Method for accurately solving capacitance broadband Q value and C value curve

Abstract

The invention provides a method for accurately solving a capacitance broadband Q value curve and a capacitance broadband C value curve. The method comprises the steps of frequency segmentation, low-frequency band and high-frequency band processing, transition area setting, curve splicing and smoothing processing. The method comprises the following specific steps: dividing a frequency range into a low-frequency band of 0-5GHz and a high-frequency band of more than 5GHz; a Q value and a C value in a 0G-5GHz frequency range are calculated by using an equivalent circuit model method in a low-frequency band; a high frequency band is calculated by using an S parameter fitting method; a transition area is arranged at 4-6 GHz; and splicing and smoothing the low-frequency-band curve and the high-frequency-band curve in the transition area to obtain a final Q-value curve and a final C-value curve. According to the method, the capacitor broadband Q value curve and the capacitor broadband C value curve can be accurately solved, and the accuracy and the reliability of capacitor performance analysis are improved.

Description

Technical Field

[0001] The present invention relates to the field of performance analysis of electronic components, and more specifically, to a method for accurately solving a wide-band Q value and C value curve of a capacitor. Background Art

[0002] In the field of electronics and communications, capacitors are key passive components, and their performance parameters such as quality factor (Q value) and capacitance value (C value) are crucial to circuit design. The characteristics of these parameters that change with frequency have a significant impact on the performance of high-frequency circuits. Traditional capacitor performance analysis methods are often not accurate enough within a wide frequency band, especially in the transition region between low-frequency and high-frequency bands. Due to the lack of effective processing methods, the calculated results of the Q value and C value curves deviate from the actual frequency response characteristics. In addition, when dealing with high-frequency bands, existing methods often rely on complex S-parameter data conversion and iterative optimization processes. These processes are not only computationally intensive, but also difficult to ensure the continuity and smoothness of the parameter curves over the entire frequency band.

[0003] In the process of implementing the embodiments of the present invention, the inventors found that there are at least the following problems or defects in the prior art: the equivalent circuit model method has limited applicability in the low frequency band, and the S parameter fitting method is difficult to balance the calculation efficiency and the accuracy of the results in the high frequency band. At the same time, there is a lack of effective smoothing processing means in the transition area between the low frequency band and the high frequency band, resulting in the final Q value and C value curves being unable to accurately reflect the actual working characteristics of the capacitor. Summary of the invention

[0004] The present invention provides a method for accurately solving a capacitor wideband Q value and C value curve, comprising:

[0005] Frequency segmentation: divide the calculation frequency range into low frequency band and high frequency band, and determine the frequency range of the low frequency band and the high frequency band;

[0006] Low frequency band processing: The equivalent circuit model method is used to calculate the Q value and C value of the capacitor in the low frequency band;

[0007] High frequency band processing: The S parameter fitting method is used to calculate the Q value and C value of the capacitor in the high frequency band;

[0008] Transition area setting: set a smooth transition area at the boundary between the low frequency band and the high frequency band;

[0009] Curve splicing: splice the Q value and C value curves calculated in the low frequency band and high frequency band in the smooth transition area;

[0010] Smoothing: Smoothing the spliced ​​Q value and C value curves to obtain the final Q value and C value curves.

[0011] Furthermore, in the frequency segmentation step, the low frequency band has a frequency range of 0 GHz-5 GHz, and the high frequency band has a frequency range of above 5 GHz.

[0012] Furthermore, in the low frequency band processing step, the equivalent circuit model method includes the following sub-steps:

[0013] Selecting an equivalent circuit topology structure, the equivalent circuit topology structure including a capacitance value, an inductance value, and a parasitic resistance value;

[0014] Taking the frequency point of 0.1GHz-5GHz as the fitting target, the optimization algorithm is called to adjust the parameters of the equivalent circuit. The optimization algorithm takes minimizing the frequency response error as the objective function to obtain the equivalent circuit model with the best fitting effect;

[0015] The Q and C values ​​of 0GHz-0.1GHz are extrapolated through the optimal equivalent circuit model.

[0016] Furthermore, the S parameter fitting method is used to calculate the Q value and C value of the capacitor in the high frequency band, and the S parameter fitting method includes:

[0017] Select the initial frequency point according to the binary principle to ensure that the high frequency range is covered;

[0018] Convert the S parameter data into a linear equation system represented by poles and residuals, perform iterative optimization, adjust the poles and residual positions to obtain a vector fitting model with the minimum error, and thus obtain a vector fitting result;

[0019] The frequency data in the vector fitting model is used to construct the Loewner matrix, and the generalized eigenvalue problem is solved to extract the poles and residuals of the system. The rational approximation function of the S parameters is generated from the poles and residuals to obtain the Loewner fitting results.

[0020] Select the best fitting result from the vector fitting results and the loewner fitting results.

[0021] The smooth transition region is set in the boundary region between the low frequency band and the high frequency band, and the frequency range of the transition region is 4 GHz-6 GHz.

[0022] Furthermore, in the transition region setting step, the frequency range of the transition region is 4 GHz-6 GHz.

[0023] Furthermore, in the curve splicing step, a weighted average method is used for splicing, and the weighting function is: Csmooth(f)=w(f)×Clow(f)+(1-w(f))×Chigh(f);

[0024] Among them, Csmooth(f) is the capacitance value curve after the transition area is spliced, w(f) is the weight function, Clow(f) is the capacitance value curve of the low frequency band, Chigh(f) is the capacitance value curve of the high frequency band, and w(f) gradually decreases from 1 to 0 in the transition frequency range.

[0025] Furthermore, in the smoothing step, sliding polynomial fitting is used for processing, data of 10 frequency points are selected near each frequency point, and the original data values ​​are replaced by quadratic polynomial fitting.

[0026] Furthermore, in the smoothing step, during the sliding polynomial fitting process, the calculated Q value curve is continuously smoothed in the entire frequency band, and the maximum error is less than 5%.

[0027] Furthermore, in the smoothing step, during the sliding polynomial fitting process, the C value curve exhibits a gradual frequency response behavior in the high frequency band.

[0028] Furthermore, the final Q value and C value curves conform to the frequency response characteristics of an actual capacitor.

[0029] The above-mentioned embodiments of the present invention have at least the following beneficial effects: the present invention can improve the calculation accuracy of capacitor performance parameters under wide frequency band by accurately dividing the calculation frequency range into low frequency band and high frequency band, and respectively using equivalent circuit model method and S parameter fitting method to calculate the Q value and C value of the capacitor. In the low frequency band, the frequency response characteristics of the capacitor can be effectively simulated by using the equivalent circuit model method; while in the high frequency band, the Q value and C value of the capacitor can be accurately extracted from the S parameter data by using the S parameter fitting method. In addition, the present invention sets a smooth transition area between the low frequency band and the high frequency band, and uses the weighted average method for curve splicing, which can ensure the continuity and smoothness of the Q value and C value curves in the full frequency band, thereby more accurately reflecting the actual working characteristics of the capacitor.

[0030] The present invention further adopts sliding polynomial fitting for smoothing, and multiple data points can be selected near each frequency point, and the original data value can be replaced by quadratic polynomial fitting to further optimize the smoothness of the Q value and C value curves. This method can not only maintain the continuous smoothness of the Q value curve in the entire frequency band, but also ensure that the C value curve exhibits a gradual frequency response behavior in the high frequency band, with a maximum error of less than 5%. Therefore, the present invention can not only provide a method for accurately solving the wide-band Q value and C value curves of capacitors, but also ensure that the final curves conform to the frequency response characteristics of actual capacitors, providing more reliable data support for the design and application of capacitors. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] The above and other objects, features and advantages of the exemplary embodiments of the present invention will become readily understood by reading the detailed description below with reference to the accompanying drawings. In the accompanying drawings, several embodiments of the present invention are shown in an exemplary and non-limiting manner, in which:

[0032] Figure 1 A schematic flow chart of a method for accurately solving a capacitor wideband Q value and C value curve provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0033] The principles and spirit of the present invention will be described below with reference to several exemplary embodiments. It should be understood that these embodiments are provided only to enable those skilled in the art to better understand and implement the present invention, and are not intended to limit the scope of the present invention in any way. On the contrary, these embodiments are provided to make the present invention more thorough and complete, and to fully convey the scope of the present invention to those skilled in the art.

[0034] Those skilled in the art will appreciate that the embodiments of the present invention may be implemented as a system, device, apparatus, method or computer program product. Therefore, the present invention may be implemented in the following forms, namely: complete hardware, complete software (including firmware, resident software, microcode, etc.), or a combination of hardware and software.

[0035] It should be noted that any number of elements in the drawings is for illustration rather than limitation, and any naming is only for distinction and does not have any limiting meaning.

[0036] Reference below Figure 1 , Figure 1 A flow chart of a method for accurately solving a capacitor wideband Q value and C value curve provided by an embodiment of the present invention. Figure 1 As shown, a method 100 for accurately solving a capacitor wideband Q value and C value curve includes:

[0037] Step 101, frequency segmentation: dividing the calculated frequency range into a low frequency band and a high frequency band, and determining the frequency ranges of the low frequency band and the high frequency band;

[0038] Step 102, low frequency band processing: using an equivalent circuit model method to calculate the Q value and C value of the capacitor in the low frequency band;

[0039] Step 103, high frequency band processing: using S parameter fitting method to calculate the Q value and C value of the capacitor in the high frequency band;

[0040] Step 104, transition area setting: setting a smooth transition area at the boundary area between the low frequency band and the high frequency band;

[0041] Step 105, curve splicing: splicing the Q value and C value curves calculated in the low frequency band and the high frequency band in the smooth transition area;

[0042] Step 106, smoothing: smoothing the spliced ​​Q value and C value curves to obtain the final Q value and C value curves.

[0043] It should be noted that the method first involves dividing the calculation frequency range into a low frequency band and a high frequency band, and determining the frequency ranges of the two frequency bands. Frequency segmentation here refers to dividing the entire calculation frequency range into two different intervals so that different calculation methods can be used for processing. The low frequency band usually refers to the lower frequency part, while the high frequency band refers to the higher frequency part. In this method, the specific frequency ranges of the low frequency band and the high frequency band are pre-set to meet different calculation requirements.

[0044] Specifically, the frequency range of the low frequency band is set to 0GHz to 5GHz, while the frequency range of the high frequency band is above 5GHz. The division of these two frequency bands is based on the changing characteristics of capacitor performance at different frequencies. In the low frequency band, the Q value and C value of the capacitor change relatively slowly, which is suitable for calculation using the equivalent circuit model method; while in the high frequency band, due to the large fluctuations and interference of the signal, it is more appropriate to use the S parameter fitting method. This setting can ensure that more accurate calculation results can be obtained in different frequency bands.

[0045] Preferably, for low frequency processing, an equivalent circuit model method can be used, which includes selecting a suitable equivalent circuit topology structure, which includes capacitance, inductance and parasitic resistance. This equivalent circuit model is used to simulate the behavior of an actual capacitor in a circuit. By adjusting these parameters, the frequency response of the model can be made as consistent as possible with the response of the actual capacitor.

[0046] Furthermore, in actual operation, the frequency point from 0.1GHz to 5GHz can be used as the fitting target, and the optimization algorithm can be called to adjust the parameters of the equivalent circuit, with the objective function of minimizing the frequency response error, to obtain the equivalent circuit model with the best fitting effect. Through this optimal model, the Q value and C value from 0GHz to 0.1GHz can be extrapolated, thereby achieving accurate calculation of the entire low-frequency band.

[0047] In some embodiments, in the frequency segmentation step, the low frequency band has a frequency range of 0 GHz-5 GHz, and the high frequency band has a frequency range of above 5 GHz.

[0048] It should be noted that this implementation describes in detail the specific frequency range of the frequency segmentation, that is, the low frequency band is 0 GHz to 5 GHz, and the high frequency band is above 5 GHz. The frequency range here refers to the specific frequency interval used to calculate the Q value and C value in the performance analysis of the capacitor. The division of the low frequency band and the high frequency band is based on the performance changes of the capacitor at different frequencies to adapt to different calculation methods.

[0049] Specifically, the equivalent circuit model is used in the low-frequency band to ensure the accuracy of the low-frequency characteristics; the S parameter fitting is used in the high-frequency band to improve the calculation accuracy in the high-frequency range, so that the measurement results of the capacitance characteristics over the entire wide frequency band are more accurate. It can effectively avoid the defect of insufficient accuracy of the circuit model in the high-frequency band and avoid the problem that the circuit model cannot accurately reflect the parasitic effects of the capacitor at high frequencies. The division of these two frequency bands is based on the understanding of the performance changes of capacitors at different frequencies and the consideration of the applicability of different calculation methods.

[0050] Preferably, the processing of the low frequency band can be further refined to use a specific equivalent circuit model, such as an RLC circuit model including a series resistor, a parallel resistor and an inductor. In this model, the actual performance of the capacitor in the low frequency band can be simulated by adjusting circuit parameters such as resistance value, inductance value and capacitance value.

[0051] Furthermore, for high frequency bands, a data fitting method based on S parameters can be used. By selecting an appropriate initial frequency point and using vector fitting technology, the S parameter data can be converted into the form of poles and residuals, and iterative optimization can be performed to obtain a fitting model with the minimum error. Such processing can ensure that more accurate Q and C values ​​are obtained in the high frequency band. In addition, other optimization algorithms or fitting techniques can also be considered to improve the accuracy and efficiency of the calculation.

[0052] In some embodiments, in the low frequency band processing step, the equivalent circuit model method includes the following sub-steps:

[0053] Selecting an equivalent circuit topology structure, the equivalent circuit topology structure including a capacitance value, an inductance value, and a parasitic resistance value;

[0054] Taking the frequency point of 0.1GHz-5GHz as the fitting target, the optimization algorithm is called to adjust the parameters of the equivalent circuit. The optimization algorithm takes minimizing the frequency response error as the objective function to obtain the equivalent circuit model with the best fitting effect;

[0055] The Q and C values ​​of 0GHz-0.1GHz are extrapolated through the optimal equivalent circuit model.

[0056] It should be noted that this embodiment describes in detail the specific operation of the equivalent circuit model method in the low-frequency band processing step. The equivalent circuit model method is a method for calculating the performance parameters of a capacitor by simulating its behavior in a circuit. This method involves selecting an equivalent circuit topology structure including capacitance, inductance, and parasitic resistance values, which together determine the frequency response characteristics of the capacitor.

[0057] Specifically, the equivalent circuit topology refers to a simplified circuit model that can simulate the actual behavior of the capacitor in the circuit. This model usually includes a main capacitor element, and possible inductor and resistor elements in series or parallel to simulate the parasitic effects of the capacitor. In the implementation process, it is first necessary to determine the topology of the equivalent circuit and then select appropriate parameter values. These parameter values ​​can be determined by experimental data or specifications provided by the manufacturer. Then, with the frequency point of 0.1GHz to 5GHz as the fitting target, the optimization algorithm is called to adjust these parameters, with minimizing the frequency response error as the objective function, so as to obtain an equivalent circuit model with the best fitting effect.

[0058] Preferably, the optimization algorithm can be one of a variety of algorithms, such as gradient descent, genetic algorithm or particle swarm optimization algorithm. These algorithms iteratively search the parameter space to find the parameter combination that best fits the experimental data. In actual operation, the number of iterations, learning rate or other related parameters of the algorithm can be set to ensure the convergence and efficiency of the algorithm.

[0059] Furthermore, we can also explore different optimization algorithms, or combine the advantages of multiple algorithms to improve the model's fitting accuracy and computational efficiency. Through the optimal equivalent circuit model, we can extrapolate the Q and C values ​​from 0 GHz to 0.1 GHz, thereby achieving accurate calculation of the entire low-frequency band.

[0060] In some embodiments, in the high frequency band processing step, the S parameter fitting method includes the following sub-steps:

[0061] The S parameter fitting method is used to calculate the Q value and C value of the capacitor in the high frequency band. The S parameter fitting method includes:

[0062] Select the initial frequency point according to the binary principle to ensure that the high frequency range is covered;

[0063] Convert the S parameter data into a linear equation system represented by poles and residuals, perform iterative optimization, adjust the poles and residual positions to obtain a vector fitting model with the minimum error, and thus obtain a vector fitting result;

[0064] The frequency data in the vector fitting model is used to construct the Loewner matrix, and the generalized eigenvalue problem is solved to extract the poles and residuals of the system. The rational approximation function of the S parameters is generated from the poles and residuals to obtain the Loewner fitting results.

[0065] Select the best fitting result from the vector fitting results and the loewner fitting results.

[0066] It should be noted that this embodiment describes in detail the specific operation of the S parameter fitting method in the high frequency band processing step. S parameters, i.e. scattering parameters, are a set of parameters used to describe the reflection and transmission characteristics of signals in radio frequency circuit networks. This method includes converting S parameter data into a set of linear equations represented by poles and residuals, and performing iterative optimization to adjust the pole and residual positions, thereby obtaining a Vector Fitting fitting model with the minimum error.

[0067] The Vector Fitting model is based on the idea of ​​decomposing complex frequency domain responses into the sum of multiple simple fractions. By introducing the concepts of poles and residuals, frequency-related characteristics can be expressed in a relatively concise mathematical form. The poles determine the singularity position of the function in the complex frequency domain and reflect the inherent frequency characteristics of the system; the residuals indicate the contribution of each pole to the overall response.

[0068] The Loewner matrix is ​​based on the frequency data obtained by the Vector Fitting model, and uses the difference relationship between the fitted model data at different frequencies to organize these relationships in the form of a matrix. This matrix structure can effectively capture the changes in the dynamic characteristics of the system at different frequencies, and provides a powerful mathematical tool for the subsequent extraction of the poles and residuals of the system. By constructing the Loewner matrix, the information in the frequency domain data can be represented in a matrix form that is easier to analyze and process, so that the system characteristics can be deeply studied using methods such as matrix operations and eigenvalue solutions.

[0069] Specifically, Vector Fitting in the S-parameter fitting method is a technology used to extract parameters of RF and microwave circuits. It fits the S-parameter data into a model in the form of a rational function, which can be represented by poles and residuals. In the implementation process, it is first necessary to select the initial frequency points according to the binary principle to ensure that the transition region and high-frequency region bands are covered, which means that the selection of frequency points should be evenly distributed throughout the frequency band so that the frequency response characteristics of the capacitor can be fully captured. Next, the S-parameter data is converted into a set of linear equations represented by poles and residuals, and iterative optimization is performed to adjust the pole and residual positions to minimize the fitting error, and the Vector Fitting fitting model is obtained.

[0070] Preferably, the frequency data in the Vector Fitting model can be used to construct the Loewner matrix, which is a matrix used to solve the generalized eigenvalue problem, which can help extract the poles and residuals of the system. From these poles and residuals, rational approximation functions of S parameters can be generated, and then the Loewner fitting S parameter results can be obtained.

[0071] Specifically, the S parameter fitting method includes the following steps:

[0072] 1. Select the initial frequency point according to the binary principle to ensure that the high frequency range is covered;

[0073] 2. Convert the S parameter data into a linear equation system represented by poles and residuals, perform iterative optimization, adjust the pole and residual positions to obtain the vector fitting model with the minimum error, and thus obtain the vector fitting S parameter results. The specific conversion and iterative optimization process is as follows:

[0074] Assume that the S parameter is S=a+jb; where a is the real part, b is the imaginary part, and j is the imaginary unit, and convert it to Y=1 / Z=(1-S) / (1+S);

[0075] In the RF circuit, for the reflection coefficient S of a port, here taking the single-port case as an example, there is the following relationship between the input impedance Z and the transmission line characteristic impedance Z0:

[0076] The reflection coefficient S is defined as:

[0077] Transform this formula to solve Z:

[0078] Depend on It can be obtained that S(Z+Z0)=Z-Z0.

[0079] Move the terms containing Z to one side and the constant terms to the other side: SZ-Z=-SZ0-Z0.

[0080] Extracting the common factor yields Z(S-1)=-(S+1)Z0.

[0081] The final solution When Z0=1,

[0082]

[0083] Admittance Y is defined as the reciprocal of impedance Z, that is, Y = 1 / Z.

[0084] (When Z0=1),

[0085] So

[0086] The poles and residual forms are further expressed by favorable approximation functions:

[0087] s=jω is a complex frequency variable, r k is the residual, p k is the pole, d and e are constants.

[0088] Construct a system of linear equations:

[0089] m is the number of sampling points.

[0090] The equations are solved by iterative algorithms such as the least squares method to obtain the poles and residuals, and then the vectorfitting model and results are obtained;

[0091] 3. Use the frequency data in the vector fitting model to construct the Loewner matrix, solve the generalized eigenvalue problem to extract the poles and residuals of the system, and generate the rational approximation function of the S parameters from the poles and residuals to obtain the Loewner fitting S parameter results;

[0092] 4. From S 11 Calculate the input impedance Z in , calculated as: Z in =(1+S 11 ) / (1-S11;

[0093] Then the input impedance Z in Convert to admittance Y in =G+jB, where G is conductance, B is susceptance, and j is an imaginary unit. The calculation method of conductance G and susceptance B is:

[0094] G=Re(Y in ), B=Im(Y in ).

[0095] The capacitance C is calculated by B = 2πfC, where f is the frequency), and the calculation method is:

[0096] C = B / (2πf);

[0097] Finally, the quality factor Q is calculated by Q=B / G;.

[0098] 5. According to the smoothness of the Q value and C value curves, select the best fitting result from the vector fitting results and the Loewner fitting results. The specific judgment method is: calculate the root mean square error of the two curves, the standard deviation of the difference between adjacent data points and other indicators, and select the one with the smaller indicator value as the best fitting result.

[0099] It should be noted that in radio frequency and microwave technology, S 11 It is a parameter used to describe the reflection characteristics of a two-port network (such as a capacitor can be regarded as a two-port element in a circuit). 11 Defined as the reflection coefficient, it indicates the ratio of the signal reflected from port 1 to the input signal when a signal is input to port 1. In a physical sense, it reflects how much energy is reflected back when the signal encounters a component (such as a capacitor) at port 1, instead of being fully transmitted to the inside of the component or other ports.

[0100] For a two-port network, according to transmission line theory and network analysis, there is the following relationship between the input impedance \(Z_{in}\) and \(S_{11}\):

[0101]

[0102] Where Z0 is the characteristic impedance of the transmission line, which can be assumed to be a normalized value of 1. The formula is simplified to:

[0103] When a signal is incident on port 1 and interacts with the component, the relationship between the reflected wave and the incident wave is expressed by S 11 To describe, and through this relationship, we can infer the equivalent impedance of the component seen from port 1, that is, the input impedance Z in . Calculate the input impedance Z in The behavior of the capacitor in the circuit can be understood, which is related to the actual electrical characteristics of the capacitor (such as capacitive reactance, etc.), and can be used to subsequently calculate the capacitance value C and quality factor Q parameters to fully characterize the performance of the capacitor within a wide frequency band.

[0104] Assume that at a certain frequency, the capacitance S is measured. 11 =0.2, if the normalized characteristic impedance Z0=1 is used, the input impedance Z is calculated according to the formula in for:

[0105]

[0106] In order to convert the denominator into a real number, multiply both the numerator and the denominator by 0.8+0.3j, and we get:

[0107]

[0108] Because J 2 =-1, so it can be further simplified to:

[0109]

[0110] In some embodiments, in the transition region setting step, the transition region frequency range is 4 GHz-6 GHz.

[0111] It should be noted that this implementation involves setting a smooth transition region at the boundary between the low frequency band and the high frequency band, and the frequency range of this transition region is set to 4GHz-6GHz. The transition region is set to ensure that the Q value and C value curves calculated by two different processing methods can be smoothly connected to avoid sudden changes at the boundary point, which is crucial to maintaining the continuity and accuracy of the capacitor performance parameters within the entire frequency band.

[0112] Specifically, the transition region refers to a frequency interval set between the low frequency band and the high frequency band, and the Q value and C value curves within this interval need to be specially processed to achieve a smooth transition. In this embodiment, the frequency range of the transition region is clearly defined as 4GHz-6GHz, which means that within this frequency range, a specific method will be used to process the Q value and C value to ensure that their changes between the low frequency band and the high frequency band are continuous. The selection of this range is based on the performance change characteristics of the capacitor at the junction of the two frequency bands, and the need to ensure a smooth transition of the curve.

[0113] Preferably, in order to achieve a smooth transition in the transition region, a weighted average method can be used to process the Q value and C value curves. This method involves assigning a weight to each frequency point in the transition region, and this weight gradually decreases as the frequency increases, thereby achieving a smooth transition from the low frequency band to the high frequency band. For example, a weight function w(f) can be designed, which takes a value of 1 at 4GHz and a value of 0 at 6GHz, and changes linearly between these two frequency points. In this way, it can be ensured that in the transition region, the processing results of the low frequency band are gradually replaced by the processing results of the high frequency band, thereby achieving the continuity and accuracy of the capacitor performance parameters in the entire frequency band. In addition, other smoothing techniques, such as polynomial interpolation or spline interpolation, can also be considered to further improve the processing effect of the transition region.

[0114] In some embodiments, in the curve splicing step, a weighted average method is used for splicing, and the weighting function is: Csmooth(f)=w(f)×Clow(f)+(1-w(f))×Chigh(f);

[0115] Among them, Csmooth(f) is the capacitance value curve after the transition area is spliced, w(f) is the weight function, Clow(f) is the capacitance value curve of the low frequency band, Chigh(f) is the capacitance value curve of the high frequency band, and w(f) gradually decreases from 1 to 0 in the transition frequency range.

[0116] It should be noted that this implementation describes a specific method for splicing the Q value and C value curves calculated in the low frequency band and the high frequency band in the transition region. The curve splicing mentioned here refers to smoothly connecting the parameter curves calculated in two different frequency bands in the transition region to ensure the continuity of the parameter curves in the entire frequency band. The weighted average method is a commonly used mathematical method for combining two or more data sets, where the weight of each data set is determined according to specific rules.

[0117] Specifically, the weighted average method is used to splice the capacitance value curve of the transition region in this embodiment. The weight function w(f) is a function that changes with the frequency f, which determines the respective contributions of the low-frequency capacitance value curve Clow(f) and the high-frequency capacitance value curve Chigh(f) during the splicing process. Within the transition frequency range, the weight function w(f) gradually decreases from 1 to 0, which means that at the low end of the transition region (close to the low frequency band), the capacitance value curve of the low frequency band contributes more to the final splicing curve Csmooth(f), while at the high end of the transition region (close to the high frequency band), the contribution of the capacitance value curve of the high frequency band gradually increases.

[0118] Preferably, the weight function w(f) can be designed in a linear or nonlinear manner to ensure a smooth transition of the capacitance value curve in the transition region. For example, a linearly decreasing weight function can be used so that w(f)=1 at 4 GHz and w(f)=0 at 6 GHz.

[0119] Furthermore, nonlinear weight functions, such as exponential decay or logarithmic decreasing functions, can also be considered to achieve a smoother transition effect. In practical applications, the form and parameters of the weight function can be adjusted according to the specific performance and design requirements of the capacitor to achieve the best splicing effect. Other splicing techniques, such as spline-based interpolation methods, can also be explored to provide more flexibility and accuracy.

[0120] In some embodiments, in the smoothing step, sliding polynomial fitting is used for processing, data of 10 frequency points are selected near each frequency point, and the original data values ​​are replaced by quadratic polynomial fitting.

[0121] It should be noted that this embodiment involves the step of smoothing the spliced ​​Q value and C value curves. The smoothing mentioned here refers to smoothing the curve by mathematical methods to reduce or eliminate fluctuations and noise in the curve, making the curve smoother and more continuous. In this embodiment, the smoothing is achieved by sliding polynomial fitting, which is a commonly used data smoothing technology.

[0122] Specifically, sliding polynomial fitting is a local regression method that selects a certain number of data points near each frequency point and then uses a polynomial function to fit these data points. In this embodiment, quadratic polynomial fitting is selected, which means that data of 10 frequency points are selected near each frequency point and a quadratic polynomial is used to fit these data points. This method can effectively capture local trends and patterns of data while reducing the impact of random fluctuations.

[0123] Preferably, the specific implementation of quadratic polynomial fitting can be further refined. For example, the coefficients of the quadratic polynomial can be determined by using the least square method so that the sum of square errors between the fitting curve and the actual data points is minimized.

[0124] Furthermore, it is also possible to consider using polynomials of other orders for fitting, or combining other types of local regression methods, such as Gaussian process regression or spline regression, to improve the accuracy and smoothness of the fitting. In practical applications, the size of the fitting window (i.e., the number of selected data points) and the order of the polynomial can be adjusted according to the characteristics and requirements of the data to achieve the best smoothing effect.

[0125] In some embodiments, in the smoothing step, during the sliding polynomial fitting process, the calculated Q value curve is continuously smoothed in the entire frequency band, and the maximum error is less than 5%.

[0126] It should be noted that this embodiment describes the requirements for the Q value curve in the smoothing step, that is, continuous smoothing in the entire frequency band, and the maximum error is less than 5%. The continuous smoothing mentioned here means that the change of the Q value curve in the entire frequency range should be uniform and without mutation, and the maximum error is less than 5% means that after smoothing, the maximum deviation of the Q value curve from the original data should not exceed 5%, ensuring the accuracy of the curve.

[0127] Specifically, the smoothing of the Q value curve is achieved by sliding polynomial fitting. This method selects a certain number of data points near each frequency point and uses a polynomial function to fit these data points. In this embodiment, the Q value curve is required to be continuous and smooth throughout the frequency band, which means that the fitted curve should not have drastic fluctuations or discontinuous points to ensure the physical meaning of the curve and the accuracy of practical applications. At the same time, the requirement of a maximum error of less than 5% can be achieved by setting the tolerance parameters of the fitting algorithm or through a post-processing step. For example, the fitted curve can be fine-tuned to ensure that the error is within the specified range.

[0128] Preferably, in order to meet the requirement that the Q value curve is continuously smooth in the entire frequency band and the maximum error is less than 5%, the smoothing process can be further refined. For example, the number of data points in the fitting window can be increased to improve the accuracy of the fitting; or a higher-order polynomial can be used for fitting to better capture the local changes of the data.

[0129] Furthermore, an error correction mechanism can be introduced, such as adding a regularization term during the fitting process to control the smoothness of the fitting curve, or further smoothing the curve after fitting, such as using moving average or Gaussian filtering techniques. These methods can help optimize the smoothness and accuracy of the Q value curve to ensure that it meets the maximum error requirements.

[0130] In some embodiments, in the smoothing step, during the sliding polynomial fitting process, the C value curve exhibits a gradual frequency response behavior in the high frequency band.

[0131] It should be noted that this embodiment involves the requirement for the C value curve in the smoothing step, that is, to show a gradual frequency response behavior in the high frequency band. The gradual frequency response behavior mentioned here means that the change trend of the C value curve in the high frequency band should be smooth and predictable, without sudden jumps or discontinuities, which helps to ensure the stability and reliability of the capacitor performance.

[0132] Specifically, the smoothing of the C value curve is achieved through sliding polynomial fitting, which selects a certain number of data points near each frequency point and uses a polynomial function to fit these data points. In the high frequency band, the gradual behavior of the C value curve can be achieved by selecting an appropriate polynomial order and fitting window size. For example, a larger fitting window can be selected to include more data points to capture the gradual change trend of the C value in the high frequency band. At the same time, the flexibility and smoothness of the fitting can be balanced by setting the order of the polynomial to ensure that the curve can reflect the true trend of the data without overfitting.

[0133] Preferably, in order to ensure that the C value curve exhibits a gradual frequency response behavior in the high frequency band, the smoothing step can be further refined. For example, an adaptive fitting window size can be used, that is, the window size is automatically adjusted in the high frequency band to better capture the change trend of the C value.

[0134] Furthermore, a frequency-dependent weight factor can be introduced to give more weight to the high-frequency band when fitting, thereby emphasizing the importance of the high-frequency band data. In addition, different types of polynomials can be considered, such as Chebyshev polynomials or Legendre polynomials, which may be more effective in dealing with boundary effects. Through these refined steps, the fitting quality and asymptotic behavior of the C value curve in the high-frequency band can be improved.

[0135] In some embodiments, the final Q value and C value curve conforms to the frequency response characteristics of an actual capacitor.

[0136] It should be noted that this implementation emphasizes that the final Q value and C value curves must conform to the frequency response characteristics of the actual capacitor. The frequency response characteristics here refer to the performance of the capacitor at different frequencies, such as the law of changes in its impedance, phase and other parameters with frequency. Ensuring that the curve conforms to the actual characteristics means the accuracy and practicality of the calculation results, which is crucial for the design and application of capacitors.

[0137] Specifically, in order to make the Q value and C value curves conform to the frequency response characteristics of the actual capacitor, it is necessary to use precise methods and conduct strict verification in the calculation and fitting process. This includes selecting appropriate model parameters, optimization algorithms, and smoothing techniques. For example, experimental data can be used to verify the accuracy of the model, and the model parameters can be adjusted by comparing the consistency of the calculated Q value and C value curves with the actual measured data. In addition, statistical methods can be used to evaluate the fitting error to ensure that the error is within an acceptable range.

[0138] Preferably, in order to further improve the accuracy of the Q-value and C-value curves, a variety of validation and optimization techniques can be used. For example, a cross-validation method can be used to evaluate the generalization ability of the model to ensure that the model can provide accurate predictions at different frequency points.

[0139] Furthermore, expert knowledge can be introduced to guide the selection of model parameters, or machine learning methods can be used to automatically optimize model parameters. In the smoothing step, more advanced mathematical tools, such as wavelet transform or Fourier transform, can be used to further smooth the curve and remove noise. Through these refined steps and alternatives, it can be ensured that the final Q value and C value curves are not only reasonable in theory, but also accurate and reliable in practical applications.

[0140] The above-mentioned various embodiments of the present invention have the following beneficial effects: the method for accurately solving the wide-band Q value and C value curve of the capacitor described in the present invention can adopt the most suitable calculation method in different frequency bands, thereby improving the calculation efficiency and accuracy. Secondly, the equivalent circuit model method is adopted in the low frequency band, and the S parameter fitting method is adopted in the high frequency band, which can ensure that the best fitting effect is obtained in the respective frequency bands, thereby improving the accuracy of the Q value and C value curves. In addition, setting the transition area and adopting the weighted average method for curve splicing can smoothly connect the results of the low frequency band and the high frequency band, avoid the discontinuity that may occur in the boundary area, and ensure the overall continuity of the curve.

[0141] Furthermore, the method also includes a smoothing step. Through the sliding polynomial fitting technology, multiple data points can be selected near each frequency point for fitting, thereby improving the smoothness and aesthetics of the curve. This method can not only maintain the continuous smoothness of the Q value curve in the entire frequency band, but also ensure that the C value curve exhibits a progressive frequency response behavior in the high frequency band, and the maximum error is controlled within 5%. Therefore, the present invention can not only provide a method for accurately solving the wide-band Q value and C value curves of capacitors, but also ensure that the final curve conforms to the frequency response characteristics of the actual capacitor, providing more reliable data support for the design and application of capacitors.

[0142] Furthermore, the storage medium of the embodiment of the present application stores program instructions that can implement all the above methods, wherein the program instructions can be stored in the above storage medium in the form of a software product, including several instructions for enabling a computer device (which can be a personal computer, server, or network device, etc.) or a processor to execute all or part of the steps of the methods described in each embodiment of the present application. The aforementioned storage medium includes: various media that can store program codes, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk, or terminal devices such as a computer, a server, a mobile phone, and a tablet.

[0143] The above descriptions are only some preferred embodiments of the present invention and an explanation of the technical principles used. Those skilled in the art should understand that the scope of the invention involved in the embodiments of the present invention is not limited to the technical solutions formed by a specific combination of the above technical features, but should also cover other technical solutions formed by any combination of the above technical features or their equivalent features without departing from the above inventive concept. For example, the above features are replaced with (but not limited to) technical features with similar functions disclosed in the embodiments of the present invention to form a technical solution.

Claims

1. A method for accurately solving the Q value and C value curve of capacitor broadband, characterized in that: The following steps are involved: Frequency segmentation: divide the calculation frequency range into low frequency band and high frequency band, and determine the frequency range of the low frequency band and the high frequency band; Low frequency band processing: The equivalent circuit model method is used to calculate the Q value and C value of the capacitor in the low frequency band; High frequency band processing: The S parameter fitting method is used to calculate the Q value and C value of the capacitor in the high frequency band; Transition area setting: set a smooth transition area at the boundary between the low frequency band and the high frequency band; Curve splicing: splice the Q value and C value curves calculated in the low frequency band and high frequency band in the smooth transition area; Smoothing: Smoothing the spliced ​​Q value and C value curves to obtain the final Q value and C value curves.

2. The method for accurately solving the wideband Q value and C value curve of capacitor according to claim 1, characterized in that: The calculation frequency range is divided into a low frequency band and a high frequency band, and the frequency ranges of the low frequency band and the high frequency band are determined, wherein the frequency range of the low frequency band is 0 GHz-5 GHz, and the frequency range of the high frequency band is above 5 GHz.

3. The method for accurately solving the wideband Q value and C value curve of capacitor according to claim 1, characterized in that: In the method of calculating the Q value and C value of the capacitor by using the equivalent circuit model method in the low frequency band, the equivalent circuit model method includes the following steps: Selecting an equivalent circuit topology structure, wherein the equivalent circuit topology structure includes a capacitance value, an inductance value, and a parasitic resistance value; Taking the frequency point of 0.1GHz-5GHz as the fitting target, the optimization algorithm is called to adjust the parameters of the equivalent circuit. The optimization algorithm takes minimizing the frequency response error as the objective function to obtain the equivalent circuit model with the best fitting effect; The Q value and C value of 0GHz-0.1GHz are calculated by the optimal equivalent circuit model.

4. The method for accurately solving the wideband Q value and C value curve of capacitor according to claim 1, characterized in that: The S parameter fitting method is used to calculate the Q value and C value of the capacitor in the high frequency band. The S parameter fitting method includes: Select the initial frequency point according to the binary principle to ensure that the high frequency range is covered; Convert the S parameter data into a linear equation system represented by poles and residuals, perform iterative optimization, adjust the poles and residual positions to obtain a vector fitting model with the minimum error, and thus obtain a vector fitting result; The frequency data in the vector fitting model is used to construct the Loewner matrix, and the generalized eigenvalue problem is solved to extract the poles and residuals of the system. The rational approximation function of the S parameters is generated from the poles and residuals to obtain the Loewner fitting results. Select the best fitting result from the vector fitting results and the loewner fitting results.

5. The method for accurately solving the wideband Q value and C value curve of capacitor according to claim 1, characterized in that: The smooth transition region is set in the boundary region between the low frequency band and the high frequency band, and the frequency range of the transition region is 4-6 GHz.

6. The method for accurately solving the wideband Q value and C value curve of capacitor according to claim 1, characterized in that: In the splicing of the Q value and C value curves calculated in the low frequency band and the high frequency band in the smooth transition region, a weighted average method is used for splicing, and the weighting function is: Csmooth(f)=w(f)×Clow(f)+(1-w(f))×Chigh(f); Among them, Csmooth(f) is the capacitance value curve after the transition area is spliced, w(f) is the weight function, Clow(f) is the capacitance value curve of the low frequency band, Chigh(f) is the capacitance value curve of the high frequency band, and w(f) gradually decreases from 1 to 0 in the transition frequency range.

7. The method for accurately solving the wideband Q value and C value curve of capacitor according to claim 1, characterized in that: The spliced ​​Q value and C value curves are smoothed to obtain the final Q value and C value curves, which are processed by sliding polynomial fitting, and data of 10 frequency points are selected near each frequency point, and the original data values ​​are replaced by quadratic polynomial fitting.

8. The method for accurately solving the wideband Q value and C value curve of capacitor according to claim 7, characterized in that: In the processing using sliding polynomial fitting, the calculated Q value curve is continuous and smooth in the entire frequency band, and the maximum error is less than 5%.

9. The method for accurately solving the wideband Q value and C value curve of capacitor according to claim 8, characterized in that: In the processing using sliding polynomial fitting, the C value curve shows a gradual frequency response behavior in the high frequency band.

10. The method for accurately solving the wideband Q value and C value curve of capacitor according to claim 1, characterized in that: The final Q-value and C-value curves correspond to the frequency response of an actual capacitor.

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