Frequency compensation system based on low-noise operational amplifier

Abstract

The invention discloses a frequency compensation system based on a low-noise operational amplifier, and relates to the technical field of analog circuit frequency domain modeling and stability optimizing.The unity gain frequency, the maximum phase lag angle and the low-frequency cut-off point of the operational amplifier are obtained; constructing a frequency compensation parameter group, and establishing an initial frequency domain stability model based on an open-loop transfer function; sequentially importing the compensation parameter groups into the model, performing frequency scanning simulation, extracting a phase response value under each compensation configuration, constructing a stability function, and performing label marking; further screening out a compensation parameter which meets the stability requirement and has the minimum capacitive reactance amplitude, and feeding back the compensation parameter for adjusting a frequency compensation loop; according to the method, fine modeling and optimal selection of the frequency compensation strategy are realized, the stability and efficiency of the system in low-noise and high-precision application are improved, and the method has good engineering applicability.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of analog circuit frequency domain modeling and stability optimization, and particularly relates to a frequency compensation system based on a low-noise operational amplifier. BACKGROUND

[0002] With the wide application of precision sensors and high-speed data acquisition systems in medical monitoring, aerospace and quantum measurement fields, the system has put forward very high requirements on the performance of low-noise operational amplifiers in the analog signal processing link. Especially in the low-frequency band (<10Hz) weak signal amplification scene, the traditional operational amplifier has problems such as frequency compensation mismatch, open-loop gain drop and insufficient phase margin, which leads to the problems of the whole system such as increased zero drift, high-frequency output noise and even closed-loop oscillation, and seriously affects the signal accuracy and system stability.

[0003] The current common frequency compensation method (such as Miller compensation) can provide basic phase margin in the medium frequency band, but it has the following difficult problems to solve at very low frequency signals (<1Hz): The compensation capacitor value must be very large to maintain stability, which leads to a significant increase in chip area; the very low frequency compensation capacitor cannot realize frequency self-adaptation, which leads to response delay of the amplifier when the signal jumps; The coupling effect of the multi-stage compensation structure leads to the frequency drift of the noise floor, causing the low-frequency resonance point of the system to shift to the working bandwidth. Especially in the low-temperature, high-magnetic, high-impedance measurement scene, the frequency compensation instability problem of this kind is more significant, which directly threatens the accuracy index of the system to meet the standard and the long-term working reliability. SUMMARY

[0004] The purpose of the present application is to provide a frequency compensation system based on a low-noise operational amplifier to solve the problems in the background art.

[0005] In order to achieve the above purpose, the present application provides the following technical scheme: a frequency compensation system based on a low-noise operational amplifier, comprising: a frequency characteristic extraction module: obtaining the open-loop gain and phase response curve of the target low-noise operational amplifier at different frequency points, and extracting the low-frequency cutoff point ω1, the unity gain frequency ωu and the maximum phase lag θm; a compensation parameter construction module: constructing a frequency compensation parameter group P={P1, P2,..., Pn}, wherein Pi={Ci, Ri}, Ci is the compensation capacitor value, Ri is the equivalent compensation resistance value, and Pn is the maximum compensation capacitive reactance range; Frequency domain stability modeling module: Based on the obtained ω1, ωu, and θm features, an initial frequency domain stability model M0 is constructed. Specifically, this includes: defining the target phase response curve and open-loop gain envelope within the frequency range using unity-gain frequency, maximum phase lag angle, and low-frequency cutoff point as input boundary conditions; and establishing an open-loop transfer function model. Where ω1 is the low-frequency pole frequency, ωz is the compensation zero frequency, A is the low-frequency gain constant, and s is the independent variable in the complex frequency domain; the open-loop transfer function model is coupled with each compensation parameter unit in the compensation parameter group to form a frequency response mapping model; the initial frequency domain stability model M0 is defined as a set of response functions containing the frequency response mapping relationship; Frequency scanning simulation module: The frequency compensation parameter group P is sequentially imported into the initial frequency domain stability model M0. The stability function F(Pi) under each compensation configuration is obtained through frequency scanning simulation. Each group of Pi is marked as to whether the stability critical condition F(Pi)≥Φ0 is satisfied, where Φ0 is the preset minimum phase margin. The optimal compensation extraction module extracts the minimum compensation parameter set P* that meets the stability requirements based on the F(Pi) marking results. P* is then used to adjust the original amplifier's frequency compensation circuit. Specifically, this includes: selecting all parameters with stability function values ​​greater than zero from the compensation parameter units that have been assigned qualified labels; calculating the total equivalent capacitive reactance of each parameter unit based on the pre-set optimization objective, using the capacitive reactance amplitude formed by the compensation capacitor value and the equivalent compensation resistor value as an evaluation index; extracting the parameter unit with the smallest capacitive reactance amplitude from the selection results, under the condition that the stability function value is non-negative, to form the minimum compensation parameter set; and feeding back the minimum compensation parameter set to adjust the original amplifier's frequency compensation circuit structure.

[0006] Preferably, the frequency response extraction module includes: performing an open-loop connection test on a low-noise operational amplifier to obtain open-loop gain and phase response data curves within a preset frequency scanning range; performing feature point extraction processing on the obtained frequency response curves to identify the unity-gain frequency ωu corresponding to the first drop in open-loop gain to 0dB; fitting the phase response data using a third-order curve fitting method to calculate the phase angle corresponding to the unity-gain frequency and determine its maximum phase lag θm; and detecting the inflection point position using the derivative method based on the gain-frequency response slope change law, thereby extracting the corresponding low-frequency cutoff point ω1.

[0007] Preferably, the compensation parameter construction module includes: determining the range of compensation capacitor values ​​based on the pre-measured unity-gain frequency, maximum phase lag angle, and low-frequency cutoff frequency of the low-noise operational amplifier, with the lower limit limited by the minimum phase margin requirement and the upper limit limited by the DC stability condition; generating multiple compensation capacitor values ​​within the range of compensation capacitor values ​​according to a preset incremental step size, and performing analytical calculation on the equivalent compensation resistance value corresponding to each compensation capacitor value based on the equivalent small-signal model, so that the two form a one-to-one parameter pair; combining each compensation capacitor value with the corresponding equivalent compensation resistance value to form a compensation parameter unit Pi={Ci,Ri}, where Ci is the compensation capacitor value, Ri is the equivalent compensation resistance value, and Pn is the maximum compensation capacitive reactance range; sorting all compensation parameter units according to the capacitive reactance amplitude formed by the compensation capacitor value and the equivalent compensation resistance value, and defining the compensation parameter unit with the largest capacitive reactance amplitude as the maximum compensation capacitive reactance range, so as to construct a complete frequency compensation parameter group P.

[0008] Preferably, the frequency scanning simulation module includes: sequentially substituting each compensation parameter unit in the frequency compensation parameter group into the initial frequency domain stability model to generate a corresponding frequency response function; performing numerical simulation on each frequency response function within a set frequency scanning range to extract the phase response value at the unity gain frequency; and comparing the extracted phase response value with a preset minimum phase margin threshold to construct a stability function. ,in To determine the phase response under the corresponding compensation parameter unit, we need to determine whether each stability function value is greater than or equal to zero, and label each group of compensation parameter units according to the determination result to distinguish those that meet the stability requirements and those that do not.

[0009] Preferably, the method involves determining whether each stability function value is greater than or equal to zero, and labeling each group of compensation parameter units based on the determination result. This includes: numerically determining the stability function value corresponding to each compensation parameter unit in the frequency scanning simulation result; if the function value is greater than or equal to zero, it is considered to meet the stability requirements; assigning a qualified label to compensation parameter units that meet the determination conditions, and assigning an unqualified label to compensation parameter units that do not meet the determination conditions; organizing all labeled compensation parameter units into a structured label result set, including compensation capacitor value, compensation resistor value, stability function value, and corresponding label; and sorting the qualified label units in ascending or descending order according to the size of the stability function value.

[0010] The technical effects and advantages provided by this invention in the above technical solution are as follows: The frequency compensation method based on a low-noise operational amplifier provided by this invention fully utilizes frequency domain characteristic parameters, including unity-gain frequency, maximum phase lag angle, and low-frequency cutoff point. By constructing an initial frequency domain stability model and combining it with frequency compensation parameter sets for frequency scanning simulation, it achieves quantitative evaluation of phase margin and stability function mapping of compensation configuration effect. This method, through stability function value judgment and labeling mechanism, can efficiently screen compensation parameter units that meet phase margin constraints, ensuring that the system maintains sufficient stability margin under different compensation conditions, and avoiding the uncertainty caused by relying on experience to select parameters in traditional designs.

[0011] Furthermore, this invention employs a minimum capacitive reactance optimization strategy. While ensuring stability, it extracts the compensation parameter set with the lowest resource consumption from the capacitor-resistor combination and feeds it back into the actual frequency compensation stage of the operational amplifier, significantly improving compensation efficiency and resource utilization. This technical solution combines modeling accuracy with feasibility, and is suitable for scenarios with high requirements for low noise and frequency stability, such as low-frequency signal amplification, high-precision analog-to-digital conversion, and electrophysiological signal detection. It reduces power consumption, area, and device complexity while ensuring stable system operation. Attached Figure Description

[0012] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this invention. For those skilled in the art, other drawings can be obtained based on these drawings.

[0013] Figure 1 This is a flowchart of the system modules of the present invention. Detailed Implementation

[0014] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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, 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.

[0015] For examples, please refer to Figure 1 As shown in this embodiment, a frequency compensation system based on a low-noise operational amplifier includes: Frequency response extraction module: Obtain the open-loop gain and phase response curves of the target low-noise operational amplifier at different frequency points, and extract its low-frequency cutoff point ω1, unity-gain frequency ωu, and maximum phase hysteresis θm.

[0016] Open-loop connection testing was performed on the low-noise operational amplifier. By disconnecting its closed-loop feedback path and applying a constant amplitude sinusoidal excitation signal to the input, the output response was measured using a vector network analyzer. The frequency scan range was set from 10 Hz to 10 MHz, and the open-loop gain (in dB) and phase response (in angle) data at each frequency point were recorded at linear intervals to obtain a complete frequency response curve.

[0017] Feature point extraction is performed on the acquired frequency response curve. Using open-loop gain as the vertical axis and frequency as the horizontal axis, the trend of gain variation with frequency is analyzed to identify the position where the open-loop gain first decreases and approaches 0 dB. The frequency value corresponding to the intersection of the gain curve and the 0 dB line is defined as the unity-gain frequency, denoted as ωu. If this intersection point falls between two sampling points, linear interpolation is used to calculate the accurate frequency value corresponding to the intersection point to improve measurement accuracy.

[0018] A third-order polynomial curve fitting method was used to fit the phase response data. The phase response data were fitted using a polynomial with frequency f as the independent variable, resulting in the following fitting function: Where a, b, c, and d are fitting coefficients, and the optimal solution is determined using the least squares method. At the point corresponding to the unity-gain frequency ωu, the fitting function φ(f) is substituted to calculate the phase response angle at that frequency point, thereby identifying the minimum phase angle value near that position, and defining this minimum phase angle as the maximum phase lag angle, denoted as θm. This parameter is used to reflect the stability margin of the op-amp near the unity-gain point.

[0019] Based on the gain-frequency response slope variation law, the derivative method is used to detect the inflection point of the frequency response curve in order to extract the low-frequency cutoff frequency. First, the first derivative of the gain curve is calculated to construct a function G′(f), which represents the rate of gain decrease per unit frequency change. In the lower frequency region, the location of the maximum value of G′(f) is detected, which is the point where the gain decreases most rapidly. The corresponding frequency is defined as the low-frequency cutoff point, denoted as ω1.

[0020] Compensation parameter construction module: Constructs a frequency compensation parameter group P={P1,P2,...,Pn}, where Pi={Ci,Ri}, Ci is the compensation capacitor value, Ri is the equivalent compensation resistance value, and Pn is the maximum compensation capacitive reactance range.

[0021] Based on the obtained unity-gain frequency, maximum phase lag angle, and low-frequency cutoff point frequency, the range of values ​​for the compensation capacitor is determined. The lower limit of the compensation capacitor value is calculated based on the target minimum phase margin. The upper limit is determined according to the stability constraints of the closed-loop system under DC conditions. When the compensation capacitor value exceeds this upper limit, it may lead to a significant decrease in DC gain or uncontrolled pole shift, thereby causing zero drift or closed-loop oscillation.

[0022] Within the aforementioned range of compensation capacitor values, multiple candidate values ​​are generated by dividing the range using a fixed linear step size. Specifically, the step size is set to ΔC, the initial value is C1, and the maximum value is Cn, resulting in the following compensation capacitor sequence: Let i = 1 to n. For each compensation capacitor value, its corresponding equivalent compensation resistor value is calculated using an equivalent small-signal model. This model is based on the second-order frequency response equation. Under the condition that the preset gain-bandwidth product remains unchanged, the RC relationship that can equivalently achieve the target zero-pole configuration is analytically solved. The equivalent compensation resistor value can be obtained using the formula... The calculated value is fi, which represents the target frequency position corresponding to the compensation pole, and is configured according to the actual application scenario.

[0023] Each compensation capacitor value is paired with its corresponding calculated equivalent compensation resistance value to form a complete compensation parameter unit, denoted as . Where Ci is the value of the i-th compensation capacitor and Ri is the equivalent compensation resistor value that matches it. All generated parameter units constitute the frequency compensation parameter set P={P1, P2, ..., Pn}, where Pn is the parameter unit with the highest number.

[0024] Finally, all parameter units are sorted according to the capacitive reactance amplitude formed by the compensation capacitor value and the equivalent compensation resistor value in each parameter unit. The capacitive reactance amplitude is defined as follows: ,in The reference frequency is used. The compensation parameter unit with the largest capacitive reactance amplitude is extracted by sorting and defined as the parameter corresponding to the maximum compensation capacitive reactance range, denoted as Pn. This parameter unit provides the strongest compensation capability while ensuring the system's ultimate stability and is used to determine the boundary characteristics of the frequency compensation parameter group.

[0025] Frequency domain stability modeling module: Construct an initial frequency domain stability model M0 based on the obtained ω1, ωu and θm features.

[0026] Using unity-gain frequency, maximum phase lag angle, and low-frequency cutoff point as input boundary conditions, a target phase response curve and open-loop gain envelope are defined within the frequency range. These three parameters limit the start and end points of the model's operating bandwidth, the lower limit of stability, and the reference points for zero-pole placement. Based on this, an ideal phase response curve is constructed as the objective function for subsequent transfer function fitting.

[0027] Establish an open-loop transfer function model. The transfer function is defined as follows: Here, G(s) represents the open-loop response function of the low-noise operational amplifier in the Laplace domain, A is the low-frequency gain constant, ω1 is the low-frequency pole frequency, corresponding to the low-frequency cutoff point, and ωz is the compensation zero frequency, used to improve the phase margin near the unity-gain frequency. s is the independent variable in the complex frequency domain (complex Laplace domain), used to represent the frequency response or dynamic behavior of a system. This transfer function is a standard second-order single-input single-output system function, with one low-frequency pole and one mid-frequency zero. By adjusting the three variables A, ω1, and ωz, it is fitted to the measured gain-phase response data under the aforementioned boundary conditions, making the model response curve approximate the measured curve.

[0028] The above open-loop transfer function model is coupled with each compensation parameter unit in the compensation parameter group to form a frequency response mapping model. The compensation parameter unit is Pi={Ci,Ri} formed during the aforementioned construction process, where Ci is the compensation capacitor value and Ri is the corresponding equivalent compensation resistance value. Based on the definition of ωz in the transfer function, ωz is expressed as... This is then substituted into the G(s) expression to achieve quantitative coupling between the compensation parameters and the model's frequency characteristics. Thus, each compensation parameter unit Pi corresponds to a unique Gi(s) expression, thereby obtaining its frequency response function.

[0029] The initial frequency domain stability model is defined as a set of response functions containing the frequency response mapping relationship described above, denoted as M0={G1(s),G2(s),...,Gn(s)}, where n is the number of compensation parameter units. Each Gi(s) expression is analytical within the same frequency sweep range, facilitating the subsequent extraction of stability indices such as phase margin and gain margin using numerical methods.

[0030] Frequency scanning simulation module: The frequency compensation parameter group P is sequentially imported into the initial frequency domain stability model M0. The stability function F(Pi) under each compensation configuration is obtained through frequency scanning simulation. Each group of Pi is marked as to whether the stability critical condition F(Pi)≥Φ0 is satisfied, where Φ0 is the preset minimum phase margin.

[0031] Each compensation parameter unit generated in the frequency compensation parameter set is sequentially substituted into the initial frequency domain stability model to generate its corresponding frequency response function. Specifically, for any set of compensation parameter units Pi={Ci,Ri}, where Ci is the compensation capacitor value and Ri is the equivalent compensation resistance value, based on the coupling relationship established in the aforementioned frequency domain modeling steps, it is substituted into the open-loop transfer function expression G(s) to form the complete frequency response function Gi(s). This function can describe the gain and phase response characteristics of the system in the frequency domain under compensation conditions.

[0032] Numerical simulations were performed on the frequency response function within a defined frequency scanning range. The frequency scanning range was set to 10 Hz to 10 MHz, and discrete scanning was performed using uniform sampling on logarithmic coordinates. For each response function Gi(s), its phase response curve was solved at the scanning frequency points, and the phase angle value corresponding to the unity-gain frequency was extracted. The unity-gain frequency is the frequency point at which the gain in the frequency response function first drops to 0 dB.

[0033] The extracted phase response value is compared with a preset minimum phase margin threshold to construct a stability function expression. Let... To compensate for the phase response of parameter unit Pi at unity gain frequency, and with Φ0 as the stability threshold (usually set to 45 degrees), the stability function is defined as follows: ,in This represents the phase response under the corresponding compensation parameter unit; when F(Pi) is greater than or equal to 0, it indicates that the phase margin under this compensation configuration meets the minimum stability requirement.

[0034] The stability function value corresponding to each compensation parameter unit is numerically evaluated. If the stability function value of a unit is greater than or equal to zero, i.e., the stability margin condition is met, the compensation parameter unit is assigned a "qualified" label; if it is less than zero, it is assigned a "unqualified" label, which is used to eliminate parameter combinations that are not engineering feasible in subsequent optimization processes.

[0035] All compensation parameter units that have been evaluated and tagged are compiled into a structured result set. This structured result set includes the compensation capacitance value, compensation resistance value, stability function value, and corresponding validity label for each compensation parameter unit. The result set is recorded in a two-dimensional structure and can be represented in tabular or data matrix form for easy sorting and filtering operations.

[0036] To facilitate the selection of the optimal compensation strategy, the compensation parameter units marked as "qualified" are sorted according to the magnitude of their stability function values. The sorting can be in ascending or descending order, depending on the system design objectives. For example, if maximizing phase margin is a priority, the units can be sorted in descending order of F(Pi), and the compensation parameter units corresponding to the maximum values ​​can be extracted for final feedback to the amplifier circuit design.

[0037] Optimal compensation extraction module: Based on the F(Pi) marking results, extract the minimum compensation parameter set P* that meets the stability requirements, and use P* as feedback to adjust the original amplifier frequency compensation circuit.

[0038] From the compensation parameter units that have been marked "qualified" in the aforementioned frequency scan simulation and stability function judgment steps, select the set of parameters whose stability function values ​​are all greater than zero. Let the stability function be... ,in Φ represents the phase response angle at the unity-gain frequency, and Φ0 is the minimum phase margin threshold (e.g., 45 degrees). Only when F(Pi) > 0 does it indicate that the corresponding compensation parameter unit not only meets the minimum phase margin requirement but also has a certain margin space, possessing further optimization potential. All parameter units that meet this condition are denoted as the candidate compensation set S1.

[0039] Based on a preset optimization objective, the total equivalent capacitive reactance of each compensation parameter unit is defined as an evaluation index to measure the resource consumption of the compensation loop. The capacitance amplitude... Calculated using the equivalent formula for resistor-capacitor series circuitry, it is defined as follows: ;in, This is the equivalent compensation resistance value. To compensate for the capacitance value, This is the unity-gain frequency, and the capacitive reactance is in ohms. This specification comprehensively considers the impedance characteristics under the combined influence of capacitance and resistance, and is used to compress compensation resources while maintaining stability.

[0040] Under the premise of ensuring that the stability function value is positive, the capacitive reactance amplitude is extracted from the candidate compensation set S1. The smallest parameter unit is denoted as P*. P* is the set of parameters that consumes the least circuit resources and has the highest frequency response efficiency among all compensation parameters that meet the phase margin requirements, and it is feasible and optimal.

[0041] The obtained minimum compensation parameter set P* is fed back into the frequency compensation loop of the original low-noise operational amplifier, and specific device parameters or circuit structure adjustments are made based on its compensation capacitor value C* and equivalent compensation resistor value R*. Specific methods include replacing the compensation capacitor components in the feedback network, adjusting the transconductance stage resistor matching unit, or updating the internal frequency compensation pole design of the operational amplifier based on the zero-point location calculated by P*, thereby ensuring frequency stability performance consistent with simulation expectations in practical applications.

[0042] Through the above-mentioned minimum compensation parameter extraction and feedback process, the minimum configuration of frequency compensation resources can be achieved while meeting the circuit stability requirements, effectively improving the synergy of the analog front end in multiple performance indicators such as power consumption, area, and phase margin.

[0043] The frequency compensation method based on low-noise operational amplifiers provided by this invention constructs an initial frequency domain stability model around frequency domain characteristic parameters such as unity-gain frequency, maximum phase lag angle, and low-frequency cutoff point. Combined with frequency scanning simulation using a set of compensation parameters, it achieves quantitative evaluation of phase margin and functional mapping of compensation effect. Through stability function judgment and labeling mechanism, it accurately selects compensation parameter units that meet stability requirements. Furthermore, it adopts a minimum capacitive reactance selection strategy to extract the capacitor-resistor combination with the minimum resource consumption while ensuring phase margin, and feeds this back into the frequency compensation circuit design, significantly improving compensation efficiency and system stability.

[0044] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.

Claims

1. A frequency compensation system based on a low-noise operational amplifier, characterized in that: include: Frequency response extraction module: Obtain the open-loop gain and phase response curves of the target low-noise operational amplifier at different frequency points, and extract its low-frequency cutoff point ω1, unity-gain frequency ωu, and maximum phase hysteresis θm; Compensation parameter construction module: Constructs a frequency compensation parameter group P={P1,P2,...,Pn}, where Pi={Ci,Ri}, Ci is the compensation capacitor value, Ri is the equivalent compensation resistance value, and Pn is the maximum compensation capacitive reactance range; Frequency domain stability modeling module: Based on the obtained ω1, ωu, and θm features, an initial frequency domain stability model M0 is constructed. Specifically, this includes: defining the target phase response curve and open-loop gain envelope within the frequency range using unity-gain frequency, maximum phase lag angle, and low-frequency cutoff point as input boundary conditions; and establishing an open-loop transfer function model. Where ω1 is the low-frequency pole frequency, ωz is the compensation zero frequency, A is the low-frequency gain constant, and s is the independent variable in the complex frequency domain; the open-loop transfer function model is coupled with each compensation parameter unit in the compensation parameter group to form a frequency response mapping model; the initial frequency domain stability model M0 is defined as a set of response functions containing the frequency response mapping relationship; Frequency scanning simulation module: The frequency compensation parameter group P is sequentially imported into the initial frequency domain stability model M0. The stability function F(Pi) under each compensation configuration is obtained through frequency scanning simulation. Each group of Pi is marked as to whether the stability critical condition F(Pi)≥Φ0 is satisfied, where Φ0 is the preset minimum phase margin. The optimal compensation extraction module extracts the minimum compensation parameter set P* that meets the stability requirements based on the F(Pi) marking results. P* is then used to adjust the original amplifier's frequency compensation circuit. Specifically, this includes: selecting all parameters with stability function values ​​greater than zero from the compensation parameter units that have been assigned qualified labels; calculating the total equivalent capacitive reactance of each parameter unit based on the pre-set optimization objective, using the capacitive reactance amplitude formed by the compensation capacitor value and the equivalent compensation resistor value as an evaluation index; extracting the parameter unit with the smallest capacitive reactance amplitude from the selection results, under the condition that the stability function value is non-negative, to form the minimum compensation parameter set; and feeding back the minimum compensation parameter set to adjust the original amplifier's frequency compensation circuit structure.

2. The frequency compensation system based on a low-noise operational amplifier according to claim 1, characterized in that: The frequency characteristic extraction module includes: Open-loop connection tests were performed on the low-noise operational amplifier to obtain open-loop gain and phase response data curves within a preset frequency scanning range; Feature point extraction processing was performed on the acquired frequency response curve to identify the unity gain frequency ωu corresponding to the first drop in open-loop gain to 0dB. The phase response data were fitted using a third-order curve fitting method to calculate the phase angle at the unity-gain frequency and determine its maximum phase lag θm. Based on the gain-frequency response slope variation law, the inflection point position is detected by the derivative method, thereby extracting the corresponding low-frequency cutoff point ω1.

3. The frequency compensation system based on a low-noise operational amplifier according to claim 2, characterized in that: The compensation parameter construction module includes: Based on the pre-measured unity-gain frequency, maximum phase lag angle, and low-frequency cutoff frequency of the low-noise operational amplifier, the range of values ​​for the compensation capacitor is determined. The lower limit is limited by the minimum phase margin requirement, and the upper limit is limited by the DC stability condition. Multiple compensation capacitor values ​​are generated within the range of compensation capacitor values ​​according to a preset incremental step size. Based on the equivalent small signal model, the equivalent compensation resistance value corresponding to each compensation capacitor value is analytically calculated so that the two form a one-to-one parameter pair. Each compensation capacitor value is combined with its corresponding equivalent compensation resistor value to form a compensation parameter unit Pi={Ci,Ri}, where Ci is the compensation capacitor value, Ri is the equivalent compensation resistor value, and Pn is the maximum compensation capacitive reactance range. All compensation parameter units are sorted according to the capacitive reactance amplitude formed by the compensation capacitor value and the equivalent compensation resistor value, and the compensation parameter unit with the largest capacitive reactance amplitude is defined as the maximum compensation capacitive reactance range, so as to construct a complete frequency compensation parameter group P.

4. The frequency compensation system based on a low-noise operational amplifier according to claim 1, characterized in that: The frequency scanning simulation module includes: Substitute each compensation parameter unit in the frequency compensation parameter group into the initial frequency domain stability model in sequence to generate the corresponding frequency response function; Within the set frequency scanning range, numerical simulations are performed on each frequency response function to extract the phase response value at the unity gain frequency. The extracted phase response value is compared with a preset minimum phase margin threshold to construct a stability function. ,in The phase response under the corresponding compensation parameter unit; Determine whether each stability function value is greater than or equal to zero, and label each set of compensation parameter units according to the determination result to distinguish those that meet the stability requirements and those that do not.

5. A frequency compensation system based on a low-noise operational amplifier according to claim 4, characterized in that: Determine whether each stability function value is greater than or equal to zero, and label each set of compensation parameter units according to the determination result, including: The stability function values ​​corresponding to each compensation parameter unit in the frequency scanning simulation results are numerically judged. If the function value is greater than or equal to zero, the stability requirement is considered to be met. Compensation parameter units that meet the judgment conditions are assigned a qualified mark, and compensation parameter units that do not meet the judgment conditions are assigned a unqualified mark. All labeled compensation parameter units are organized into a structured label result set, which includes compensation capacitor value, compensation resistor value, stability function value and corresponding label; The qualified identification units are sorted in ascending or descending order according to the magnitude of the stability function value.

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