Trans-impedance amplification circuit of MEMS capacitive transducer with high gain and stable phase

Abstract

The invention discloses a high-gain and phase-stable trans-impedance amplification circuit of an MEMS (Micro Electro Mechanical System) capacitive transducer, which is used for converting a current signal of an MEMS resonator into a stable voltage signal. The trans-impedance amplification circuit of the MEMS capacitive transducer comprises a first-stage integrator and a second-stage phase shifter, wherein the first-stage integrator is used for receiving a differential induction current signal of the MEMS resonator and performing integral amplification, and a feedback capacitor of the first-stage integrator is directly composed of an output capacitor of the MEMS resonator; mechanical homologous capacitance feedback is realized; and the second-stage phase shifter is connected to the output end of the first-stage integrator and is used for carrying out phase compensation on the integrated signal so as to meet the phase condition of loop oscillation. According to the amplification circuit provided by the invention, by adopting a mechanical homologous capacitance feedback technology and a two-stage cascade structure of the integrator and the phase shifter, the zero temperature drift characteristic of transimpedance gain and the accurate and stable control of a loop phase are realized.

Description

Technical Field

[0001] This invention relates to the field of integrated circuit design, and more particularly to a high-gain and phase-stable MEMS capacitive transimpedance amplifier circuit. Background Technology

[0002] Microelectromechanical systems (MEMS) resonators are widely used in high-precision time references, inertial sensors, and other fields due to their compatibility with integrated circuit processes and ability to achieve high mechanical quality factors. They are core components for realizing positioning, navigation, and timing (PNT) functions. In a closed-loop detection system for a MEMS resonator, the front-end transimpedance amplifier is responsible for converting the weak induced current signal output by the resonator into a voltage signal.

[0003] However, existing transimpedance amplifiers have significant drawbacks. Firstly, the gain of traditional integrator-differentiator transimpedance amplifiers relies on mismatched resistors in the second stage. These resistors are susceptible to temperature variations, leading to gain instability over a wide temperature range and causing amplitude fluctuations and frequency drift. Secondly, the resonator itself contains parasitic capacitance and resistance, which, together with the compensation capacitors in the front-end amplifier, introduce additional phase shifts into the loop, disrupting the phase conditions required for self-oscillation and affecting frequency stability. Furthermore, traditional transimpedance amplifiers use CMOS process capacitors as feedback capacitors, while the input capacitors are from MEMS processes. These two processes inherently differ in temperature coefficients and process variations, and this mismatch further exacerbates gain drift with temperature changes.

[0004] In summary, existing technologies struggle to simultaneously meet the requirements of high gain stability and high phase stability, especially in high-precision applications with wide temperature variations, where this contradiction is particularly pronounced. Therefore, a novel transimpedance amplifier circuit architecture is urgently needed that can effectively suppress temperature-induced gain drift while ensuring loop phase requirements are met. Summary of the Invention

[0005] In view of the above-mentioned shortcomings of the existing technology, the present invention provides a high-gain and phase-stable MEMS capacitive transimpedance amplifier circuit. This amplifier circuit achieves zero temperature drift characteristics of transimpedance gain and precise and stable control of loop phase by adopting mechanical homogeneous capacitor feedback technology and a two-stage cascaded structure of integrator and phase shifter.

[0006] To achieve the above objectives, the embodiments of the present invention adopt the following technical solutions: A high-gain and phase-stable MEMS capacitive transimpedance amplifier circuit is provided for converting the current signal of a MEMS resonator into a stable voltage signal. The MEMS capacitive transimpedance amplifier circuit includes a first-stage integrator and a second-stage phase shifter. The first-stage integrator is used to receive the differential induced current signal of the MEMS resonator and perform integration and amplification. The feedback capacitor of the first-stage integrator is directly composed of the output capacitor of the MEMS resonator, realizing mechanical homogeneous capacitor feedback. The second-stage phase shifter is connected to the output of the first-stage integrator and is used to perform phase compensation on the integrated signal to meet the phase condition of the loop oscillation.

[0007] According to one aspect of the present invention, the first-stage integrator includes a first-stage operational amplifier, a first pseudo-resistor, and a second pseudo-resistor, wherein the first pseudo-resistor is connected in series between the inverting input terminal and the non-inverting output terminal of the first-stage integrator; and the second pseudo-resistor is connected in series between the non-inverting input terminal and the inverting output terminal of the first-stage operational amplifier.

[0008] According to one aspect of the present invention, the first pseudo resistor and the second pseudo resistor have the same resistance parameters.

[0009] According to one aspect of the present invention, both the first pseudo resistor and the second pseudo resistor are PMOS transistors with their gates and sources shorted.

[0010] According to one aspect of the present invention, the inverting input terminal and the non-inverting input terminal of the first-stage operational amplifier are respectively connected to the positive input terminal and the inverting input terminal of the differential induced current signal; The MEMS resonator is a linear resonator or a hemispherical resonator, wherein the output capacitor is the differential detection capacitor of the MEMS resonator, including a first output capacitor and a second output capacitor, which are respectively connected to the feedback path of the first-stage integrator.

[0011] According to one aspect of the invention, the common terminal of the MEMS resonator is connected to the virtual ground of the input terminal of the first operational amplifier; In the MEMS resonator, one end of each differential detection electrode is connected to a high-voltage bias source, and the other end of each differential detection electrode is connected to the output of the first-stage operational amplifier. Thus, the capacitance between the MEMS resonator detection electrodes and the common terminal constitutes the feedback capacitance of the first-stage operational amplifier.

[0012] According to one aspect of the present invention, the second-stage phase shifter includes a first resistor, a second resistor, a third resistor, a fourth resistor, a first capacitor, a second capacitor, a third capacitor, a fourth capacitor, and a second-stage operational amplifier; The non-inverting output of the first-stage integrator is connected to the non-inverting input of the second-stage operational amplifier through the first resistor; The inverting output of the first-stage integrator is connected to the inverting input of the second-stage operational amplifier through the second resistor; The non-inverting output of the first-stage integrator is connected to the inverting input of the second-stage operational amplifier through the first capacitor; The inverting output of the first-stage integrator is connected to the non-inverting input of the second-stage operational amplifier via the second capacitor; The third resistor and the third capacitor are connected in parallel between the non-inverting output terminal and the inverting input terminal of the operational amplifier; The fourth resistor and the fourth capacitor are connected in parallel between the inverting output terminal and the inverting input terminal of the operational amplifier.

[0013] According to one aspect of the present invention, the first resistor and the second resistor have the same resistance value, the first capacitor and the second capacitor have the same capacitance value, the third resistor and the fourth resistor have the same resistance value, and the third capacitor and the fourth capacitor have the same capacitance value.

[0014] According to one aspect of the present invention, the transfer function of the second-stage phase shifter circuit is: ,in, The voltage at the non-inverting input terminal of the differential signal. This is the voltage at the negative input terminal of the differential signal. This is the voltage at the non-inverting output terminal of the operational amplifier. This is the voltage at the inverting output terminal of the operational amplifier. For complex frequency variables, The resistance value is the input to the network. The capacitance value is the input to the network. To provide the resistance value of the feedback network, This represents the capacitance value of the feedback network.

[0015] According to one aspect of the present invention, the high-gain and phase-stable MEMS capacitive transimpedance amplifier circuit further includes a quadrature phase controller, which includes a mixer, a charge pump, a loop filter, and a buffer. The input terminal of the quadrature phase controller receives two quadrature signals output from the first-stage integrator and the second-stage phase shifter; The mixer detects the phase error between the two orthogonal signals. When the phase deviates from the 90-degree orthogonal relationship, the controller outputs a control voltage. The control voltage is fed back to the second-stage phase shifter to dynamically adjust the resistance values ​​of the first, second, third, and fourth resistors in the second-stage phase shifter.

[0016] The advantages of this invention are as follows: First, by using the MEMS resonator's own capacitance as the feedback capacitor through mechanical homogeneous capacitor feedback technology, a perfect match between the input and feedback path capacitor temperature drift and process is achieved, fundamentally solving the mismatch problem of traditional CMOS capacitor feedback and ensuring extremely high gain stability. Second, by utilizing a two-stage structure of integrator and phase shifter, a precise 0-degree total phase shift is achieved at the resonance point. The phase shifter has high gain stability due to resistance matching, and the residual phase deviation is dynamically compensated by an orthogonal phase controller, ensuring long-term phase stability of the closed-loop oscillation circuit. Third, gain and phase stability stabilize the resonant frequency of the MEMS resonator, effectively suppressing temperature hysteresis, improving the accuracy of the quality factor monitoring based on the controller output, and significantly improving the accuracy and reliability of the sensor system. Fourth, the fully differential phase shifter structure based on negative resistance provides precise phase shift while possessing good common-mode noise suppression capability, which helps to improve the circuit signal-to-noise ratio. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 This is a circuit structure diagram of the high-gain and phase-stable MEMS capacitive transimpedance amplifier circuit described in this invention. Figure 2 This is a schematic diagram of the linear vibration resonator described in this invention; Figure 3 This is a schematic diagram of the hemispherical resonator described in this invention; Figure 4 This is a block diagram of the quadrature phase controller described in this invention. Detailed Implementation

[0019] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0020] like Figure 1 The circuit diagram of a high-gain and phase-stable MEMS capacitive transimpedance amplifier circuit according to the present invention is shown. Figure 1 As shown, the amplifier circuit adopts a fully differential structure to convert the weak current signal of the MEMS resonator into a stable voltage signal, including a first-stage integrator and a second-stage phase shifter.

[0021] The first-stage integrator is the front end of the entire circuit, used to convert the weak differential induced current signal output by the MEMS resonator ( and The integrator performs integration and amplification. The first-stage integrator includes a first-stage operational amplifier 100, a first pseudo-resistor 200, and a second pseudo-resistor 201.

[0022] The first pseudo-resistor 200 and the second pseudo-resistor 201 are respectively connected across the inverting input terminal and the non-inverting output terminal, and the non-inverting input terminal and the inverting output terminal of the first-stage operational amplifier 100. Specifically, the first pseudo-resistor 200 is connected in series between the inverting input terminal and the non-inverting output terminal of the first-stage operational amplifier 100; and the second pseudo-resistor 201 is connected in series between the non-inverting input terminal and the inverting output terminal of the first-stage operational amplifier 100.

[0023] In this embodiment, the first pseudo-resistor 200 and the second pseudo-resistor 201 have the same parameters. The pseudo-resistor is a PMOS transistor with its gate and source shorted, and its function is to establish a common-mode point for the input of the first-stage operational amplifier 100 and ensure the stability of the first-stage loop. When the input common-mode point of the first-stage operational amplifier 100 is established close to the output common-mode point, the PMOS transistor enters the cutoff region, forming a large resistance.

[0024] In this embodiment of the invention, the common terminal of the MEMS resonator is connected to the virtual ground point of the input terminal of the first-stage operational amplifier 100. Simultaneously, one end of each differential detection electrode in the MEMS resonator is connected to a high-voltage bias source (e.g., 10V DC), and the other end of each differential detection electrode is connected to the output terminal of the first-stage operational amplifier 100. Thus, the capacitance between the MEMS resonator detection electrodes and the common terminal ( and This forms the feedback capacitor of the first-stage operational amplifier 100.

[0025] Due to the feedback capacitance of the MEMS resonator ( and ) and the input capacitance of the MEMS resonator ( and Originating from the same MEMS differential capacitor structure: both share the common terminal plate of the resonator ( and Both capacitors are manufactured using the same MEMS process, with the same materials, dimensions, and process deviations. This ensures that their key characteristics, such as temperature coefficient, capacitance deviation, and parasitic parameters, change completely synchronously. This eliminates the mismatch problem caused by material and process differences in independent capacitors in traditional solutions from a physical perspective, thereby achieving a homogeneous match between temperature coefficient and process deviation. It also solves the mismatch problem between CMOS capacitors and MEMS capacitors in traditional designs, effectively suppressing common-mode interference and temperature drift.

[0026] In this embodiment of the invention, this circuit connection method connects the output capacitor of the MEMS resonator ( and It can be directly reused as the feedback capacitor of the first-stage operational amplifier 100, thereby realizing mechanical homogeneous capacitor feedback.

[0027] The MEMS resonator can be either a linear resonator or a hemispherical resonator. Both of these resonators are specific implementations of MEMS capacitive transducers, but their mechanical structures and electrode layouts differ significantly. The circuit architecture of the transimpedance amplifier circuit of this invention is compatible with both of these different structures.

[0028] Figure 2 and Figure 3 The specific structures of these two resonators are shown. Figure 2 and Figure 3 As shown, in a linear resonator, the common moving plate of the MEMS differential capacitor ( and The part located) is situated between two differential fixed plates ( and , and In the middle of the hemispherical resonator, the common movable plate is located on the same side of the two differential fixed plates.

[0029] in: , The input capacitor of the MEMS differential capacitor is used to receive the induced current signal of the transducer. , The output capacitor of the MEMS differential capacitor, together with subsequent circuits (such as operational amplifiers), forms the feedback path of the transimpedance amplifier circuit. , The common active plate of the MEMS differential capacitor (a resonant beam-like vibration structure in linear vibration, and a vibration-related part of a hemispherical harmonic oscillator in hemispherical vibration) will cause the capacitance value to change due to its vibration. High-voltage bias voltage provides bias for MEMS capacitors, enabling them to effectively sense changes in capacitance caused by vibration. , : The connection point to subsequent circuits (such as operational amplifiers), used to convert capacitance changes into voltage signals and transmit them to subsequent circuits.

[0030] As can be seen from the physical characteristics of the MEMS resonator, in this embodiment of the invention, the common terminal plate of the MEMS resonator is connected to the virtual ground of the first-stage operational amplifier, thereby ensuring the MEMS input capacitance ( and The change in capacitance is entirely due to the change in physical capacitance caused by mechanical displacement, not the change in plate voltage. This simplifies signal detection, making the current signal... and It purely reflects mechanical motion.

[0031] During operation, the induced current affects the feedback capacitor. and Perform charging integration, thereby reaching the output of the first-stage operational amplifier 100 ( and This generates a differential voltage signal proportional to the mechanical displacement of the resonator. Simultaneously, due to integration, this stage introduces a 90-degree phase lag.

[0032] The second-stage phase shifter is connected after the first-stage integrator and is used to perform phase compensation on the signal to meet the phase conditions of loop oscillation.

[0033] Among them, the non-inverting output of the first-stage integrator The first resistor 300 is connected to the non-inverting input of the second-stage operational amplifier 101; while the inverting output of the first-stage integrator is connected to the non-inverting input. It is then connected to the inverting input of the second-stage operational amplifier 101 via a second resistor 301. This cross-connection method achieves an equivalent negative resistance.

[0034] Meanwhile, the non-inverting output of the first-stage integrator The first capacitor 400 is connected to the inverting input of the second-stage operational amplifier 101, and the inverting output of the first-stage integrator is also connected to it. The second capacitor 401 is connected to the non-inverting input of the second-stage operational amplifier 101.

[0035] Among them, the resistance values ​​of the first resistor 300 and the second resistor 301 are the same, and the capacitance values ​​of the first capacitor 400 and the second capacitor 401 are the same.

[0036] In this embodiment of the invention, the second-stage operational amplifier 101 is a fully differential operational amplifier as the active core device. This amplifier receives the differential signal processed by the input network and drives the generation of a differential output signal. The non-inverting output terminal of the second-stage operational amplifier 101 is... The inverting output of the operational amplifier is .

[0037] Among them, the non-inverting output terminal of the second-stage operational amplifier 101 of the second-stage phase shifter Inverting input terminal, inverting output terminal A feedback branch is connected between the positive input terminal and a resistor and a capacitor in parallel.

[0038] In this embodiment of the invention, the feedback branch is specifically configured as follows: at the non-inverting output terminal of the second-stage operational amplifier 101... A third resistor 302 and a third capacitor 402 are connected in parallel across the inverting input terminal; at the inverting output terminal of the operational amplifier. A fourth resistor 303 and a fourth capacitor 403 are connected in parallel across the positive input terminal.

[0039] In this configuration, the third resistor 302 and the fourth resistor 303 have the same resistance value, and the third capacitor 402 and the fourth capacitor 403 have the same capacitance value. Thus, the parameters of the two feedback paths are strictly symmetrical, forming a fully differential feedback structure.

[0040] This stage of the circuit constitutes a fully differential active phase-shifting network based on negative resistance. Its transfer function is: .

[0041] in: This is the voltage at the non-inverting input terminal of the differential signal; This is the voltage at the negative input terminal of the differential signal; This is the voltage at the non-inverting output terminal of the operational amplifier; This is the voltage at the inverting output terminal of the operational amplifier; This is the fully differential input voltage, representing the differential input signal received by the circuit; This is the fully differential output voltage, representing the differential signal output by the circuit; For complex frequency variables (complex frequency domain representation in Laplace transform); The resistance values ​​for the input network are (i.e., the resistance values ​​of the first resistor 300 and the second resistor 301, which have the same resistance value). The capacitance value of the input network (i.e., the capacitance values ​​of the first capacitor 400 and the second capacitor 401, which have the same capacitance value). The resistance values ​​of the feedback network (i.e., the resistance values ​​of the third resistor 302 and the fourth resistor 303, which have the same resistance value). The capacitance value of the feedback network (i.e., the capacitance values ​​of the third capacitor 402 and the fourth capacitor 403, which have the same capacitance value).

[0042] As can be seen from the transfer function of the phase shifter above, by reasonably designing the resistance value ( , ) and capacitance value ( , The structural parameters allow the circuit to generate a 90-degree phase lead at the system's resonant frequency, precisely compensating for the 90-degree phase lag introduced by the first-stage integrator. Finally, at the second-stage output... and The result is a differential voltage signal that is in phase with the input current signal and has been sufficiently amplified.

[0043] To address parameter drift and achieve long-term phase stability, the MEMS capacitive transimpedance amplifier circuit of this invention also includes an orthogonal phase controller.

[0044] Figure 4 A block diagram of the orthogonal phase controller of this invention is shown. For example... Figure 4 As shown, the phase controller includes a mixer, a charge pump, a loop filter, and a buffer.

[0045] The input of the quadrature phase controller simultaneously receives the output of the first-stage integrator 100. and The quadrature signals of the second-stage phase shifter 101 and the final output of the second-stage phase shifter 101 are ( and The controller outputs a control voltage. The phase error between these two signals is detected by an internal mixer. If the phase deviates from the ideal 90-degree quadrature relationship (corresponding to a total loop phase shift of 0 degrees), the controller will output a control voltage. .

[0046] The control voltage The feedback dynamically adjusts the resistance values ​​of the first resistor 300, the second resistor 301, the third resistor 302, and the fourth resistor 303 in the second-stage phase shifter. Through this negative feedback mechanism, the system can automatically lock the loop phase in the optimal state, thereby achieving high-precision phase stability.

[0047] In summary, the MEMS capacitive transimpedance amplifier circuit of this invention achieves the core objectives of high gain stability and high phase stability through a two-stage precisely matched architecture and the innovative introduction of mechanical homogeneous capacitors and dynamic phase compensation.

[0048] The advantages of this invention are as follows: First, by using the MEMS resonator's own capacitance as the feedback capacitor through mechanical homogeneous capacitor feedback technology, a perfect match between the input and feedback path capacitor temperature drift and process is achieved, fundamentally solving the mismatch problem of traditional CMOS capacitor feedback and ensuring extremely high gain stability. Second, by utilizing a two-stage structure of integrator and phase shifter, a precise 0-degree total phase shift is achieved at the resonance point. The phase shifter has high gain stability due to resistance matching, and the residual phase deviation is dynamically compensated by an orthogonal phase controller, ensuring long-term phase stability of the closed-loop oscillation circuit. Third, gain and phase stability stabilize the resonant frequency of the MEMS resonator, effectively suppressing temperature hysteresis, improving the accuracy of the quality factor monitoring based on the controller output, and significantly improving the accuracy and reliability of the sensor system. Fourth, the fully differential phase shifter structure based on negative resistance provides precise phase shift while possessing good common-mode noise suppression capability, which helps to improve the circuit signal-to-noise ratio.

[0049] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A high-gain and phase-stable MEMS capacitive transimpedance amplifier circuit for converting the current signal of a MEMS resonator into a stable voltage signal, characterized in that, The MEMS capacitive transimpedance amplifier circuit includes a first-stage integrator and a second-stage phase shifter. The first-stage integrator is used to receive the differential induced current signal of the MEMS resonator and perform integration and amplification. The feedback capacitor of the first-stage integrator is directly composed of the output capacitor of the MEMS resonator, realizing mechanical homogeneous capacitor feedback. The second-stage phase shifter is connected to the output of the first-stage integrator and is used to perform phase compensation on the integrated signal to meet the phase condition of the loop oscillation.

2. The high-gain and phase-stable MEMS capacitive transimpedance amplifier circuit according to claim 1, characterized in that, The first-stage integrator includes a first-stage operational amplifier (100), a first pseudo resistor (200), and a second pseudo resistor (201). The first pseudo resistor (200) is connected in series between the inverting input terminal and the non-inverting output terminal of the first-stage integrator; the second pseudo resistor (201) is connected in series between the non-inverting input terminal and the inverting output terminal of the first-stage operational amplifier (100).

3. The high-gain and phase-stable MEMS capacitive transimpedance amplifier circuit according to claim 2, characterized in that, The first pseudo resistor (200) and the second pseudo resistor (201) have the same resistance parameters.

4. The high-gain and phase-stable MEMS capacitive transimpedance amplifier circuit according to claim 2, characterized in that, The first pseudo resistor (200) and the second pseudo resistor (201) are both PMOS transistors with their gate and source shorted.

5. The high-gain and phase-stable MEMS capacitive transimpedance amplifier circuit according to claim 2, characterized in that, The inverting input and non-inverting input of the first-stage operational amplifier are respectively connected to the positive input and inverting input of the differential induced current signal; The MEMS resonator is a linear resonator or a hemispherical resonator, wherein the output capacitor is the differential detection capacitor of the MEMS resonator, including a first output capacitor and a second output capacitor, which are respectively connected to the feedback path of the first-stage integrator.

6. The high-gain and phase-stable MEMS capacitive transimpedance amplifier circuit according to claim 2, characterized in that, The common terminal of the MEMS resonator is connected to the virtual ground point of the input terminal of the first-stage operational amplifier (100); In the MEMS resonator, one end of each differential detection electrode is connected to a high-voltage bias source, and the other end of each differential detection electrode is connected to the output of the first-stage operational amplifier (100). Thus, the capacitance between the MEMS resonator detection electrodes and the common terminal constitutes the feedback capacitance of the first-stage operational amplifier (100).

7. The high-gain and phase-stable MEMS capacitive transimpedance amplifier circuit according to claim 1, characterized in that, The second-stage phase shifter includes a first resistor (300), a second resistor (301), a third resistor (302), a fourth resistor (303), a first capacitor (400), a second capacitor (401), a third capacitor (402), a fourth capacitor (403), and a second-stage operational amplifier (101). The non-inverting output of the first-stage integrator is connected to the non-inverting input of the second-stage operational amplifier (101) through the first resistor (300); The inverting output of the first-stage integrator is connected to the inverting input of the second-stage operational amplifier (101) through the second resistor (301); The non-inverting output of the first-stage integrator is connected to the inverting input of the second-stage operational amplifier (101) through the first capacitor (400); The inverting output of the first-stage integrator is connected to the non-inverting input of the second-stage operational amplifier (101) through the second capacitor (401); The third resistor (302) and the third capacitor (402) are connected in parallel between the non-inverting output terminal and the inverting input terminal of the operational amplifier; The fourth resistor (303) and the fourth capacitor (403) are connected in parallel between the inverting output terminal and the inverting input terminal of the operational amplifier.

8. The high-gain and phase-stable MEMS capacitive transimpedance amplifier circuit according to claim 6, characterized in that, The first resistor (300) and the second resistor (301) have the same resistance value, the first capacitor (400) and the second capacitor (401) have the same capacitance value, the third resistor (302) and the fourth resistor (303) have the same resistance value, and the third capacitor (402) and the fourth capacitor (403) have the same capacitance value.

9. The high-gain and phase-stable MEMS capacitive transimpedance amplifier circuit according to claim 6, characterized in that, The transfer function of the second-stage phase shifter circuit is: ,in, The voltage at the non-inverting input terminal of the differential signal. This is the voltage at the negative input terminal of the differential signal. This is the voltage at the non-inverting output terminal of the operational amplifier. This is the voltage at the inverting output terminal of the operational amplifier. For complex frequency variables, The resistance value is the input to the network. The capacitance value is the input to the network. To provide the resistance value of the feedback network, This represents the capacitance value of the feedback network.

10. The high-gain and phase-stable MEMS capacitive transimpedance amplifier circuit according to any one of claims 1 to 9, characterized in that, The high-gain and phase-stable MEMS capacitive transimpedance amplifier circuit also includes a quadrature phase controller, which includes a mixer, a charge pump, a loop filter, and a buffer. The input terminal of the quadrature phase controller receives two quadrature signals output from the first-stage integrator and the second-stage phase shifter; The mixer detects the phase error between the two orthogonal signals. When the phase deviates from the 90-degree orthogonal relationship, the controller outputs a control voltage. The control voltage is fed back to the second-stage phase shifter to dynamically adjust the resistance values ​​of the first resistor (300), the second resistor (301), the third resistor (302), and the fourth resistor (303) in the second-stage phase shifter.

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