Method for accurately solving for wideband q-factor and c-value curves of capacitor

Abstract

Provided in the present invention is a method for accurately solving for wideband Q-factor and C-value curves of a capacitor, the method comprising frequency segmentation, low-frequency band and high-frequency band processing, transition region setting, curve splicing and smoothing processing. The specific steps comprise: dividing a frequency range into a low-frequency band of 0-5 GHz and a high-frequency band of above 5 GHz; in the low-frequency band, using an equivalent circuit model method to calculate a Q factor and a C value within the frequency range of 0-5 GHz; in the high-frequency band, using an S parameter fitting method to calculate a Q factor and a C value; setting a transition region at 4-6 GHz; and splicing curves of the low-frequency band and the high-frequency band and then performing smoothing processing on the curves in the transition region, so as to obtain final Q-factor and C-value curves. The present invention can accurately solve for the wideband Q-factor and C-value curves of the capacitor, thereby improving the accuracy and reliability of capacitor performance analysis.

Description

A method for accurately solving wideband Q-value and C-value curves of capacitors Technical Field

[0001] This invention relates to the field of performance analysis of electronic components, and more specifically, to a method for accurately solving wideband Q-value and C-value curves of capacitors. Background Technology

[0002] In the fields of electronics and communications, capacitors are critical passive components, and their performance parameters, such as quality factor (Q) and capacitance (C), are crucial for circuit design. The frequency-dependent characteristics of these parameters significantly impact the performance of high-frequency circuits. Traditional capacitor performance analysis methods are often inaccurate over a wide frequency range, particularly in the transition region between low and high frequencies. Due to a lack of effective processing methods, the calculated Q and C curves deviate from the actual frequency response characteristics. Furthermore, existing methods, when dealing with high frequencies, often rely on complex S-parameter data conversion and iterative optimization processes. These processes are not only computationally intensive but also struggle to guarantee the continuity and smoothness of the parameter curves across the entire frequency band.

[0003] In the process of implementing the embodiments of the present invention, the inventors have found that the prior art has at least the following problems or defects: the applicability of the equivalent circuit model method is limited in the low frequency band, while the S-parameter fitting method is difficult to balance computational efficiency and result accuracy in the high frequency band. At the same time, there is a lack of effective smoothing methods in the transition region between the low frequency band and the high frequency band, which results in the Q value and C value curves that cannot accurately reflect the actual working characteristics of the capacitor. Summary of the Invention

[0004] This invention provides a method for accurately solving the wideband Q-value and C-value curves of a capacitor, comprising:

[0005] Frequency segmentation: Divide the calculated frequency range into low-frequency and high-frequency bands, and determine the frequency range of the low-frequency and high-frequency bands;

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

[0007] High-frequency processing: The Q and C values ​​of the capacitor are calculated using the S-parameter fitting method in the high-frequency band;

[0008] Transition region setting: Set a smooth transition region in the boundary area between the low frequency band and the high frequency band;

[0009] Curve splicing: The Q-value and C-value curves calculated from the low-frequency and high-frequency bands are spliced ​​together within a smooth transition region;

[0010] Smoothing: The spliced ​​Q-value and C-value curves are smoothed 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 0GHz-5GHz, and the high-frequency band has a frequency range of above 5GHz.

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

[0013] Choose an equivalent circuit topology, which includes capacitance, inductance, and parasitic resistance values.

[0014] Using the frequency range 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 and obtains the equivalent circuit model with the best fitting effect.

[0015] The Q and C values ​​for 0 GHz to 0.1 GHz are extrapolated using the optimal equivalent circuit model.

[0016] Furthermore, the calculation of the Q and C values ​​of the capacitor using the S-parameter fitting method in the high-frequency band includes:

[0017] The initial frequency point is selected according to the binary principle to ensure coverage of the high-frequency band.

[0018] The S-parameter data is converted into a system of linear equations expressed in terms of poles and residuals. Iterative optimization is performed, and the positions of poles and residuals are adjusted to obtain the vector fitting model with the minimum error, thus obtaining the vector fitting result.

[0019] The Loewner matrix is ​​constructed by using vector fitting to fit the frequency data in the model. The generalized eigenvalue problem is solved to extract the system's poles and residuals. The rational approximation function of the S-parameters is generated from the poles and residuals to obtain the Loewner fitting result.

[0020] Choose the best fit result from the vector fitting results and the Loewner fitting results.

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

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

[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] Where Csmooth(f) is the capacitance value curve after splicing the transition region, w(f) is the weighting function, Clow(f) is the low-frequency capacitance value curve, Chigh(f) is the high-frequency capacitance value curve, and w(f) gradually decreases from 1 to 0 in the transition frequency range.

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

[0026] Furthermore, in the smoothing process, during the sliding polynomial fitting process, the calculated Q-value curve is continuously smooth throughout the entire frequency band, with a maximum error of less than 5%.

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

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

[0029] The embodiments of the present invention have at least the following beneficial effects: By precisely dividing the calculation frequency range into low-frequency and high-frequency bands, and calculating the Q and C values ​​of the capacitor using the equivalent circuit model method and the S-parameter fitting method respectively, the present invention can improve the calculation accuracy of capacitor performance parameters over a wide frequency band. In the low-frequency band, the equivalent circuit model method can effectively simulate the frequency response characteristics of the capacitor; while in the high-frequency band, the S-parameter fitting method can accurately extract the Q and C values ​​of the capacitor from the S-parameter data. Furthermore, the present invention sets a smooth transition region between the low-frequency and high-frequency bands and uses a weighted average method for curve splicing, which can ensure the continuity and smoothness of the Q and C value curves across the entire frequency band, thereby more accurately reflecting the actual operating characteristics of the capacitor.

[0030] This invention further employs sliding polynomial fitting for smoothing, selecting multiple data points near each frequency point and replacing the original data values ​​with quadratic polynomial fitting to further optimize the smoothness of the Q and C value curves. This method not only maintains the continuous smoothness of the Q value curve across the entire frequency band but also ensures that the C value curve exhibits a gradual frequency response behavior in the high-frequency range, with a maximum error of less than 5%. Therefore, this invention not only provides a method for accurately solving the wideband Q and C value curves of capacitors but also ensures that the final curves conform to the frequency response characteristics of actual capacitors, providing more reliable data support for capacitor design and application. Attached Figure Description

[0031] The above and other objects, features, and advantages of exemplary embodiments of the present invention will become readily apparent from the following detailed description taken in conjunction with the accompanying drawings. Several embodiments of the invention are illustrated in the drawings by way of example and not limitation, wherein:

[0032] Figure 1 is a flowchart illustrating a method for accurately solving the Q-value and C-value curves of a capacitor over a wide bandwidth, according to an embodiment of the present invention. Detailed Implementation

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

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

[0035] It should be noted that the number of any elements in the accompanying drawings is for illustrative purposes only and not as a limitation, and any naming is for distinction only and has no limiting meaning.

[0036] Referring to Figure 1 below, Figure 1 is a flowchart illustrating a method for accurately determining the Q-value and C-value curves of a capacitor over a wide bandwidth according to an embodiment of the present invention. As shown in Figure 1, a method 100 for accurately determining the Q-value and C-value curves of a capacitor over a wide bandwidth includes:

[0037] Step 101, Frequency Segmentation: Divide the calculated frequency range into low-frequency and high-frequency bands, and determine the frequency range of the low-frequency and high-frequency bands;

[0038] Step 102, Low-frequency processing: Calculate the Q and C values ​​of the capacitor using the equivalent circuit model method in the low-frequency range;

[0039] Step 103, High-frequency processing: Calculate the Q and C values ​​of the capacitor using the S-parameter fitting method within the high-frequency band;

[0040] Step 104, Transition Region Setting: Set a smooth transition region in the boundary area between the low-frequency band and the high-frequency band;

[0041] Step 105, Curve splicing: Splice the Q-value and C-value curves calculated for the low-frequency and high-frequency bands within the smooth transition region;

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

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

[0044] Specifically, the low-frequency band is set to 0 GHz to 5 GHz, while the high-frequency band is above 5 GHz. This division is based on the characteristics of capacitor performance at different frequencies. In the low-frequency band, the Q and C values ​​of the capacitor change relatively smoothly, making it suitable for calculation using the equivalent circuit model method; while in the high-frequency band, due to greater signal fluctuations and interference, the S-parameter fitting method is more appropriate. This setup ensures relatively accurate calculation results across 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 containing capacitance, inductance, and parasitic resistance values. 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 practice, a frequency range of 0.1 GHz to 5 GHz can be used as the fitting target. An optimization algorithm can be invoked to adjust the parameters of the equivalent circuit, with the goal of minimizing the frequency response error, to obtain the equivalent circuit model with the optimal fitting effect. Through this optimal model, the Q and C values ​​from 0 GHz to 0.1 GHz can be extrapolated, thereby achieving accurate calculations across 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 to 5 GHz, and the high-frequency band has a frequency range of 5 GHz and above.

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

[0049] Specifically, the use of an equivalent circuit model in the low-frequency band ensures the accuracy of low-frequency characteristics; the use of S-parameter fitting in the high-frequency band improves the calculation accuracy in the high-frequency range, thus making the measurement results of capacitance characteristics more accurate across the entire bandwidth. This effectively avoids the shortcomings of insufficient accuracy of circuit models in the high-frequency band and prevents the circuit model from failing to accurately reflect the parasitic effects of capacitance 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 consideration of the applicability of different calculation methods.

[0050] Preferably, for low-frequency processing, it can be further refined to use a specific equivalent circuit model, such as an RLC circuit model that includes series resistance, parallel resistance, and inductance. In this model, the actual performance of a capacitor in the low-frequency range can be simulated by adjusting circuit parameters such as resistance, inductance, and capacitance values.

[0051] Furthermore, for the high-frequency band, a data fitting method based on S-parameters can be employed. By selecting appropriate initial frequency points and utilizing vector fitting techniques, the S-parameter data is converted into the form of poles and residuals, and iterative optimization is performed to obtain a fitting model with minimal error. This approach ensures more accurate Q and C values ​​in the high-frequency band. In addition, other optimization algorithms or fitting techniques can be considered to improve computational accuracy and efficiency.

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

[0053] Choose an equivalent circuit topology, which includes capacitance, inductance, and parasitic resistance values.

[0054] Using the frequency range 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 and obtains the equivalent circuit model with the best fitting effect.

[0055] The Q and C values ​​for 0 GHz to 0.1 GHz are extrapolated using the optimal equivalent circuit model.

[0056] It should be noted that this implementation details the specific operation of the equivalent circuit model method in the low-frequency processing steps. 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 that includes 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 simulates the actual behavior of a capacitor in a circuit. This model typically includes a main capacitive element, along with possible series or parallel inductors and resistors to simulate the parasitic effects of the capacitor. In implementation, the topology of the equivalent circuit must first be determined, followed by the selection of appropriate parameter values. These parameter values ​​can be determined using experimental data or manufacturer specifications. Next, using a frequency range of 0.1 GHz to 5 GHz as the fitting target, an optimization algorithm is invoked to adjust these parameters, with minimizing the frequency response error as the objective function, thereby obtaining an equivalent circuit model with optimal fitting performance.

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

[0059] Furthermore, different optimization algorithms can be explored, or the advantages of multiple algorithms can be combined to improve the model's fitting accuracy and computational efficiency. Through the optimal equivalent circuit model, the Q and C values ​​from 0 GHz to 0.1 GHz can be extrapolated, thereby achieving accurate calculations across the entire low-frequency band.

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

[0061] The method for calculating the Q and C values ​​of the capacitor using S-parameter fitting in the high-frequency band includes:

[0062] The initial frequency point is selected according to the binary principle to ensure coverage of the high-frequency band.

[0063] The S-parameter data is converted into a system of linear equations expressed in terms of poles and residuals. Iterative optimization is performed, and the positions of poles and residuals are adjusted to obtain the vector fitting model with the minimum error, thus obtaining the vector fitting result.

[0064] The Loewner matrix is ​​constructed by using vector fitting to fit the frequency data in the model. The generalized eigenvalue problem is solved to extract the system's poles and residuals. The rational approximation function of the S-parameters is generated from the poles and residuals to obtain the Loewner fitting result.

[0065] Choose the best fit result from the vector fitting results and the Loewner fitting results.

[0066] It should be noted that this implementation describes in detail the specific operation of the S-parameter fitting method in the high-frequency band processing steps. S-parameters, or scattering parameters, are a set of parameters used to describe the signal reflection and transmission characteristics in an RF circuit network. This method involves converting the S-parameter data into a system of linear equations represented by poles and residuals, and performing iterative optimization to adjust the positions of the poles and residuals, thereby obtaining a Vector Fitting model with minimal error.

[0067] Vector Fitting models are 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-dependent characteristics can be represented in a relatively concise mathematical form. Poles determine the singularity of the function in the complex frequency domain, reflecting the inherent frequency characteristics of the system; residuals represent the contribution of each pole to the overall response.

[0068] The Loewner matrix is ​​based on frequency data obtained through vector fitting of the model. It utilizes the differences between the fitted model data at different frequencies, organizing these relationships into a matrix. This matrix structure effectively captures the dynamic characteristics of the system at different frequencies, providing a powerful mathematical tool for subsequent extraction of the system's poles and residuals. By constructing the Loewner matrix, information in the frequency domain data can be represented in a more easily analyzed and processed matrix form, enabling in-depth study of system characteristics using matrix operations and eigenvalue solving.

[0069] Specifically, Vector Fitting in S-parameter fitting is a technique for extracting parameters from radio frequency and microwave circuits. It fits S-parameter data into a rational function model, which can be represented by poles and residuals. In implementation, the initial frequency points are first selected according to the bisection principle to ensure coverage of the transition and high-frequency regions. This means that the frequency points should be evenly distributed across the entire frequency band to comprehensively capture the frequency response characteristics of the capacitor. Next, the S-parameter data is converted into a system of linear equations represented by poles and residuals, and iterative optimization is performed, adjusting the positions of the poles and residuals to minimize the fitting error, resulting in the Vector Fitting model.

[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 and can help extract the system's poles and residuals. From these poles and residuals, a rational approximation function for the S-parameters can be generated, thus obtaining the Loewner-fitted S-parameter results.

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

[0072] 1. Select the initial frequency point according to the binary division principle to ensure coverage of the high-frequency band;

[0073] 2. The S-parameter data is converted into a system of linear equations expressed in terms of poles and residuals. Iterative optimization is then performed, and the positions of the poles and residuals are adjusted to obtain the vector fitting model with the minimum error. This yields the vector fitting S-parameter result. The specific conversion and iterative optimization process is as follows:

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

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

[0076] The reflection coefficient S is defined as follows:

[0077] Solve for Z by transforming this expression:

[0078] Depend on We can obtain 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] Factoring out the common factor, we get Z(S-1) = -(S+1)Z0.

[0081] The final solution is When Z0 = 1

[0082] Admittance Y is defined as the reciprocal of impedance Z, i.e., Y = 1 / Z.

[0083] (When Z0 = 1),

[0084] So

[0085] Furthermore, the poles and residuals are expressed in terms of favorable approximation functions:

[0086] s = jω is a complex frequency variable, r k For the residual, p k The pole is denoted as d, and e are constants.

[0087] Construct a system of linear equations:

[0088] i = 1, 2, ..., m, where m is the number of sampling points.

[0089] The poles and residuals are obtained by solving the system of equations using iterative algorithms such as the least squares method, and then the vector fitting model and results are obtained.

[0090] 3. Construct the Loewner matrix using the frequency data in the model by using vector fitting, solve the generalized eigenvalue problem to extract the system's poles and residuals, and generate a rational approximation function for the S-parameters from the poles and residuals to obtain the Loewner fitting S-parameter results;

[0091] 4. From S 11 Calculate the input impedance Z in The calculation method is: Z in =(1+S) 11 ) / (1-S11;

[0092] Next, the input impedance Z in Convert to admittance Y in = G + jB, where G is conductance, B is susceptance, and j is the imaginary unit. The conductance G and susceptance B are calculated as follows:

[0093] G = Re(Y) in ), B = Im(Y in ).

[0094] The capacitance C is calculated using the formula B = 2πfC, where f is the frequency. The calculation method is as follows:

[0095] C = B / (2πf);

[0096] Finally, the quality factor Q is calculated using Q = B / G.

[0097] 5. Based on the smoothness of the Q-value and C-value curves, select the optimal fitting result from the vector fitting and Loewner fitting results. The specific judgment method is to 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 optimal fitting result.

[0098] It should be noted that in radio frequency and microwave technology, S 11 S is a parameter used to describe the reflection characteristics of a two-port network (such as a capacitor, which can be considered a two-port element in a circuit). 11Defined as the reflection coefficient, it represents the ratio of the signal reflected back from port 1 to the input signal when a signal is input at port 1. Physically speaking, it reflects how much energy of the signal is reflected back when it encounters a component (such as a capacitor) at port 1, and is not completely transmitted into the component or to other ports.

[0099] For a two-port network, according to transmission line theory and network analysis, the input impedance \(Z_{in}\) and \(S_{11}\) have the following relationship:

[0100] Where Z0 is the characteristic impedance of the transmission line, which can be assumed to be a normalized value of 1. In this case, the formula simplifies to:

[0101] When a signal is incident on port 1 and interacts with the component, the relationship between the reflected wave and the incident wave is determined by S. 11 This can be described by the relationship between the input impedance and the output impedance Z, which can be derived from the equivalent impedance of the component as seen from port 1. in Calculate the input impedance Z. in Understanding the behavior of a capacitor in a circuit is crucial, as it relates to the capacitor's actual electrical characteristics (such as capacitive reactance). This understanding can then be used to calculate the capacitance value C and the quality factor Q, thus comprehensively characterizing the capacitor's performance over a wide frequency band.

[0102] Suppose that at a certain frequency, the capacitance S is measured. 11 =0.2, if the normalized characteristic impedance Z0 = 1 is used, then the input impedance Z is calculated according to the formula. in for:

[0103] To make the denominator a real number, multiply both the numerator and denominator by 0.8 + 0.3j, resulting in:

[0104] Because j 2 =-1, so further simplification is:

[0105] In some embodiments, the frequency range of the transition region in the transition region setting step is 4GHz-6GHz.

[0106] It should be noted that this implementation involves setting a smooth transition region at the boundary between the low-frequency and high-frequency bands, with the frequency range of this transition region set to 4GHz-6GHz. The transition region is designed to ensure a smooth connection between the Q-value and C-value curves calculated using two different processing methods, avoiding abrupt changes at the boundary point. This is crucial for maintaining the continuity and accuracy of capacitor performance parameters throughout the entire frequency band.

[0107] Specifically, the transition region refers to a frequency range defined between the low-frequency and high-frequency bands. The Q-value and C-value curves within this range require special processing to achieve a smooth transition. In this embodiment, the frequency range of the transition region is explicitly defined as 4GHz-6GHz. This means that within this frequency range, specific methods will be used to process the Q-value and C-value to ensure their changes between the low-frequency and high-frequency bands are continuous. This range is chosen based on the performance characteristics of the capacitor at the boundary between these two frequency bands and the need to ensure a smooth transition of the curves.

[0108] Preferably, to achieve a smooth transition within 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 within the transition region, which gradually decreases as the frequency increases, thereby achieving a smooth transition from the low-frequency band to the high-frequency band. For example, a weighting function w(f) can be designed, which has a value of 1 at 4 GHz and a value of 0 at 6 GHz, and varies linearly between these two frequency points. In this way, it can be ensured that the processing results of the low-frequency band are gradually replaced by the processing results of the high-frequency band within the transition region, thereby achieving continuity and accuracy of capacitor performance parameters throughout 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 in the transition region.

[0109] In some embodiments, the curve splicing step is performed using a weighted average method, and the weighting function is: Csmooth(f)=w(f)×Clow(f)+(1-w(f))×Chigh(f);

[0110] Where Csmooth(f) is the capacitance value curve after splicing the transition region, w(f) is the weighting function, Clow(f) is the low-frequency capacitance value curve, Chigh(f) is the high-frequency capacitance value curve, and w(f) gradually decreases from 1 to 0 in the transition frequency range.

[0111] It should be noted that this implementation describes a specific method for stitching together the Q-value and C-value curves calculated from the low-frequency and high-frequency bands within the transition region. Curve stitching, as mentioned here, refers to smoothly connecting the parameter curves calculated in two different frequency bands within the transition region to ensure the continuity of the parameter curves throughout the entire frequency band. The weighted average method is a commonly used mathematical method for combining two or more datasets, where the weight of each dataset is determined according to specific rules.

[0112] Specifically, in this embodiment, the weighted average method is used to stitch together the capacitance curves in the transition region. The weighting function w(f) is a function that varies with frequency f, determining the respective contributions of the low-frequency capacitance curve Clow(f) and the high-frequency capacitance curve Chigh(f) during the stitching process. Within the transition frequency range, the weighting function w(f) gradually decreases from 1 to 0, meaning that at the lower end of the transition region (closer to the low-frequency band), the low-frequency capacitance curve contributes more to the final stitched curve Csmooth(f), while at the higher end of the transition region (closer to the high-frequency band), the contribution of the high-frequency capacitance curve gradually increases.

[0113] Preferably, the weighting function w(f) can be designed in a linear or nonlinear manner to ensure a smooth transition of the capacitance curve in the transition region. For example, a linearly decreasing weighting function can be used, such that w(f) = 1 at 4 GHz and w(f) = 0 at 6 GHz.

[0114] Furthermore, nonlinear weighting functions, such as exponentially decaying or logarithmically decreasing functions, can be considered to achieve a smoother transition. In practical applications, the form and parameters of the weighting 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 greater flexibility and accuracy.

[0115] In some embodiments, the smoothing process involves using sliding polynomial fitting, where data from 10 frequency points are selected near each frequency point and replaced with quadratic polynomial fitting to replace the original data values.

[0116] It should be noted that this implementation involves a step of smoothing the spliced ​​Q-value and C-value curves. The smoothing process mentioned here refers to smoothing the curves using mathematical methods to reduce or eliminate fluctuations and noise, making the curves smoother and more continuous. In this implementation, the smoothing process is achieved through sliding polynomial fitting, a commonly used data smoothing technique.

[0117] 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 chosen, which means selecting 10 frequency points near each frequency point and using a quadratic polynomial to fit these data points. This method can effectively capture the local trends and patterns of the data while reducing the impact of random fluctuations.

[0118] Preferably, the specific implementation of the quadratic polynomial fitting can be further refined. For example, the coefficients of the quadratic polynomial can be determined using the least squares method, so as to minimize the sum of squared errors between the fitted curve and the actual data points.

[0119] Furthermore, other orders of polynomials can be used for fitting, or combined with other types of local regression methods, such as Gaussian process regression or spline regression, to improve the accuracy and smoothness of the fit. In practical applications, the size of the fitting window (i.e., the number of data points selected) and the order of the polynomial can be adjusted according to the characteristics and needs of the data to achieve the best smoothing effect.

[0120] In some embodiments, during the smoothing process, the Q-value curve calculated during the sliding polynomial fitting process is continuously smoothed across the entire frequency band, with a maximum error of less than 5%.

[0121] It should be noted that this implementation describes the requirements for the Q-value curve in the smoothing process, namely, continuous smoothing across the entire frequency band and a maximum error of less than 5%. Continuous smoothing here means that the Q-value curve should change uniformly and without abrupt changes across the entire frequency range, while a maximum error of less than 5% means that after smoothing, the maximum deviation between the Q-value curve and the original data should not exceed 5%, ensuring the accuracy of the curve.

[0122] Specifically, the smoothing of the Q-value curve is achieved through 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 entire frequency band. This means that the fitted curve should not have drastic fluctuations or discontinuities to ensure the accuracy of the curve's physical meaning and practical applications. Meanwhile, the requirement of a maximum error of less than 5% can be achieved by setting the tolerance parameter of the fitting algorithm or through post-processing steps. For example, the fitted curve can be fine-tuned to ensure that the error is within the specified range.

[0123] Preferably, to meet the requirement that the Q-value curve is continuously smooth across 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 local variations in the data.

[0124] Furthermore, error correction mechanisms can be introduced, such as adding a regularization term during the fitting process to control the smoothness of the fitted curve, or performing further smoothing processing on the curve after fitting, such as using moving averages or Gaussian filtering. These methods can help optimize the smoothness and accuracy of the Q-value curve, ensuring that it meets the requirements for maximum error.

[0125] In some embodiments, during the smoothing process, the C-value curve exhibits a gradual frequency response behavior in the high-frequency range during the sliding polynomial fitting process.

[0126] It should be noted that this implementation involves requirements for the C-value curve during the smoothing process, namely, exhibiting a gradual frequency response behavior in the high-frequency range. This gradual frequency response behavior means that the C-value curve should exhibit a smooth and predictable trend in the high-frequency range, without sudden jumps or discontinuities. This helps ensure the stability and reliability of the capacitor's performance.

[0127] Specifically, the smoothing of the C-value curve is achieved through sliding polynomial fitting. This method selects a certain number of data points around each frequency point and uses a polynomial function to fit these data points. In the high-frequency range, the asymptotic 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, thereby capturing the asymptotic trend of the C-value in the high-frequency range. At the same time, the flexibility and smoothness of the fitting can be balanced by setting the polynomial order to ensure that the curve reflects the true trend of the data without overfitting.

[0128] Preferably, to ensure that the C-value curve exhibits a gradual frequency response behavior in the high-frequency range, the smoothing process 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 range to better capture the changing trend of the C-value.

[0129] Furthermore, frequency-dependent weighting factors can be introduced to give more weight to high-frequency data during fitting, thereby emphasizing the importance of high-frequency data. Additionally, different types of polynomials, such as Chebyshev polynomials or Legendre polynomials, can be considered, as these may be more effective in handling boundary effects. These refined steps can improve the fitting quality and asymptotic behavior of the C-value curve in the high-frequency range.

[0130] In some embodiments, the final Q and C value curves conform to the frequency response characteristics of a real capacitor.

[0131] 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. Here, frequency response characteristics refer to the performance of the capacitor at different frequencies, such as the variation of its impedance, phase, and other parameters with frequency. Ensuring that the curves conform to actual characteristics means the accuracy and practicality of the calculation results, which is crucial for capacitor design and application.

[0132] Specifically, to ensure that the Q-value and C-value curves accurately reflect the frequency response characteristics of an actual capacitor, precise methods and rigorous verification are required during the calculation and fitting processes. This includes selecting appropriate model parameters, optimization algorithms, and smoothing techniques. For example, experimental data can be used to verify the model's accuracy, and model parameters can be adjusted by comparing the consistency of the calculated Q-value and C-value curves with actual measured data. Furthermore, statistical methods can be used to evaluate the fitting error, ensuring that the error remains within an acceptable range.

[0133] Preferably, to further improve the accuracy of the Q-value and C-value curves, various validation and optimization techniques can be employed. For example, cross-validation can be used to evaluate the model's generalization ability, ensuring that the model provides accurate predictions at different frequency points.

[0134] Furthermore, expert knowledge can be introduced to guide the selection of model parameters, or machine learning methods can be used to automatically optimize the model parameters. In the smoothing step, more advanced mathematical tools, such as wavelet transform or Fourier transform, can be employed to further smooth the curves 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 theoretically sound but also accurate and reliable in practical applications.

[0135] The above embodiments of the present invention have the following beneficial effects: The method for accurately solving the wide-band Q-value and C-value curves of capacitance described in the present invention can employ the most suitable calculation method in different frequency bands, thereby improving calculation efficiency and accuracy. Secondly, the equivalent circuit model method is used in the low-frequency band, and the S-parameter fitting method is used in the high-frequency band, which can ensure that the best fitting effect is obtained in their respective frequency bands, thereby improving the accuracy of the Q-value and C-value curves. In addition, setting a transition region and using a weighted average method for curve splicing can smoothly connect the results of the low-frequency band and the high-frequency band, avoiding discontinuities that may occur in the boundary region and ensuring the overall continuity of the curves.

[0136] Furthermore, the method includes a smoothing step. By employing a sliding polynomial fitting technique, multiple data points can be selected near each frequency point for fitting, thereby improving the smoothness and aesthetics of the curve. This method not only maintains the continuous smoothness of the Q-value curve across the entire frequency band but also ensures that the C-value curve exhibits a gradual frequency response behavior in the high-frequency range, with the maximum error controlled within 5%. Therefore, this invention not only provides a method for accurately solving the wideband Q-value and C-value curves of capacitors but also ensures that the final curve conforms to the frequency response characteristics of actual capacitors, providing more reliable data support for capacitor design and application.

[0137] Furthermore, the storage medium in the embodiments of this application stores program instructions capable of implementing all the above methods. These program instructions can be stored in the storage medium in the form of a software product, including several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) or processor to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks, or terminal devices such as computers, servers, mobile phones, and tablets.

[0138] The above description is merely a selection of preferred embodiments of the present invention and an explanation of the technical principles employed. Those skilled in the art should understand that the scope of the invention as described in the embodiments is not limited to technical solutions formed by specific combinations of the above-described technical features, but should also cover other technical solutions formed by arbitrary combinations of the above-described technical features or their equivalents without departing from the inventive concept. For example, technical solutions formed by substituting the above-described features with (but not limited to) technical features with similar functions disclosed in the embodiments of the present invention.

Claims

1. A method for accurately solving the Q value and C value curves of a wide frequency band capacitor, characterized in that, Includes the following steps: Frequency segmentation: Divide the calculated frequency range into low-frequency and high-frequency bands, and determine the frequency range of the low-frequency and high-frequency bands; Low-frequency processing: The equivalent circuit model method is used to calculate the Q value and C value of the capacitor in the low-frequency range; High-frequency processing: The Q and C values ​​of the capacitor are calculated using the S-parameter fitting method in the high-frequency band; Transition region setting: Set a smooth transition region in the boundary area between the low frequency band and the high frequency band; Curve splicing: The Q-value and C-value curves calculated from the low-frequency and high-frequency bands are spliced ​​together within a smooth transition region; Smoothing: The spliced ​​Q-value and C-value curves are smoothed to obtain the final Q-value and C-value curves.

2. The method of claim 1, wherein, The calculation frequency range is divided into low-frequency band and high-frequency band. The frequency range of the low-frequency band is 0GHz-5GHz, and the frequency range of the high-frequency band is above 5GHz.

3. The method of claim 1, wherein, The calculation of the Q and C values ​​of capacitance using the equivalent circuit model method in the low-frequency band includes the following steps: Select an equivalent circuit topology, wherein the equivalent circuit topology includes capacitance, inductance, and parasitic resistance values; Using the frequency range 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 and obtains the equivalent circuit model with the best fitting effect. The Q and C values ​​for the 0 GHz-0.1 GHz range were calculated using the optimal equivalent circuit model.

4. The method of claim 1, wherein, The method for calculating the Q and C values ​​of the capacitor using S-parameter fitting in the high-frequency band includes: The initial frequency point is selected according to the binary principle to ensure coverage of the high-frequency band. The S-parameter data is converted into a system of linear equations expressed in terms of poles and residuals. Iterative optimization is performed, and the positions of poles and residuals are adjusted to obtain the vector fitting model with the minimum error, thus obtaining the vector fitting result. The Loewner matrix is ​​constructed by using vector fitting to fit the frequency data in the model. The generalized eigenvalue problem is solved to extract the system's poles and residuals. The rational approximation function of the S-parameters is generated from the poles and residuals to obtain the Loewner fitting result. Choose the best fit result from the vector fitting results and the Loewner fitting results.

5. The method of claim 1, wherein, A smooth transition region is set in the boundary area 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 of claim 1, wherein, In the process of stitching together the Q-value and C-value curves calculated for the low-frequency and high-frequency bands in the smooth transition region, a weighted average method is used for stitching. The weighting function is: Csmooth(f)=w(f)×Clow(f)+(1-w(f))×Chigh(f); Where Csmooth(f) is the capacitance value curve after splicing the transition region, w(f) is the weighting function, Clow(f) is the low-frequency capacitance value curve, Chigh(f) is the high-frequency capacitance value curve, and w(f) gradually decreases from 1 to 0 in the transition frequency range.

7. The method of claim 1, wherein, The spliced ​​Q and C value curves are smoothed to obtain the final Q and C value curves. Sliding polynomial fitting is used to process the curves, and data from 10 frequency points near each frequency point are selected and replaced with the original data values ​​by quadratic polynomial fitting.

8. The method of claim 7, wherein, In the process of using sliding polynomial fitting, the calculated Q-value curve is continuous and smooth throughout the entire frequency band, with a maximum error of less than 5%.

9. The method of claim 8, wherein, In the process of using sliding polynomial fitting, the C-value curve exhibits a gradual frequency response behavior in the high-frequency range.

10. The method of claim 1, wherein, The final Q and C value curves correspond to the frequency response of the actual capacitor.

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