additional components would be required to match the antenna and the LNA, or a significant portion of the available power would be reflected back to the antenna and re-radiated.

[0409] In contrast, tuning of a circuit called an ATLF (ATL-based filter circuit), described below, can be achieved by enabling automatic conjugate impedance matching between the antenna and receiver. In this way, the ATLF can be used to achieve a high degree of energy transfer between the antenna and 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 for 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; 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 as the susceptibility becomes zero at the same time. Such an antenna therefore matches the impedance to a fixed value of about 72 ohms.

[0412] Specifically, for example, in the common 2.4 GHz and 5 GHz type frequency bands, a half-wave dipole or quarter-wave monopole is physically too large and many applications require a more compact antenna.

[0413] Such small ESAs have highly reactive components and low radiation resistance. In Figure 5, consider the input impedance of a much shorter antenna, nominally 0.1 wavelengths. A direct 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. Efficiently compensating for this large capacitive reactance requires a resonant circuit with a significant Q and component accuracy. A matching circuit to convert 2 ohms to 50 ohms is not trivial, and using real lumped matching components would represent significant losses.

[0414] If you make the dipole antenna a little longer you can achieve a reasonable antenna Q. Figure 56 shows the impedance of a dipole nominally 0.35 wavelengths long. The radiation resistance increases to 30 ohms, and the series capacitive reactance becomes 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 requirements for ESA antenna design are to achieve 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.

[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 fixed and relatively constant average impedance over the transceiver's operating band, across the transceiver's operating range. 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 transceiver's range.

[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 transmission bandwidth. This circuit is called the Arotec ATL Filter Tena, or simply ATLF. The ATLF can be applied to both transmit and receive functions.

[0420] It is particularly important that the ATLF conjugate-matched antenna circuit be functional even when the antenna impedance is not static. The control of the circuit used to complex-conjugate-match an antenna in situations or applications where the target antenna's local environment changes the target antenna's reflection coefficient to achieve conjugate coupling with the antenna is not static. Changes in the reflection coefficient can be caused by 1) local environmental factors, or 2) coupling between the target antenna and nearby objects, or 3) application-specific changes in antenna impedance. Antenna optimization techniques for communications systems and other applications in such dynamic environments may lose track of the target antenna's true reflection coefficient, resulting in antenna optimization failure or effectively isolating the antenna from the transceiver system.

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

[0422] Impedance matching for 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 examines 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. Measuring VSWR requires special equipment on the antenna tower.

[0425] In this method, the center frequency of transmission is tuned so that the VSWR is adjusted to minimize the antenna impedance mismatch over the entire bandwidth of the transmission. This is in contrast to the approach described below, which optimizes the match 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, such as the ATL mentioned above, can be optimized by combining 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 Filter (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 toward a desired result.

[0428] The term "filtenna" is sometimes used to refer to a circuit containing 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 filter in a filtenna is a bandpass structure that is essentially a matched circuit. A filtenna can simply be thought of as a grouping of an antenna and a matched network, usually with bandpass characteristics. Filtenna bandpass matching circuits can be high-order and complex, such as the conventional example in Figure 60, producing a high-order Chebyshev-like bandpass response from an otherwise narrowband antenna.

[0429] The term "reconfigurable antenna" can be used to refer to a type of control applied to an antenna that changes the frequency response or radiation pattern of that antenna. This may be achieved through diode control or PIN switches coupled at different portions of the antenna. One prior art example of a diode-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 using active secondary radiators to achieve reconfigurable antenna characteristics.

[0430] What will be presented is a circuit topology and method for achieving dynamic antenna matching without the use of an antenna impedance matching circuit. The discussion herein will be in terms of ATL-based circuits and will therefore 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 antenna's unknown reflection coefficient is achieved by analyzing the SNR feedback from the receiver demodulation available from the receiver chain and dithering both amplitude and phase within the ATLF to achieve the required conjugate impedance match. Once this is achieved, the ATLF further increases the absolute value of the effective reflection coefficient, thereby effectively narrowing the signal bandwidth and increasing the Q of the received signal. The bandwidth narrowing is limited by the ATLF's self-calibration and stability control, 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 are available 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 estimation 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 in Figure 62 as two coupled resonators in receive mode, allowing for typical antenna matching components to be distributed and transceiver devices to be directly connected to the ATLF resonator link antenna subsystem. Figure 62 shows an impedance-matched antenna 6210, a recirculating loop at the antenna and ATL port 6212, an ATL resonator 6214, an ATL gain block 6216, and a receive signal output 6218. This is because the electrically small, low-loss antenna is a resonant circuit element that is absorbed into the ATL 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] Reconfigurable antennas, optionally frequency control, apply to antennas, usually in the form of varactor diodes.

[0439] However, because the antenna is directly coupled to the ATLn as an embedded resonator, traditional antenna impedance matching is eliminated within the ATLF. This is achieved through the ATLn's self-calibration, 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 required to accommodate the ATLF is a minor cost driver. Inductors are often size-critical, and Qs above 15 are considered cost-ineffective. Therefore, an ATLn resonator Q of approximately 10 is a reasonable starting point. ATLn enhancement factor (the ratio of closed-loop Q to open-loop Q) can be successfully achieved, resulting in an 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, we will assume a shortened dipole with a Q of the order of 10. This antenna is still too long for practical sensor implementation, but there are ways to achieve a more compact antenna with 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 the antenna port impedance is normalized to 1 ohm. zA is specified as:

number

[0444] The reflection coefficient (looking at 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 that 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 its resonant frequency, such that R=1. The pole-zero plot for this case can be seen to be as shown in Figure 66. Other possibilities for a resonant but mismatched antenna can be considered, but the range R=0 to R=1 will limit the problem.

[0448] In contrast, the ATLF block diagram shown in the lower portion of Figure 67 dispenses with matching components and connects the transceiver device directly to the chip antenna. Because the chip antenna effectively becomes part of the resonator within the ATLn, the ATLF demonstrates that the circuit can be operated without impedance matching. The ATLn self-calibrates and optimizes the performance of this antenna subsystem, regardless of whether an antenna is attached, as described below. Figure 67 shows two block diagrams of a transceiver without matching network functionality. The top diagram shows the antenna 6710, L and 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 mentioned above, 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 adjustable scaling block are controlled to condition the signal received by the antenna to modify it toward the desired signal. Preferably, the signal conditioning block also includes an adjustable resonator. It is also understood that the signal conditioning block can 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 should be recognized 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 ATLF's two resonant structures: the mismatched target antenna and the tunable analog ATLn filter. Here, we start with the simplest idealized model of the ATL1, shown in Figure 40, consisting of a resonator and 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 a loop whose secondary importance is the actual physical location of the ATL adaptive filter's input and output ports.

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

number

[0454] The characteristic plot of the resonator at normalized frequency is shown in Figure 63. ωr=1 and Dr=0.05, which results in an open loop Q of 10, or 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 is adjustable by the reactor diode control voltage, and

[0457] The ATL1 scaling block provides a gain of G 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 of any resonator, the change in Q from the open-loop resonator to the closed-loop, is represented by RQ and given by the following equation:

Number

[0463] From this expression, the two ratios of the open-loop to the closed-loop Q, ·When the values of RQ > 1 and 0 < G < 1 correspond to Q enhancement, ·When the values of RQ < 1 and G < 0 correspond to Q spoiling, note that can be obtained.

[0464] Note R. It becomes indeterminate for the value of QG = 1. This corresponds to a pole that crosses the RHP of the S-plane, which is an unstable state.

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

[0466] Zooming in on the component size issue, the resonant frequency is given by:

number

[0467] As shown in Figure 64, ATL1 includes a directional coupler 6410 and an output splitter 6412. Here, a resonator 6414 is included in the feedback loop 6416, and a scaling block 6418 appears to act as 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 ATL's input port 6420. For ATL1, a small return gain is necessary, but too much may overwhelm the target antenna's resonance, making calibration difficult. Therefore, a moderate amount of directivity from the directional coupler is desirable. The splitter in Figure 64 may be easily implemented with a simple reversible resistor circuit.

[0468] Adding a phase shifter to the ATLF

[0469] The phase shifter implementation of ATL1 is described above. Now consider combining a phase shifter into the feedback loop of the ATLF, as shown in Figure 68, which consists 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 applied. For now, assume the input is a current impressed on the antenna and the output is taken from the output of a gain block. Now we can take into account the combined 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 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 fall conveniently deep into the left-hand plane, becoming the second-order closed-loop poles.

[0473] Figure 69 shows the case of an 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 must be adjusted to compensate for the phase error in the phase shifter in order 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, we can 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 a single peak (F(j)Ω) in 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 they also show 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 value 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-shifting 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 360-degree increments associated with the round-trip delay become cumulative. 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 illustrated 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 at the top of Figure 75 and the Thévinin equivalent circuit shown at the bottom of Figure 75. The 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, with a source 7610, resistor 7612, and load 7614 terminated at Z. The significance of this circuit is that the equivalent source impedance of the generator is now Z. Load = Z22*Z so that the best power transfer is achieved by conjugate load impedance matching of 22Z.

[0484] The ATLF analysis uses both the antenna impedance and reflection coefficient. The advantage of the reflection coefficient is that it 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 discussion of impedance matching, let's first consider a typical example of narrowband matching 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 connects a source 7710 , an inductor 7712 , a resistor 7714 , a receiver 7716 , a capacitor 7718 , an SNR measurement 7720 , and an SNR optimizer 7722 to the inductor 7712 and capacitor 7718 .

[0487] With the proper values ​​of physical L and C, the impedance from the antenna to the matching network and looking into the receiver is exactly 20 ohms. Also, because only lossless inductors and capacitors are used in the match, 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 |Γr|2 as a function of L and C, obtaining the contour plot in Figure 78. This is a favorable convex error surface that can be easily optimized when L and C are used with 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 |Γr|2. Then, by maximizing the SNR, we can find |Γr|. In this example, |Γr| is a simple, nearly convex function of the matching parameters. Putting all this together, a simple gradient search for the SNR will find the global minimum |Γr(L,C)|. The only caveat is that ISI and narrowband interference spectral peaks are not considered here.

[0490] Matching L is simple and suitable 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 matching bandwidth is very small. If the resulting bandwidth is too small to accommodate the desired antenna signal, a more complex physical matching network with a more physical L and C is required.

[0491] The challenge of chip integration of L matching can be significant when the range of L and C required to accommodate the antenna's range 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. While it is possible to integrate an inductor for C, variable physical L requires 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, a function of only two parameters. However, for severe matching problems (such as large antenna reactances, or R = Rr), it has been observed that the bandwidth becomes too narrow before the match is complete. In this case, SNR optimization limits the match by effectively imposing a loose constraint on the tolerable ISI noise.

[0493] Reactive Antenna Component Matching for ATLF Using Adaptive Resistor 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's reactance is zero. 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 at the top of Figure 112. The circuit in Figure 112 shows the antenna model 11210 with resistor 11212, capacitor 11214, and inductor 11216, along with the negative resistance provided by resistor 11220 and inductor 11222, along with coupling cap 11218. The root locus and Nyquist plot for this circuit are shown at the bottom of Figure 112. Applying a large magnitude of negative resistance pushes the magnitude of the ATLF reflection coefficient above unity, resulting in an enhancement of the Q. Note how the poles wrap around and cross the axis at a significantly different frequency than the Jw antenna resonance. Also, a second resonance occurs at a much lower frequency, which is 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 photodiode. 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 portion 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 with a 0 degree output port 2 in the gain block, followed by a 3 dB splitter as the ATL1 output coupler. The return signal from the output coupler is coupled to 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] When the phase is set correctly in this embodiment, the 90-degree coupler is lossless, and no signal is sent to port 3, resulting in no dissipation in the termination resistor. 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, when the phase matching is done correctly and ideally there is no loop loss, the noise figure (NF) of ATL1 is minimized. 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 recognized 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. Scheme 11512 at the bottom uses several stages of inductors and capacitors. Both schemes 11510 and 11512 show resistor 11514, inductor 11516, and capacitor 11518.

[0510] When designing an ATLF, the required phase delay correction can be minimized through 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 of delay over a wide frequency range. If the required phase adjustment is small, a simple variable phase shifter can be used, combining the ATL negative resistance implementation with the phase shifter described above.

[0511] Active antenna reflection coefficient synthesis in ATLF.

[0512] The purpose of the ATLF is to synthesize an inductance-matched 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 the capacitor, the circuit will react as if a physical capacitor were actually creating 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 * ΓA, then the antenna is matched to the receiver and the available power in the antenna signal is fully utilized. This condition also entails the caveat of Snr B above. Nevertheless, maximizing Snr B is the best thing we can do to recover the antenna signal.

[0515] Next, consider how to implement the black-box receiver shown in Figure 79, which includes the black-box receiver circuit 7910 and the source 7912. A possible implementation is a Category 1 ATLF implementation using a circulator. Here, the signal enters the circulator, couples to the gain stage and phase shifter, and then returns to the circulator and to the antenna. Unfortunately, the circulator is not completely separate due to the required ferrite and magnetic field source, but it can be implemented in a non-chip configuration. Based on this active scheme, we can certainly generate any reflection coefficient: ΓR|>1 as needed. Therefore, we can satisfy the conjugate matching condition ΓR=ΓA*, which means we have fully utilized the signal power available from the antenna.

[0516] Regarding NF, it appears that the noise associated with the gain stage 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 can 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 can 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 source 8110, resistor 8112, inductor 8114, and RF voltage source 8116. The current flowing out of the antenna, i(t), is reduced due to the inductive impedance. If there were no inductance,

number

[0518] This corresponds to the case when an inductor is coupled to a matched resistive load, R, without the 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 (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 8216. Then the voltage across the capacitor is given by:

number

[0521] As a result, we must have

number

[0522] This is to be expected as the series L and C resonates 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, which controls the gain G and phase φ. The voltage signal from the antenna to circulator port 1 is V in. Thus the return signal to the antenna, VF, is given as:

number

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

number

[0525] For now, we will assume that the circulator port and the input impedance of the subsequent gain block have an impedance R. We will later develop this general information by adding a small component to Γ. Based on the antenna impedance, 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 want to plot the power loss coefficient of the antenna source. To do this, we subtract the inductive component of the antenna impedance, ZR, from the reflection coefficient, which we call Γa. Next, we calculate the coefficient of Γa.

number

[0528] Note that as the antenna reactance increases, the region where antenna coupling is valid decreases, requiring higher gain. This is expected because the active feedback must match the antenna's larger amplitude reflection coefficient. The larger the reflection coefficient, the stronger the resonance and the smaller the region.

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

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

number

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

number

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

number

[0533] We also

number

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

number

number

[0535] Once Vr 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 the current is 0.5 because R = 1 and V = 1, so I = V / 2R = 0.5. However, notice the following: 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 thing here is that the forward power wave emanating from the antenna enters the active load of the circulator and is then reflected back to the antenna by combining b. Therefore, the information of a is available at the receiver. As a result, we actually need to look at the voltage at a, not the voltage at port 1 of the circulator.

[0538] However, a = 0.5, regardless of the reflection coefficient produced by the receiver. Thus, the whole active feedback scheme does not seem to be realized very well - this is because the antenna is starting to match. Once the 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, and the "b" signal then becomes "a" inside the antenna. This is illustrated in Figure 86 with the inductor 2-port S-parameters 8610 and recovery section 8612.

[0539] Now consider the node's receiver plots, which are shown in Figure 87 for all of the receiver's 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 input to the receiver's gain block. It may seem like we've created a "super antenna," but unfortunately, we are not. The problem is that since the a signal receives a contribution from the active receiver via path b → a2 → S22 → b2 → a, what we see is a combination of the power wave from the antenna and a recirculated signal from the receiver back to the inductor port (antenna port). The recirculated signal is coherent with the antenna power wave, but adds receiver noise. This complicates the analysis.

[0540] Feedback provides gain so that the apparent power wave from the antenna can grow, but as the apparent power wave 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 definitive indicator of the optimum operating point. The true measurement is again the SNR.

[0542] The signal graph in Figure 87 provides another way to interpret what is happening. A power wave emanating from the antenna strikes the inductor 2 port, where it is reflected and partially transmitted. Without active feedback and termination R, the power wave at the inductor output is reduced by |S21| less than 1. However, this reduction does not necessarily degrade the SNR, because the inductor does not add noise. Now we have a feedback signal b → a2 → S22 → b2 → a. If the active receiver reflection coefficient were to be serially connected to R to emulate a resonant capacitor, it would be added to the antenna power wave, restoring its amplitude. However, the process of doing this adds noise from the receiver's active gain block. The higher the inductance, the larger the magnitude of the reflection coefficient the receiver must generate to compensate for the loss. |S21| (increases with inductance) = 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 be increased 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 drop.

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

[0544] Indirect measurement of the matching conditions in the receive mode can 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 to which it is exposed, 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 receiver noise is negligible compared to the thermal and interference noise from the antenna, matching becomes irrelevant because in-band noise and signals are treated similarly, and therefore there is no benefit 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, with antenna matching, ISI noise increases if the antenna match bandwidth is too narrow. This is a factor to consider when the ATLF received signal bandwidth is too narrow to be usable in the first place, as discussed next.

[0549] Note that SNR maximization-based matching involves two processes. 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 the resonance of the matching network. Therefore, noise and interference from outside the resonance peak are suppressed relative to the desired antenna signal.

[0550] Next, Figure 89 is a block diagram of the process 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. Figure 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, which are used in the SNR optimization, which involves 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 using values ​​stored in a LUT. However, the real benefit of the ATLF is its ability to adapt to changing antenna characteristics. Furthermore, Q enhancement within the ATL requires precise feedback determination and implementation. Ultimately, then, it is the noise in the demodulated signal that matters, not the amplitude or bandwidth of the demodulated signal itself. The ATLF must respond to filtering functions performed in the demodulation process, such as by the equalizer 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. Therefore, attention to the entire processing feedback loop is important.

[0553] As described above, we use the LUT values ​​as an initial setting. We also dynamically update the LUT for instances such as frequency hopping protocols required for fast ATLF adaptation. 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 an 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 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, because it must keep up with channel variations due to multipath effects. Variations on equalizers are rake receivers and OFDM receivers, which are used in spread spectrum 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 multipath.

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

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

[0559] An example of when antenna impedance changes are 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. Therefore, 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. Therefore, there is no need to have a complex ATLF with multiple poles. However, there is a moderately enhanced NF such that frequency components outside the RF signal band are not well matched.

[0561] Implementation of ATL Filtena (ATLF)

[0562] The complication with 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 implementations. Other examples are possible.

[0563] Radiation resistance component of antenna impedance

[0564] Let's 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 sinusoid with an RMS (root-mean-square) amplitude of V. Therefore, the power available from this antenna is

number

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

number

[0566] The reflection coefficient of the antenna is defined as:

number

number

number

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

number

[0568] This is based on the assumption that the antenna's equivalent noise temperature is 293°C. This clearly illustrates 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 antenna-receiver gain is arbitrary and the FOM should focus solely on the receiver's ability to utilize the available power provided by the antenna. If the receiver's NF is NF = 1, it generates no inherent noise and there is no consequence to mismatch. In other words, mismatch only reduces the receiver's overall signal gain but does not contribute to the NF. This also means that in-band noise and signals from the antenna source are processed identically, so mismatch affects both equally. Antenna matching is only necessary if the receiver generates additional noise. Similarly, if the interfering noise at the antenna input is much greater than the receiver's inherent noise, it can be stated that there is little effect on antenna mismatch.

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

[0570] If the antenna has no substantial reactive component to the radiation resistance (such as the simple resistance model currently considered), the losses due to NF mismatch and inflation are usually modest. Consider the example of 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 antenna mismatch is not a concern. However, if the same antenna is used for transmission, the mismatch will be the same for the transmit and receive channels, as 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 antenna's desired signal output is typically buried in thermal background noise and interference. Furthermore, multipath causes the exact received signal strength to vary widely. Therefore, it is impractical to infer the condition of the antenna match from RF signal observations. 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, an antenna's reflection coefficient can be measured directly based on a VSWR (Voltage Standing Wave Ratio) measurement, which is usually easy to implement. Suppose you have antennas used for both transmit and receive at roughly the same carrier frequency. You could then, in principle, match antennas based on VSWR or other measurements for transmit mode, and by correlation, apply the same match to receive mode. This approach is sufficient if the antennas are sufficiently spread out so that the frequency separation between the transmit and receive channels is small compared to the antenna bandwidth. However, this is not an assumption we are making here, and our goal is to adjust the antenna match based solely on the typically weak received signal in order to transfer optimal energy from the antenna to the receiver.

[0575] Coupling of 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 at the top of Figure 94. The antenna resonator is represented by a series LRC model, where R represents the radiation resistance. The negative resistance ATL is represented by a reflection coefficient given as ΓG = G(g), which represents a direct dependence on G, which is set by the control g. A series RLC is shown representing the antenna, and a varactor diode with capacitance CV. This has an equivalent reflection coefficient represented as ΓA. Figure 94 shows the antenna (series LRC) 9410, negative resistance 9412, resistor 9414, inductor 9416, and 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 what is shown in the small loop antenna example of Figure 95. Figure 95 shows a small loop antenna 9510, capacitor 9512, directional coupler 9514, and 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 due to 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 coupler diode that sets up 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 enters the loop antenna as a voltage source. This is amplified by the gain section, which acts as a one-port reflector that is reflected by the mismatched antenna. The backward coupler serves to block reflections from the gain stage, 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 where the antenna port impedance is denoted as z. Given A [Number]

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

[0582] Here, impedance normalization is used such that the characteristic impedance is 1. This can be expressed as the reflection coefficient 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 reactance of the antenna, 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 within 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 for 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 within 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 we assume that the output is taken 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, and R = 0.1, we obtain the root locus shown to the left of 97 in G 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 across the JwR1 axis, i.e., provided 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(Actual(T)) + .01

[0592] This gives a closed-loop Q of about 100. The frequency response is plotted at the top of Figure 98 on 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 place 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 ΓA is now a negative value from the previous case, resulting in a Smith chart plot of line 9918 below 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 tuned short dipole antenna as shown in Figure 100. Here, the dipole is best modeled 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 seen by the backward coupler is

number

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

[0598] The reflection coefficients are plotted as shown in Figure 10110 and show similar behavior as before, but ΓA is a little 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 would be more logically placed after the inductor 10212, unfortunately has a very small tuning range. If the diode 10210 is in series with the inductor, the tuning range is restored. Figure 102 shows the antenna 10214, capacitor 10216, directional coupler 10216, and 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 can vary depending on where the output and input are placed. For now, assume the input is a current impressed on the antenna and the output is taken from the output of a gain block. Now we can take into account the combined poles and zeros and plot the closed-loop poles as a function of G as shown in Figure 104.

[0602] This now reveals some complications regarding the coupled resonance of the antenna reflection and the phase shifter. Note that the important result is that the closed-loop dominant pole is determined by the phase shifter, not the antenna reflection. The poles of Γα(s) unfortunately move towards the real axis, and then one of the poles moves along the real axis into 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 capacitor 10610 and resistor 10612. This restoration circuit can be placed anywhere within the loop of Figure 103 to enhance stability. By adding this circuit, the root locus changes to that of Figure 107, indicating the increased stability of the dominant pole.

[0604] Next, replace the phase shifter with a resonator and obtain the root locus plots shown in Figure 108 and Figure 109. Note 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 requiring any additional correction.

[0605] Note that we now essentially have ATL1 with an unwanted loop delay that can be corrected by de-energizing the resonator as described above. Figure 110. The only deviation in ATL1 is that the directional coupler is configured differently and reversed to send a feedback signal that reflects off the antenna rather than back into the ATL1 loop. Figure 110 shows the antenna reconfiguration 11010, reverse directional coupler 11012, gain stage 11014, and resonator 11016.

[0606] This can be extended to an 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 well-behaved dominant pole moving towards the Jw axis as well as spurious poles at higher frequencies. However, for high Q extensions this becomes much less noticeable. The pole to the left of the resonator is the antenna pole and finally, at the far left, is the all-path circuit pole simulating the loop delay.

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

[0608] For calibration purposes, given a desired frequency, we can vary the capacitances of the antenna's transducers 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, when everything is set correctly, the dominant pole for the ATL3 filter antenna moves straight toward the jw axis, with no spurious passbands. This is a minimum-G solution that can be used for calibration as described above. Therefore, the previous calibration rule remains in place, with the four transducers set to {f1,f2,f3,fAnt} such that G is minimized for a constrained Q expansion or bandwidth.

[0609] ATLn as a negative resistance element

[0610] As shown above, the key element of the ATLF is that the directional coupler is reversed from the normal ATLn configuration, with the antenna coupled inside the ATLn's resonant structure, which has a controllable bandwidth. When the normal directional coupler is reversed, this causes the ATLn to act as a negative resistance, providing a return gain for the input power. When the ATLF is implemented in this manner, the need for a directional coupler is eliminated. This can be highly desirable, as suitable directional couplers are difficult to realize on a chip with physically small L and C. Therefore, in this section, we take a different approach to the ATLF, eliminating the directional coupler and instead implementing 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, rather than a detailed design, we return to the ATLF with ATL1 for further discussion.

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

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 voltage source, inductor, and negative resistance ZG. The diagram at the bottom of Figure 116 is the Thévenin equivalent circuit of the circuit shown above. VA is a voltage source that can be derived 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 lookup table (LUT) entries for specific inputs {Q, desired 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 once the antenna is in steady state. If the antenna is changed for another antenna, or if the antenna impedance changes due to near-field interactions, the LUT entries will be in error. To be useful, the ATLF must have a run-time calibration method.

[0617] One approach is to maximize the SNR of the demodulated signal from the receiver: {g,p,f} are dithered to maximize the SNR of the processed output. Consider a constant-power data-modulated signal coupled into an ATLF antenna. Assume the position and orientation of the ATLF antenna remain fixed. The ATLF output is demodulated, and the SNR of the data samples is calculated continuously in time. Assume the processing receiver demodulator has its own clock and carrier synchronization scheme, which is performed as an internal process of data demodulation. For a nominal SNR, this demodulation function, with carrier and clock optimization, is relatively independent of the ATLF optimization. Next, dither the {g,p,f} controls with a time constant slower than the receiver's 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 can be optimized for the data signal's operating point (carrier frequency and bandwidth) to optimize the SNR. The input to the LUT is the data signal parameters, not the desired center frequency and bandwidth used to self-calibrate the ATLn.

[0618] The bandwidth must be 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, and if the bandwidth is too narrow, there will be ISI (Inter-Symbol Interference).

[0619] Next, assume that the ATLF is still stationary with a stationary antenna and no neighborhood changes, but the data signal is frequency hopping. However, since the hopping sequence is known, the LUT entries for the upcoming data burst are used to configure the ATLF. However, {f,g,p} are slightly dithered to new values ​​to indicate whether the SNR obtained after the burst is demodulated has increased or decreased. A gradient algorithm can then be used 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, the LUT entries are slightly nudged toward the current ATLF parameter set. In this way, the LUT entries for the current data modulation can be slowly optimized. Because 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 only 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. Because the SNR measurement is random, the dither-based {f,g,p} optimization is essentially a stochastic gradient search algorithm.

[0620] Next, allow the antenna to move, which means the multipath environment changes. However, this does not mean the antenna impedance changes. If the SNR remains maximum, the ATLF LUT parameters should be changed only if the antenna is changed. Multipath causes a fade in the dynamics, and the SNR changes from burst to 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 a 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 antenna's near environment. An example is a smart bandage where the patient changes position or rolls over periodically, affecting the antenna's near field. In such cases, the antenna's impedance changes, and the LUT entries must be modified. This 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 runtime calibration and are generally robust. However, there are pathological cases where dithering algorithms fail. 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 the series LRC model as before. The reflection coefficient looking into the antenna, ΓA, is specified as:

number

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

number

[0626] This ignored many details, but it shows that increasing G moves the poles toward the jw axis, narrowing the bandwidth commensurate with the phase value.

[0627] Regardless of the details of the root locus, as R / L decreases, the starting point of the root locus moves closer to the jw-axis and the bandwidth becomes smaller. Note that this is the case for effective Q spoiling, as a larger bandwidth may be required: the ATLF active feedback gain can push the poles further inside the LHP, away from the jw-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 unstable region and a narrower bandwidth with an increase in the region of S. Thus, for 0 < G < 1, since the circle radius is larger than 1, 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 an incoming electromagnetic (EM) signal in the receive mode. This FOM is flexible in that it can vary depending on the allowable or preferred values according to a specific design scenario, since different antennas may be accommodated by ATLF. Therefore, it is necessary 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] The antenna intercepts the signal contained in the input EM field and converts it into conducted power. The effectiveness of the antenna in performing this task is quantified by the radiation resistance, denoted as R in this specification. The power available from the antenna, of course, depends on the signal amplitude as voltage or current. The complexity of determining the signal amplitude is simply a characteristic of the antenna and not of ATLF, and may be ignored in this FOM calculation. Therefore, it may be assumed that there is available power at the antenna terminal output. Specify Pav as follows.

Number

[0632] Where IA is the RMS level of the current leaving the antenna terminals. Otherwise, you can consider VA as the RMS voltage at the antenna terminals, 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. Instead, what is important is how much available power the ATLF uses 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 for the ATLF is shown in Figure 118, showing resistor 11810 and source 11812.

[0634] The purpose 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 desired form of showing power loss due to impedance mismatch.

[0637] Next, assume that the receiver has a load resistance, RR, which 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] This is based on the assumption that the antenna's equivalent noise temperature is 293°C. This relationship illustrates the inflation of NF due to antenna-to-receiver mismatch. The antenna-receiver figure of merit (FOM) may be defined as this NF. This makes sense, since antenna-receiver gain is arbitrary and FOM should focus solely on the receiver's ability to utilize the available power provided by the antenna. For NF, R does not introduce inherent noise into the receiver, and there is no consequence to antenna mismatch. In other words, mismatch only reduces the receiver's overall signal gain but does not contribute to NF. This also means that in-band noise and signals from antenna sources are processed identically, so mismatch affects both equally. Antenna matching is only necessary if the receiver generates additional noise. Similarly, if the interfering noise at the antenna input is much greater than the receiver's inherent noise, it can be stated that 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 ATLF's Noise Figure (NF), denoted as NfAtlF. The overall ATLF NF 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 the conducted noise spectral density at the antenna terminals is ΗA. Similarly, the ATLF negative resistor has the same input noise density 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 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 because 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, particularly between the antenna radiation resistance and active electronics used as a negative resistance. Determining this impedance is tricky: ΓF (ΓF) > Γ due to negative resistance.

[0645] Consider a negative element equivalent circuit, as shown in Figure 119, in which an 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 into the coupler. Assume a high-ratio coupler so that ports {1,2} and {3,4} are strongly coupled. Assume 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, port 1 is equivalent to a negative resistance if the phase shifter is properly configured to offset the 90-degree shift in the hybrid coupler. It is clear that, regardless of frequency dependence, signal reflection occurs at port 1 at the resonant frequency due to the mismatch in R. A characteristic impedance of the circuit in Figure 119 leads to a signal loss associated with 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 of

number

number

[0648] ATLF configuration

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

[0650] A shows a direct connection from antenna 12010 to ATLn 12012, where ATLn 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 filter. If the antenna 12010 does not match the characteristic impedance on the band of interest, it will not effectively couple to ATL1 12012. Therefore, B includes matching network 12016 and LNA 12014.

[0652] C shows a small antenna 12010 which can be modeled as an LRC circuit, where the transducer 12018 modifies the effective antenna capacitance, which changes the antenna resonance and partially aligns 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 inverter 12018. The reason for this circuit is to provide partial Q enhancement, creating a dominant pole pair that is further enhanced by the second ATLn. This approach makes it easier to accommodate a wider range of antennas.

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

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

[0656] G is similar to F, but shows that if the phase shifter can be removed and replaced with three resonators 12022, slight adjustments as described above will provide a range of suitable phase correction. G shows the 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, scaling, phase and resonator are 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 configured based on the following principle: In this example, for ATL1, there can be three such LUTs, for ATL3 there can be nine.

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

[0662] Next, we describe 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, typically a system resource, adjusts the frequency and Q control of the ATL1 7502 via a DAC implemented as a pulse-width modulation (PWM) circuit 7506, adjusting it based on readings from a temperature sensor 7508. The microprocessor drives the ATL1 7502 until it begins to self-oscillate. The frequency of this self-oscillation is downconverted in block 7510 by a frequency synthesizer signal generated by a crystal reference 7505 and frequency synthesizer 7507, also set by the microprocessor 7504. A frequency counter 7509 or other measurement means determines the frequency of the downconverted signal. In this way, the resonant frequency of the ATL1 core module may be determined. Additionally, a power detector 7512 and an ADC block 7514 are provided that can estimate the rate of increase of the self-oscillation signal at the output of the ATL1 7502. The microprocessor 7504 estimates this exponential power rise and thereby determines the location of the closed-loop poles of the ATL1 7502. Currently, it is just to the right of the Jw axis. If the Q enhancement is slightly reduced, self-oscillation continues at the same frequency with high accuracy, but begins to decay exponentially. Now, Paul points out that while the ATL1 calibration is stable over time but varies primarily based on ambient temperature, the ATLF calibration depends on transitions to intentionally 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 to the current context.

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

[0665] The first consequence of complex variable theory is that the open-loop transfer function is stable and has no poles within the right-hand plane. This is true as long as the components are unconditionally stable. In our architecture, we assume that the resonators and gain blocks are stable, which is certainly true for the resonators since they are passive auxiliary circuits with no active gain. Since the gain blocks can be assumed to be unconditionally stable, this is also considered appropriate. However, a situation can arise when the gain blocks are based on transistor configurations that are not unconditionally stable; slight changes in the impedance of other loop components can cause poles to gradually move closer to the right-hand plane, changing the Nyquist stability criteria. This is a design issue that can be avoided or minimized. However, implementing negative resistance in an ATLF presents some additional challenges in that the gain blocks are not unconditionally stable. Reflections from the resonators or phase shifters and reflections from the negative resistance can easily push poles into 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 analytic continuity, which 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 the unstable region. Conversely, outside this boundary, we have strictly stable behavior.

[0668] Furthermore, operating points a short distance from the Nyquist constellation have predictable natural modes that decay exponentially in the stable region and grow exponentially 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 as if we were flying a plane 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 characteristic is that the Nyquist locus is likely to have small loops visible due to antenna reflections from near-field antennas. These loops always fall inside the unstable region, as shown in Figure 128. The reason for this is that the feathers of the Nyquist locus (for a 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, we can see that only inward-facing loops are possible. This means that near-field scattering will result in adjustable frequency gaps. However, because loops cannot grow outward, they will not suddenly destabilize the ATLF, thus aiding stability. This is shown in Figure 129.

[0670] ATLF calibration

[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 shown below. Other procedures may also be possible.

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

[0674] Increase g until the RF detector shows an oscillation mode, and then slightly 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 to frequency. If the RF detector still exhibits 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 simultaneously move from the active state to the extinction state. From the shape of G(g), we know

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 because you only need a gradient along the direction of the g and f variations. The gradient is found numerically by dithering g and f by small amounts.

[0682] This is more difficult with variable multipath and variable antenna impedance, as the SNR fluctuates randomly. If the multipath and antenna impedance are slowly changing, we can assume they are quasi-static and complete iterations 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 variation is 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 provide a vector of f and g settings as a function of hopping frequency. One calibration procedure can calibrate each hopping frequency as if it were a single frequency. However, other, more efficient procedures may also be used.

[0685] An obvious improvement would be to calibrate the frequencies in order 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 a first guess for the next higher frequency.

[0686] It is clear that the parametric curves for g (frequency) and f (frequency) are then fairly smooth. Spline interpolation can be used to combine calibration data. This may be more useful in tracking. In tracking, SNR is again used. The problem is that the SNR available to the ATLF transceiver can be highly frequency-dependent in areas of multipath. Therefore, dithering only makes sense when comparing specific frequencies. This means that the dithering calculation of the numerical gradient must wait until a specific frequency appears. If multipath varies in time more than the convergence time of the SNR optimization, the ATLF bandwidth must be opened so that more SNR data is available. This is a compromise, as the ATLF only provides optimal matching for segments of the tuning range, not individual frequencies. The innovation here is the choice of this matching for the size of the frequency segments and the number of segments to actively track.

[0687] This grouping does not work well when the multipath frequency changes rapidly. In conclusion, grouping hopping frequencies relative to the coherence bandwidth of the multipath channel is preferable 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 quite limiting, the optimization algorithm only needs to keep up with changes in antenna impedance and 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 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 it as having three states:

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

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

[0696] For multi-frequency sensors, calibration is done in the same way, but for each of the aforementioned hopping frequencies. We assume that commissioning provides a procedure that handles calibration in an efficient way, such as using spline fitting, 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, a self-calibration step can be performed 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 at a specific frequency. When a packet arrives, it displays 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 as needed. If necessary, you 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, once the LUT entries are accurate and receive performance is optimal, you exit acquisition mode.

[0698] Tracking phase: Upon completion of acquisition, self-calibration based on self-oscillation is no longer necessary and the system may enter track mode. This means that only SNR is used to fine-tune the ATLF during reception. SNR tuning is very low power, but requires a series of data packets because a stochastic gradient method is used. Such stochastic gradient determination requires dithering, which results in slight degradation of ATLF tuning. As discussed, if the coherence bandwidth or coherence time is too short, the SNR gradient estimation becomes unreliable and noisy, preventing track mode from working. In this case, the system 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 acquisition energy is too high, there is an option to control the bandwidth to achieve acceptable average results for a segment of the hopping frequency band. That is, instead of retuning the ATLF for each specific frequency hopping packet, the frequency hopping band can be grouped into two or three segments. The ATLF uses a wider bandwidth. Because packets for a group of hopping frequencies occur more frequently than for individual frequencies, there is now significantly more data available. Therefore, 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] ATLn and ATLF runtime calibration

[0704] Next, consider runtime 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 in which a transceiver chip wakes up every second, transmits a data packet on a specific frequency, and then goes back to sleep. If ATL1b is used in mode 3 (Figure 150) for transmission, mode 4 (Figure 151) may be run a few milliseconds before transmission to precisely set the control voltage of ATL1b based on the ATL1a VCO set to the transmit frequency. Then, just before transmission, the ATLF is reconfigured for mode 3 (Figure 150) with ATL1b precisely tuned in frequency. A receive mode is generally required so that the bandage sensor can be controlled to a) what to transmit, b) when to transmit, and c) on which frequency channel. To conserve power, the receiver typically wakes up at a predetermined time based on the radio telemetry protocol being used. Before the receive mode epoch mode 4 (Figure 151) is configured, ATL1b is VCO-set at the expected receive frequency. The ATL1a control is dithered to properly center the passband and have 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 should be done periodically. The problem is that calibration requires additional battery energy, which should also be minimized. For every calibration measurement, the LUT may be annealed with new information. Thus, 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 performed only at the receiver MOD. Depending on the baseband processing, there is generally some utility for measuring signal quality. This is likely the result of some clocking phase tracking loop for optimal demodulation of the communications signal. The control voltage can be dithered to optimize this demodulation process.

[0708] ATLF self-calibration overview

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

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

[0711] Dynamically change coefficients in response to changes in the antenna environment, changes in circuit temperature, or other influences 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 resonance matching, which is the output of the ATLF self-calibration process, accomplishes several goals simultaneously. As explained above, matching components are eliminated, which not only reduces the part count by eliminating the need for matching components, but also eliminates the losses associated with more typical impedance matching. Simply put, 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's radiated power and the transmitted 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 across the entire tuning bandwidth of the ATLn.

[0714] This ATLF optimization is not a compromise for best match that can be achieved with a small number of discontinuous matching components. This becomes more 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 for best match at 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] Conjugate antenna impedance matching network (ATLF) based on vertical integration of ATL.

[0720] The 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 was 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 over time as scattering objects in the near field change.

[0723] In the case of ATLn, it is possible to consider a calibration look-up table (LUT) for coarse control and use SNR measurements 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 through SNR optimization. Essentially, the more information that can be stored in the LUT, the fewer fine-tuning adjustments that need to be made in runtime control. The LUT can be constructed as an initial calibration step or developed at runtime as a priority. Regardless of the step, as the calibration matures and the LUT becomes more accurate, the emphasis on runtime control becomes less important. Calibration can be thought of as a form of supervised learning, where the labeled data used for training is the output of a communication process. At runtime, after a coarse adjustment by the LUT, the objective of maximizing SNR drives the control. Feedback from this process regarding 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, creating three very different cases for ATLF control. These cases are discussed: static, quasi-static, and dynamic antenna impedance.

[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 perspective of an ATLn control with static input and output port impedances. In this case, the ATLF LUT can be pre-calibrated or accumulated over time. Ultimately, only the unmodeled components of the LUT need to be tracked based on the SNR optimization procedure. For example, if the LUT does not include provisions for temperature fluctuations, the ATLF control will track slow fluctuations. Note that multipath frequency selectivity may occur between a static sensor and reader, but does not affect the antenna impedance because the effect of a moving reader is small from the perspective of moving scattering objects.

[0727] Quasi-static antenna impedance: Consider a sensor mounted on some equipment outdoors, where temperature and humidity variations can be significant, affecting the antenna impedance. One method of control is to build a high-dimensional LUT that takes these environmental effects into account. Assuming a sufficiently sophisticated LUT, there is no difference compared to the static case. However, if calibrating a high-dimensional LUT is impractical, 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), meaning 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 cause significant changes in the antenna impedance. If the signal to be demodulated is largely unknown, only the SNR can be used for optimization. If the signal structure is known, a more powerful optimization process can be implemented to make the optimization faster and more robust. However, this more sophisticated process requires energy. Therefore, at some point, the energy saved by more optimal tuning of the ATLF is more than offset by the additional increments of energy required for processing.

[0729] For the ATLF to be successful in these cases, the following mechanisms are required: First we build the LUT so that the 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 for the static antenna impedance case is that it is likely to be fully self-calibrating once attached to the antenna, sensor, etc. For example, a pipeline sensor installation can be as simple as placing the sensor on the pipe from its packaging, then initiating a self-calibration algorithm that builds a route. If the LUT is satisfactory, it can be put into service. A mechanism to detect the need for recalibration (if the runtime SNR optimization is not sufficient for tracking, or if the optimization is off track) is part of the control algorithm so that the sensor can always return to its initial self-calibration mode.

[0731] Clearly, it is impossible to describe the installation, commissioning, and use of every conceivable sensor in the required algorithms. Instead, we will focus on the calibration tools that must be incorporated. This is similar to a transceiver chip in a cell phone. It consists primarily of hardware processing blocks that perform different functions with associated software drivers. The smartphone designer must then generate a "main program" that calls all the subroutines that call the hardware processing blocks, targeting the final application target. This integration is not a trivial task, and this is where power consumption minimization comes in. There are application-specific questions that the system designer must address. Setting the parameter for the duration of the first ATLF calibration Specify the required precision for the LUT before releasing it at runtime Allows runtime calibration feedback data to affect LUT values If this change continues over time If the ATLF needs to be periodically recalibrated 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 locus is central to visualizing the mechanism of the ATLF. As explained above, if s = jω is a complex frequency, then we have H0L(s) as the open-loop response of the resonator, the antenna reflection coefficient Γa, and any loop parasitics such as the propagation delay and phase shift of the gain block. 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 by g and the polarity control denoted by p. Also, G is frequency independent. Therefore, we assume that we factorize H0L(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 fH(s|g,p,f), where the function H(s) is tuned with respect to the parameters g, p, and f, is the function to which the open-loop response will continue 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 not a function of either the frequency s or 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 a dependence 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 accommodate the frequency variation of the gain block, but it cannot accommodate the degree to which the frequency variation varies with p or g. The approximation is reasonable to a first order approximation, but the implications must be understood.

[0738] The motivation for factorization is that it yields a clear Nyquist plot from which fundamental behavior can be extracted. Consider the initial introductory figure 130, where the left contour represents the Nyquist locus when the system is calibrated, and the black dots represent 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 1 / G operating point and is based on the g and p settings. As mentioned above, the operating point is based on criteria. It must lie outside the outer circle of the Nyquist locus for stability. The closer to the Nyquist plot, the higher the Q enhancement. On the negative real axis segment, as g increases, 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, approaching the origin. Eventually, g becomes so large that the operating point crosses the Nyquist locus, which is a point of infinite-Q enhancement and also a point of instability.

[0739] Now consider a small change in antenna impedance (or other effect) that 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 characteristic, which can be sketched as shown in Figure 131, with a significant reduction in Q enhancement and a shifted 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] An even worse scenario is when the ATLF becomes unstable with changes in antenna impedance, as shown in Figure 132. Figure 132 shows the Nyquist locus during actual operation 13210, the Nyquist locus during initial calibration 13212, the initial operating point 13214, and the new operating point during operation 13216. As shown, the left contour in Figure 132 shifts to the left so that the Nyquist contour surrounds the operating point. Now, the ATLF becomes unstable and begins to oscillate, typically at a frequency independent of the desired signal. With sufficient Q enhancement, the operating point remains relatively close to the Nyquist locus, and even slight perturbations in the antenna impedance always pose a risk of oscillation. From this Nyquist plot visualization, the objective of the ATLF control algorithm can be clearly stated.

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

[0742] An idealized ATLF consisting of a non-reactive antenna and a loop with controllable delay.

[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] Here, the delay T monotonically decreases as f increases. The Nyquist locus has a radius, G(g)r. Therefore, there is a redundant specification regarding the radius. We know that oscillations occur when G(g)r ≥ 1 at some frequency. In reality, G(g)r cannot exceed unity because the oscillation amplitude becomes large and the gain block begins to saturate. For control purposes, we assume 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, without any scaling offset. The shape may be known to within a few percent from the chip design, which is accurate enough. However, because there is a small difference between a highly Q-enhanced stable state and unstable oscillations, we need to know the scaling very accurately. Therefore, this scaling can only be realized through calibration. To simplify control, we arbitrarily assume that r is exactly unity and that the difference is absorbed by G. We can now meaningfully scale G via calibration: G(g) = 1 for values ​​of g that just initiate oscillation conditions. Then, if we know the shape of G(g), we 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 when oscillations occur, the frequency can in principle be measured accurately relative to the clock crystal time. Thus, the frequency of oscillations is given by a fuzzy probability:

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[0746] In this idealistic ATLF, consisting of pure delays, an infinite set of all frequencies is possible. However, a practical ATLF would only have an open-loop response sufficient for the desired tuning range. Therefore, we assume that only one frequency component is active. If baseband processing following the ATLF were sufficient, we could envision a wideband Fourier-based analysis in which the oscillation frequency could be observed immediately after downconversion. However, this is not consistent with the very low-power processing considered inherent in ATLF-based network sensor applications. A suitable circuit may be a diode power-detection circuit, as shown in Figure 133.

[0747] Here, there is an RF diode power detector immediately following the ATLF, which is wide enough to detect oscillations within the ATLF's tuning range. The ADC can be a simple 1-bit threshold comparator. Because this detector is wideband but does not need to respond quickly, detector circuits using ADCs consume very little power. The ATLF output is typically downconverted for further processing to baseband to demodulate and decode the signal. This may be completed at a zero IF, a near IF, or a full IF stage before...

Claims

1. A communication circuit, comprising: an antenna block for receiving a desired electromagnetic signal; a signal loop including an input port, an output port, and a signal conditioning block between the input port and the output port, the antenna block being in bidirectional communication with the input port of the signal loop, the signal conditioning block applying a phase shift and a gain factor to the desired signal; a controller block configured to adjust the phase shift and the gain factor of the signal conditioning block to improve a signal quality factor of the desired signal from the antenna block. Communication circuit.

2. The communications circuit of claim 1 , wherein the signal conditioning block includes one or more variable frequency resonators and a gain block that applies the gain factor.

3. The communication circuit of claim 2 , wherein the controller block adjusts the phase shift by adjusting the one or more variable frequency resonators.

4. The communications circuit of claim 2 , wherein the antenna block includes an antenna having an impedance, and the controller block controls the signal conditioning block to match the impedance of the antenna block.

5. The communications circuit of claim 1 , wherein the signal quality factor comprises 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.

6. The communication circuit of claim 5 , wherein the controller block adjusts the gain factor to improve the signal-to-noise ratio or to modify a bandwidth of the desired signal.

7. The communications circuit of claim 1 , further comprising a receiver block that receives the desired signal from the signal conditioning block and processes the desired signal.

8. 8. The communications circuit of claim 7, wherein the desired signal is modulated onto a carrier and the receiver block includes a demodulator.

9. The communication circuit of claim 1 , further comprising a bidirectional coupling element connected to the antenna block and the signal conditioning block.

10. 8. The communication circuit of claim 7, wherein the communication circuit has an impedance, and the signal conditioning block adjusts the impedance of the communication circuit to enhance available energy transferred from an antenna of the antenna block to the receiver block.

11. 4. The communication circuit of claim 3, wherein the signal loop includes an encoder that encodes a data stream to be transmitted by the antenna block onto a return path from the signal loop to the antenna block.

12. The communications circuit of claim 11 , wherein the encoded data stream on the return path is provided by a sensor.

13. The communications circuit of claim 11 , wherein the signal conditioning block includes a negative impedance element and a phase shifter element.

14. 2. The communications circuit of claim 1, wherein the signal conditioning block includes a phase shifter that applies the phase shift and a gain block that applies the gain factor.

15. The communication circuit of claim 1 , wherein the controller block is configured to improve the signal quality factor by varying the gain factor between positive and negative values.

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