A broadband frequency sweeping method

Abstract

The present invention discloses a broadband frequency sweeping method, which comprises: S1: acquiring frequency domain response data of a circuit system in a preset frequency band; S2: obtaining Loewner interpolation according to the frequency domain response data; S3: removing spikes of the Loewner interpolation by using a spike removal method to obtain a smooth interpolation result; S4: outputting the smooth interpolation result as the broadband frequency sweeping result. The broadband frequency sweeping method provided by the present invention can obtain a stable interpolation result by using the least frequency points, and accurately approximate the broadband frequency response of the electronic system.

Description

Technical Field

[0001] The present invention relates to the technical field of circuit systems, and in particular to a broadband frequency sweeping method. Background Art

[0002] With the rapid development of communication reconnaissance and electronic countermeasure technologies, more and more electronic devices are using broadband working mode. Correspondingly, frequency domain computational electromagnetic methods such as moment method and finite element method also need broadband frequency sweeping. Usually, these methods may take a long time to calculate each frequency point.

[0003] Mainstream electromagnetic simulation software has already used some broadband sweep frequency methods, such as the asymptotic waveform estimation method (AWE), the adaptive Lanczos-Padé sweep frequency method (ALPS), and the rational interpolation method.

[0004] The AWE algorithm only needs one matrix inversion operation to get the frequency response within a certain frequency band. However, the basic starting point of the algorithm is to approximate the integral kernel through the Taylor series. However, the accuracy of the Taylor series at the expanded frequency point is very high, and the farther away from the expanded frequency point, the lower the accuracy. Therefore, the AWE algorithm is a narrowband frequency sweeping method, and the accuracy is not high.

[0005] ALPS is a deep improvement of AWE technology, mainly used in the finite element method. This technology first expands the system matrix at a certain frequency point, then uses the Lanczos method to determine the pole frequency of the system, and finally uses the Padé approximation to solve the matrix equation within a certain frequency band. ALPS can perform frequency sweeps on a wider frequency band. However, in actual simulations, a very wide frequency band is often divided into several narrower frequency bands, and then ALPS is used to perform frequency sweep analysis on each narrower frequency band. This requires many frequency points for frequency sweeping, and the efficiency is low.

[0006] Since all electronic devices work in a resonant state, some resonant frequencies are real numbers, and some are complex numbers. At this time, most electromagnetic parameters can be expressed as rational polynomials. Therefore, using rational interpolation for broadband frequency sweeping is a more efficient method. The existing interpolation method generally uses the simplest rational interpolation, that is, both the numerator and the denominator are simple polynomials. However, this method requires solving the Vandermonde matrix equation, so it is very unstable and can only be applied to situations with fewer interpolation points. When there are more interpolation points, this simple rational polynomial will have some spikes, and these spikes can easily be confused with the function peaks of the resonance points. Summary of the invention

[0007] The object of the present invention is to provide a broadband frequency sweeping method, so as to obtain a stable interpolation result by using the least frequency points and accurately approximate the broadband frequency response of the electronic system.

[0008] The technical solution of the present invention to solve the above technical problems is as follows:

[0009] The present invention provides a broadband frequency sweeping method, the broadband frequency sweeping method comprising:

[0010] S1: Obtain frequency domain response data of the circuit system within a preset frequency band;

[0011] S2: Obtaining Loewner interpolation according to the frequency domain response data;

[0012] S3: using a spike removal method to remove spikes from the Loewner interpolation to obtain a smooth interpolation result;

[0013] S4: Outputting the smooth interpolation result as the broadband frequency sweep result.

[0014] Optionally, the frequency domain response data includes an odd number of frequency points, and step S2 includes:

[0015] S21: performing normalization processing on the odd number of frequency points to obtain normalized frequencies;

[0016] S22: Obtaining a corresponding frequency response according to the normalized frequency;

[0017] S23: constructing a Loewner interpolation matrix according to the normalized frequency and the frequency response;

[0018] S24: Obtaining Loewner interpolation using an adaptive interpolation algorithm according to the Loewner interpolation matrix.

[0019] Optionally, the step S22 is obtained by the following formula:

[0020]

[0021] in, represents the frequency response function, Indicates The normalized frequency of the point, Indicates The frequency response value of the point, is a natural number and .

[0022] Optionally, the step S23 includes:

[0023] S231: Divide the normalized frequency and the frequency response into a first data group and a second data group;

[0024] S232: constructing a rational polynomial of a Loewner interpolation matrix using the first data group;

[0025] S233: Obtaining a matrix equation according to the rational polynomial and the second data group;

[0026] S234: Obtain a Loewner interpolation matrix according to the matrix equation.

[0027] Optionally, in step S232, the rational polynomial of the Loewner interpolation matrix is for:

[0028]

[0029] in, represents a complex constant, Indicates The frequency response of the points in the first data set is, Indicates The normalized frequency of points in the first data set, represents the normalized frequency and , Indicates the lowest frequency point, Indicates the highest frequency point, Indicates frequency.

[0030] Optionally, in step S233, the matrix equation is:

[0031]

[0032] in, represents the Loewner interpolation matrix, represents a complex constant and , represents the frequency domain response at the frequency point of the second data set and , represents the normalized frequency of the second data set and , Indicates The frequency response of the points in the first data set is, Indicates The normalized frequency of the points in the first data set and .

[0033] Optionally, the step S24 includes:

[0034] S241: Initialize the Loewner interpolation matrix;

[0035] S242: Obtaining a corresponding Loewner interpolation according to the Loewner interpolation matrix;

[0036] S243: Calculate the global error and local error of the Loewner interpolation within the preset frequency band, and determine whether the global error is less than a convergence threshold. If so, proceed to step S244; otherwise, proceed to step S245;

[0037] S244: Outputting the Loewner interpolation as Loewner interpolation;

[0038] S245: taking the center frequencies of the two frequency intervals with the largest local errors as added interpolation points, adding 1 to the frequency domain response data, and returning to step S242.

[0039] Optionally, step S3 includes:

[0040] S31: Calculate the poles and residues of the Loewner interpolation;

[0041] S32: Obtain a new Loewner interpolation polynomial according to the poles and the residues;

[0042] S33: Determine whether the new Loewner interpolation polynomial satisfies the spike existence condition, if yes, proceed to step S34, otherwise, proceed to step S4;

[0043] S34: modifying the new Loewner interpolation polynomial to obtain a modified Loewner interpolation polynomial;

[0044] S35: Correct the interpolation points according to the corrected Loewner interpolation polynomial and return to step S242.

[0045] Optionally, in step S32, the new Loewner interpolation polynomial for:

[0046]

[0047] in, is a natural number and , For the remainder, For the extreme point, is a constant term that does not change with frequency, represents the normalized frequency and , Indicates the lowest frequency point, Indicates the highest frequency point, Indicates frequency.

[0048] Optionally, in step S33, the condition for the existence of the spike is that one of the polynomial summation terms of the new Loewner interpolation has the smallest residue and the imaginary part of the pole is the smallest.

[0049] The present invention has the following beneficial effects:

[0050] The algorithm of the present invention utilizes three advantages of Loewner matrix interpolation. First, the rational polynomial based on Loewner matrix interpolation is an expression similar to Lagrange interpolation, which is relatively concise and intuitive. Second, the number of sampling points required for Loewner matrix interpolation is the least among all rational interpolations. Finally, Loewner matrix interpolation is very stable, with few spikes and can be completely removed. In summary, the algorithm of the present invention can use the least frequency points to obtain a stable interpolation result and accurately approximate the broadband frequency response of the electronic system. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 A flow chart of the broadband frequency sweeping method provided by the present invention;

[0052] Figure 2 It is a 37-port passive network;

[0053] Figure 3 Schematic diagram of the convergence process of adaptive Loewner interpolation;

[0054] Figure 4 To clear the spikes, 1,26 The real part and the local enlarged diagram;

[0055] Figure 5 To clear the spikes, 1,26 The imaginary part and the local enlarged view. DETAILED DESCRIPTION

[0056] The principles and features of the present invention are described below in conjunction with the accompanying drawings. The examples given are only used to explain the present invention and are not used to limit the scope of the present invention.

[0057] Example 1

[0058] The present invention provides a broadband frequency sweeping method, referring to Figure 1 As shown, the broadband frequency sweeping method comprises:

[0059] S1: Obtain frequency domain response data of the circuit system within a preset frequency band;

[0060] The present invention performs broadband interpolation on the frequency domain response of any circuit system, such as voltage, current, S parameters, etc.

[0061] S2: Obtaining Loewner interpolation according to the frequency domain response data;

[0062] The frequency domain response data here can be a set of discrete frequency point data obtained by simulation or measurement. In the present invention, the number of forced data is an odd number, that is, ( ) of which is a natural number greater than or equal to 2. arrive Arrange in order from low to high, Indicates the lowest frequency point, Indicates the highest frequency point. Therefore, in the present invention, the preset frequency band is arrive On this basis, the step S2 comprises:

[0063] S21: performing normalization processing on the odd number of frequency points to obtain normalized frequencies;

[0064] That is, for the convenience of calculation, the frequency Normalized to .

[0065] S22: Obtaining a corresponding frequency response according to the normalized frequency;

[0066] According to the normalized frequency above, the data of all interpolation points are recorded as:

[0067]

[0068] in, represents the frequency response function, Indicates The normalized frequency of the point, Indicates The frequency response value of the point, is a natural number and .

[0069] S23: constructing a Loewner interpolation matrix according to the normalized frequency and the frequency response;

[0070] Optionally, the step S23 includes:

[0071] S231: Divide the normalized frequency and the frequency response into a first data group and a second data group;

[0072] Similarly, all normalized frequency points are arranged in order from low to high. Then all data are divided into two groups and re-recorded as the first data group: , and the second data set: .

[0073] in, and Respectively represent the numbers for dividing the data into the first data group and the second data group, and represent the normalized frequency of the first data set and the normalized frequency of the second data set respectively, and Respectively represent the frequency domain responses at the first data set frequency point and the second data set frequency point.

[0074] S232: constructing a rational polynomial of a Loewner interpolation matrix using the first data group;

[0075] That is, using the first data group Construct an interpolation expression using the points:

[0076]

[0077] in, represents a complex constant, Indicates The frequency response of the points in the first data set is, Indicates The normalized frequency of points in the first data set, represents the normalized frequency and , Indicates the lowest frequency point, Indicates the highest frequency point, Indicates frequency.

[0078] in, is the complex constant to be solved.

[0079] S233: Obtaining a matrix equation according to the rational polynomial and the second data group;

[0080] Before getting the matrix equation, we first get an equation, namely:

[0081]

[0082] Therefore, the matrix equation is:

[0083]

[0084] in, represents the Loewner interpolation matrix, represents a complex constant and , represents the frequency domain response at the frequency point of the second data set and , represents the normalized frequency of the second data set and , Indicates The frequency response of the points in the first data set is, Indicates The normalized frequency of the points in the first data set and .

[0085] S234: Obtain a Loewner interpolation matrix according to the matrix equation.

[0086] That is, the Loewner interpolation matrix is:

[0087] .

[0088] The premise of using the above Loewner interpolation is that all interpolation points are given. However, in practical applications, it is unknown where these interpolation points are, and they need to be determined step by step through the following adaptive interpolation algorithm.

[0089] S24: Obtaining Loewner interpolation using an adaptive interpolation algorithm according to the Loewner interpolation matrix.

[0090] Optionally, the step S24 includes:

[0091] S241: Initialize the Loewner interpolation matrix;

[0092] In the present invention, the convergence threshold is set ,set up , since the data point is , so when When , there are 3 data points, so the first 3 interpolation points are set as: .

[0093] S242: Obtaining a corresponding Loewner interpolation according to the Loewner interpolation matrix;

[0094] use The Loewner interpolation matrix constructed from the data of points is obtained. , we can get the interpolation value .

[0095] S243: Calculate the global error and local error of the Loewner interpolation within the preset frequency band, and determine whether the global error is less than a convergence threshold. If so, proceed to step S244; otherwise, proceed to step S245;

[0096] In order to perform adaptive interpolation, the error of the interpolation polynomial must be estimated. Define the complex function In the interval The norm of is:

[0097]

[0098] By observing the expressions of two adjacent interpolations and The norm of the difference between the two can be used to estimate the global error of the interpolation polynomial over the entire frequency band.

[0099]

[0100] In addition, observe the interval formed by two adjacent interpolation points , called the interval, then the norm of the interpolation polynomial in this interval is:

[0101]

[0102] Accordingly, k The error estimate for the interval is:

[0103]

[0104] Using the global error estimation formula, we can evaluate the degree to which the interpolation polynomial approximates the interpolated function, and thus decide whether to continue adding interpolation points. Using the local error estimation, we can find the two intervals with the largest errors, and use the midpoints of these two intervals as new interpolation points.

[0105] S244: Outputting the Loewner interpolation as Loewner interpolation;

[0106] S245: taking the center frequencies of the two frequency intervals with the largest local errors as added interpolation points, adding 1 to the frequency domain response data, and returning to step S242.

[0107] If the data of the interpolation points are not accurate but contain a small amount of error, then the interpolated function is not a strict rational polynomial. In this case, the Loewner interpolation rational polynomial may have one or two erroneous spikes.

[0108] S3: using a spike removal method to remove spikes from the Loewner interpolation to obtain a smooth interpolation result;

[0109] Optionally, step S3 includes:

[0110] S31: Calculate the poles and residues of the Loewner interpolation;

[0111] It is known that the rational polynomial based on the Loewner matrix is:

[0112]

[0113] Then the denominator of the above formula is:

[0114]

[0115] The zero point of the denominator D This is the solution to the following generalized eigenvalue problem.

[0116]

[0117] S32: Obtain a new Loewner interpolation polynomial according to the poles and the residues;

[0118] Since the zero point of D is The poles of , so the rational polynomial based on the Loewner matrix can be transformed into a rational polynomial based on the poles and residues:

[0119]

[0120] Since both sides of the above equation have the same pole , and the coefficient is unknown and is called the residue. Considering that the expression on the right side of the above formula must go through p Interpolation points , so we have:

[0121]

[0122] Solve the equation to get all the residues The value of , thus determining the rational polynomial based on the poles and residues, that is, the new Loewner interpolation polynomial for:

[0123]

[0124] in, is a natural number and , For the remainder, For the extreme point, is a constant term that does not change with frequency, represents the normalized frequency and , Indicates the lowest frequency point, Indicates the highest frequency point, Indicates frequency.

[0125] If there are small errors in the interpolated data, the interpolated function is not a strict rational function. If you force a rational function to approximate, one or two spikes may appear. You can see the spikes by drawing a curve based on the poles and residues of the rational polynomial. The reason for the spikes is that when the numerator of a summation term on the right side of the rational polynomial based on the poles and residues is Very small, and at the same time the denominator When the imaginary part of is also very small, this term will produce a spike in the curve. The spike can be removed by simply deleting this summation term on the right side of the rational polynomial based on the poles and residues. The resulting function may deviate slightly from the given interpolation point, but it will still be a close approximation to the interpolated function.

[0126] S33: Determine whether the new Loewner interpolation polynomial satisfies the spike existence condition, if yes, proceed to step S34, otherwise, proceed to step S4;

[0127] The condition for the existence of the spike is that one of the polynomial summation terms of the new Loewner interpolation has the smallest residue and the imaginary part of the pole is the smallest.

[0128] S34: modifying the new Loewner interpolation polynomial to obtain a modified Loewner interpolation polynomial;

[0129] The polynomial of the modified Loewner interpolation is:

[0130]

[0131] S35: Correct the interpolation points according to the corrected Loewner interpolation polynomial and return to step S242.

[0132] The original interpolation points are corrected to , and then, using the corrected interpolation point data, re-perform Loewner interpolation:

[0133]

[0134] S4: Outputting the smooth interpolation result as the broadband frequency sweep result.

[0135] Example 2

[0136] Figure 2 It is a 37-port passive network. The S parameters in the frequency band from 0.1 GHz to 250 GHz are simulated by finite element method. 26,1The interpolation process verifies the performance of the method of the present invention. As a comparison standard, a uniformly spaced scan with a step size of 0.1 GHz is used, and the finite element method is used to simulate the reference values ​​of 2500 frequency points. In the present invention, the above step S2 is used to perform broadband scanning, and the results are shown in FIG. Figure 3 . It can be seen that starting from the three interpolation points, the method of the present invention can automatically find the frequency interval with the largest error and increase the interpolation points, so that the interpolation curve quickly approaches the reference value. When the number of points increases to 21, the global error is reduced to below 0.01, which can be considered converged. However, at 21 points, an erroneous spike appears on the curve at 157.6GHz. At this time, the spike can be removed by using the spike removal method to obtain a smooth curve. The real and imaginary parts of the interpolation result are as follows: Figure 4 and Figure 5 shown.

[0137] The present invention has the following beneficial effects:

[0138] The algorithm of the present invention utilizes three advantages of Loewner matrix interpolation. First, the rational polynomial based on Loewner matrix interpolation is an expression similar to Lagrange interpolation, which is relatively concise and intuitive. Second, the number of sampling points required for Loewner matrix interpolation is the least among all rational interpolations. Finally, Loewner matrix interpolation is very stable, with few spikes and can be completely removed. In summary, the algorithm of the present invention can use the least frequency points to obtain a stable interpolation result and accurately approximate the broadband frequency response of the electronic system.

[0139] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A broadband frequency sweeping method, characterized in that: The broadband frequency sweeping method comprises: S1: Obtain frequency domain response data of the circuit system within a preset frequency band; S2: Obtaining Loewner interpolation according to the frequency domain response data; S3: using a spike removal method to remove spikes from the Loewner interpolation to obtain a smooth interpolation result; S4: outputting the smooth interpolation result as the broadband frequency sweep result; The frequency domain response data includes an odd number of frequency points, and the step S2 includes: S21: performing normalization processing on the odd number of frequency points to obtain normalized frequencies; S22: Obtaining a corresponding frequency response according to the normalized frequency; S23: constructing a Loewner interpolation matrix according to the normalized frequency and the frequency response; S24: Obtaining Loewner interpolation using an adaptive interpolation algorithm according to the Loewner interpolation matrix; The step S22 is obtained by the following formula: in, represents the frequency response function, Indicates The normalized frequency of the point, Indicates The frequency response value of the point, is a natural number and ; The step S23 comprises: S231: Divide the normalized frequency and the frequency response into a first data group and a second data group; S232: constructing a rational polynomial of a Loewner interpolation matrix using the first data group; S233: Obtaining a matrix equation according to the rational polynomial and the second data group; S234: Obtaining a Loewner interpolation matrix according to the matrix equation; In step S232, the rational polynomial of the Loewner interpolation matrix is for: in, represents a complex constant, Indicates The frequency response of the points in the first data set is, Indicates The normalized frequency of points in the first data set, represents the normalized frequency and , Indicates the lowest frequency point, Indicates the highest frequency point, Indicates frequency; In step S233, the matrix equation is: in, represents the Loewner interpolation matrix, represents a complex constant and , represents the frequency domain response at the frequency point of the second data set and , represents the normalized frequency of the second data set and , Indicates The frequency response of the points in the first data set is, Indicates The normalized frequency of the points in the first data set and ; The step S24 comprises: S241: Initialize the Loewner interpolation matrix; S242: Obtaining a corresponding Loewner interpolation according to the Loewner interpolation matrix; S243: Calculate the global error and local error of the Loewner interpolation within the preset frequency band, and determine whether the global error is less than a convergence threshold. If so, proceed to step S244; otherwise, proceed to step S245; S244: Outputting the Loewner interpolation as Loewner interpolation; S245: taking the center frequencies of the two frequency intervals with the largest local errors as added interpolation points, adding 1 to the frequency domain response data, and returning to step S242.

2. The broadband frequency sweeping method according to claim 1, characterized in that: The step S3 comprises: S31: Calculate the poles and residues of the Loewner interpolation; S32: Obtain a new Loewner interpolation polynomial according to the poles and the residues; S33: Determine whether the new Loewner interpolation polynomial satisfies the spike existence condition, if yes, proceed to step S34, otherwise, proceed to step S4; S34: modifying the new Loewner interpolation polynomial to obtain a modified Loewner interpolation polynomial; S35: Correct the interpolation points according to the corrected Loewner interpolation polynomial and return to step S242.

3. The broadband frequency sweeping method according to claim 2, characterized in that: In step S32, the new Loewner interpolation polynomial for: in, is a natural number and , For the remainder, For the extreme point, is a constant term that does not change with frequency, represents the normalized frequency and , Indicates the lowest frequency point, Indicates the highest frequency point, Indicates frequency.

4. The broadband frequency sweeping method according to claim 2 or 3, characterized in that: In step S33, the condition for the existence of the spike is that one of the polynomial summation terms of the new Loewner interpolation has the smallest residue and the imaginary part of the pole is the smallest.

Images