Compensation method for non-ideal characteristics in analog signal amplification link

Abstract

The invention provides a compensation method for non-ideal characteristics in an analog signal amplification link, and relates to the technical field of weak signal detection. The method comprises the following steps: determining an equivalent low-pass filter circuit of the amplifying circuit; determining a transfer function of the equivalent low-pass filter circuit; determining an attenuation coefficient; determining an equivalent transfer function of the non-ideal characteristic of the amplification circuit at the phase-sensitive detection output end; performing inverse operation to obtain an inverse system transfer function; carrying out regular design on the inverse system transfer function; and designing an analog system or a digital system according to the inverse system transfer function of the regular design to compensate the non-ideal characteristics of the analog signal amplification link. According to the invention, the problem of signal distortion caused by non-ideal characteristics such as uneven amplitude-frequency response and phase nonlinearity in an analog signal amplification link is solved, and especially the technical problems of measurement precision reduction and measurement accuracy reduction caused by non-ideal frequency response characteristics of a detection system in a weak signal detection scene are solved.

Description

Technical Field

[0001] This invention relates to the field of weak signal detection technology, and in particular to a compensation method for non-ideal characteristics in analog signal amplification links. Background Technology

[0002] Lock-in amplification (LIA) technology, as the cornerstone of weak signal detection, extracts weak signals from strong noise backgrounds through coherent demodulation mechanisms. It is widely used in cutting-edge fields such as sensor signal detection, bioelectric sensing, and quantum measurement. Its core chain consists of three main modules: preamplifier, phase-sensitive detector, and low-pass filter.

[0003] When the resonant sensor outputs a double-sideband modulated signal, the analog preamplifier circuit is limited by factors such as parasitic capacitance and component tolerances, making it difficult to maintain a flat amplitude-frequency response and phase-frequency response. As the double-sideband modulated signal passes through the circuit, different frequencies experience varying attenuation and phase shift, reducing the accuracy of the phase-sensitive detector output signal.

[0004] The current mainstream improvement method for preamplifier circuits is to insert an RLC network or a negative feedback equalizer into the amplification link to compensate for amplitude-frequency fluctuations. This introduces additional noise, degrades the signal-to-noise ratio, and the phase shift generated by the compensation circuit itself exacerbates phase distortion, making it difficult to synchronously and accurately compensate for amplitude-frequency and phase-frequency distortions.

[0005] Faced with the aforementioned bottlenecks, a simple new method for frequency response compensation is urgently needed. Summary of the Invention

[0006] In view of the above-mentioned shortcomings in the prior art, the present invention provides a compensation method for non-ideal characteristics in analog signal amplification links, which can compensate for the influence of the amplification circuit without modifying the analog circuit design, and realize the accurate detection function of reducing the phase-locked amplification error.

[0007] To achieve the above objectives, the technical solution adopted by this invention is: a compensation method for non-ideal characteristics in an analog signal amplification link, comprising the following steps: Determine the equivalent low-pass filter circuit for the amplifier circuit; Determine the transfer function of the equivalent low-pass filter circuit; The attenuation coefficient is determined based on the transfer function; Based on the attenuation coefficient, the equivalent transfer function of the amplifier circuit at the phase-sensitive detector output terminal is determined to obtain the equivalent transfer function of the non-ideal characteristics of the amplifier circuit at the phase-sensitive detector output terminal. The inverse system transfer function is obtained by performing an inverse operation on the equivalent transfer function of the non-ideal characteristics of the amplifier circuit at the output of the phase-sensitive detector. Regularization design of the transfer function of the inverse system; Based on the inverse system transfer function designed using regularization, analog or digital systems are designed to compensate for the non-ideal characteristics of analog signal amplification links.

[0008] Furthermore, the determination of the transfer function of the equivalent low-pass filter circuit is specifically as follows: Based on the cutoff frequency and order of the equivalent low-pass filter circuit, the order, cutoff frequency, and filter type are set in the software to design the filter and derive the state-space model of the filter. Based on the relationship between the state-space model and the transfer function, the transfer function of the equivalent low-pass filter circuit can be obtained.

[0009] Furthermore, the transfer function of the equivalent low-pass filter circuit is obtained by solving, and it is specifically as follows: The state-space model is determined using the following formula: ; ; in, Indicates time, Represents the state vector. , , and Both represent system matrices. Represents the input vector. Indicates the output vector; Under zero-input conditions, perform a Laplace transform on the state-space model: ; ; in, , , and Both represent system matrices. express Laplace transform, express Laplace transform, express Laplace transform, Represents the Laplace operator; Based on the Laplace transform, the transfer function of the equivalent low-pass filter circuit is obtained: ; in, Represents the transfer function. Represents the identity matrix.

[0010] Furthermore, the expression for the attenuation coefficient is as follows: ; ; ; ; in, Indicates the attenuation coefficient. This represents the response of the difference frequency signal. Represents the response of the sum-frequency components. This represents the response of the equivalent low-pass filter circuit to the difference frequency component. This represents the frequency domain representation of the difference frequency component in the input signal. This represents the response of the equivalent low-pass filter circuit to the sum-frequency components. This represents the frequency domain representation of the sum frequency component in the input signal. The form of the transfer function of the equivalent low-pass filter circuit of the amplifier circuit in the frequency domain is given by the transfer function. The transformation is obtained, and the transformation relationship is: , Represents the Laplace operator. Indicates the real part, Indicates the imaginary part. This indicates the carrier frequency of the double-sideband modulated signal. This indicates the frequency of the double-sideband modulated input signal. , , and Both represent system matrices.

[0011] Furthermore, the expression for the equivalent transfer function is as follows: ; in, This represents the equivalent transfer function of the amplifier circuit at the output of the phase-sensitive detector. Indicates the attenuation coefficient. , , and Both represent system matrices. Represents the identity matrix. This represents the Laplace operator.

[0012] Furthermore, the regularization design of the transfer function of the compensation system is expressed as follows: ; ; in, This represents a canonical approximation of the transfer function of the inverse system. Represents the transfer function of the inverse system. Represents the time constant. Represents the Laplace operator. k This represents the highest order of the transfer function of the inverse system. Indicates the attenuation coefficient. , , and Both represent system matrices. Represents the identity matrix. The beneficial effects of this invention are: The present invention provides a method for compensating the non-ideal characteristics of an analog amplification link through inverse system compensation. The compensation is performed at the output of the phase-sensitive detector, and the compensation is applied to the low-frequency signal. This avoids the noise accumulated in the amplified AC link, preserves the dynamic characteristics and stability margin of the original phase-locked amplifier link, improves the signal-to-noise ratio and robustness of the detection system, and makes the compensation design more flexible.

[0013] The present invention provides a method for compensating for non-ideal characteristics of an analog amplification link through inverse system compensation. It employs transfer function equivalence to simultaneously compensate for the amplitude and phase of the signal, thereby improving the accuracy of the detection system.

[0014] The present invention provides a method for compensating for non-ideal characteristics of analog amplification links through inverse system compensation. It performs equivalent transformation on the amplifier circuit, abstracting the complex transimpedance amplifier into a single-pole system, which greatly simplifies the analysis process while preserving key dynamic characteristics. Attached Figure Description

[0015] Figure 1 The flowchart of the analog amplification link non-ideal characteristic compensation method for inverse system compensation is shown; Figure 2 The response curve of the equivalent single-pole low-pass filter circuit of the amplifier circuit in the embodiment is shown; Figure 3 The response curves of the compensation inverse system and the equivalent low-pass filter circuit at the phase-sensitive detector output terminal of the embodiment are shown. Detailed Implementation

[0016] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0017] Example The embodiment applies a non-ideal characteristic correction method for an analog lock-in amplifier link using inverse system compensation according to the present invention, to achieve high-precision demodulation of the output signal of a resonant voltage sensor, reducing errors caused by components in the analog conditioning circuit. (Reference) Figure 1 This invention provides a compensation method for non-ideal characteristics in an analog signal amplification link, characterized by comprising the following steps: S1. Determine the equivalent low-pass filter circuit for the amplifier circuit; In this embodiment, based on the response curve of the amplifier circuit to the input signal, characteristic analysis is performed to obtain the cutoff frequency of the equivalent low-pass filter, and a corresponding low-pass filter circuit is designed. By comparing the curves of the two circuits, it is determined that the equivalent circuit is correct and effective.

[0018] like Figure 2 As shown, the response characteristics of the amplifier circuit are simulated using circuit simulation software. The frequency at which the gain reaches -3dB is used as the cutoff frequency of the equivalent low-pass filter circuit. In this embodiment, the cutoff frequency of the equivalent low-pass filter circuit is 16.3kHz.

[0019] S2. Determine the transfer function of the equivalent low-pass filter circuit; In this embodiment, based on the cutoff frequency and order of the equivalent low-pass filter, the order, cutoff frequency, and filter type are set using the Analog Filter Design module in Simulink software. The filter is then designed, and its state-space model is derived. Based on the relationship between the state-space model and the transfer function, the expression for the transfer function is derived.

[0020] The state-space model is shown in equations (1) and (2): (1) (2) in, Indicates time, Represents the state vector. , , and Both represent system matrices. Represents the input vector. Indicates the output vector; Under zero-input conditions, the Laplace transform of equations (1) and (2) is shown in equations (3) and (4): (3) (4) in, , , and Both represent system matrices. express Laplace transform, express Laplace transform, Represents the input vector. express Laplace transform, Indicates the output vector. Let represent the Laplace operator. The transfer function, obtained by combining equations (3) and (4), is shown in equation (5): (5) in, , , and Both represent system matrices. express Laplace transform, express Laplace transform, Represents the input vector. express Laplace transform, Indicates the output vector. This represents the Laplace operator.

[0021] S3. Determine the attenuation coefficient based on the transfer function; In this embodiment, the mathematical expression of the input signal is subjected to Laplace transform, multiplied with the transfer function, and the responses of the difference frequency component and the sum frequency component are calculated. The ratio of the amplitude response of the sum frequency component to the amplitude response of the difference frequency component is used as the attenuation coefficient α.

[0022] The signal expression of the input amplifier circuit is shown in equation (6): (6) in, This indicates the signal input to the amplifier circuit. Represents a functional relationship. Is with Relevant variables, This indicates the carrier frequency of the double-sideband modulated signal. This indicates the frequency of the double-sideband modulated input signal.

[0023] The transfer function of the equivalent low-pass filter circuit of the amplifier circuit in the frequency domain is shown in equation (7): (7) Based on the calculation results of step two, the responses of the difference frequency signal and the sum frequency signal input after passing through the amplifier circuit are calculated as shown in equations (8) and (9): (8) (9) The attenuation coefficient is calculated according to equations (8) and (9) as shown in equation (10): (10) in, Indicates the attenuation coefficient. This represents the response of the difference frequency signal. Represents the response of the sum-frequency components. This represents the response of the equivalent low-pass filter circuit to the difference frequency component. This represents the frequency domain representation of the difference frequency component in the input signal. This represents the response of the equivalent low-pass filter circuit to the sum-frequency components. This represents the frequency domain representation of the sum frequency component in the input signal. The form of the transfer function of the equivalent low-pass filter circuit of the amplifier circuit in the frequency domain is given by the transfer function. The transformation is obtained, and the transformation relationship is: , Represents the Laplace operator. Indicates the real part, Indicates the imaginary part. This indicates the carrier frequency of the double-sideband modulated signal. This indicates the frequency of the double-sideband modulated input signal. , , and Both represent system matrices.

[0024] S4. Based on the attenuation coefficient, the equivalent transfer function of the amplifier circuit at the phase-sensitive detector output terminal is determined to obtain the equivalent transfer function of the non-ideal characteristics of the amplifier circuit at the phase-sensitive detector output terminal. In this embodiment, the phase-sensitive detection system is a linear time-varying system, and the transfer function of the amplifier circuit at the output of the phase-sensitive detection system is shown in equation (11): (11) in, This represents the equivalent transfer function of the amplifier circuit at the output of the phase-sensitive detector. Indicates the attenuation coefficient. , , and Both represent system matrices. Represents the identity matrix. This represents the Laplace operator.

[0025] S5. Perform inverse operation on the equivalent transfer function of the non-ideal characteristics of the amplifier circuit at the output of the phase-sensitive detector to obtain the inverse system transfer function; In this embodiment, the non-ideal characteristics are corrected by designing an inverse system at the phase-sensitive detector output. The equivalent transfer function of the non-ideal characteristics of the amplifier circuit obtained in step four at the phase-sensitive detector output is inversely calculated to obtain the compensation system transfer function (i.e., the inverse system transfer function). Specifically: According to S4, the equivalent transfer function of the non-ideal characteristics of the amplifier circuit at the phase-sensitive detector output is obtained. To correct the non-ideal characteristics, an inverse system is designed at the phase-sensitive detector output, making the composite system at the output an identity mapping, such as... Figure 3 As shown.

[0026] The transfer function of the inverse system is shown in equation (12): (12) Represents the transfer function of the inverse system. Indicates the attenuation coefficient. , , and Both represent system matrices. Represents the identity matrix. This represents the Laplace operator.

[0027] In the example, the amplifier circuit is equivalent to a first-order low-pass filter circuit with D=0, which is a single-input single-output system. In the example, the inverse system transfer function is shown in equation (13): (13) in, Represents the transfer function of the inverse system. Indicates the attenuation coefficient. , , Both represent system matrices. Represents the identity matrix. This represents the Laplace operator.

[0028] S6. Perform regularization design on the transfer function of the inverse system; S7. Based on the inverse system transfer function designed by regularization, design an analog or digital system to compensate for the non-ideal characteristics of the amplification link.

[0029] In this embodiment, the inverse system transfer function is non-regular, containing ideal differential terms that are unrealizable in the physical system. Therefore, a regularization design for the inverse system transfer function is required. ;in, Represents the transfer function of the inverse system. k This represents the highest order of the transfer function of the inverse system. It is the time constant, which controls the approximate accuracy and the robustness of the system. The selection requirement is moderate, and the optimal value can be selected through simulation. Based on the transfer function of the compensation system, an analog or digital system is designed to compensate for the non-ideal characteristics of the amplification link.

[0030] Specifically, the amplifier circuit is equivalent to a low-pass filter circuit. The numerator order of the compensation system transfer function is greater than the denominator order, it contains a differential term, and it is non-regular and non-causal, making it physically unrealizable. Therefore, it is necessary to regularize the inverse system transfer function and construct an approximate inverse system transfer function as shown in equation (14): (14) in, This represents a canonical approximation of the transfer function of the inverse system. Represents the Laplace operator. k This represents the highest order of the transfer function of the inverse system. It represents the time constant, controls the approximate accuracy, and the robustness of the system. The selection requirements are moderate, and the optimal value can be selected through simulation. , , Both represent system matrices.

[0031] The regularization design of the inverse system transfer function in the embodiment is shown in equation (15): (15) Simulation results show that the non-ideal characteristics of the amplifier circuit cause significant errors in the phase-sensitive detection results. The method described in this invention compensates for these non-ideal characteristics, effectively reducing the errors and improving the accuracy of the signal detection system. An analog or digital system is designed based on a canonically designed transfer function to compensate for the non-ideal characteristics of the amplifier circuit.

[0032] This invention is particularly applicable to transimpedance amplifier-locked-phase amplifier combined links, such as weak signal processing systems like photoelectric detection, bioelectric signal acquisition, and sensor interfaces.

[0033] The above detailed description further illustrates the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method of compensating for non-ideal characteristics in an analog signal amplification link, the method comprising: determining a non-ideal characteristic of the analog signal amplification link; and adjusting a gain of the analog signal amplification link based on the determined non-ideal characteristic. Includes the following steps: Determine the equivalent low-pass filter circuit for the amplifier circuit; Determine the transfer function of the equivalent low-pass filter circuit; The attenuation coefficient is determined based on the transfer function; Based on the attenuation coefficient, the equivalent transfer function of the amplifier circuit at the phase-sensitive detector output terminal is determined to obtain the equivalent transfer function of the non-ideal characteristics of the amplifier circuit at the phase-sensitive detector output terminal. The inverse system transfer function is obtained by performing an inverse operation on the equivalent transfer function of the non-ideal characteristics of the amplifier circuit at the output of the phase-sensitive detector. Regularization design of the transfer function of the inverse system; Based on the inverse system transfer function designed using regularization, analog or digital systems are designed to compensate for the non-ideal characteristics of analog signal amplification links.

2. The method of claim 1, wherein, The transfer function of the equivalent low-pass filter circuit is specifically determined as follows: Based on the cutoff frequency and order of the equivalent low-pass filter circuit, the order, cutoff frequency, and filter type are set in the software to design the filter and derive the state-space model of the filter. Based on the relationship between the state-space model and the transfer function, the transfer function of the equivalent low-pass filter circuit can be obtained.

3. The method of claim 2, wherein the method further comprises: The transfer function of the equivalent low-pass filter circuit obtained by the solution is as follows: Determine the state-space model; Under zero-input conditions, perform a Laplace transform on the state-space model; Based on the Laplace transform results, the transfer function of the equivalent low-pass filter circuit is obtained.

4. The compensation method for non-ideal characteristics in an analog signal amplification link according to claim 3, wherein the expression of the state-space model is as follows: ； ； in, denotes time, denotes state vector, , , and denote system matrix, denotes input vector, denotes output vector.

5. The compensation method for non-ideal characteristics in an analog signal amplification link according to claim 3, wherein the expression for the Laplace transform of the state-space model is as follows: ； ； in, , , and Both represent system matrices. express Laplace transform, express Laplace transform, Represents the input vector. express Laplace transform, Indicates the output vector. This represents the Laplace operator.

6. The compensation method for non-ideal characteristics in an analog signal amplification link according to claim 3, wherein the transfer function of the equivalent low-pass filter circuit is expressed as follows: ； in, Represents the transfer function. , , and Both represent system matrices. Represents the identity matrix. This represents the Laplace operator.

7. The compensation method for non-ideal characteristics in an analog signal amplification link according to claim 1, characterized in that, The expression for the attenuation coefficient is as follows: ； ； ； ； in, Indicates the attenuation coefficient. This represents the response of the difference frequency signal. Represents the response of the sum-frequency components. This represents the response of the equivalent low-pass filter circuit to the difference frequency component. This represents the frequency domain representation of the difference frequency component in the input signal. This represents the response of the equivalent low-pass filter circuit to the sum-frequency components. This represents the frequency domain representation of the sum frequency component in the input signal. The form of the transfer function of the equivalent low-pass filter circuit of the amplifier circuit in the frequency domain is given by the transfer function. The transformation is obtained, and the transformation relationship is: , Represents the Laplace operator. Indicates the real part, Indicates the imaginary part. This indicates the carrier frequency of the double-sideband modulated signal. This indicates the frequency of the double-sideband modulated input signal. , , and Both represent system matrices.

8. The compensation method for non-ideal characteristics in an analog signal amplification link according to claim 1, characterized in that, The expression for the equivalent transfer function is as follows: ； in, This represents the equivalent transfer function of the amplifier circuit at the output of the phase-sensitive detector. Indicates the attenuation coefficient. , , and Both represent system matrices. Represents the identity matrix. This represents the Laplace operator.

9. The compensation method for non-ideal characteristics in an analog signal amplification link according to claim 1, characterized in that, The regularization design of the transfer function of the compensation system is expressed as follows: ； ； in, This represents a canonical approximation of the transfer function of the inverse system. Represents the transfer function of the inverse system. Represents the time constant. Represents the Laplace operator. k This represents the highest order of the transfer function of the inverse system. Indicates the attenuation coefficient. , , and Both represent system matrices. Represents the identity matrix.

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