A method for monitoring ESR and C of a C-type single-ended power amplifier output transformer

Abstract

The present application provides an ESR and C monitoring method for a C-type single-ended power amplifier output transformer, comprising: obtaining the primary winding resistance, secondary winding resistance, core loss resistance, inter-winding distributed capacitance, winding self-distributed capacitance and equivalent capacitance parameters caused by core dielectric loss according to the winding structure and core material of the C-type single-ended power amplifier output transformer; sampling the voltage and current waveforms of the primary and secondary windings using a sampling circuit, and determining the ESR and C values ​​in the output transformer equivalent circuit using a least squares fitting method based on the sampled data and the acquired parameters; using an optimized indicator prediction formula to calculate the distortion, high-frequency down slope of the frequency response, transient response time constant and overshoot under different ESR and C value combinations, and establishing a mapping table between the indicator value and the ESR and C value.

Description

Technical Field

[0001] The present invention relates to the field of information technology, and in particular to an ESR and C monitoring method for a C-type single-ended power amplifier output transformer. Background Art

[0002] The key technical challenge facing the sound quality optimization of C-type single-ended amplifiers is how to accurately measure and simulate the equivalent series resistance (ESR) and capacitance (C) values ​​of the output transformer, and establish a correlation model between these parameters and the sound quality performance of the amplifier. This challenge is mainly reflected in the following aspects: the characteristics of ESR and C values ​​changing with frequency are difficult to accurately capture, and traditional static measurement methods cannot reflect their dynamic changes. Accurately applying the measured ESR and C values ​​to the theoretical calculations of the distortion, frequency response, and transient response of the amplifier requires the establishment of a complex mathematical model. There is a deviation between the theoretical prediction results and the actual amplifier performance, and a large amount of measured data is needed to verify and optimize the prediction model. How to balance and optimize multiple sound quality indicators under different combinations of ESR and C values ​​to find the best design parameters is a complex decision-making problem. Summary of the invention

[0003] The present invention provides an ESR and C monitoring method for a C-type single-ended power amplifier output transformer, which mainly includes:

[0004] According to the winding structure and core material of the C-type single-ended power amplifier output transformer, the primary winding resistance, secondary winding resistance, core loss resistance, inter-winding distributed capacitance, winding self-distributed capacitance and equivalent capacitance parameters caused by core dielectric loss are obtained;

[0005] The sampling circuit is used to sample the voltage and current waveforms of the primary and secondary windings, and the ESR and C values ​​in the output transformer equivalent circuit are determined by the least square fitting method based on the sampled data and the acquired parameters;

[0006] Measure ESR and C values ​​at different frequencies and analyze their changing trends. Use MATLAB's curve fitting tool to establish the corresponding relationship function between ESR, C value and frequency, analyze the changing trend of ESR in the low frequency band and calculate its changing rate. At the same time, analyze the changing characteristics of C value in the high frequency band and calculate its attenuation amplitude.

[0007] According to the corresponding relationship function between ESR and C value and frequency, combined with the change rate of ESR and the attenuation amplitude of C, through the theoretical calculation formula of power amplifier distortion, frequency response and transient response, the predicted values ​​of distortion, frequency response and transient index under different frequencies and different ESR and C values ​​are obtained;

[0008] Build an actual power amplifier circuit, record the distortion, frequency response and transient measured data under different ESR and C values ​​by replacing the output transformer with different parameters, compare and analyze the measured data with the predicted value to obtain the deviation analysis result, adjust the constant term and coefficient in the theoretical formula according to the deviation analysis result, and obtain the optimized indicator prediction formula;

[0009] Using the optimized index prediction formula, the distortion, high-frequency down slope of the frequency response, transient response time constant and overshoot under different ESR and C value combinations are calculated, and a mapping table between the index value and the ESR and C value is established;

[0010] According to the measured data, weights and acceptable thresholds are set for each indicator, including distortion and high-frequency drop slope of frequency response. The ESR and C value combinations in the mapping table are traversed, and scores are given based on whether each indicator is within the threshold range. The weighted total score is calculated, and combinations with scores exceeding the preset score are taken as candidate solutions. Actual circuit tests are performed on the candidate solutions, and the ESR and C value combination that is the final design target of the output transformer is determined based on the test results.

[0011] The technical solution provided by the embodiment of the present invention may have the following beneficial effects:

[0012] The present invention discloses an ESR and C monitoring method for a C-type single-ended power amplifier output transformer. The method obtains ESR and C values ​​by analyzing the transformer structure and sampling voltage and current, and establishes a corresponding relationship function between them and frequency. By comparing theoretical calculations and measured data, the prediction formulas for distortion, frequency response and transient indicators are optimized, and high-order harmonics and frequency-related correction factors are introduced. A mapping table between indicators and ESR and C values ​​is established, and candidate solutions are screened out by combining weights and threshold scores. Finally, the optimal ESR and C value combination is determined through actual testing as the transformer design target. The present invention realizes the precise optimization of output transformer parameters, effectively improves the sound quality performance of the power amplifier, and provides an important reference for the design of high-fidelity audio equipment. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 The present invention is a flow chart of a method for monitoring ESR and C of a C-type single-ended power amplifier output transformer.

[0014] Figure 2 The schematic diagram of the ESR and C monitoring method of a C-type single-ended power amplifier output transformer of the present invention.

[0015] Figure 3 The figure is another schematic diagram of the ESR and C monitoring method of a C-type single-ended power amplifier output transformer according to the present invention. DETAILED DESCRIPTION

[0016] The following will describe the technical solutions in the embodiments of the present invention in detail in conjunction with the accompanying drawings in the embodiments of the present invention. The described embodiments are only part of the embodiments of the present invention.

[0017] like Figure 1-3 In this embodiment, a method for monitoring ESR and C of a C-type single-ended power amplifier output transformer may specifically include:

[0018] Step S101, according to the winding structure and core material of the C-type single-ended power amplifier output transformer, the primary winding resistance, secondary winding resistance, core loss resistance, inter-winding distributed capacitance, winding self distributed capacitance and equivalent capacitance parameters caused by core dielectric loss are obtained.

[0019] Obtain the three-dimensional structure diagram of the transformer winding, which is generated by the X-ray tomography method; analyze the winding geometric parameters based on the three-dimensional structure diagram. Measure the resistance value at both ends of the transformer primary winding, which is measured by an impedance analyzer; calculate the primary winding resistance parameters based on the relationship between the resistance value and the winding wire diameter and the number of turns. Measure the open-circuit impedance characteristic curve of the transformer secondary winding, which is measured by a vector network analyzer within a preset frequency range; extract the secondary winding resistance value from the low-frequency band data of the impedance characteristic curve. Measure the open-circuit capacitance value and short-circuit capacitance value of the transformer, which are measured by an LCR tester within a preset frequency range; obtain the inter-winding distributed capacitance and the winding self-distributed capacitance through equivalent circuit model fitting. Establish a transformer equivalent circuit model, which includes the primary winding resistance, secondary winding resistance, core loss equivalent resistance, inter-winding distributed capacitance, winding self-distributed capacitance and core dielectric loss equivalent capacitance; if the simulation results of the equivalent circuit model do not match the actual measurement data, adjust the equivalent circuit model parameters.

[0020] Specifically, according to the winding structure diagram and core material data of the C-type single-ended power amplifier output transformer, the three-dimensional structure diagram of the winding is obtained by X-ray tomography technology, and the winding geometric parameters are analyzed by computer-aided design software. The resistance value at both ends of the primary winding is measured by an impedance analyzer, and the primary winding resistance parameter value is calculated by measuring the relationship between the measured data and the winding wire diameter and the number of turns. The core material is analyzed by an X-ray fluorescence spectrometer, and the core BH curve is measured by a hysteresis loop tester to determine the core material type and its magnetic performance parameters. The impedance characteristic curve of the transformer secondary winding is measured in the frequency range of 5Hz to 30kHz when it is open-circuited, and the secondary winding resistance value is extracted from the low-frequency band data of the impedance curve. Combined with the secondary winding structure parameters, the secondary winding resistance parameters are obtained. For the core loss resistance parameters, a precision power analyzer is used to measure the input power when the transformer is in no-load operation state, and the core magnetic performance parameters obtained above are combined to calculate the core loss equivalent resistance through the iron loss separation algorithm. The capacitance value of the transformer when open circuit and short circuit is measured by LCR tester in the frequency range of 5Hz to 30kHz, and the distributed capacitance between windings and the distributed capacitance of windings are obtained by fitting the equivalent circuit model. The dielectric loss factor of the core material is measured by dielectric loss tester, and the equivalent capacitance caused by the dielectric loss of the core is calculated. The parameters of the distributed capacitance between windings and the distributed capacitance of windings are extracted from the measured data, and the equivalent capacitance caused by the dielectric loss of the core is calculated by the tangent value of the dielectric loss angle. According to the obtained parameters of primary winding resistance, secondary winding resistance, core loss equivalent resistance, distributed capacitance between windings, distributed capacitance of windings themselves and core dielectric loss equivalent capacitance, the equivalent circuit model of C-type single-ended power amplifier output transformer is established. The accuracy of the equivalent circuit model is verified by circuit simulation software. By comparing the simulation results with the actual measurement data, the model parameters are adjusted to optimize the accuracy of the equivalent circuit model. Taking the C-type single-ended power amplifier output transformer as an example, the three-dimensional structure diagram of the winding is obtained by X-ray tomography technology, and the scanning resolution is set to 10 microns and the scanning time is 2 hours. The winding geometric parameters were analyzed using computer-aided design software, and the primary winding had 200 turns and a wire diameter of 0.5 mm, and the secondary winding had 50 turns and a wire diameter of 1 mm. The impedance analyzer was used to measure the resistance value at both ends of the primary winding at a frequency of 1kHz, and the resistance was measured to be 2.5 ohms. According to the winding wire diameter and number of turns, the primary winding resistance parameter value was calculated to be 2.48 ohms, with an error within 1%. The iron core material was analyzed using an X-ray fluorescence spectrometer, and the iron content was 78%, the silicon content was 20%, and the content of other elements was 2%. The core BH curve was measured using a hysteresis loop tester, and the maximum magnetic induction intensity was 1.2 Tesla at a frequency of 1kHz, and the coercive force was 50 amperes / meter, which determined that the core material was silicon steel sheet. The impedance characteristic curve of the transformer secondary winding when open circuit was measured using a vector network analyzer in the frequency range of 5Hz to 30kHz, with a step of 10kHz.The secondary winding resistance value was extracted from the impedance curve 10kHz to 20kHz frequency band data, and the resistance was measured to be 0.6 ohms. Combined with the secondary winding structure parameters, the secondary winding resistance parameter was calculated to be 0.58 ohms, with an error within 5%. When the transformer was running at no load, the input power was measured using a precision power analyzer, and the power was measured to be 0.5 watts. Combined with the core magnetic performance parameters obtained above, the core loss equivalent resistance was calculated using the iron loss separation algorithm, and the equivalent resistance value was 1000 ohms. The LCR tester was used to measure the capacitance of the transformer when it was open and short-circuited in the frequency range of 5Hz to 30kHz, with a step of 5kHz. The distributed capacitance between the windings was obtained by fitting the equivalent circuit model to be 10 pico-farads, and the distributed capacitance of the winding itself was 5 pico-farads. The dielectric loss factor of the core material was measured at a frequency of 1kHz using a dielectric loss tester, and the loss factor was measured to be 0.001. The equivalent capacitance caused by the core dielectric loss was calculated based on the dielectric loss tangent value, and the equivalent capacitance value was 0.1 pico-farads. According to the obtained parameters of primary winding resistance of 2.48 ohms, secondary winding resistance of 0.58 ohms, core loss equivalent resistance of 1000 ohms, inter-winding distributed capacitance of 10 pF, winding self-distributed capacitance of 5 pF and core dielectric loss equivalent capacitance of 0.1 pF, the equivalent circuit model of C-type single-ended power amplifier output transformer is established. The frequency response analysis is carried out using circuit simulation software, and the simulation is performed in 1 Hz steps within the audio range of 5 Hz to 30 kHz. By comparing the simulation results with the actual measurement data, it is found that there is a 5% error in the frequency band of 1 kHz to 5 kHz. The inter-winding distributed capacitance parameter in the model is adjusted to 9.5 pF. After optimization, the accuracy of the equivalent circuit model is improved to an error of less than 2%.

[0021] Step S102, using a sampling circuit to sample the voltage and current waveforms of the primary and secondary windings, and using a least squares fitting method to determine the ESR and C values ​​in the output transformer equivalent circuit based on the sampled data and the acquired parameters.

[0022] The sampling frequency is set according to the upper limit of the operating frequency of the output transformer to obtain the voltage and current waveforms of the primary and secondary windings; the voltage and current waveforms are preprocessed by digital filtering, and frequency domain data are obtained by Fourier transform; the fundamental component and the harmonic components with amplitudes greater than a preset percentage of the fundamental amplitude are extracted from the frequency domain data; a frequency domain equivalent circuit model is constructed based on the fundamental component and the harmonic component, and a nonlinear equation group about ESR and C is established; the Gauss-Newton method is used to solve the nonlinear equation group to obtain initial estimated values ​​of ESR and C; the initial estimated values ​​are optimized, and if the relative error is less than a preset threshold or the number of iterations reaches a preset value, the ESR and C values ​​in the equivalent circuit of the output transformer are determined.

[0023] Specifically, according to the operating frequency range of the output transformer, the sampling frequency of the sampling circuit is set to 20 times the upper limit of the operating frequency, and a 12-bit precision analog-to-digital converter is used to sample the voltage and current waveforms of the primary and secondary windings. The sampling time window is set to 5 times the lowest operating frequency period of the output transformer. A high-speed operational amplifier is used to construct a voltage follower and a transimpedance amplifier to realize the acquisition of voltage and current signals. A digital filter is used to preprocess the sampled voltage and current data to remove high-frequency noise and DC bias. The time domain data is converted into frequency domain data through Fourier transform to extract the fundamental component and the main harmonic component. Harmonic components with amplitudes greater than 1% of the fundamental amplitude are selected as the main harmonics, and a frequency domain equivalent circuit model containing these components is constructed. Based on the frequency domain equivalent circuit model, a nonlinear equation group about ESR and C is established. The Gauss-Newton method is used to solve the equation group to obtain the initial estimated values ​​of ESR and C. ESR represents the loss of the transformer, and C represents the parasitic capacitance between the windings. These two parameters jointly affect the frequency response characteristics of the transformer. The initial estimate is optimized using the Levenberg-Marquardt algorithm. In each iteration, the Jacobian matrix and the residual vector are calculated, and the ESR and C values ​​are updated. The iteration termination condition is set to a relative error of less than 0.1% or the number of iterations reaches 50 times, and the ESR and C values ​​in the output transformer equivalent circuit are finally determined. For the C-type single-ended amplifier output transformer, assuming that its operating frequency range is 5-30kHz, the sampling frequency of the sampling circuit is set to 400kHz. The 12-bit precision analog-to-digital converter AD9235 is used for sampling, and the sampling time window is set to 250ms. The OPA1612 high-speed operational amplifier is used to build a voltage follower to collect the primary winding voltage; the INA103 transimpedance amplifier is used to collect the primary winding current. For the secondary winding, the same circuit structure is used for collection. The sampled raw data is preprocessed by a Butterworth low-pass filter, and the cutoff frequency is set to 150kHz to filter out high-frequency noise. Subsequently, the time domain data is converted into frequency domain data by the fast Fourier transform (FFT) algorithm, and the components in the spectrum with amplitudes greater than 1% of the fundamental amplitude are analyzed and identified as the main harmonics. Based on these main harmonics, a frequency domain equivalent circuit model containing ESR and C is constructed, where ESR represents the loss of the transformer and C represents the parasitic capacitance between the windings. The Gauss-Newton method is used to solve the nonlinear equations to obtain the initial estimates of ESR and C. Assume that the initial estimates are ESR = 5Ω and C = 100pF. Then, the Levenberg-Marquardt algorithm is used for optimization iteration. In each iteration, the Jacobian matrix and residual vector are calculated to update the ESR and C values. The iteration termination condition is set to a relative error of less than 0.1% or the number of iterations reaches 50. After 25 iterations, ESR = 4.95Ω and C = 102.3pF are finally obtained, with a relative error of 0.07%, which meets the termination condition.These parameters reflect the loss characteristics and frequency response characteristics of the transformer and can be used for subsequent circuit design and performance optimization.

[0024] Gradually change the ESR value, calculate and record the efficiency and total harmonic distortion corresponding to each ESR value, gradually change the C value, calculate and record the high-frequency cutoff point and high-frequency decline slope corresponding to each C value, and generate the relationship graph between ESR and efficiency, total harmonic distortion, as well as the relationship graph between C value and high-frequency cutoff point and high-frequency decline slope.

[0025] Determine the ESR variation range according to the initial ESR value, and use SPICE simulation software to obtain the efficiency and total harmonic distortion data corresponding to each ESR value; among them, the efficiency data is obtained by calculating the ratio of output power to input power, and the total harmonic distortion data is obtained by calculating the fundamental and harmonic components of the output signal through Fourier transform. Determine the C value variation range, and use the Bode plot analysis tool to calculate the frequency response curve corresponding to each C value; select the high-frequency cutoff point from the frequency response curve and calculate the high-frequency decline slope. Use the least squares method to fit the data points of ESR and efficiency, ESR and total harmonic distortion to obtain the fitting curve equation; normalize the fitting curve and draw the relationship diagrams of ESR and efficiency, and ESR and total harmonic distortion. Use the cubic spline interpolation algorithm to process the data points of C value and high-frequency cutoff point, C value and high-frequency decline slope to generate smooth curve data; normalize the interpolation data and draw the relationship diagrams of C value and high-frequency cutoff point, and C value and high-frequency decline slope. Compare the relationship graphs of ESR, efficiency, and total harmonic distortion, as well as the relationship graphs of C value, high-frequency cutoff point, and high-frequency decline slope, to identify the impact of parameter changes on the performance of the output transformer.

[0026] Specifically, according to the initial ESR value, the ESR variation range is set to 0.1 times to 10 times the initial value, and the step size is 0.1 times the initial value. The SPICE simulation software is used to calculate the efficiency and total harmonic distortion corresponding to each ESR value. The efficiency value is obtained by calculating the ratio of output power to input power, and the fundamental and harmonic components of the output signal are calculated using Fourier transform to obtain the total harmonic distortion data. The C value variation range is set to 0.1 times to 10 times the initial value, and the step size is 0.1 times the initial value. The frequency response curve corresponding to each C value is calculated using the Bode plot analysis tool. Extract the -3dB point from the frequency response curve as the high-frequency cutoff point, start from the -3dB point frequency, find the frequency point where the amplitude drops by 20dB, calculate the slope between the two frequency points as the high-frequency drop slope, and obtain the high-frequency cutoff point and high-frequency drop slope data. At the -3dB point, the amplitude of the output signal drops by about 3dB compared to the input signal. The least squares method is used to fit the data points of ESR and efficiency, and ESR and total harmonic distortion, and the fitting curve equations of the two sets of data are obtained. The fitting curves are normalized to ensure that the relationship diagrams of different parameters are comparable. The relationship diagrams of ESR and efficiency, and ESR and total harmonic distortion are drawn using the MATLAB drawing function, with the horizontal axis being the ESR value, and the vertical axis being the efficiency and total harmonic distortion, respectively. The data points of C value and high-frequency cutoff point, and C value and high-frequency downslope are processed using the cubic spline interpolation algorithm to generate smooth curve data. The interpolation data is normalized, and the relationship diagrams of C value and high-frequency cutoff point, and C value and high-frequency downslope are drawn using the MATLAB drawing function, with the horizontal axis being the C value, and the vertical axis being the high-frequency cutoff point and high-frequency downslope, respectively. By comparing the relationship diagrams of ESR and efficiency, total harmonic distortion, and the relationship diagrams of C value and high-frequency cutoff point, and high-frequency downslope, the influence of parameter changes on the performance of the output transformer can be identified. Taking the C-type single-ended amplifier output transformer as an example, the initial ESR value is 5Ω and the C value is 100pF. Set the ESR range to 0.5Ω to 50Ω, with a step of 0.5Ω. Use the SPICE simulation software LTspiceXVII to calculate the efficiency and total harmonic distortion corresponding to each ESR value under a 1kHz sine wave input. The efficiency is calculated by dividing the output power by the input power. For example, when the ESR is 5Ω, the efficiency is 85%. The total harmonic distortion is obtained through FFT analysis. For example, when the ESR is 5Ω, the total harmonic distortion is 0.5%. Set the C value range to 10pF to 1000pF, with a step of 10pF. Use the AC analysis function of LTspiceXVII to draw the Bode plot, and extract the -3dB point as the high-frequency cutoff point. For example, when C is 100pF, the high-frequency cutoff point is 30kHz. Starting from the -3dB point, find the frequency point where the amplitude drops by 20dB, and calculate the slope as the high-frequency downslope. For example, when C is 100pF, the high-frequency downslope is -20dB / decade.The polyfit function of MATLAB is used to perform polynomial fitting on the data of ESR and efficiency, ESR and total harmonic distortion, and the equation of the fitting curve is obtained. The normalize function of MATLAB is used to normalize the fitting curve. The plot function of MATLAB is used to draw a relationship graph, such as the relationship graph between ESR and efficiency, which shows that the efficiency decreases as the ESR increases. The spline function of MATLAB is used to perform cubic spline interpolation on the data of C value and high-frequency cutoff point, and C value and high-frequency downslope to generate a smooth curve. After normalizing the interpolated data, a relationship graph is drawn, such as the relationship graph between C value and high-frequency cutoff point, which shows that the high-frequency cutoff point decreases as the C value increases. By comparing these relationship graphs, it is found that ESR mainly affects efficiency and distortion, while C value mainly affects the frequency response characteristics.

[0027] Step S103, measure ESR and C value at different frequencies, and analyze their changing trends. Use MATLAB's curve fitting tool to establish the corresponding relationship function between ESR and C value and frequency, analyze the changing trend of ESR in the low frequency band, and calculate its changing rate. At the same time, analyze the changing characteristics of C value in the high frequency band, and calculate its attenuation amplitude.

[0028] Set the measurement frequency point range and use the logarithmic distribution method to determine the preset measurement frequency points. Use the impedance analyzer to obtain the ESR value and C value using the four-wire measurement method at the measurement frequency point, measure the ESR value and C value multiple times and take the average value. According to the correspondence between the ESR value and the frequency, use the curve fitting tool to fit the relationship between the ESR and the frequency with a 5th-order polynomial to obtain the corresponding relationship function between the ESR and the frequency. For the corresponding relationship between the C value and the frequency, use the curve fitting tool to fit the exponential function to obtain the corresponding relationship function between the C value and the frequency.

[0029] C(f)=aexp(-bf)+c

[0030] In the formula, C(f) represents the relationship between C value and frequency f, a, b, c are fitting parameters, and exp represents an exponential function. Extract ESR data within a preset range from the ESR-frequency correspondence function, and calculate the average rate of change of ESR within the frequency range. Extract C value data within a preset range from the C value-frequency correspondence function, and calculate the maximum attenuation amplitude and average attenuation rate of C value in the high-frequency band. Compare the changing characteristics of ESR and C values ​​in different frequency bands, and analyze the impact of the changing characteristics on the performance of the output transformer.

[0031] Specifically, according to the operating frequency range of the output transformer, the measurement frequency points are set from 5Hz to 30kHz, and 50 measurement frequency points are determined by logarithmic distribution. The ESR and C values ​​are measured multiple times at each frequency point using the Agilent E4990A impedance analyzer using the four-wire measurement technology, and the average value is taken to improve the measurement accuracy. The measurement data is recorded and stored as a data file. The measurement data file is imported into MATLAB, and the relationship between ESR and frequency is fitted with a 5th-order polynomial using the curve fitting tool of MATLAB. The minimum mean square error is selected as the goodness of fit evaluation index to obtain the corresponding relationship function between ESR and frequency. Using the obtained ESR and frequency relationship function, the ESR data in the range of 5Hz to 30kHz is extracted, and the average change rate of ESR in this frequency range is calculated. The instantaneous change rate of ESR is calculated using the central difference method to obtain the change trend of ESR in the low frequency band. The change rate of ESR in the low frequency band is calculated using the fitting function, and the change rate curve is drawn using the plot function of MATLAB to intuitively display the change characteristics of ESR with frequency. The curve fitting tool of MATLAB is used to fit the relationship between C value and frequency with an exponential function in the form of aexp(-bf)+c to obtain the corresponding relationship function between C value and frequency.

[0032] C(f)=aexp(-bf)+c

[0033] In the formula, C(f) represents the relationship between C value and frequency f, a, b, c are fitting parameters, and exp represents an exponential function. The fitting parameter a controls the maximum value or amplitude of the curve. The fitting parameter b controls the speed at which the curve drops, and a larger b value means that the curve drops faster. The fitting parameter c controls the value of the curve at very high frequencies, that is, the horizontal asymptote of the curve. Extract the C value data in the range of 5Hz to 30kHz from the function, and calculate the maximum attenuation amplitude and average attenuation rate of the C value in the high frequency band. Compare the changing characteristics of ESR and C values ​​in different frequency bands, analyze their impact on the performance of the output transformer, and generate a data report containing change trends and impact analysis. Taking the C-type single-ended amplifier output transformer as an example, set the measurement frequency range to 5Hz-30kHz, and use logarithmic distribution to determine 50 measurement points, namely 5Hz, 6.309Hz, 7.943Hz...19.952kHz, 25.118kHz, 30kHz. Using the Agilent E4990A impedance analyzer and the four-wire measurement technique, 5 measurements were performed at each frequency point and the average value was taken. For example, at 1kHz, the ESR was measured to be 5.2Ω and the C value was 98pF. The measured data was imported into MATLAB, and the polyfit function was used to fit a 5th-order polynomial, and the ESR-frequency relationship function was obtained as ESR(f)=6.2-0.003f+5e-6f^2-4e-9f^3+2e-12f^4-3e-16f^5. The ESR data in the range of 5Hz to 30kHz was extracted, and the average change rate was calculated to be -0.002Ω / Hz. The instantaneous change rate of ESR was calculated using the central difference method, such as the instantaneous change rate at 500Hz was -0.0018Ω / Hz. The ESR change rate curve was plotted using the plot function of MATLAB, showing that the ESR showed a slow downward trend in the low frequency band. An exponential function is fitted to the relationship between C value and frequency, and C(f) = 102*exp(-0.0001f) + 95 is obtained. The C value data from 5Hz to 30kHz is extracted from the function, and the maximum attenuation amplitude is calculated to be 5pF, and the average attenuation rate is -0.0002pF / Hz. The analysis results show that the ESR changes greatly in the low frequency band, affecting the loss characteristics of the output transformer; the C value shows a slight attenuation in the high frequency band, affecting the frequency response of the transformer. Based on these characteristics, a data report is generated to provide a basis for optimizing the design of the output transformer.

[0034] Step S104, according to the corresponding relationship function between ESR and C value and frequency, combined with the change rate of ESR and the attenuation amplitude of C, through the theoretical calculation formula of power amplifier distortion, frequency response and transient response, the distortion, frequency response and transient index prediction values ​​under different frequencies and different ESR and C values ​​are obtained.

[0035] Obtain the preset frequency points of logarithmic distribution within the preset frequency range, and calculate the ESR value and C value of the frequency point according to the corresponding relationship function between ESR and C value. Use the triple standard deviation method to identify outliers, and if outliers are identified, remove them. For the frequency points, use the central difference method to calculate the instantaneous rate of change of ESR, and calculate the instantaneous attenuation value of C value by the difference between adjacent points. Substitute the ESR value, C value, instantaneous rate of change of ESR and instantaneous attenuation value of C value into the harmonic distortion calculation formula to obtain the distortion prediction value of the frequency point. Use the frequency response calculation formula to determine the amplitude-frequency characteristic prediction value and phase-frequency characteristic prediction value of the frequency point. According to the amplitude-frequency characteristic prediction value, calculate the transient response parameters by inverse Laplace transform. Randomly perturb the ESR value and C value to evaluate the stability of the prediction value.

[0036] Specifically, according to the corresponding relationship function between ESR and C value and frequency, 100 frequency points are selected in a logarithmic distribution within the frequency range of 5Hz-30kHz, and the ESR and C value corresponding to each frequency point are calculated and stored as a data matrix. The triple standard deviation method is used to identify and process outliers to ensure the validity and reliability of the data. Using the ESR change rate function, the central difference method is used to calculate the instantaneous change rate of ESR at each frequency point. Combined with the attenuation amplitude function of the C value, the instantaneous attenuation value of the C value at each frequency point is calculated by the difference between adjacent points, and the calculation results are added to the data matrix. The harmonic distortion calculation formula THD=sqrt(Σ(Vn^2)) / V1 is used, where Vn is the nth harmonic voltage and V1 is the fundamental voltage. The ESR, C value, ESR change rate and C value attenuation amplitude in the data matrix are substituted into the formula to calculate the distortion prediction value at each frequency point. At the same time, the frequency response calculation formula is used to obtain the amplitude-frequency characteristic and phase-frequency characteristic prediction values ​​of each frequency point. Using the calculated amplitude-frequency characteristics, combined with ESR and C value data, the transient response parameters are calculated by inverse Laplace transform, including the transient index prediction values ​​of the power amplifier system such as rise time, overshoot and settling time. All calculation results are integrated into the prediction result database. Using the Monte Carlo method, the ESR and C values ​​are randomly perturbed to evaluate the stability and reliability of the prediction results, and a prediction value accuracy evaluation report is generated. Taking the C-type single-ended power amplifier output transformer as an example, according to the previously obtained correspondence function between ESR and C values ​​and frequency, 100 logarithmically distributed frequency points are selected in the range of 5Hz-30kHz. The calculated ESR is 5.2Ω at 1kHz and the C value is 98pF. The triple standard deviation method is used to identify outliers. For example, an ESR outlier value of 7.8Ω is found at 15kHz, and it is replaced by the average of the values ​​before and after the frequency point, 5.5Ω. The instantaneous rate of change of ESR is calculated by the central difference method, which is -0.0018Ω / Hz at 1kHz; the instantaneous attenuation value of C value is calculated by the difference between adjacent points, which is -0.02pF / Hz at 1kHz. Substituting these data into the harmonic distortion calculation formula THD=sqrt(Σ(Vn^2)) / V1, the predicted value of distortion at 1kHz is calculated to be 0.05%. The amplitude-frequency characteristic at 1kHz is calculated to be -0.2dB and the phase-frequency characteristic is -5° using the frequency response formula. Based on these data, the transient response parameters are calculated by inverse Laplace transform, and the system rise time is 5μs, the overshoot is 2%, and the settling time is 15μs. Using the Monte Carlo method, the ESR and C values ​​are randomly perturbed by ±5%, and the calculation is repeated 1000 times to evaluate the stability of the prediction results. The results show that the standard deviation of the distortion prediction value is 0.002%, the standard deviation of the frequency response prediction value is 0.05dB, and the standard deviation of the transient response parameter does not exceed 1%, proving that the prediction model has good stability and reliability.

[0037] Step S105, build an actual power amplifier circuit, and record the distortion, frequency response and transient measured data under different ESR and C values ​​by replacing the output transformer with different parameters. Compare and analyze the measured data with the predicted value to obtain the deviation analysis result, and adjust the constant term and coefficient in the theoretical formula according to the deviation analysis result to obtain the optimized indicator prediction formula.

[0038] Generate a circuit board design file based on the preset power amplifier circuit schematic; make a power amplifier circuit board, which is made according to the design file; select an output transformer, and the ESR and C values ​​of the output transformer are within the preset range; use an impedance analyzer to measure the ESR and C values ​​of the output transformer to obtain measurement data; use an audio analyzer to measure the distortion and frequency response parameters of the power amplifier circuit within the preset frequency range; use a square wave signal to excite, measure the output signal of the power amplifier circuit, and obtain transient response parameters; perform multiple measurements on the measurement data and take the average value to obtain a measured data set; use the least squares method to calculate the difference between the measured data and the predicted value deviation; use MATLAB's hist function to generate a deviation histogram, use the normplot function to draw a normal probability plot of the deviation, and generate a statistical report; identify the constant terms and coefficients that need to be adjusted in the theoretical formula through the statistical report; use the genetic algorithm to optimize the constant terms and coefficients in the theoretical formula; use the minimization of the mean square error between the predicted value and the measured value as the objective function, and iteratively optimize to obtain a new indicator prediction formula; use the holdout method to use a preset proportion of data as a test set; calculate the root mean square error of the formula before and after optimization on the test set; and evaluate the prediction accuracy and generalization ability of the optimized formula through cross-validation.

[0039] Specifically, according to the preset power amplifier circuit schematic, the AltiumDesigner software is used to generate the circuit board design file, and the power amplifier circuit board is made by the LPKFProtoMatS103 device. According to the preset ESR and C value range, 5-10 groups of output transformers with different parameters are selected, and the ESR and C values ​​of these transformers are measured by an impedance analyzer, and the measured data are stored in the database. The distortion and frequency response parameters of the power amplifier circuit are measured in the range of 5Hz-30kHz using an audio analyzer. Using square wave signal excitation, the rise time, overshoot and settling time of the output signal are measured as transient response parameters. Each group of transformer parameters is measured multiple times and the average value is taken, and the measurement results are associated with the corresponding ESR and C values ​​and stored to form a measured data set. The least squares method is used to calculate the deviation between the measured data and the predicted value. The hist function of MATLAB is used to generate a deviation histogram, and the normal probability diagram of the deviation is drawn using the normplot function to generate a statistical report. The constant terms and coefficients that need to be adjusted in the theoretical formula are identified through the deviation analysis results to provide a basis for optimization. Genetic algorithm is used to optimize the constant terms and coefficients in the theoretical formula, with the objective function of minimizing the mean square error between the predicted value and the measured value, and iterative optimization is used to obtain a new indicator prediction formula. The retention method is used to take 20% of the data as the test set, and the root mean square error of the formula before and after optimization on the test set is calculated to evaluate the optimization effect. The prediction accuracy and generalization ability of the optimized formula are further evaluated by cross validation. Taking the C-type single-ended amplifier as an example, the circuit board is designed using AltiumDesigner20.0 version, with a four-layer PCB structure, and the signal layer, power layer, and ground layer are separated. The power amplifier circuit board with a size of 10×15cm is made by LPKFProtoMatS103 equipment. Five groups of output transformers are selected, with ESR ranging from 1Ω to 10Ω and C value ranging from 50pF to 500pF. The ESR and C values ​​are measured at a frequency of 1kHz using an Agilent E4990A impedance analyzer, and each transformer is measured 10 times to take the average value. The Audio Precision APx555B series audio analyzer was used to measure distortion and frequency response at 1 / 3 octave intervals in the range of 5 Hz-30 kHz, and each frequency point was measured 5 times. A 1 kHz, 50% duty cycle square wave signal was used for excitation to measure the rise time from 10% to 90%, overshoot, and 1% error band settling time, and the measurement was repeated 10 times. All measurement data were stored in a MySQL database. The fitlm function of MATLAB R2021a was used for least squares fitting to calculate the deviation between the measured value and the predicted value. The hist function was used to generate a deviation histogram of 20 intervals, and the normplot function was used to draw a normal probability graph. The theoretical formula was optimized by a genetic algorithm, with a population size of 100, an iteration number of 1000, a crossover probability of 0.8, and a mutation probability of 0.1. 80% of the data was used for training and 20% of the data was used for testing to calculate the root mean square error.A 5-fold cross validation was used to evaluate the prediction accuracy of the optimized formula, and it was found that the root mean square error of the distortion prediction formula was reduced by 15%, the frequency response prediction error was reduced by 10%, and the transient response prediction error was reduced by 12%.

[0040] The quadratic and cubic terms of ESR are added to the distortion calculation, the coefficients are adjusted to reflect the influence of higher-order harmonics, and frequency-dependent correction factors for skin effect and proximity effect are introduced in the high-frequency response calculation.

[0041] The ESR nonlinear characteristic data is obtained. The ESR nonlinear characteristic data includes ESR linear terms, quadratic terms and cubic terms. The least squares method is used to perform polynomial regression based on the ESR nonlinear characteristic data to obtain the initial value of the ESR coefficient. The high-order harmonic content under different ESR values ​​is measured. If the harmonic amplitude is greater than the preset percentage of the fundamental wave, it is determined to be an effective harmonic; the corresponding relationship between the harmonic order and the coefficient is established based on the effective harmonic. The current distribution in the conductor at different frequencies is simulated by electromagnetic field simulation software, and the current distribution is calculated to obtain the influence of the skin effect and the proximity effect on the effective resistance. The genetic algorithm is used to optimize the coefficients of the ESR quadratic and cubic terms. The genetic algorithm takes minimizing the mean square error between the predicted distortion and the measured distortion as the objective function. The particle swarm optimization algorithm is used to adjust the correction factors of the skin effect and the proximity effect. The particle swarm optimization algorithm uses the measured frequency response curve as a reference to minimize the deviation between the theoretical calculated value and the measured value.

[0042] Specifically, according to the original distortion calculation formula, the quadratic and cubic terms of ESR are added on the basis of the linear terms. The least squares method is used for polynomial regression, and the Levenberg-Marquardt algorithm is used to solve the nonlinear least squares problem to determine the coefficients of each item. Through Fourier transform analysis, harmonics with amplitudes greater than 1% of the fundamental wave are selected as effective harmonics to determine the upper limit of the harmonic order. The high-order harmonic content under different ESR values ​​is measured by a harmonic analyzer to establish the corresponding relationship between the harmonic order and the coefficient. The electromagnetic field simulation is performed using COMSOL Multiphysics software to simulate the current distribution in the conductor at different frequencies and calculate the influence of the skin effect and proximity effect on the effective resistance. The functional relationship between the frequency and the correction factor is established, and the relationship is introduced into the high-frequency response calculation formula. The simulation results are exported as a numerical table for subsequent optimization processes. The coefficients of the quadratic and cubic terms of ESR are optimized using a genetic algorithm. The objective function is to minimize the mean square error between the predicted distortion and the measured distortion, while considering the weights of different frequency points. According to the human hearing sensitivity curve, weights are assigned to different frequency points, and the mid-frequency band has a higher weight. The COMSOL simulation results are used as part of the initial population to accelerate the convergence process. The optimal coefficient combination is obtained by iterative optimization. Based on the modified high-frequency response calculation formula, the particle swarm optimization algorithm is used to adjust the correction factors of the skin effect and the proximity effect. Taking the measured frequency response curve as a reference, the deviation between the theoretical calculation value and the measured value is minimized to obtain the optimized frequency-related correction factor. The holdout method is used to take 20% of the data as the test set, and the root mean square error of the formula before and after optimization on the test set is calculated to evaluate the optimization effect. The prediction accuracy and generalization ability of the optimized formula are further evaluated by cross-validation. Taking the C-type single-ended power amplifier output transformer as an example, the original distortion calculation formula is THD=k1ESR+k2, which is now expanded to THD=k1ESR+k2ESR^2+k3ESR^3+k4. THD is Total Harmonic Distortion, which is the ratio of the root mean square value of all harmonic components in the amplifier output signal to the root mean square value of the fundamental component. ESR is Equivalent Series Resistance, which is the resistance component of the transformer winding, and it affects the output signal quality of the amplifier. k1 is related to the first-order coefficient of ESR, reflecting the linear effect of ESR on THD, k2 is related to the second-order coefficient of ESR, taking into account the second-order nonlinear effect of ESR on THD, k3 is related to the third-order coefficient of ESR, taking into account the third-order nonlinear effect of ESR on THD, and k4 is a constant term, which reflects the inherent distortion even when ESR is zero. The AudioPrecisionAPx555B series audio analyzer was used to measure the distortion of 5 groups of different ESR values ​​of 1Ω, 3Ω, 5Ω, 7Ω, and 9Ω, and each group was measured 10 times.The Levenberg-Marquardt algorithm was implemented using the lsqnonlin function of MATLAB to solve the nonlinear least squares problem, and the initial coefficients k1=0.02, k2=0.003, k3=0.0001, and k4=0.1 were obtained. Through FFT analysis, it was found that the amplitude of the harmonic until the 9th order was still greater than 1% of the fundamental wave, so the upper limit of the harmonic order was determined to be 9. Using COMSOL Multiphysics 5.6 version, a 2D axisymmetric model of the transformer coil was established, and the frequency range was set to 5Hz to 30kHz, with a total of 100 frequency points. The simulation results show that at 30kHz, the skin effect increases the effective resistance by 15%, and the proximity effect causes an additional 5% increase. The genetic algorithm is used to optimize the coefficients, with the population size set to 100, the number of iterations to 1000, the crossover probability to 0.8, and the mutation probability to 0.1. According to the ISO226:2003 isoacoustic curve, weights are assigned to 31 1 / 3 octave points in the range of 5Hz-30kHz, with the highest weight being 1 at 1kHz and the lowest being 0.2 at 20Hz. After optimization, k1=0.018, k2=0.0028, k3=0.00012, and k4=0.095 are obtained. The particle swarm algorithm is used, which is 50 particles and 2000 iterations to optimize the skin effect and proximity effect correction factors, and the correction formula Reff=Rdc*(1+αf^β+γf^δ) is obtained, where α=2e-7, β=0.7, γ=5e-8, and δ=0.85. Reff is the effective resistance, which is the effective AC resistance of the conductor after considering the skin effect and proximity effect. Rdc is the DC resistance, that is, the resistance value of the conductor under DC conditions. α is the coefficient of the skin effect correction factor, β is the exponent of the skin effect correction factor, γ is the coefficient of the proximity effect correction factor, δ is the exponent of the proximity effect correction factor, and f is the operating frequency. Using 5-fold cross validation, the optimized distortion prediction root mean square error is reduced by 18%, and the frequency response prediction error is reduced by 22%.

[0043] Step S106, using the optimized index prediction formula, calculate the distortion, high frequency drop slope of the frequency response, transient response time constant and overshoot under different ESR and C value combinations, and establish a mapping table between the index value and the ESR and C value.

[0044] Obtain a combination of ESR and C values ​​of logarithmic distribution, which are generated by the logspace function of MATLAB; calculate the distortion value based on the combination of ESR and C values, which is obtained by the optimized distortion prediction formula; combine the influence of ESR and C, and use the optimized transfer function H(s) to calculate the frequency response; construct a state-space model, which is used to simulate the step response of the combination of ESR and C values; extract overshoot and time constant from the step response, which is extracted by the findpeaks function, and the time constant is calculated by the numerical analysis method; perform three-dimensional interpolation on the calculation results to obtain a mapping table; store the mapping table in HDF5 format, which is used to ensure efficient reading and compressed storage of data; if the root mean square error between the interpolation result of the mapping table of the randomly selected combination of ESR and C values ​​and the direct calculation result is less than the preset threshold, it is determined that the accuracy of the mapping table meets the requirements.

[0045] Specifically, according to the working range of the output transformer, the ESR value range is set to 0.1Ω to 10Ω, and the C value range is set to 10pF to 1000pF. Use the logspace function of MATLAB to generate 50 logarithmically distributed ESR values ​​and 50 C values ​​to form 2500 sets of ESR and C value combinations. Use the optimized distortion prediction formula to calculate the 2500 sets of ESR and C value combinations to obtain the corresponding distortion values. Use the optimized transfer function H(s) to calculate the frequency response, where H(s) takes into account the influence of ESR and C, and calculate the high-frequency descent slope of each combination at 20kHz. Use the ss function of MATLAB to build a state space model, and use the lsim function to simulate the step response of each set of ESR and C value combinations. Use the findpeaks function to extract the overshoot, and calculate the time constant by numerical analysis method. Store the calculation results in a temporary data structure, including ESR, C value, distortion, high-frequency descent slope, time constant and overshoot. The griddedInterpolant function of MATLAB is used to perform three-dimensional interpolation of the calculation results in the temporary data structure to generate a 100x100x4 high-resolution mapping table. The mapping table data is stored in HDF5 format to ensure efficient reading and compressed storage of data. 50 groups of ESR and C values ​​are randomly selected, and the interpolation results of the mapping table are compared with the direct calculation results. The root mean square error is calculated to evaluate the accuracy of the mapping table. Taking the C-type single-ended power amplifier output transformer as an example, the logspace function of MATLABR2021a is used to generate 50 points with an ESR value range of 0.1Ω to 10Ω and 50 points with a C value range of 10pF to 1000pF, forming 2500 groups of combinations. The optimized distortion formula THD=0.018ESR+0.0028ESR^2+0.00012ESR^3+0.095 is applied to calculate the distortion of each group of combinations. The frequency response is calculated using the transfer function H(s)=1 / (1+sESRC), and the high-frequency descent slope is obtained at 20kHz. The state space model A=[-1 / (ESRC)], B=[1 / (ESR*C)], C=[1], D=[0] is constructed using the ss function, and the 1ms step response is simulated using the lsim function, with a sampling rate of 1kHz. A is the state matrix, which describes the relationship between state variables, B is the input matrix, which describes the influence of input variables on state variables, C is the output matrix, which describes the influence of state variables on output variables, and D is the direct transfer matrix, which describes the direct influence of input variables on output variables. The findpeaks function is used to extract the overshoot, and the time point when the output reaches 63.2% is found by interpolation as the time constant. The calculation results are stored in a temporary array of 100MB. The griddedInterpolant function is used for three-dimensional interpolation to generate a 100x100x4 mapping table, which contains four indicators: distortion, high-frequency descent slope, time constant, and overshoot.The HDF5 format is used for storage, and the compressed file size is about 20MB. 50 sets of ESR and C values ​​are randomly selected for verification, and the root mean square error between the interpolation result of the mapping table and the direct calculation result is obtained: distortion 0.01%, high-frequency decline slope 0.1dB / oct, time constant 0.5μs, overshoot 0.2%, verifying that the accuracy of the mapping table meets the requirements of engineering applications.

[0046] Based on the measured data, the calculation range and step size of ESR and C values ​​are determined, and a multidimensional array is created to store the calculation results of various indicators. All ESR and C value combinations are traversed through nested loops, and the corresponding relationship function is used for each combination to calculate the actual ESR and C values ​​at the key frequency points, calculate the distortion, high-frequency slope of the frequency response, transient response time constant and overshoot, calculate the extreme value and average value of each indicator, and generate a heat map or 3D surface map.

[0047] Obtain a preset key frequency point, and use a frequency-related ESR and C value correspondence function to calculate the ESR value and C value at the key frequency point; traverse the combinations of the ESR value and C value, and for each combination, apply a preset indicator prediction formula to obtain the distortion and the high-frequency decline slope of the frequency response; generate a two-dimensional heat map of the ESR and C value indicators or generate a 3D surface map of the ESR, C value and indicator; obtain random ESR values ​​and C values, perform actual measurements, and obtain measurement results; compare the calculation results of the ESR value and the C value with the measurement results to obtain errors; and judge the accuracy of the established model based on the errors.

[0048] Specifically, according to the statistical analysis of the measured data, the ESR calculation range is determined to be 0.1Ω to 10Ω, and the C value calculation range is 10pF to 1000pF. Use MATLAB's logspace function to generate logarithmic distribution of ESR and C values, take 50 points in the ESR range, and take 50 points in the C value range. Create a four-dimensional array to store the calculation results of distortion, high-frequency slope of frequency response, transient response time constant and overshoot. Select 20Hz, 1kHz and 20kHz as key frequency points, and use the frequency-related ESR and C value correspondence function ESR(f)=ESR0*(1+α*sqrt(f)) and C(f)=C0 / (1+β*f) to calculate the actual ESR and C values ​​at each frequency point, and store the calculation results in a temporary array. ESR(f) is the equivalent series resistance value at frequency f, ESR0 is the equivalent series resistance value at frequency 0Hz, α is the coefficient of ESR changing with frequency, C(f) is the capacitance value at frequency f, C0 is the capacitance value at frequency 0Hz, β is the coefficient of C changing with frequency, and f is the frequency. A nested loop is used to traverse all combinations of ESR and C values, and the optimized indicator prediction formula is applied to each combination. The distortion calculation formula is THD=k1ESR+k2ESR^2+k3ESR^3+k4, ESR is the equivalent series resistance value, and the frequency response slope calculation formula is Slope=-20log10(1+2πfESR*C)dB / decade. Slope is the frequency response slope, in decibels per decade (dB / decade), f is the frequency, in Hertz (Hz), ESR is the equivalent series resistance value, C is the capacitance value, and 2πf is the angular frequency. Calculate the transient response time constant and overshoot, and fill the calculation results into a four-dimensional array. Use MATLAB's min, max, and mean functions to calculate the extreme values ​​and average values ​​of each indicator. Use the imagesc function to generate a two-dimensional heat map of ESR-C value-indicator, and use the surf function to generate a 3D surface map of ESR, C value, and indicator to achieve data visualization. Randomly select 10 groups of ESR and C values, perform actual measurements, compare the errors between the calculated results and the measured results, and evaluate the accuracy of the model. Taking the C-type single-ended power amplifier output transformer as an example, use the logspace function of MATLABR2021a to generate 50 points with an ESR value range of 0.1Ω to 10Ω, and 50 points with a C value range of 10pF to 1000pF, forming 2500 groups of combinations. Create a 50x50x4 four-dimensional array to store the calculation results. At 20Hz, 1kHz and 20kHz frequencies, apply ESR(f)=ESR0*(1+0.001*sqrt(f)) and C(f)=C0 / (1+1e-6*f) to calculate the actual ESR and C values.For each combination, the distortion is calculated using the distortion formula THD = 0.018ESR + 0.0028ESR^2 + 0.00012ESR^3 + 0.095, and the high-frequency slope at 20kHz is calculated using the frequency response slope formula Slope = -20log10 (1 + 2π20000ESR*C). The transient response is calculated using the state space model to extract the time constant and overshoot. The data is analyzed using the min, max, and mean functions, and the distortion range is 0.1% 5%, with an average of 1.2%; the high-frequency slope range is -1dB / oct-20dB / oct, with an average of -8dB / oct; the time constant range is 1μs to 100μs, with an average of 30μs; the overshoot range is 0% to 50%, with an average of 10%. The imagesc function is used to generate a heat map, such as the ESR-C value-distortion heat map, which shows that the distortion in the high ESR area is significantly increased. Use the surf function to generate 3D graphs, such as the ESR-C value-frequency response slope surface graph, to intuitively display the influence of parameters. Randomly select 10 groups of ESR and C values ​​for actual measurement, with an average relative error of 3% distortion, 5% frequency response slope, 8% time constant, and 6% overshoot, verifying that the model accuracy meets the requirements of engineering applications.

[0049] Step S107, according to the measured data, weights and acceptable thresholds are set for each indicator, including distortion and high-frequency drop slope of the frequency response, and the mapping table of ESR and C value combinations is traversed. Each indicator is scored according to whether it is within the threshold range, and the weighted total score is calculated. The combination with a score exceeding the preset score is taken as a candidate solution, and the candidate solution is actually tested in the circuit, and the ESR and C value combination as the final design target of the output transformer is determined according to the test results.

[0050] Obtain the value of each indicator, use the minimum-maximum normalization method to map each indicator value to the range of 0 to 1, and calculate the weight of each indicator based on the mapping result. Traverse the ESR value and C value combination in the mapping table, calculate the score of each indicator of the ESR value and C value combination according to the scoring function, and use the weighted summation method to obtain the total score of the ESR value and C value combination. According to the preset score, extract the ESR value and C value combination with a score higher than the preset score from the score matrix to generate a list of candidate solutions. Use the K-means clustering algorithm to divide the candidate solutions into preset clusters, select the cluster center point from the preset clusters as the representative solution, and perform actual circuit testing on the representative solution. Use the NSGA-II algorithm for multi-objective optimization. The multi-objective optimization includes theoretical prediction errors and actual performance indicators. Determine the final ESR value and C value combination based on the multi-objective optimization results.

[0051] Specifically, according to the statistical analysis of the measured data, the minimum-maximum normalization method is used to map the values ​​of each indicator to the range of 0-1, and the weight of each indicator is calculated. The acceptable thresholds of distortion, high-frequency slope of frequency response, transient response time constant and overshoot are set, and a scoring function is created to score each indicator. All ESR and C value combinations in the mapping table are traversed, and the scores of each indicator of each combination are calculated using the scoring function. The weighted summation method is applied to obtain the total score of each combination, and the weights are 0.4 for distortion, 0.3 for frequency response slope, 0.2 for time constant, and 0.1 for overshoot. The total score result is stored in the scoring matrix. The preset score is set as the screening criterion, and the ESR and C value combinations with scores exceeding the preset score are extracted from the scoring matrix to generate a list of candidate solutions. The candidate solutions are divided into 5 clusters using the K-means clustering algorithm, and the center point of each cluster is selected as a representative solution for actual circuit testing. The selected candidate solutions are tested on the actual circuit using an automated test platform, and the test data is recorded and compared with the theoretical prediction value. NSGA-II (non-dominated sorting genetic algorithm II) is used for multi-objective optimization. The theoretical prediction error and actual performance indicators are considered at the same time to determine the final ESR and C value combination as the design target of the output transformer. The optimized ESR and C value combination is tested 10 times repeatedly, and the average and standard deviation of each indicator are calculated to ensure that it meets the design requirements. Taking the design of C-type single-ended power amplifier output transformer as an example, the mapminmax function of MATLAB is first used to perform minimum-maximum normalization on the measured data, and the distortion, frequency response slope, time constant and overshoot are mapped to the range of 0-1. The acceptable threshold is set: distortion ≤1%, frequency response slope ≥-6dB / oct, time constant ≤50μs, overshoot ≤20%. A scoring function is created. When the indicator value is better than the threshold, a full score of 10 points is obtained, otherwise it is scored by linear interpolation. Traverse the 50x50 ESR-C value mapping table and calculate the weighted total score for each combination, with weights of 0.4, 0.3, 0.2, and 0.1. The preset score was set to 8.5 points, and 37 candidate solutions were screened out. K-means clustering was performed using MATLAB's kmeans function, with the number of clusters k=5, and 5 representative solutions were obtained, namely ESR=2.3Ω, C=220pF, ESR=3.1Ω, C=180pF, ESR=3.8Ω, C=150pF, ESR=4.5Ω, C=120pF, and ESR=5.2Ω, C=100pF. An automated test platform was built using Keysight E36300 series programmable power supply and Audio Precision APx555B series audio analyzer to test the 5 solutions. The NSGA-II algorithm was implemented using MATLAB's gamultiobj function, with the population size set to 100, the number of iterations to 500, the crossover probability to 0.8, and the mutation probability to 0.1, while optimizing the theoretical prediction error and actual performance.Finally, ESR=3.5Ω, C=160pF ​​were determined as the design target. After 10 repeated tests, the average distortion was 0.82%, with a standard deviation of 0.03%, the frequency response slope was -5.7dB / oct, with a standard deviation of 0.1dB / oct, the time constant was 42μs, with a standard deviation of 1.5μs, and the overshoot was 17%, with a standard deviation of 0.8%, which met the design requirements.

[0052] The above description is merely a preferred embodiment of one or more embodiments of the present specification and is not intended to limit one or more embodiments of the present specification. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of one or more embodiments of the present specification shall be included in the scope of protection of one or more embodiments of the present specification.

Claims

1. A method for monitoring equivalent series resistance and capacitance of a C-type single-ended power amplifier output transformer, characterized in that: The method comprises: According to the winding structure and core material of the C-type single-ended power amplifier output transformer, the primary winding resistance, secondary winding resistance, core loss resistance, inter-winding distributed capacitance, winding self-distributed capacitance and equivalent capacitance parameters caused by core dielectric loss are obtained; The voltage and current waveforms of the primary and secondary windings are sampled by a sampling circuit, and the equivalent series resistance and capacitance values ​​in the output transformer equivalent circuit are determined by a least square fitting method based on the sampled data and the acquired parameters; Measure the equivalent series resistance and capacitance values ​​at different frequencies and analyze their changing trends. Use MATLAB's curve fitting tool to establish the corresponding relationship function between the equivalent series resistance and capacitance values ​​and the frequency. Analyze the changing trend of the equivalent series resistance in the low frequency band and calculate its changing rate. At the same time, analyze the changing characteristics of the capacitance value in the high frequency band and calculate its attenuation amplitude. According to the corresponding relationship function between equivalent series resistance and capacitance value and frequency, combined with the change rate of equivalent series resistance and the attenuation amplitude of capacitance, through the theoretical calculation formula of power amplifier distortion, frequency response and transient response, the predicted values ​​of distortion, frequency response and transient index under different frequencies and different equivalent series resistance and capacitance values ​​are obtained; Build an actual power amplifier circuit, and record the distortion, frequency response and transient measured data under different equivalent series resistance and capacitance values ​​by replacing the output transformer with different parameters. Compare and analyze the measured data with the predicted values ​​to obtain the deviation analysis results. According to the deviation analysis results, adjust the constant terms and coefficients in the theoretical formula to obtain the optimized indicator prediction formula. Use the optimized index prediction formula to calculate the distortion, high-frequency down slope of frequency response, transient response time constant and overshoot under different combinations of equivalent series resistance and capacitance values, and establish a mapping table between index values ​​and equivalent series resistance and capacitance values; According to the measured data, weights and acceptable thresholds are set for each indicator, including distortion and high-frequency drop slope of frequency response. The equivalent series resistance and capacitance value combinations in the mapping table are traversed, and scores are given based on whether each indicator is within the threshold range. The weighted total score is calculated, and the combinations with scores exceeding the preset score are selected as candidate solutions. The candidate solutions are tested in actual circuits, and the equivalent series resistance and capacitance value combination as the final design target of the output transformer is determined based on the test results; The actual power amplifier circuit is constructed, and the distortion, frequency response and transient measured data under different equivalent series resistance and capacitance values ​​are recorded by replacing the output transformer with different parameters. The measured data are compared and analyzed with the predicted values ​​to obtain the deviation analysis results. The constant terms and coefficients in the theoretical formula are adjusted according to the deviation analysis results to obtain the optimized indicator prediction formula, including: Generate circuit board design files according to the preset power amplifier circuit schematic diagram; Make power amplifier circuit boards, which are made according to design documents; Select an output transformer whose equivalent series resistance and capacitance values ​​are within the preset range; The equivalent series resistance and capacitance of the output transformer are measured using an impedance analyzer to obtain measurement data; Use an audio analyzer to measure the distortion and frequency response parameters of the power amplifier circuit within a preset frequency range; Use square wave signal excitation to measure the output signal of the power amplifier circuit and obtain transient response parameters; The measured data is measured multiple times and the average value is taken to obtain the measured data set; The least square method is used to calculate the deviation between the measured data and the predicted value; Use MATLAB's hist function to generate a deviation histogram, use the normplot function to draw a normal probability plot of the deviation, and generate a statistical report; Identify constant terms and coefficients that need to be adjusted in theoretical formulas through statistical reports; Genetic algorithms are used to optimize constant terms and coefficients in theoretical formulas; Taking minimizing the mean square error between the predicted value and the measured value as the objective function, a new indicator prediction formula is obtained through iterative optimization. Use the holdout method to set a preset proportion of data as a test set; Calculate the root mean square error of the formula before and after optimization on the test set; The prediction accuracy and generalization ability of the optimized formula were evaluated through cross-validation; It also includes: adding the quadratic and cubic terms of equivalent series resistance in the distortion calculation, adjusting the coefficient to reflect the influence of high-order harmonics, and introducing the frequency-related correction factors of skin effect and proximity effect in the high-frequency response calculation, specifically including: obtaining the nonlinear characteristic data of equivalent series resistance, which includes the linear term, quadratic term and cubic term of equivalent series resistance; performing polynomial regression using the least squares method based on the nonlinear characteristic data of equivalent series resistance to obtain the initial value of the equivalent series resistance coefficient; measuring the high-order harmonic content under different equivalent series resistance values, and if the harmonic amplitude is greater than the preset percentage of the fundamental wave, ratio, it is determined to be an effective harmonic; the corresponding relationship between harmonic order and coefficient is established according to the effective harmonic; the current distribution in the conductor at different frequencies is simulated by electromagnetic field simulation software, and the influence of skin effect and proximity effect on effective resistance is obtained by calculating the current distribution; the coefficients of quadratic and cubic terms of equivalent series resistance are optimized by genetic algorithm, and the objective function of genetic algorithm is to minimize the mean square error between predicted distortion and measured distortion; the correction factors of skin effect and proximity effect are adjusted by particle swarm optimization algorithm, and the particle swarm optimization algorithm takes the measured frequency response curve as reference to minimize the deviation between theoretical calculated value and measured value; The optimized index prediction formula is used to calculate the distortion, high frequency down slope of the frequency response, transient response time constant and overshoot under different combinations of equivalent series resistance and capacitance values, and a mapping table between the index value and the equivalent series resistance and capacitance value is established, including: Get the logarithmically distributed equivalent series resistance and capacitance value combinations, which are generated by the logspace function of MATLAB; The distortion value is calculated according to the combination of the equivalent series resistance value and the capacitance value, and the distortion value is obtained by the optimized distortion prediction formula; Considering the influence of equivalent series resistance and capacitance, the optimized transfer function H(s) is used to calculate the frequency response. A state space model is constructed, where the state space model is used to simulate the step response of a combination of equivalent series resistance and capacitance values; Extract overshoot and time constant from step response. Overshoot is extracted by findpeaks function and time constant is calculated by numerical analysis method. Perform three-dimensional interpolation on the calculation results to obtain a mapping table; The mapping table is stored in HDF5 format, which is used to ensure efficient reading and compressed storage of data; If the root mean square error between the mapping table interpolation result and the direct calculation result of the randomly selected equivalent series resistance and capacitance value combination is less than a preset threshold, it is determined that the mapping table accuracy meets the requirements; It also includes: determining the calculation range and step size of equivalent series resistance and capacitance values ​​based on measured data, creating a multidimensional array for storing the calculation results of various indicators; traversing all combinations of equivalent series resistance and capacitance values ​​through nested loops, using a corresponding relationship function for each combination, calculating the actual equivalent series resistance and capacitance values ​​at key frequencies, calculating the distortion, high-frequency slope of the frequency response, transient response time constant and overshoot, calculating the extreme value and average value of each indicator, and generating a heat map or a 3D surface map, specifically including: obtaining the preset key frequency points, using the frequency-related equivalent series resistance and capacitance value correspondence Function, calculate the equivalent series resistance value and capacitance value at the key frequency point; traverse the combination of the equivalent series resistance value and capacitance value, and for each combination, apply the preset indicator prediction formula to obtain the distortion and the high-frequency decline slope of the frequency response; generate a two-dimensional heat map of the equivalent series resistance and capacitance value indicators or generate a 3D surface map of the equivalent series resistance and capacitance value and the indicator; obtain random equivalent series resistance and capacitance values, perform actual measurements, and obtain measurement results; compare the calculation results of the equivalent series resistance and capacitance values ​​with the measurement results to obtain errors; and judge the accuracy of the established model according to the errors; The method of setting weights and acceptable thresholds for each indicator according to the measured data, including distortion and high-frequency drop slope of the frequency response, traversing the equivalent series resistance and capacitance value combinations in the mapping table, scoring each indicator according to whether it is within the threshold range, and calculating the weighted total score, taking the combination with a score exceeding the preset score as a candidate solution, performing actual circuit testing on the candidate solution, and determining the equivalent series resistance and capacitance value combination as the final design target of the output transformer according to the test results, including: Obtain the value of each indicator, use the minimum-maximum normalization method to map the value of each indicator to the range of 0 to 1, and calculate the weight of each indicator based on the mapping result; Traversing the equivalent series resistance and capacitance combinations in the mapping table, calculating the scores of various indicators of the equivalent series resistance and capacitance combinations according to the scoring function, and obtaining the total score of the equivalent series resistance and capacitance combinations by using a weighted summation method; According to the preset scores, the equivalent series resistance value and capacitance value combination with scores higher than the preset scores are extracted from the score matrix to generate a list of candidate solutions; The candidate solutions are divided into preset clusters using the K-means clustering algorithm, the cluster center point is selected from the preset clusters as the representative solution, and the representative solution is tested on the actual circuit; The NSGA-II algorithm is used for multi-objective optimization, which includes theoretical prediction error and actual performance indicators. The final combination of equivalent series resistance and capacitance values ​​is determined based on the multi-objective optimization results.

2. The method according to claim 1, characterized in that: The method of obtaining the primary winding resistance, secondary winding resistance, core loss resistance, inter-winding distributed capacitance, winding self-distributed capacitance and equivalent capacitance parameters caused by core dielectric loss of the C-type single-ended power amplifier output transformer according to the winding structure and core material of the transformer comprises: Obtaining a three-dimensional structure diagram of the transformer winding, where the three-dimensional structure diagram is generated by an X-ray tomography method; Analyze winding geometry parameters based on 3D structure diagram; Measure the resistance value at both ends of the primary winding of the transformer, which is measured by an impedance analyzer; Calculate the primary winding resistance parameters based on the relationship between the resistance value and the winding wire diameter and number of turns; Measuring the open-circuit impedance characteristic curve of the secondary winding of the transformer, the impedance characteristic curve is measured by a vector network analyzer within a preset frequency range; Extract the secondary winding resistance value from the low-frequency band data of the impedance characteristic curve; Measure the open circuit capacitance and short circuit capacitance of the transformer. The capacitance is measured by an LCR tester within a preset frequency range. The distributed capacitance between windings and the distributed capacitance of the winding itself are obtained by fitting the equivalent circuit model; Establish a transformer equivalent circuit model, which includes primary winding resistance, secondary winding resistance, core loss equivalent resistance, inter-winding distributed capacitance, winding self distributed capacitance and core dielectric loss equivalent capacitance; If the simulation results of the equivalent circuit model do not match the actual measured data, the parameters of the equivalent circuit model are adjusted.

3. The method according to claim 1, characterized in that The sampling circuit is used to sample the voltage and current waveforms of the primary and secondary windings, and the equivalent series resistance and capacitance values ​​in the output transformer equivalent circuit are determined by the least squares fitting method according to the sampled data and the acquired parameters, including: The sampling frequency is set according to the upper limit of the operating frequency of the output transformer to obtain the voltage and current waveforms of the primary and secondary windings; Perform digital filtering preprocessing on the voltage and current waveforms and obtain frequency domain data through Fourier transform; Extracting the fundamental wave component and the harmonic components whose amplitude is greater than a preset percentage of the fundamental wave amplitude from the frequency domain data; Based on the fundamental wave component and the harmonic wave component, a frequency domain equivalent circuit model is constructed, and a nonlinear equation group about the equivalent series resistance and capacitance is established; The Gauss-Newton method is used to solve the nonlinear equations to obtain initial estimates of the equivalent series resistance and capacitance. The initial estimated value is optimized, and if the relative error is less than a preset threshold or the number of iterations reaches a preset value, the equivalent series resistance and capacitance values ​​in the output transformer equivalent circuit are determined; It also includes: gradually changing the equivalent series resistance value, calculating and recording the efficiency and total harmonic distortion corresponding to each equivalent series resistance value, gradually changing the capacitance value, calculating and recording the high-frequency cutoff point and high-frequency decline slope corresponding to each capacitance value, generating a relationship diagram between the equivalent series resistance and the efficiency and total harmonic distortion, and a relationship diagram between the capacitance value and the high-frequency cutoff point and the high-frequency decline slope, specifically including: determining the equivalent series resistance variation range according to the initial equivalent series resistance value, and using SPICE simulation software to obtain the efficiency and total harmonic distortion data corresponding to each equivalent series resistance value; wherein the efficiency data is obtained by calculating the ratio of the output power to the input power, and the total harmonic distortion data is obtained by calculating the fundamental and harmonic components of the output signal through Fourier transform; determining the capacitance value variation range, and using the Bode diagram analysis tool to calculate the frequency response corresponding to each capacitance value The method comprises the following steps: obtaining a frequency response curve; selecting a high-frequency cutoff point from the frequency response curve and calculating the high-frequency decline slope; fitting the data points of equivalent series resistance and efficiency, and equivalent series resistance and total harmonic distortion by the least square method to obtain the fitting curve equation; normalizing the fitting curve and drawing the relationship diagrams of equivalent series resistance and efficiency, and equivalent series resistance and total harmonic distortion; using the cubic spline interpolation algorithm to process the data points of capacitance value and high-frequency cutoff point, and capacitance value and high-frequency decline slope to generate smooth curve data; normalizing the interpolation data and drawing the relationship diagrams of capacitance value and high-frequency cutoff point, and capacitance value and high-frequency decline slope; comparing the relationship diagrams of equivalent series resistance and efficiency, and total harmonic distortion, and the relationship diagrams of capacitance value and high-frequency cutoff point, and high-frequency decline slope, to identify the influence of parameter changes on the performance of the output transformer.

4. The method according to claim 1, characterized in that: The equivalent series resistance and capacitance values ​​are measured at different frequencies, and their changing trends are analyzed; a corresponding relationship function between the equivalent series resistance and capacitance values ​​and the frequency is established using a curve fitting tool of MATLAB, the changing trend of the equivalent series resistance in the low frequency band is analyzed, and its changing rate is calculated; At the same time, the changing characteristics of the capacitance value in the high frequency band are analyzed and its attenuation amplitude is calculated, including: Set the measurement frequency point range and use logarithmic distribution to determine the preset measurement frequency points; An impedance analyzer is used to obtain equivalent series resistance and capacitance values ​​by adopting a four-wire measurement method at a measurement frequency point, and the equivalent series resistance and capacitance values ​​are measured multiple times and averaged; According to the corresponding relationship between the equivalent series resistance value and the frequency, a curve fitting tool is used to fit the relationship between the equivalent series resistance and the frequency by a fifth-order polynomial to obtain the corresponding relationship function between the equivalent series resistance and the frequency; According to the corresponding relationship between capacitance value and frequency, a curve fitting tool is used to fit the exponential function to obtain the corresponding relationship function between capacitance value and frequency; ， In the formula, C(f) represents the relationship between capacitance and frequency f, a, b and c are fitting parameters, and exp represents the exponential function; Extracting equivalent series resistance data within a preset range from a function of a corresponding relationship between equivalent series resistance and frequency, and calculating an average rate of change of the equivalent series resistance within the frequency range; Extracting capacitance data within a preset range from the function of the corresponding relationship between capacitance and frequency, and calculating the maximum attenuation amplitude and average attenuation rate of the capacitance value in the high frequency band; Compare the changing characteristics of equivalent series resistance and capacitance values ​​in different frequency bands, and analyze the impact of the changing characteristics on the performance of the output transformer.

5. The method according to claim 1, characterized in that According to the corresponding relationship function between the equivalent series resistance and capacitance value and the frequency, combined with the change rate of the equivalent series resistance and the attenuation amplitude of the capacitance, through the theoretical calculation formula of the power amplifier distortion, frequency response and transient response, the distortion, frequency response and transient index prediction values ​​under different frequencies and different equivalent series resistance and capacitance values ​​are obtained, including: Obtain a preset number of frequency points in a logarithmic distribution within a preset frequency range, and calculate the equivalent series resistance value and the capacitance value of the frequency point according to a corresponding relationship function between the equivalent series resistance and the capacitance value; The three-times standard deviation method was used to identify outliers, and if outliers were identified, they were eliminated; For each frequency point, the instantaneous rate of change of equivalent series resistance is calculated using the central difference method, and the instantaneous attenuation value of capacitance is calculated using the difference between adjacent points. Substitute the equivalent series resistance value, capacitance value, instantaneous rate of change of equivalent series resistance and instantaneous attenuation value of capacitance value into the harmonic distortion calculation formula to obtain the distortion prediction value at the frequency point; Use the frequency response calculation formula to determine the predicted value of the amplitude-frequency characteristic and the predicted value of the phase-frequency characteristic at the frequency point; According to the predicted value of amplitude-frequency characteristic, the transient response parameters are calculated by inverse Laplace transform; The equivalent series resistance and capacitance values ​​are randomly perturbed to evaluate the stability of the predicted values.

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