Method and apparatus for calibrating a capacitive resonator - Patents.com

Abstract

1. A method of calibrating a resonator having a resonator member vibrating in a first vibration mode and a calibration electrode spaced from and capacitively coupled to the resonator member, comprising: 1. A method comprising: applying a polarization voltage to a resonant member and a calibration voltage to a calibration electrode, the polarization voltage being a negative voltage; vibrating the resonant member such that the resonant member vibrates in a first vibration mode; measuring a frequency parameter of the resonant member; determining whether the frequency parameter complies with a predetermined threshold; and if the frequency parameter does not comply with the predetermined threshold, adjusting the frequency parameter to comply with the predetermined threshold by adjusting at least one of the polarization voltage and the calibration voltage.

Description

[Technical field]

[0001] FIELD OF THE DISCLOSURE This application relates generally to capacitive resonators, and more particularly to a method and apparatus for calibrating capacitive resonators. [Background technology]

[0002] Many conventional micro-electro-mechanical (MEMS) resonators are physical structures designed to vibrate at high frequencies. Such resonators can be incorporated into a variety of devices, such as timing oscillators, mass sensors, gyroscopes, accelerometers, switches, and electromagnetic fuel sensors, among others. MEMS resonators play an important role in a variety of applications, including mass sensing, timing reference applications, inertial sensing, and filtering applications. Summary of the Invention [Problem to be solved by the invention]

[0003] A resonator typically includes a resonating member capable of vibrating in one or more modes. In applications such as gyroscopic sensing, two modes are utilized: a drive mode and a sense mode. For example, the drive mode vibration can correspond to a linear vibration along a first axis, and the sense mode vibration can correspond to a linear vibration along a second axis that is generally perpendicular to the first axis. The resonator may further include a plurality of drive electrodes spaced apart from and capacitively coupled to the resonating member. A voltage may be applied to the one or more drive electrodes to excite the resonating member such that the resonating member vibrates in its drive mode and at a particular frequency. When the resonating member rotates, the Coriolis effect transfers energy from the drive mode to the sense mode, causing the resonating member to vibrate in the sense mode. In general, it is desirable to match the frequencies of the drive mode and the sense mode, as this tends to increase the signal-to-noise ratio of the resonator. However, due to imperfections or other errors introduced during the manufacturing process of the resonator, the frequencies may differ from one another. It is therefore desirable to calibrate the resonator after manufacturing to compensate for these errors so that the resonator can operate in a mode-matched state. [Brief description of the drawings]

[0004] The above and other aspects of the present invention will become apparent to those skilled in the art to which the present invention pertains upon reading the following description in conjunction with the accompanying drawings. [Figure 1] FIG. 2 is a schematic diagram of an exemplary resonator and control system. [Diagram 2] 13 is a graph showing how the stiffness change of a resonator can vary as a function of polarization voltage and calibration voltage. [Diagram 3] 13 is another graph showing how the stiffness change of the resonator can vary as a function of the polarization voltage and the calibration voltage. [Figure 4] 4 is a graph showing the slope / derivative of the curves of FIG. 3. [Diagram 5] FIG. 2 illustrates an exemplary circuit for a control system of a resonator. [Figure 6]FIG. 2 illustrates a regulated charge pump feedback loop of the circuit. [Figure 7A] FIG. 2 illustrates one exemplary embodiment of a charge pump in a regulated charge pump feedback loop. [Figure 7B] FIG. 2 illustrates a clock generation circuit for a regulated charge pump feedback loop. [Figure 8] FIG. 2 illustrates another exemplary embodiment of a charge pump in a regulated charge pump feedback loop. [Figure 9] FIG. 1 is a cross-sectional view of an integrated circuit for a regulated charge pump feedback loop. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0005] Exemplary embodiments are described and illustrated in the drawings. These examples are not intended to limit the invention. For example, one or more aspects may be utilized in other embodiments and even other types of devices. Moreover, certain terminology is used herein for convenience only and should not be construed as limiting.

[0006] 1, an exemplary capacitive transduction resonator 10 corresponding to a gyroscope sensor is shown. The resonator 10 includes a substrate 12, a cylindrical anchor 14 fixed to the substrate 12, a resonator member 16 supported by and extending radially outward from the anchor 14 so as to be suspended above the substrate 12, and a number of electrodes 18 spaced apart from and surrounding the resonator member 16. The electrodes 18 are capacitively coupled to the resonator member 16 and include a number of drive electrodes 18a, a number of sense electrodes 18b, and a number of calibration electrodes 18c.

[0007] The resonant member 16 is flexibly supported by the anchors 14 such that it can vibrate in two resonant modes: a first (e.g., drive) mode and a second (e.g., sense) mode. In this embodiment, the drive mode vibration corresponds to a radial vibration along a first axis X, and the sense mode vibration corresponds to a radial vibration along a second axis Y that is substantially perpendicular to the first axis X (e.g., such that axes X, Y are orthogonal to within 10°, and preferably within about 5°). However, the drive mode vibration and the sense mode vibration can correspond to other types of vibration and / or other vibration directions in other embodiments. Indeed, the resonant member 16 may be vibrated in any number and type of one or more modes without departing from the scope of the present disclosure.

[0008] The modal vibrations can be actuated by applying a voltage to the resonant member 16 and / or one or more electrodes 18. For example, a voltage can be applied to one or more drive electrodes 18a, thereby exciting the resonant member 16 to vibrate in a drive mode and at its inherent drive mode frequency. Similarly, a voltage can be applied to one or more sense electrodes 18b, thereby exciting the resonant member 16 to vibrate in a sense mode and at its inherent sense mode frequency. Applying a voltage to the resonant member 16 and / or one or more calibration electrodes 18c can also induce or affect the drive and / or sense mode vibrations.

[0009] In one embodiment, the resonator 10 can be positioned in a first orientation (e.g., as shown in FIG. 1 ) and a drive voltage can be applied to one or more drive electrodes 18a, which applies a drive force to the resonant member 16 to excite the resonant member 16 to vibrate in the drive mode and at its natural frequency. When the resonant member 16 is rotated to a different orientation, the Coriolis effect transfers energy from the drive mode to the sense mode, causing the resonant member 16 to vibrate in the sense mode. Additionally, the sense electrode 18b is configured to generate a current in response to the sense mode motion of the resonant member 16. This current can be analyzed to determine the rotational speed of the resonant member 16.

[0010] It should be understood that the resonator 10 described above may have alternative configurations without departing from the scope of the present disclosure. Additionally, the resonator 10 may be configured for other applications besides gyroscopic sensing. For example, the resonator 10 may be incorporated into various devices such as timing oscillators, mass sensors, accelerometers, switches, and electromagnetic fuel sensors. In general terms, the resonator 10 may have any configuration having a resonating member capable of vibrating in one or more modes and a number of electrodes operable to vibrate the resonating member, the electrodes including at least one drive electrode and at least one calibration electrode.

[0011] In gyroscope sensing applications, it is generally desirable to vibrate the resonator 10 in two vibration modes (e.g., drive mode and sense mode) that have matching frequencies of vibration, as this tends to increase the signal-to-noise ratio of the resonator 10. However, due to imperfections or other errors introduced during the manufacturing process of the resonator 10, the frequencies may differ from each other. Thus, to compensate for these errors, the resonator 10 may be calibrated after manufacture so that it operates in a mode-matched state. To this end, the inventors have developed a novel and useful method and apparatus for calibrating the resonator 10 so that the frequencies of its drive mode vibration and sense mode vibration are substantially similar.

[0012] More specifically, a control system 30 can be provided that includes a programmable controller 32 operably coupled to the resonant member 16 and the electrodes 18 (e.g., via circuitry and wiring). The control system 30 can further include one or more measurement devices configured to measure one or more parameters of the resonator 10 (e.g., voltage, current, frequency of vibration in a particular mode, stiffness of a vibration mode, cross stiffness of two vibration modes, etc.). For example, the control system 30 in this embodiment includes a measurement device 34 (e.g., a network analyzer, a lock-in amplifier, or a portion of an integrated circuit) configured to measure the frequency difference between the sense mode vibration and the drive mode vibration of the resonant member 16. Each measurement device can be operably coupled to the controller 32 to communicate its measured parameter to the controller 32. Additionally, each measurement device can be operably coupled to the resonant member 16 and / or the electrodes 18 as needed to measure its respective parameter.

[0013] The controller 32 may be programmed to perform a calibration process that adjusts the frequency parameters of the resonator 10, preferably so that the resonator 10 operates in a mode-matched condition. During this process, the controller 32 may initially operate the resonator 10 such that the resonant member 16 vibrates in both vibration modes. For example, the controller 32 may apply a voltage to one or more drive electrodes 18a such that the resonant member 16 vibrates in a drive mode, and another voltage to one or more sense electrodes 18b such that the resonant member 16 vibrates in a sense mode. The controller 32 may then control the polarization voltage V p to the resonant member 16, and the calibration voltage V cal may further be applied to one or more calibration electrodes 18c.

[0014] The resonator member 16 is vibrating in both modes and the polarization voltage V p and the calibration voltage V cal is applied to the resonator 10, the controller 32 controls the frequency parameter f of the resonator member 16. p(For purposes of this disclosure, a "frequency parameter" of a resonant member may refer to the frequency of one of two vibrational modes, the frequencies of both vibrational modes, the frequency difference between the two frequencies, or any other parameter or parameters indicative of said frequency, frequency, or frequency difference). For example, in this embodiment, the controller 32 operates a measurement device 34 that measures the frequency difference between the two vibrational modes of the resonant member and sends an output indicative of the frequency difference to the controller 34. In other embodiments, the controller 32 may operate a separate measurement device that measures the frequency of each respective vibrational mode and provides an output indicative of the frequency to the controller 32. The controller 32 may then calculate the frequency difference between the two vibrational modes.

[0015] The controller 32 then calculates a frequency parameter f p It may be possible to determine whether the frequency parameter f complies with a predetermined threshold. For example, the controller 32 in this embodiment determines whether the frequency difference between the two vibration modes is less than or equal to a predetermined maximum threshold. The maximum threshold may be a fixed value (e.g., 0.1 Hz) or the maximum threshold may be a function of some other variable (e.g., 0.1 ppm of the frequency of the drive mode vibration). In other examples, the frequency parameter f p corresponds to the frequencies of the two vibration modes, the controller 32 can determine whether the ratio of the two frequencies is within a predetermined threshold range (eg, 0.8 to 1.2).

[0016] Frequency parameter f p does not comply with the predetermined threshold, the controller 32 adjusts the frequency parameter f p One or more calibration parameters of the resonator 10 can be adjusted (for purposes of this disclosure, a “calibration parameter” of a resonator is defined as a frequency parameter f p (This refers to any parameter of the resonator that can be adjusted to affect the drive mode k, which can be varied based on certain parameters, such as:d The stiffness can be.

[0017]

number

[0018] Here, Δk d is the stiffness change of the drive mode k d , χ is the proportionality constant of the resonating member 16, V p is the polarization voltage applied to the resonator member 16, V cal is the calibration voltage applied to one of the calibration electrodes 18c.

[0019] Figure 2 shows the stiffness change Δk d is the polarization voltage V p and the calibration voltage V cal In particular, curve 50 shows how the polarization voltage V p is set to 15.0 volts, and the calibration voltage V cal The stiffness change Δk when increases from 0 volts to 15 volts d can vary, and curve 52 shows how the polarization voltage V p is set to 17.5 volts, and the calibration voltage V cal The stiffness change Δk when increases from 0 volts to 15 volts cal can vary, and curve 54 shows how the polarization voltage V p is set to 20 volts, and the calibration voltage V cal The stiffness change Δk when increases from 0 volts to 15 volts d The y-axis values ​​show how the maximum stiffness change Δk d is 1, the minimum stiffness change Δk d is normalized to be 0. Therefore, the stiffness k d and the amount of change is the polarization voltage V p and the calibration voltage V cal By adjusting these voltages, the stiffness k d and the amount of change can be changed. Furthermore, the stiffness k d By adjusting the frequency parameter f of the resonator member 16,p can be changed.

[0020] Polarization voltage V p and the calibration voltage V cal is the frequency parameter f of the resonator member 16 p It should be understood that other calibration parameters that affect the calibration voltage V may be affected as well. cal Depending on the position of the calibration electrode 18c to which the polarization voltage V p and the calibration voltage V cal can similarly affect the stiffness of the sensing mode, or the cross stiffness between the drive and sensing modes, thereby affecting the frequency parameter f of the resonating member 16. p can also have an impact on

[0021] In this manner, the controller 32 controls the frequency parameter f p The polarization voltage V p and the calibration voltage V cal may be adjusted to adjust one or more calibration parameters of the resonator 10. In addition, the controller 32 also controls the frequency parameter f p During this process, one or more other voltages or other parameters may be adjusted to adjust the frequency parameter f p It should be appreciated that the frequency parameter f can be influenced by the controller 32. p The polarization voltage V p and the calibration voltage V cal The control circuitry may be programmed to perform any number and / or series of adjustments, including adjusting one or both of the control circuitry.

[0022] As a result of the above calibration process, the drive mode frequency and the sense mode frequency are preferably approximately equal to each other (for purposes of this disclosure, two frequencies are "approximately equal" if the ratio of the frequencies is between 0.8 and 1.2). In some embodiments, the calibration process results in the drive mode frequency and the sense mode frequency being closer to each other in part by a predetermined threshold. For example, the frequency difference between the drive mode frequency and the sense mode frequency after calibration can be about 1% or less of the frequency difference between the drive mode frequency and the sense mode frequency before calibration.

[0023] In some embodiments, the controller 32 may include a plurality of calibration parameters and / or a frequency parameter f p It should be appreciated that the calibration process in some embodiments may be programmed to adjust the polarization voltage V to ultimately calibrate the drive mode frequency and the sense mode frequency. Additionally, it should be appreciated that the calibration process in some embodiments may be designed to result in a larger frequency difference between the drive mode frequency and the sense mode frequency. Additionally, in embodiments having a single vibration mode, the controller 32 may adjust one or more calibration parameters to adjust the frequency of that single mode to comply with a predetermined threshold. Broadly speaking, the controller 32 may adjust one or more calibration parameters to adjust the polarization voltage V p and the calibration voltage V cal At least one of the frequency parameters f p , and cause them to comply with one or more predetermined thresholds.

[0024] Referring again to FIG. 2, an improvement to the above calibration process will be described. As can be seen, the stiffness change Δk cal is initially the calibration voltage V cal increases with but eventually levels off, allowing for a larger calibration voltage V cal Even if the stiffness change Δk cal Therefore, the effect on the calibration voltage V cal Increase the stiffness k calThe range in which the polarization voltage V can be adjusted is limited. p The range can be amplified by increasing the polarization voltage V (for example, from 15 to 20 volts), but this is not possible with a higher polarization voltage V cal increases the noise and power consumption of the resonator 10 and is therefore generally undesirable.

[0025] Generally, the calibration voltage V cal Stiffness change Δk according to d Therefore, in order to calibrate the resonator 10, it is desirable to maximize the stiffness k cal Furthermore, in order to reduce the noise and power consumption of the resonator 10, a larger range of adjustment can be made to the polarization voltage V p and the calibration voltage V cal However, as can be seen in Fig. 2, the stiffness change Δk cal is typically the polarization voltage V p and the calibration voltage V cal These goals are typically in conflict with each other since the

[0026] We apply a negative polarization voltage V p By applying a polarization voltage V p and the calibration voltage V cal While minimizing the stiffness change Δk cal More specifically, FIG. 3 shows the same curves 50, 52, 54 of FIG. 2, but at a polarization voltage V p is set to -5.0 volts, and the calibration voltage V cal When increases from 0, the stiffness change Δk cal The y-axis value further includes a curve 56 showing how the maximum stiffness change Δk cal is 1, the minimum stiffness change Δk cal is renormalized to be 0.

[0027] As can be seen in FIG. 3, the slopes of the curves 50, 52, and 54 vary with the calibration voltage V cal This is because the larger the calibration voltage V calThis means that the efficiency of the calibration decreases as more calibration voltage V is required. Conversely, the slope of curve 56 decreases as the calibration voltage V cal increases, which is due to the negative polarization voltage V p This means that the efficiency of the calibration is better when using the calibration voltage V cal By increasing the stiffness change Δk cal The stiffness change Δk can be increased cal is the calibration voltage V cal 54. Also, for curve 56, the specific calibration voltage V cal Stiffness change Δk cal Similar or larger values ​​of can be realized, but the polarization voltage V p In fact, for curve 56, the absolute value of the stiffness change Δk cal is the calibration voltage V beyond that shown in Figure 3. cal 5. The curves 50, 52, and 54 in FIG.

[0028] The above effect is due to the calibration voltage V cal 4 which shows lines 60, 62, 64, 66 corresponding to the slopes / derivatives of curves 50, 52, 54, 56 of FIG. 3 with respect to

[0029] Therefore, the resonator member 16 is subjected to a negative polarization voltage V p By applying the calibration voltage V cal Stiffness change Δk according to d can be maximized while at the same time the polarization voltage V p and the calibration voltage V cal can also be minimized, thereby maximizing calibration efficiency while minimizing noise and power consumption. Furthermore, similar effects can be realized for other calibration parameters, such as the stiffness of the sensing mode or the cross stiffness of the two modes, which also depend on the polarization voltage V p and the calibration voltage V cal It should be understood that the polarity of the resonator member 16 is a function of the polarity of the resonator member 16. pBy applying the calibration voltage V cal The variation of these calibration parameters can be maximized according to the polarization voltage V p and the calibration voltage V cal can also be minimized.

[0030] Turning to FIG. 5, the controller 32 generates a negative polarization voltage V p An exemplary circuit 100 is now described that allows for applying a polarization voltage V to the resonant member 16. The circuit 100 may be the controller 32 itself, or the circuit 100 may be operatively coupled between the controller 32 and the resonant member 16. The circuit 100 applies a polarization voltage V to each calibration electrode 18c. P and the calibration voltage V T1 , V T2 , V QA , V QB The reference voltage Vref may include a DC reference circuit 102 configured to generate a DC reference voltage Vref.

[0031] In some embodiments, the positive programmable charge pump circuit provides a calibrated voltage V T1 , V T2 , V QA and V QB while the negative charge pump circuit may be configured to generate a polarization voltage V P , all of which are generated from a standard power supply voltage, for example up to 3 V. P and the calibration voltage V T1 , V T2 , V QA and V QB may be generated by a circuit 102, the output of which may be connected, for example, to any number of electrodes 18 of the resonator 10 (implicit connecting wires not shown). P may be controlled to provide negative values ​​in the range of −2.0 volts to −10.0 volts, and the calibration voltage V T1 , V T2 , V QA and V QBmay each be configured to provide a voltage value in the range of 0 volts to 15.0 volts.

[0032] The circuit 102 may include a negative charge pump circuit, as described further below. Unlike the positive charge pump operation, the reverse bias scheme is implemented through the negative charge pump circuit by inverting the diodes such that they turn on only when the voltage is greater than the previous voltage. In this manner, the diodes may be configured to turn on when the capacitors accumulate charge or voltage in the opposite direction. Thus, the negative charge pump circuit is configured to implement a reverse bias, and a negative polarization voltage V p The biasing scheme may include multiple stages that allow the voltage to be pumped down to a desired negative value to obtain a bias voltage of 0.01 V. This biasing scheme prevents the transistors from operating in an undesirable manner.

[0033] Figure 6 shows a regulated charge pump feedback loop circuit 108 that is part of the circuit 102 of Figure 5. The circuit 108 may include a charge pump 110, a resistive voltage divider 112 for negative feedback in the regulation loop, a reference voltage generator 114, a feedback loop error amplifier 116, a clock generation circuit 118, and a ring oscillator circuit 120.

[0034] Charge pump 110 uses its input clock to generate an input voltage V to charge circuit elements including, but not limited to, one or more capacitors C1, C2, C3 within charge pump 110. in (e.g., 2.5 volts DC) to get the output voltage V cp and may be configured to transfer charge from the output to the input (the opposite of a positive charge pump, where charge moves from the input to the output). cp is the polarization voltage V p and can therefore be applied to the resonator member 16 for calibration purposes. cpR is defined by the variables M and N, which are functions of resistor ratios, where M=1-R1 / R2, and N=R1 / R2. Without feedback, charge pump 110 can generate an output voltage V without regulation up to large voltage levels, which may depend on the number of stages in charge pump 110, the clock amplitude, the clock frequency, and other internal losses. cp may be configured to pump

[0035] The feedback loop is connected to V through a resistor divider 112. cp The divided voltage of is supplied to the error amplifier 116 to obtain the output voltage V cp The error amplifier 116 may be configured to adjust this voltage relative to the reference voltage V generated by the generator 114. ref 6, the output of the error amplifier 116 may be configured to drive a clock generation circuit 118 to control the amplitude of a clock in the charge pump 110. The frequency of the clock may include a fixed frequency derived by a ring oscillator circuit 120.

[0036] As shown in FIG. 7A, the charge pump 110 includes transistors M1, M2, M3, . . . , M n , N1, N2, N3, . . . , N n are the associated capacitors C1, C2, C3, ..., C in any number of stages such as stg1, stg2, stg3, ..., stgn, and the output stg. n The charge pump 110 may be connected to a capacitor C 1-n Multiple clocks Φ as respective inputs to 1-n In addition, the connections on the NMOS transistors of the charge pump 110 are reversed. To achieve reverse biasing, the transistors M1, M2, M3, ..., M n This inverted connection of the capacitor C 1-n and converts the charge into an output voltage V outThis change in inverting connection may be implemented for all stages in charge pump 110 so that charge flow moves in the opposite direction instead of inverting the diode connection. Thus, this change in inverting connection reverses the diode connection, which reverses the current flow.

[0037] Capacitor C 1-n may be alternately driven by clock Φ or the opposite polarity of the clock. As an example, capacitor C1 may be driven by clock Φ1, capacitor C2 may be driven by Φ2 with the opposite polarity of clock Φ1, etc., resulting in being pumped in opposite directions to sequentially move charge in a path from the input to the output of charge pump 110. As an example, the opposite polarity of clock Φ may be derived by pushing clock Φ through an inverter (not shown). The final stage or output stg may comprise a rectifier stage that conducts for half a clock cycle, converting the output of the previous stage from a clock waveform to a DC voltage.

[0038] As shown in FIG. 7B, the clock generation circuit 118 may include a voltage doubler circuit that utilizes a flying capacitor. For this charge pump application, the clock generation circuit 118 generates a voltage V oa In addition, the input and output clocks of the clock generation circuit 118 may include non-overlapping clocks to avoid turning on all stages in the charge pump 110 simultaneously and causing reverse current leakage. In particular, the input voltage V (from the operational amplifier, or error amplifier 116) oa may be configured to control the output clock of the clock generation circuit 118. The amplitude of the output clock is determined by the voltage V oa The amplitude of the input clock is equal to the amplitude of the input clock plus

[0039] Resistive voltage divider 112 is V DDand the output of the charge pump 110, and includes a first resistor R1 in series with a second resistor R2. As an example, the sum of the values ​​of the first resistor R1 and the second resistor R2 is designed so that they do not draw excessive current, and in some cases, the sum of the values ​​may exceed 9 MΩ. However, such a large resistor may cause stability problems in the feedback loop due to a low frequency pole formed by the first resistor R1, the second resistor R2, and the input capacitance of an operational amplifier such as the error amplifier 116. To solve the stability problem in the feedback loop, a capacitor may be included to create a zero in the loop transfer function and restore a proper phase margin to the feedback loop. For example, a capacitor may be added in parallel with a portion of the first resistor R1. Additionally, the input of the error amplifier 116 is connected to a node between the first resistor R1 and the second resistor R2. As a result of the resistive voltage divider 112, the voltage at that node (V cp ) is fed to the error amplifier 116, which then converts it to a reference voltage V ref and amplifying the difference, and the amplified difference (V oa ) represents the output of operational amplifier 116 which drives clock generation circuit 118. Thus, charge pump 110 generates voltage V cp Reference voltage V ref , or may be configured to pump up or down to adjust the V (via a path including R2) to a multiple of DD The connection to is for the negative charge pump.

[0040] FIG. 8 illustrates another exemplary embodiment of the charge pump 110. As shown in FIG. 8, the stages of the charge pump 110 are provided with well bias connections. The output of each stage (stg1) of the charge pump 110, which is a clock waveform, may be conditioned by a filter, such as an RC filter, to generate a DC bias voltage that is connected to a local p-well (not shown, but see FIG. 9 described below). The RC filter may be connected to the output of the next stage (such as stg2). In some embodiments, filtering the output of each stage with an RC filter is not required. Since the last stage is lossy (its input-to-output DC drop creates losses), an additional parallel pump stage may be added to generate the voltage Vwell. Because the same Vwell bias voltage generation method would turn on a parasitic PWELL_N+ diode, which may create leakage current. As further shown in FIG. 8, the bulk or local p-well node 130 may be connected to the output of the subsequent stage.

[0041] 9 illustrates a cross-sectional view of an exemplary integrated circuit 131 for the regulated charge pump feedback loop circuit 108. The integrated circuit 131 forms two cascaded pump stages of the charge pump 110. It will be appreciated that any number of additional stages, each including a transistor, may be added. The illustration of FIG. 9 allows for the implementation of a negative voltage level relative to a grounded application specific integrated circuit (ASIC) substrate and includes the use of a triple well to create a biased isolation well.

[0042] In particular, the integrated circuit 131 may include a semiconductor chip having a P-substrate 132 and two p-wells 134 formed in the P-substrate 132 and separated from each other by a plurality of n-wells 136 and a deep n-well layer 138. Each transistor M1, M2 of the integrated circuit 131 may include a bulk region, a source region, a gate region, and a drain region formed in the p-well 134. The p-wells 134 are biased below ground and the deep n-well layer 138 is biased above ground, such as 2.5 volts. The deep n-well layer 138 may be disposed to separate each p-well 134 from the P-substrate 132. In this manner, the p-wells 134 may be biased to a different DC voltage than the P-substrate 132 due to the deep n-well layer 138, and the p-wells 134 may be biased to a negative voltage. By way of example and not limitation, the p-wells 134 may be biased to -11.0 volts. The deep n-well layer 138 may be configured to be biased to the most positive voltage, such as 2.5 volts, to prevent the p-well 134 to n-well 136 and substrate 132 to n-well 136 transistors from conducting current through the connections via the n-well 136.

[0043] The voltage of each stage is applied to an RC filter 133 to bias its p-well 134, thereby keeping the oxide voltage below the maximum allowed technology voltage of the NMOS transistors M1, M2 to avoid stressing the oxide layer deposited on the p-well 134. For each stage, a bias circuit as shown in Figure 9 may be configured to generate a DC voltage for the p-well 134 of that stage. For example, the RC filter 133 may be connected to the output of the next stage.

[0044] Throughout this specification and the claims, the following terms have at least the meaning expressly associated therewith herein, unless the context clearly dictates otherwise. The term "or" is intended to mean an inclusive "or." Additionally, the terms "a," "an," and "the" are intended to mean one or more, unless otherwise specified or clear from the context to be directed to the singular form.

[0045] Although particular embodiments of the disclosed technology are described above, it is to be understood that the disclosed technology is not limited to the disclosed embodiments, but on the contrary, is intended to cover various modifications and equivalent arrangements included within the scope of the appended claims. The patentable scope of particular embodiments of the disclosed technology is defined by the claims, and may include other examples that occur to those skilled in the art.

Claims

1. 1. A method of calibrating a resonator having a resonator member capable of vibrating in a first vibration mode and a calibration electrode spaced from and capacitively coupled to the resonator member, comprising: applying a polarization voltage to the resonator member and a calibration voltage to the calibration electrode, the polarization voltage being a negative voltage; vibrating the resonator member such that the resonator member vibrates in the first vibration mode; measuring a frequency parameter of the resonant member; determining whether the frequency parameter complies with a predetermined threshold; if the frequency parameter does not comply with the predetermined threshold, adjusting the frequency parameter to comply with the predetermined threshold by adjusting at least one of the polarization voltage and the calibration voltage; A method comprising:

2. The method of claim 1 , wherein the frequency parameter corresponds to a first frequency of the first vibrational mode.

3. 2. The method of claim 1, wherein the resonant member also vibrates in a second vibration mode, and the frequency parameter corresponds to a difference between a first frequency of the first vibration mode and a second frequency of the second vibration mode.

4. a resonant member capable of vibrating in a first mode and a second mode; a plurality of electrodes spaced from and capacitively coupled to the resonant member, the plurality of electrodes including a calibration electrode, a drive electrode, and a sense electrode; a controller operatively coupled to the resonant member and the plurality of electrodes, applying a polarization voltage to the resonator member and a calibration voltage to the calibration electrode, the polarization voltage being a negative voltage; vibrating the resonator member such that the resonator member vibrates in the first vibration mode and the second vibration mode; determining whether a frequency parameter of the resonant member complies with a predetermined threshold; If the frequency parameter does not comply with the predetermined threshold, adjusting the frequency parameter to comply with the predetermined threshold by adjusting at least one of the polarization voltage and the calibration voltage. The controller and A resonator system comprising:

5. a negative charge pump configured to output an output voltage, the negative charge pump including a plurality of reverse-biased transistors; a voltage divider configured to divide down a portion of the output voltage to generate an input voltage; an amplifier configured to compare the input voltage to a reference voltage; a clock circuit configured to control a clock amplitude provided to the negative charge pump; 1. An integrated circuit comprising:

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