A MEMS electric field sensor closed loop demodulation system and method

Abstract

A MEMS electric field sensor closed loop demodulation system and method, comprising: obtaining an error signal by subtracting a reconstructed reference signal from a product of a voltage signal of a MEMS electric field sensor and a set first gain coefficient, multiplying the error signal by a quadrature reference carrier and a sine signal to obtain an in-phase mixed signal and a quadrature mixed signal, the quadrature reference carrier and the sine signal being orthogonal signals; filtering the in-phase mixed signal and the quadrature mixed signal to filter out high frequency components to obtain a baseband in-phase component and a baseband quadrature component; vector synthesizing the baseband in-phase component and the baseband quadrature component to obtain a demodulation output; multiplying the demodulation output by a set second gain coefficient and then by the quadrature reference carrier to obtain the reconstructed reference signal; and adjusting a shielding electrode driving frequency of the MEMS electric field sensor to be the frequency of the quadrature reference carrier. The demodulation output signal of the application automatically approximates the real electric field value and is not significantly affected by the slowly varying parameter offset in the signal link.

Description

Technical Field

[0001] This invention belongs to the field of electric field measurement and microelectromechanical systems (MEMS) sensing technology, and more specifically, relates to a closed-loop demodulation system and method for MEMS electric field sensors. Background Technology

[0002] MEMS resonant electric field sensors utilize piezoelectrically driven shielding electrodes to undergo periodic mechanical vibrations, alternating the exposure of the sensing electrodes to the measured electric field with periods of shielding. The induced charge generated on the sensing electrodes changes over time, forming an induced current proportional to the electric field strength. Existing MEMS resonant electric field sensors are based on single-ended or differential structures. Differential structures can suppress common-mode noise and achieve a 6dB gain in differential-mode signals. However, current manufacturing processes for MEMS resonant electric field sensors struggle to ensure complete structural symmetry, thus not only negating the advantages of differential structures but also introducing differential-mode interference.

[0003] Existing signal demodulation methods for resonant electric field sensors, such as lock-in amplification demodulation, synchronous demodulation, and fast Fourier transform spectrum analysis, only use a single reference signal or direct frequency domain analysis, without establishing orthogonal signal paths. Therefore, they cannot eliminate the coupling between the initial phase of the input signal and the amplitude demodulation at the signal processing level. The IQ transform-based method introduces a pair of orthogonal reference carriers, cos(ωt) and sin(ωt), which are mixed with the input signal to obtain in-phase and quadrature baseband components, respectively. Vector synthesis and modulus extraction eliminate the interference of phase information on amplitude demodulation. This characteristic gives the IQ method a phase-sensitive decoupling capability in principle. However, existing IQ demodulation schemes are all open-loop structures. When the transimpedance amplifier gain drifts, filter parameters shift due to temperature changes, or the analog-to-digital converter exhibits nonlinear errors, a deviation will appear between the demodulated output and the actual electric field strength, and this deviation cannot be automatically corrected. The measurement accuracy depends entirely on the pre-calibration accuracy of each component.

[0004] In summary, existing demodulation methods are limited by phase sensitivity and signal processing complexity, while open-loop IQ demodulation methods cannot eliminate the influence of the system itself and the external environment, thus restricting the high-precision and stable measurement of MEMS resonant electric field sensors in practical engineering environments. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a closed-loop demodulation system and method for MEMS electric field sensors.

[0006] The present invention adopts the following technical solution.

[0007] The first aspect of this invention proposes a closed-loop demodulation system for a MEMS electric field sensor, comprising a transimpedance amplifier, a first gain module, a feedback loop, an ADC, a PID controller, a frequency synthesizer, a non-inverting branch mixer, a quadrature branch mixer, a second-order non-inverting branch filter, a second-order quadrature branch filter, a first adder, a second adder, and a third multiplier, specifically: The induced current output by the MEMS electric field sensor is converted into a voltage signal by a transimpedance amplifier. The voltage signal is then input to the first adder. The output of the first adder is adjusted by the first gain module and then converted into a digital signal by an ADC as an error signal. The error signal is input to a PID controller. The output of the PID controller is simultaneously sent to the in-phase branch mixer and the quadrature branch mixer. The frequency synthesizer outputs a quadrature reference carrier and a sine wave signal. The quadrature reference carrier and the sine wave signal are respectively sent to the in-phase branch mixer and the quadrature branch mixer. The in-phase branch mixer and the quadrature branch mixer output an in-phase mixed signal and a quadrature mixed signal, respectively. The in-phase mixing signal is input into the second-order filter of the in-phase branch, and the quadrature mixing signal is input into the second-order filter of the quadrature branch. The outputs of the second-order filters of the in-phase branch and the second-order filters of the quadrature branch are input into the second adder; the output of the second adder is the demodulated output signal. The feedback loop includes an adaptive modulation module and a DAC. The quadrature reference carrier and the demodulated output signal are passed through the adaptive modulation module to obtain the reconstructed reference signal. After the reconstructed reference signal is converted into an analog signal by the DAC, the analog signal is inverted and input into the first adder.

[0008] Preferably, the quadrature reference carrier and the sinusoidal signal output by the frequency synthesizer are quadrature signals; the in-phase branch mixer and the quadrature branch mixer are the first multiplier and the second multiplier, respectively.

[0009] Preferably, the adaptive modulation module includes a third multiplier and a second gain module. The demodulated output signal is input to the third multiplier, and the orthogonal reference carrier is also input to the third multiplier after passing through the second gain module. The output of the third multiplier is the reconstructed reference signal.

[0010] Preferably, the frequency of the orthogonal reference carrier is passed through a DAC module and then used as the driving frequency of the shielded electrode of the MEMS electric field sensor.

[0011] Preferably, the in-phase branch second-order filter and the quadrature branch second-order filter are low-pass filters or band-pass filters, and the cutoff frequencies of the in-phase branch second-order filter and the quadrature branch second-order filter are the same.

[0012] The second aspect of the present invention proposes a closed-loop demodulation method for a MEMS electric field sensor based on the system described in the first aspect of the present invention, specifically as follows: The error signal is obtained by subtracting the reconstructed reference signal from the product of the voltage signal from the MEMS electric field sensor and the set first gain coefficient. The error signal is then multiplied by the quadrature reference carrier and the sinusoidal signal to obtain the in-phase mixer signal and the quadrature mixer signal, respectively. The quadrature reference carrier and the sinusoidal signal are orthogonal to each other. The in-phase mixer signal and the quadrature mixer signal are filtered to remove high-frequency components, resulting in the baseband in-phase component and the baseband quadrature component. The baseband in-phase component and the baseband quadrature component are then vector synthesized to obtain the demodulated output. The demodulated output is multiplied by the set second gain coefficient, and then multiplied by the quadrature reference carrier to obtain the reconstructed reference signal; Furthermore, the driving frequency of the shielded electrode of the MEMS electric field sensor is adjusted to the frequency of the quadrature reference carrier.

[0013] A third aspect of the present invention provides a terminal device including a memory, a processor, and a computer program stored in the memory and executable on the processor, the processor performing steps using the closed-loop demodulation method for a MEMS resonant electric field sensor described in the second aspect of the present invention.

[0014] A fourth aspect of the present invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, uses the steps of the closed-loop demodulation method based on a MEMS resonant electric field sensor described in the second aspect of the present invention.

[0015] The beneficial effects of this invention are compared with those of the prior art: This invention utilizes the same frequency synthesizer to simultaneously provide the sensor drive voltage and the orthogonal reference carrier required for IQ demodulation. By constructing two orthogonal signal paths, I / Q, and performing vector synthesis, the influence of the input signal phase on the electric field amplitude measurement is eliminated. This invention employs a closed-loop feedback adaptive error adjustment mechanism, reconstructing the demodulated output as a reference signal and using a PID controller to drive the error to zero, enabling the demodulated output to automatically approximate the true electric field value. This mechanism allows the demodulation system to adaptively adjust to non-ideal factors such as transimpedance amplifier gain drift, low-pass filter parameter temperature shift, and analog-to-digital converter errors. It overcomes the limitation of open-loop demodulation schemes where measurement accuracy depends entirely on the pre-calibrated accuracy of each component, and achieves the same common-mode signal suppression capability as differential structures. Therefore, when the closed loop reaches steady state, the demodulated output signal automatically approximates the true electric field value, unaffected by significant deviations in slowly varying parameters in the signal link, thus improving long-term measurement stability. The signal processing link of this invention consists of only five stages: gain adjustment, two-channel IQ mixing, second-order low-pass / band-pass filtering, adder vector synthesis, and PID control feedback. Compared with the multi-stage serial structure of synchronous demodulation methods, such as high-pass filtering-orthogonal correlation-band-pass / low-pass filtering-peak extraction, this is greatly simplified. The entire demodulation system only needs to adjust three parameters: the first gain coefficient K1, the second gain coefficient K2, and the PID controller parameters, which reduces the workload of debugging and calibration and is conducive to engineering implementation on digital platforms such as FPGA. Attached Figure Description

[0016] Figure 1 This is a framework diagram of the system of the present invention. Detailed Implementation

[0017] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of this invention. The embodiments described in this application are merely some embodiments of this invention, and not all embodiments. Based on the spirit of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the protection scope of this invention.

[0018] like Figure 1 As shown, Embodiment 1 of the present invention proposes a closed-loop demodulation system for a MEMS electric field sensor, including a transimpedance amplifier, a first gain module, a feedback loop, an ADC, a PID controller, a frequency synthesizer, a non-inverting branch mixer, a quadrature branch mixer, a second-order non-inverting branch filter, a second-order quadrature branch filter, a first adder, a second adder, and a third multiplier, specifically as follows: It should be noted that, in a DC electric field, the MEMS electric field sensor is designed with the following parameters: electric field strength E1, vacuum permittivity ε0, shielding electrode angular frequency ω1, total area of ​​sensing comb teeth nA0 (where n is the number of sensing comb teeth and A0 is the area of ​​a single sensing comb tooth), shielding coefficient k, displacement hysteresis driving force β, and induced current i. e (t) is:

[0019] Induced current i e (t) is converted into a voltage signal u by a transimpedance amplifier. e (t). The amplitude of the induced current is linearly related only to the electric field strength under the condition that the speed of the shielded electrode is constant. For AC and AC / DC mixed electric fields, the induced current contains multiple frequency components, and the amplitude of each component is proportional to the corresponding electric field component. The output of this sensor is essentially an amplitude-modulated signal with the mechanical vibration frequency ω0 as the carrier.

[0020] The induced current output by the MEMS electric field sensor is converted into a voltage signal Sig_in by a transimpedance amplifier. This voltage signal is then input to a first adder. The output of the first adder is adjusted by a first gain module (the gain coefficient of the first gain module is K1), and then converted into a digital signal by an ADC as an error signal. This error signal is input to a PID controller, and the output u of the PID controller is... e (t) Simultaneously fed into the in-phase branch mixer and the quadrature branch mixer, the frequency synthesizer outputs a quadrature reference carrier and a sine wave signal: Pd(t) = u e (t) · cos(ω1t) Pq(t) = u e (t) · sin(ω1t) Where Pd(t) is the quadrature reference carrier, Pq(t) is the sinusoidal signal, and ω1 is the angular frequency of the quadrature reference carrier and the sinusoidal signal; The quadrature reference carrier and the sinusoidal signal are fed into the in-phase branch mixer and the quadrature branch mixer, respectively. The in-phase branch mixer and the quadrature branch mixer output the in-phase mixed signal and the quadrature mixed signal, respectively. The in-phase mixing signal is input into the second-order filter of the in-phase branch, and the quadrature mixing signal is input into the second-order filter of the quadrature branch. The outputs of the second-order filters of the in-phase branch and the second-order filters of the quadrature branch are input into the second adder; the output of the second adder is the demodulated output signal Sig_Out. The feedback loop includes an adaptive modulation module and a DAC. The quadrature reference carrier and the demodulated output signal are passed through the adaptive modulation module to obtain the reconstructed reference signal. After the reconstructed reference signal is converted into an analog signal by the DAC, the analog signal is inverted and input into the first adder.

[0021] In this preferred embodiment, the quadrature reference carrier and the sinusoidal signal output by the frequency synthesizer are quadrature signals; the in-phase branch mixer and the quadrature branch mixer are the first multiplier and the second multiplier, respectively.

[0022] In this preferred embodiment, the adaptive modulation module includes a third multiplier and a second gain module. The demodulated output signal is input to the third multiplier, and the orthogonal reference carrier is also input to the third multiplier after passing through the second gain module. The output of the third multiplier is the reconstructed reference signal.

[0023] That is, the reconstructed reference signal Sig_ref is: Sig_ref = K2 · Sig_Out · cos(ω1t) The reconstructed reference signal represents the ideal waveform that the sensor output signal should exhibit under the current electric field estimate Sig_Out.

[0024] It should be noted that existing technologies have closed-loop control of the shielding door displacement signal, but the closed-loop feedback is fed back to the driving voltage of the sensor sensing unit in order to ensure that the sensor always operates stably at the resonant frequency. In contrast, this invention feeds back the demodulated voltage value reflecting the electric field strength to the signal processing system after the sensor sensing unit outputs the signal. The purpose is to eliminate the offset errors caused by the various hardware components in the signal processing system changing with time and environment, but it does not operate on the sensor sensing unit itself. Instead, it improves the demodulation accuracy of the sensing system.

[0025] In the first adder, the voltage signal Sig_in is subtracted from the Sig_ref to obtain the error signal before amplification. e(t) = Sig_in – K2 · Sig_Out · cos(ω1t) After passing through the first gain module, the final error signal u is obtained. e (t): u e (t)=k1·e(t) In this preferred embodiment, the frequency of the orthogonal reference carrier is passed through the DAC module and used as the driving frequency of the shielding electrode of the MEMS electric field sensor, so that the amplitude modulation signal ω0 of the carrier is always equal to ω1.

[0026] In this preferred embodiment, the in-phase branch second-order filter and the quadrature branch second-order filter are low-pass filters or band-pass filters, and the cutoff frequencies of the in-phase branch second-order filter and the quadrature branch second-order filter are the same.

[0027] In Embodiment 2 of the present invention, the system described in Embodiment 1 is used for control in a DC electric field. In this embodiment, a frequency synthesizer generates a 4 kHz sine wave with a peak-to-peak value of 10 V as the sensor driving voltage. The sensor is measured in a DC electric field of 0~10 kV / m.

[0028] The sensor output induced current is converted into a voltage signal Sig_in by a transimpedance amplifier with a gain of 10 MΩ. After adjustment by a gain of K1=5, the peak value of Sig_in is controlled within the range of 1~3 V. The signal is then fed into a mixer with in-phase and quadrature branches after passing through a first adder, a first gain module, an ADC, and a PID controller. The mixer multiplies the adjusted signal by cos(4kHz·t) and sin(4 kHz·t), respectively, to generate Pd(t) and Pq(t).

[0029] Pd(t) and Pq(t) are input to the in-phase and quadrature branches of the second-order low-pass filters, respectively. The second-order low-pass filters employ a Butterworth architecture with a cutoff frequency of 10 Hz. The adder performs vector synthesis on the two filtered baseband components to generate Sig_Out.

[0030] The feedback loop multiplies Sig_Out by K2·cos(4 kHz·t) to generate the reconstructed reference signal Sig_ref, where K2=0.8. The original input Sig_in is subtracted from Sig_ref to obtain the unamplified error signal e(t), which is then multiplied by K1 and fed into the PID controller. The PID controller parameters are selected as Kp=0.8 and Ki=50, and its output regulation is sent to the demodulation system to drive e(t) to approach zero.

[0031] In Embodiment 3 of the present invention, the system described in Embodiment 1 is used for regulation in an alternating electric field. In this embodiment, the sensor operates in an alternating electric field of 50 Hz, the cutoff frequency of the second-order low-pass filter is set to 100 Hz, and other system parameters are the same as in Embodiment 2. The sensor output contains frequency components of ω0 ± 50 Hz (ω0 is controlled to equal ω1). The final output Sig_Out contains a component proportional to the amplitude of the 50 Hz AC electric field. The AC electric field strength measurement can then be obtained by extracting the peak value of the 50 Hz frequency component from Sig_Out.

[0032] In Embodiment 4 of the present invention, the system described in Embodiment 1 is used for regulation in a mixed AC / DC electric field. In this embodiment, the sensor is simultaneously exposed to a mixed electric field consisting of a 2 kV / m DC electric field and an AC electric field with an amplitude of 0.5 kV / m and a frequency of 50 Hz. Other system parameters are the same as in Embodiment 2. The final output Sig_Out contains both a DC component and a 50 Hz AC component. The DC component can be extracted using a low-pass filter (cutoff frequency 10 Hz) to obtain the DC electric field measurement; the AC component peak value can be extracted using a band-pass filter (center frequency 50 Hz) to obtain the AC electric field measurement. The extraction of both components is completed within a single demodulation channel, requiring no additional hardware channels.

[0033] All the embodiments described above are implemented on an FPGA platform, using Xilinx Spartan-6 series FPGA chips, with a system clock frequency of 50 MHz.

[0034] Embodiment 5 of the present invention proposes a closed-loop demodulation method for a MEMS electric field sensor based on the system described in Embodiment 1 of the present invention, specifically as follows: The error signal is obtained by subtracting the reconstructed reference signal from the product of the voltage signal from the MEMS electric field sensor and the set first gain coefficient. The error signal is then multiplied by the quadrature reference carrier and the sinusoidal signal to obtain the in-phase mixer signal and the quadrature mixer signal, respectively. The quadrature reference carrier and the sinusoidal signal are orthogonal to each other. The in-phase mixer signal and the quadrature mixer signal are filtered to remove high-frequency components, resulting in the baseband in-phase component and the baseband quadrature component. The baseband in-phase component and the baseband quadrature component are then vector synthesized to obtain the demodulated output. The demodulated output is multiplied by the set second gain coefficient, and then multiplied by the quadrature reference carrier to obtain the reconstructed reference signal; Furthermore, the driving frequency of the shielded electrode of the MEMS electric field sensor is adjusted to the frequency of the quadrature reference carrier.

[0035] Embodiment 6 of the present invention proposes a terminal device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor performs the steps of using the closed-loop demodulation method of the MEMS resonant electric field sensor described in Embodiment 5 of the present invention.

[0036] Embodiment 7 of the present invention proposes a computer-readable storage medium storing a computer program, which, when executed by a processor, uses the steps of the closed-loop demodulation method based on a MEMS resonant electric field sensor described in Embodiment 5 of the present invention.

[0037] This disclosure can be a system, method, and / or computer program product. A computer program product may include a computer-readable storage medium having computer-readable program instructions loaded thereon for causing a processor to implement various aspects of this disclosure.

[0038] Computer-readable storage media can be tangible devices capable of holding and storing instructions for use by an instruction execution device. Computer-readable storage media can be, for example—but not limited to—electrical storage devices, magnetic storage devices, optical storage devices, electromagnetic storage devices, semiconductor storage devices, or any suitable combination of the foregoing. More specific examples (a non-exhaustive list) of computer-readable storage media include: portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), static random access memory (SRAM), portable compact disc read-only memory (CD-ROM), digital multifunction disc (DVD), memory sticks, floppy disks, mechanical encoding devices, such as punch cards or recessed protrusions storing instructions thereon, and any suitable combination of the foregoing. The computer-readable storage media used herein are not to be construed as transient signals themselves, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through waveguides or other transmission media (e.g., light pulses through fiber optic cables), or electrical signals transmitted through wires.

[0039] The computer-readable program instructions described herein can be downloaded from computer-readable storage media to various computing / processing devices, or downloaded via a network, such as the Internet, local area network, wide area network, and / or wireless network, to an external computer or external storage device. The network may include copper transmission cables, fiber optic transmission, wireless transmission, routers, firewalls, switches, gateway computers, and / or edge servers. A network adapter card or network interface in each computing / processing device receives the computer-readable program instructions from the network and forwards them to the computer-readable storage media in the respective computing / processing device.

[0040] Computer program instructions used to perform the operations of this disclosure may be assembly instructions, instruction set architecture (ISA) instructions, machine instructions, machine-dependent instructions, microcode, firmware instructions, status setting data, or source code or object code written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Smalltalk, C++, etc., and conventional procedural programming languages ​​such as the "C" language or similar programming languages. The computer-readable program instructions may execute entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving a remote computer, the remote computer may be connected to the user's computer via any type of network—including a local area network (LAN) or a wide area network (WAN)—or may be connected to an external computer (e.g., via the Internet using an Internet service provider). In some embodiments, electronic circuitry, such as programmable logic circuitry, field-programmable gate arrays (FPGAs), or programmable logic arrays (PLAs), is personalized by utilizing the status information of the computer-readable program instructions to implement various aspects of this disclosure.

[0041] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the protection scope of the claims of the present invention.

Claims

1. A closed-loop demodulation system for a MEMS electric field sensor, comprising a transimpedance amplifier, a first gain module, a feedback loop, an ADC, a PID controller, a frequency synthesizer, a non-inverting branch mixer, a quadrature branch mixer, a second-order non-inverting branch filter, a second-order quadrature branch filter, a first adder, a second adder, and a third multiplier, characterized in that: The induced current output by the MEMS electric field sensor is converted into a voltage signal by a transimpedance amplifier. The voltage signal is then input to the first adder. The output of the first adder is adjusted by the first gain module and then converted into a digital signal by an ADC as an error signal. The error signal is input to a PID controller. The output of the PID controller is simultaneously sent to the in-phase branch mixer and the quadrature branch mixer. The frequency synthesizer outputs a quadrature reference carrier and a sine wave signal. The quadrature reference carrier and the sine wave signal are respectively sent to the in-phase branch mixer and the quadrature branch mixer. The in-phase branch mixer and the quadrature branch mixer output an in-phase mixed signal and a quadrature mixed signal, respectively. The in-phase mixing signal is input into the second-order filter of the in-phase branch, and the quadrature mixing signal is input into the second-order filter of the quadrature branch. The outputs of the second-order filters of the in-phase branch and the second-order filters of the quadrature branch are input into the second adder; the output of the second adder is the demodulated output signal. The feedback loop includes an adaptive modulation module and a DAC. The quadrature reference carrier and the demodulated output signal are passed through the adaptive modulation module to obtain the reconstructed reference signal. After the reconstructed reference signal is converted into an analog signal by the DAC, the analog signal is inverted and input into the first adder.

2. The closed-loop demodulation system for a MEMS electric field sensor according to claim 1, characterized in that: The quadrature reference carrier and the sinusoidal signal output by the frequency synthesizer are quadrature signals; the in-phase branch mixer and the quadrature branch mixer are the first multiplier and the second multiplier, respectively.

3. The closed-loop demodulation system for a MEMS electric field sensor according to claim 1, characterized in that: The adaptive modulation module includes a third multiplier and a second gain module. The demodulated output signal is input to the third multiplier, and the quadrature reference carrier is also input to the third multiplier after passing through the second gain module. The output of the third multiplier is the reconstructed reference signal.

4. The closed-loop demodulation system for a MEMS electric field sensor according to claim 1, characterized in that: The frequency of the orthogonal reference carrier is passed through the DAC module and then used as the driving frequency of the shielded electrode of the MEMS electric field sensor.

5. The closed-loop demodulation system for a MEMS electric field sensor according to claim 1, characterized in that: The in-phase branch second-order filter and the quadrature branch second-order filter are low-pass filters or band-pass filters, and the cutoff frequencies of the in-phase branch second-order filter and the quadrature branch second-order filter are the same.

6. A closed-loop demodulation method for a MEMS electric field sensor based on the system described in any one of claims 1-5, characterized in that: The error signal is obtained by subtracting the reconstructed reference signal from the product of the voltage signal of the MEMS electric field sensor and the set first gain coefficient. The error signal is then multiplied by the quadrature reference carrier and the sine signal to obtain the in-phase mixing signal and the quadrature mixing signal, respectively. The quadrature reference carrier and the sine signal are quadrature signals. The in-phase and quadrature mixing signals are filtered to remove high-frequency components, resulting in baseband in-phase and baseband quadrature components, respectively. The baseband in-phase and baseband quadrature components are then vector-synthesized to obtain the demodulated output. The demodulated output is multiplied by the set second gain coefficient, and then multiplied by the quadrature reference carrier to obtain the reconstructed reference signal; Furthermore, the driving frequency of the shielded electrode of the MEMS electric field sensor is adjusted to the frequency of the quadrature reference carrier.

7. A terminal device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, The processor performs the steps of using the closed-loop demodulation method for the MEMS resonant electric field sensor as described in claim 6.

8. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, uses the steps of the closed-loop demodulation method based on a MEMS resonant electric field sensor as described in claim 6.

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