Coupled Matrix Extraction Method and Device Based on Rational Expression Fitting and Matrix Transformation

Abstract

The present application relates to a coupling matrix extraction method and an electronic device based on rational expression fitting and matrix transformation. This method can accurately extract the coupling matrix corresponding to the current tuning state from the actual measurement or simulation S-parameters of a filter. The method based on rational expression fitting and matrix transformation does not depend on the selection of an initial value and has a fast calculation speed.

Description

Technical Field

[0001] The present application relates to a coupling matrix extraction method, and in particular to a coupling matrix extraction method and device based on rational expression fitting and matrix transformation. Background Art

[0002] Unlike wired communication, wireless communication is carried out in an open public environment, and interference between signals is a key factor affecting the quality of wireless communication. Frequency selective devices represented by filters are key components for suppressing interference signals in wireless communication systems. At present, with the continuous development of mobile communication technology and the popularization of technologies such as the Internet of Things and unmanned driving, the demand for various microwave and millimeter wave filters will continue to increase.

[0003] A key issue in designing and producing filters is that their electrical characteristics are very sensitive to errors in physical dimensions or changes in material parameters. Even a small disturbance in the size of a resonator will cause its resonant frequency to shift from within the passband to outside the passband, causing the filter characteristics to deviate significantly from the target response. A filter usually has dozens of physical parameters and design variables. If the measured or simulated filter response does not meet the design specifications, it is difficult to directly determine which units need to be adjusted. However, errors are inevitably present in the production process of the filter, so precise debugging in the later stages of processing is essential. The traditional solution relies on technicians to observe the measured responses and judge how to adjust each tuning unit based on accumulated experience. This work is very challenging, boring and arduous, so manual debugging is costly.

[0004] In order to achieve mechanized automatic debugging of the filter and reduce production costs, it is necessary to be able to infer how to debug the filter based on the current filter measurement response. The core technology of this type of method is circuit model parameter extraction, and the coupling matrix is ​​a universal circuit model that describes various types of filters. It is only necessary to compare the extracted coupling matrix corresponding to the current tuning state with the coupling matrix of the filter in the ideal state, find out the elements with large differences, and then quickly determine how to further debug the filter based on the correspondence between the coupling matrix elements and the physical structure of the filter. In the process of gradually reducing the difference between the extracted coupling matrix and the target coupling matrix, the response of the filter to be tuned can gradually approach the target response.

[0005] The extraction of the coupling matrix mainly has two categories: optimization methods and analytical methods. Among them, the optimization method is based on an initial coupling matrix, and tries to modify the element values of the coupling matrix through various optimization algorithms to minimize the difference between the response of the coupling matrix and the S-parameters obtained by measurement / simulation. Whether the optimization algorithm can succeed depends very much on the selection of the initial value, and the optimization algorithm is prone to converge to a local optimal solution, which affects the accuracy of the extraction result. Another limitation of the optimization algorithm is that the matrix extraction speed is slow due to the large amount of calculation, which affects the debugging efficiency.

[0006] The existing methods for analytically extracting the coupling matrix have made varying degrees of simplification of the actual filter model, ignoring various actual factors. For example, the port transmission line will introduce a phase shift that changes with frequency, the resonator and the coupling structure will generate power losses and the loss degrees of each unit are different, and there are parasitic couplings in the filter network. Therefore, the accuracy is often poor when extracting the coupling matrix of the actual filter, and it is difficult to assist in the debugging of the actual filter. Especially for the debugging of high-order filters, there are still great difficulties. Summary of the Invention

[0007] Aiming at the problem that the existing algorithms for analytically extracting the coupling matrix are difficult to accurately extract the coupling matrix of the actual filter, this application proposes a coupling matrix extraction method and an electronic device based on rational function fitting and matrix transformation. This method can accurately extract the coupling matrix corresponding to the current tuning state from the actual measured or simulated S-parameters of the filter.

[0008] In the first aspect, this application proposes a coupling matrix extraction method based on rational function fitting and matrix transformation, including the following steps:

[0009] Step1: Obtain multiple groups of original scattering parameter matrices of the filter at multiple sampling frequency points Among them, S 11 is the reflection coefficient of the first port of the filter, S 12 is the reverse transmission coefficient of the filter, S 21 is the forward transmission coefficient of the filter, S 22 is the reflection coefficient of the second port of the filter;

[0010] Step 2: Transform the original scattering parameter matrix S from the physical band-pass domain to the normalized low-pass domain to obtain the low-pass domain scattering parameter matrix

[0011] Step 3: Perform rational function fitting on the reflection coefficients of each port in the low-pass domain scattering parameter matrix S'. The order of the rational function used is higher than the order of the filter. Convert the obtained fitted rational function into the form of zeros and poles. Calculate the loading phase of the port using the zeros and poles whose distance from the origin is greater than the distance threshold and the phase shift introduced by the transmission line that varies with frequency, and remove this phase shift from the low-pass domain scattering parameter matrix S' to obtain the phase-corrected scattering parameter matrix

[0012] Step 4: Convert the phase-corrected scattering parameter matrix S” into an admittance parameter matrix The reference impedance of all ports is 1 ohm during the conversion process;

[0013] Step 5: Fit the elements of the admittance parameter matrix Y using a set of rational functions with shared poles, and the number of shared poles is equal to the order of the filter. Among them, Y 11 and Y 22 are fitted in the form of partial fractions, while Y 12 and Y 21 The numerator polynomial of the fitted rational function is restricted to be equal to the number of transmission zeros of the filter, and weights are applied to the fitting data of Y 12 and Y 21 The smaller the modulus value of the data, the greater the weight;

[0014] Step 6: Convert the fitted rational function of the admittance parameter matrix Y into the form of poles-residues, and construct the transverse coupling matrix M and capacitance matrix C according to the poles and residues;

[0015] Step 7: Perform a series of basic matrix transformations on the transverse coupling matrix M and the capacitance matrix C to obtain the target coupling matrix corresponding to the actual coupling structure form of the filter.

[0016] In a possible implementation,

[0017] The specific content of Step 3 includes:

[0018] Perform rational function fitting on the reflection coefficient S′ of the i-th port in the low-pass domain scattering parameter matrix S' according to the following formula (1): ii According to the following formula (1):

[0019]

[0020] where i takes values in {1, 2}, r k and p k are the k-th residue and the k-th pole respectively, and z kis the k-th zero, d is the constant term, s = jω, ω is the low-pass angular frequency, j is the imaginary unit, and m is a positive integer;

[0021] According to the distances of each zero and pole from the origin in the complex plane, the zero-pole form in Equation (1) is rewritten as the following Equation (2);

[0022]

[0023] where z 1 ~z nz are nz zeros whose distances from the origin in the complex plane are greater than the distance threshold, and p 1 ~p np are np poles whose distances from the origin in the complex plane are greater than the distance threshold;

[0024] Calculate the phase factor α of the i-th port according to the following Equation (3) i ;

[0025]

[0026] Calculate the loaded phase of the i-th port and the phase shift θ(s) introduced by the transmission line that varies with frequency through the following Equation (4); i (s);

[0027] θ i (s) = arg(α i ) / 2 (4)

[0028] Construct the phase shift matrix D,

[0029]

[0030] Remove the phase shift θ(s) of the i-th port in the low-pass domain scattering parameter matrix S' through the following Equation (5), and obtain the phase-corrected scattering parameter matrix i (s),

[0031] S” = DSD (5)

[0032] The specific content of Step4 includes:

[0033] Convert the phase-corrected scattering parameter matrix S” into an admittance parameter matrix through the following Equation (6), and the reference impedance of all ports is 1 ohm during the conversion process;

[0034] Y = (I - S”)(I + S”) -1 = (I + S”) -1 (I - S”) (6)

[0035] where I is the identity matrix;

[0036] Step 5 specifically includes:

[0037] Perform rational fitting on each element of the admittance parameter matrix Y through the following formula (7):

[0038]

[0039] where d 11 , d 22 are the coefficients to be determined for rational fitting, a k are the poles of the fitting basis function, N is the order of the filter, and nfz is the number of transmission zeros;

[0040] Determine d 11 , d 22 to obtain the target fitting rational formula based on formula (7);

[0041] Convert the target fitting rational formula into the pole-residue form according to the following formula (8):

[0042]

[0043] where p k are the poles shared by the target fitting rational formula, is the residue of Y pq corresponding to the pole p k , the pq combination takes values in {11, 12, 21, 22}, K 11 and K 22 are the constant terms of the rational formulas of Y 11 and Y 22 respectively;

[0044] Step 6 specifically includes:

[0045] Construct a transverse coupling matrix M of size (N + 2)×(N + 2) according to the poles and residues in formula (8), and the calculation method of the non-zero elements in the transverse matrix M is:

[0046] M 11 = K 11 / j, M N+2,N+2 = K 22 / j;

[0047] And for k = 1, 2,..., N, there are:

[0048] M k+1，k+1 = jp k ,

[0049] If then

[0050] If then

[0051] Construct a capacitance matrix C in the form of a diagonal matrix with a size of (N + 2)×(N + 2). For each diagonal element of the capacitance matrix C, except for the first and the last one which are 0, the rest are all 1.

[0052] In a possible implementation, in the Step1, by measuring the physical object of the filter or simulating the model of the filter, multiple groups of original scattering parameter matrices S of the filter at multiple sampling frequency points are obtained, and the sampling frequency range of the measurement or simulation covers the passband of the filter and the resonant frequencies of all relevant resonant modes, and the number of sampling frequency points is not less than 20.

[0053] In a possible implementation, in the Step2, according to the band-pass - low-pass frequency mapping relationship represented by the formula ω = f 0 / B * (f / f 0 – f 0 / f), transform the original scattering parameter matrix S from the physical band-pass domain to the normalized low-pass domain;

[0054] where f 0 is the center frequency of the filter, B is the bandwidth of the filter, and f is the physical frequency.

[0055] In a possible implementation, in the Step3, m is 1 or 2, and the distance threshold takes values in the range of 2 to 5.

[0056] In a possible implementation, in the Step4, the calculation method of each element of the admittance parameter matrix Y is as follows:

[0057]

[0058]

[0059]

[0060] In a possible implementation, in the Step5, first arbitrarily select a set of initial values for a k in Equation (7), and construct a fitting equation (9) in the following form to solve the coefficients to be determined for the rational expression fitting d 11 , d 22 :

[0061]

[0062] Among them, the data of each frequency point corresponds to a row of the fitting equation (9).

[0063] Y pq is a diagonal matrix of size Ns×Ns, and the u-th diagonal element value of Y pq is Y pq (s u ).

[0064] y pq is a vector of size Ns×1, and the u-th element value of y pq is Y pq (s u ).

[0065] W 12 is a diagonal matrix of size Ns×Ns, and the u-th diagonal element value of W 12 is

[0066] The pq combination takes values in {11, 12, 21, 22}, and u = 1, 2, 3... Ns;

[0067] A 1 is a matrix of size Ns×(N + 1), where Ns is the number of sampling frequency points, and the u-th row elements of A 1 are:

[0068]

[0069] A 2 is a matrix of size Ns×N, and the u-th row elements of A 2 are:

[0070]

[0071] A 3 is a matrix of size Ns×(nfz + 1), and the u-th row elements of A 3 are:

[0072]

[0073] c 11 ,c 12 ,c 22 and The four vectors contain the coefficients to be determined in the formula (7), where:

[0074]

[0075]

[0076]

[0077] Among them, the pp combination takes values in {11, 22};

[0078] Solve from the fitting equation (9) Update the pole a of the fitting basis function in the following way k of the position:

[0079] Construct a matrix Find all the eigenvalues of this matrix as the poles a of the new fitting basis function k of the position, where A is a diagonal matrix of size N×N, and the diagonal elements of A are the poles a k of the original position, b is a vector of N×1 and all its elements are 1;

[0080] The pole a of the fitting basis function k After the position of is updated, reconstruct a rational fitting equation in the form of the fitting equation (9), and solve it iteratively in this way until the rational fitting process converges, that is, the target rational expression is obtained.

[0081] In a possible implementation manner, in the Step5, when the difference in the positions of the poles a calculated successively twice in a row k is less than the first set threshold, or the length of the vector is less than the second set threshold, it is determined that the constructed rational fitting process converges.

[0082] In a possible implementation manner, in the Step7, the basic matrix transformation includes node scale transformation, row-column superposition transformation, and rotation transformation.

[0083] In a second aspect, the present application proposes an electronic device, including:

[0084] A memory,

[0085] A processor connected to the memory, and

[0086] Instructions stored in the memory and executable by the processor;

[0087] Among them, when the processor executes the instructions, the method described in the first aspect is implemented.

[0088] The coupling matrix extraction method provided by this application can quickly and accurately extract the coupling matrix corresponding to the current tuning state from the simulated or measured S-parameters of a filter. Compared with the coupling matrix extraction method based on optimization, the method of this application does not depend on the selection of initial values and has a fast calculation speed. One coupling matrix extraction can be completed within a few seconds. This method can be used to assist debuggers in debugging microwave and millimeter-wave filters, and can also be combined with a debugging machine to achieve mechanical automatic debugging of filters. Description of the Drawings

[0089] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings of the embodiments will be briefly introduced below. Obviously, the drawings in the following description only relate to some embodiments of this application and do not limit this application.

[0090] Figure 1 It is a flowchart of the method according to an embodiment of this application.

[0091] Figure 2 It is a picture of a filter provided by an embodiment of this application.

[0092] Figure 3 It is Figure 2 the S-parameter amplitude curve measured for the filter shown in a tuning state.

[0093] Figure 4 It is the coupling matrix corresponding to the filter shown obtained by using the coupling matrix extraction method provided by the embodiment of this application Figure 2 for the filter shown.

[0094] Figure 5 It is the coupling matrix corresponding to the filter shown obtained by using the coupling matrix extraction method provided by the embodiment of this application Figure 2 for the filter shown.

[0095] Figure 6 It is a picture of a filter provided by another embodiment of this application.

[0096] Figure 7 It is Figure 6 the S-parameter amplitude curve measured for the filter shown in a tuning state.

[0097] Figure 8 It is the coupling matrix corresponding to the filter shown obtained by using the coupling matrix extraction method provided by the embodiment of this application Figure 6 for the filter shown.

[0098] Figure 9 It is the coupling matrix corresponding to the filter shown obtained by using the coupling matrix extraction method provided by the embodiment of this application Figure 6 for the filter shown.

[0099] Figure 10Schematic diagram of the process for assisting filter debugging provided by the embodiments of the present application. Detailed implementation manners

[0100] To make the objectives, technical solutions and advantages of the present application clearer, the technical solutions of the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present application. Apparently, the described embodiments are some but not all of the embodiments of the present application. All other embodiments obtained by those of ordinary skill in the art based on the described embodiments of the present application without creative efforts shall fall within the protection scope of the present application. It can be understood that, without conflict, some technical means described in the various embodiments herein may be replaced or combined with each other.

[0101] In the description of the specification and claims of the present application, if there are terms such as "first" and "second", they are only used to distinguish the described objects and do not have any sequential or technical meanings. Thus, the objects defined with "first", "second", etc. may explicitly or implicitly include one or more of such objects.

[0102] In the description of the specification of the present application, referring to "one embodiment" or "some embodiments" etc. means that a specific feature, structure or characteristic described in conjunction with the embodiment is included in one or more embodiments of the present application. Thus, the statements "in one embodiment", "in some embodiments", "in other some embodiments", "in still other embodiments" etc. that appear in different places in this specification do not necessarily refer to the same embodiment, but mean "one or more but not all of the embodiments", unless otherwise specifically emphasized in other ways.

[0103] To facilitate readers to better understand the technical solutions of the embodiments of the present application, relevant terms and concepts will be introduced below.

[0104] 1) S-parameters

[0105] That is, scattering parameters, which are electrical parameters that can be directly measured in the microwave and millimeter-wave frequency bands. These parameters characterize the reflection or transmission coefficients between the various ports of a network.

[0106] 2) Y-parameters

[0107] That is, short-circuit admittance parameters, which are one of the commonly used parameters for describing microwave networks. These parameters characterize the self-admittance of each port and the mutual admittance between the ports. After the reference impedance of each port of a given network is given, the Y-parameters can be obtained by converting the S-parameters.

[0108] 3) Rational expressions

[0109] A rational expression is a single-variable expression where both the numerator and denominator are polynomials. Rational expressions have different forms, and common forms include the form of polynomial division, the zero-pole form, and the partial fraction form.

[0110] 4) Vector fitting method

[0111] A calculation method for rational expression fitting that can directly obtain the pole-residue form of a rational expression.

[0112] 5) Coupled resonator network

[0113] A passive network formed by coupling multiple resonators together in a specific topology. The network can have one to multiple ports and is usually used to construct microwave filters, power splitters / combiners, matching networks, etc.

[0114] 6) Coupling matrix

[0115] A matrix model used to describe a coupled resonator network. Usually, there is a clear correspondence between the elements of the coupling matrix and the physical units of the filter: each diagonal element corresponds to a resonance mode, the value of the diagonal element is related to that resonance mode, and each non-diagonal element corresponds to a normalized coupling coefficient.

[0116] 7) Capacitance matrix

[0117] Another matrix model generated along with the coupling matrix, which acts together with the coupling matrix to describe the circuit model of the filter. The capacitance matrix is required when calculating the response of the coupling matrix.

[0118] 8) Transverse coupling matrix

[0119] A special form of the coupling matrix where the first row and first column and the last row and last column are all non-zero elements, and the central part is a diagonal matrix. The transverse matrix can be directly constructed from the poles and residues of the Y-parameter polynomial. Other forms of the coupling matrix are obtained by applying equivalent transformations to the transverse coupling matrix.

[0120] The following combines Figure 1 Describe a coupling matrix extraction method based on rational expression fitting and matrix transformation according to an embodiment of the present application. The method includes the following steps:

[0121] Step1: Obtain multiple groups of original scattering parameter matrices of the filter at multiple sampling frequency points Among them, S 11 is the reflection coefficient of the first port of the filter, S 12 is the reverse transmission coefficient of the filter, S 21 is the forward transmission coefficient of the filter, S 22 is the reflection coefficient of the second port of the filter.

[0122] In some embodiments, the above-mentioned multiple groups of original scattering parameter matrices S can be obtained by measuring the physical filter.

[0123] In other embodiments, the above-mentioned multiple groups of original scattering parameter matrices S can be obtained by simulating the filter model.

[0124] In this Step1, the sampling frequency range of measurement or simulation should cover the passband of the filter and the resonant frequencies of all relevant resonant modes, and the number of sampling frequency points (i.e., the number of sampling frequency points) is preferably not less than 20.

[0125] Step 2: Transform the original scattering parameter matrix S from the physical band-pass domain to the normalized low-pass domain to obtain the low-pass domain scattering parameter matrix where S′ 11 corresponds to S 11 S′ 12 corresponds to S 12 S′ 21 corresponds to S 21 S′ 22 corresponds to S 22 corresponds.

[0126] Specifically, according to the band-pass to low-pass frequency mapping relationship represented by the formula ω = f 0 / B * (f / f 0 – f 0 / f), the original scattering parameter matrix S is transformed from the physical band-pass domain to the normalized low-pass domain to obtain the above-mentioned low-pass domain scattering parameter matrix S'. Where f 0 is the center frequency of the filter, B is the bandwidth of the filter, f is the physical frequency, and ω is the low-pass angular frequency.

[0127] The band-pass to low-pass frequency transformation establishes a one-to-one correspondence between the physical frequency f and the normalized low-pass angular frequency ω. The characteristic of this frequency transformation is that it can map the upper and lower passband edge frequencies of the band-pass filter to -1 and 1 rad / s respectively, and the center frequency f 0 is mapped to 0 rad / s, corresponding to the origin of the complex plane.

[0128] In this Step2, the low-pass angular frequency ω is further transformed into the complex frequency s = jω, and this complex frequency s will be used as the independent variable for fitting rational expressions in the following Step3 and Step5.

[0129] Step3: Rationalize the reflection coefficient S′ ii of the i-th port in the low-pass domain scattering parameter matrix S' according to the following formula (1):

[0130]

[0131] Among them, i takes values in {1, 2}, that is, i can take 1 and 2 respectively. Therefore, the reflection coefficient S′ of the first port in the low-pass domain scattering parameter matrix S' 11 and the reflection coefficient S′ of the second port 22 are respectively fitted with the above formula (1) and transformed into the zero-pole form according to the above formula respectively.

[0132] In the above formula (1), r k and p k are the k-th residue and the k-th pole respectively, z k is the k-th zero; m is a positive integer, representing the number of zero-poles more than the order of the filter, and m can generally take 1 or 2, that is, rational expressions slightly higher than the order of the filter are used to fit the reflection coefficients of each port respectively; d is a constant term; s is a complex frequency. Specifically, s = jω, where ω has been introduced above and is the low-pass angular frequency, and j is the imaginary unit.

[0133] According to the distances of each zero-pole to the origin in the complex plane, the zero-pole form in the above formula (1) can be written in the form of the following formula (2);

[0134]

[0135] Among them, z 1 ~z nz are nz zeros whose distances to the origin in the complex plane are greater than the distance threshold, p 1 ~p np are np poles whose distances to the origin in the complex plane are greater than the distance threshold. Obviously, both nz and np are integers.

[0136] Specifically, according to the distances of the zero-poles to the origin in the complex plane, that is, the modulus values of the zero-poles, the zero-poles can be divided into two categories. Among them, the first category of zero-poles is closer to the origin - less than or equal to the set distance threshold. They are the zero-poles generated by resonance and have a greater impact on the amplitude response; the second category of zero-poles is farther from the origin - greater than the set distance threshold. They are the zero-poles generated by the port transmission line and have a smaller impact on the amplitude response, mainly introducing a phase shift that changes with frequency. The aforementioned distance threshold for distinguishing these two categories of zero-poles is generally preferably in the range of 2 - 5.

[0137] In the above zero-pole expression, that is, formula (2), z nz+1 ~z N+m and p np+1 ~p N+m are the first category of zero-poles, while z 1 ~z nz and p 1 ~pzp They are the second type of zeros and poles, which together with the constant term d form the phase factor α. i .

[0138] It can be understood that the second equal sign in Equation (1) above is in the zero-pole form. Equation (2) further rewrites the zero-pole form in Equation (1) to facilitate the discussion of estimating the port phase using zeros and poles farther from the origin.

[0139] After that, the phase factor α of the i-th port is calculated according to Equation (3) below i ;

[0140]

[0141] As mentioned above, i takes values in {1, 2}. Therefore, according to Equation (3), the phase factor α of the first port can be obtained 1 and the phase factor α of the second port 2 .

[0142] The loaded phase of the i-th port and the phase shift introduced by the transmission line that varies with frequency can be deduced from the phase of the phase factor α i . The specific calculation method is as follows:

[0143] The loaded phase of the i-th port and the phase shift θ introduced by the transmission line that varies with frequency can be calculated through Equation (4) below i (s);

[0144] θ i (s) = arg(α i ) / 2 (4)

[0145] As mentioned above, i takes values in {1, 2}. Therefore, according to Equation (4), the loaded phase of the first port and the phase shift θ introduced by the transmission line that varies with frequency can be obtained 1 (s) and the loaded phase of the second port and the phase shift θ introduced by the transmission line that varies with frequency 2 (s).

[0146] After the loaded phases of the two ports and the transmission line phases are calculated according to the above steps, a phase shift matrix D is constructed.

[0147]

[0148] At this time, the loaded phase and the transmission line phase can be removed from the low-pass domain scattering parameter matrix S'. The specific removal method is as follows:

[0149] The phase shifts of each port in the low-pass domain scattering parameter matrix S' (i.e., the above θ 1 (s) and θ2 (s)) to obtain the phase-corrected scattering parameter matrix where S″ 11 corresponds to S′ 11 S″ 12 corresponds to S′ 12 S″ 21 corresponds to S′ 21 S″ 22 corresponds to S′ 22 and so on.

[0150] S” = DSD (5)

[0151] As mentioned above, S” is the phase-corrected scattering parameter matrix, S is the original scattering parameter matrix obtained by measurement or simulation, and D is the constructed phase shift matrix.

[0152] As can be seen from the above, in this Step 3, the present embodiment uses a rational expression containing N + m poles and zeros to fit the reflection coefficients of each port, that is, the diagonal elements S ii of the S-parameter matrix, respectively. Among them, N is the order of the filter, and m can usually take 1 or 2, that is, a rational expression slightly higher than the order of the filter is used to fit the reflection coefficients of each port respectively. More specifically, the present embodiment uses the vector fitting method to complete the rational expression fitting, obtains the pole-residue form of the rational expression, and then converts the pole-residue form of the rational expression into the zero-pole form.

[0153] Step 4: Convert the phase-corrected scattering parameter matrix S” into an admittance parameter matrix through Equation (6) The reference impedance of all ports is 1 ohm during the conversion process;

[0154] Y = (I - S”)(I + S”) -1 = (I + S”) -1 (I - S”) (6)

[0155] where I is the identity matrix; S” has been introduced above and is the phase-corrected scattering parameter matrix.

[0156] Expanding the above Equation (6), it can be seen that the specific calculation formulas for each element in the admittance parameter matrix Y are respectively:

[0157]

[0158]

[0159]

[0160] Step 5: Rationalize the fitting of each element in the admittance parameter matrix Y using the following formula (7) (it is not difficult to see that the right side of the equal sign in formula (7) is a set of rational expressions sharing poles):

[0161]

[0162] where d 11 , d 22 are the coefficients to be determined for rational fitting (specifically, d 11 and d 22 are the constant terms of the numerator rational expressions of Y 11 and Y 22 respectively), a k is the pole of the fitting basis function, N is the order of the filter, and nfz is the number of transmission zeros. The meaning of S has been explained above and is the complex frequency. Specifically, s = jω.

[0163] Determine d 11 , d 22 to obtain the target fitting rational expression based on formula (7).

[0164] Specifically, when using formula (7) to fit the admittance parameter matrix Y, a set of initial values can be arbitrarily selected for a k in formula (7), and the following fitting equation (9) can be constructed to solve the coefficients to be determined for rational fitting d 11 , d 22 :

[0165]

[0166] where each frequency point data corresponds to a row of the above fitting equation (9). Since Y 11 , Y 12 (Y 21 = Y 12 ) and Y 22 are simultaneously fitted, the above fitting equation (9) has a total of 3Ns rows, where Ns is the number of sampling frequency points (i.e., the number of sampling frequency points).

[0167] Y pq is a diagonal matrix of size Ns×Ns, and the u-th diagonal element value of Y pq is Y pq (s u );

[0168] y pq is a vector of size Ns×1, and the u-th element value of y pq is Y pq (su )

[0169] W 12 is a diagonal matrix of size \(N_s\times N_s\), and the \(u\)-th diagonal element value of \(W\) 12 is

[0170] where the \(pq\) combination takes values in \(\{11, 12, 21, 22\}\), that is, the \(pq\) combination takes 11, 12, 21, and 22 respectively; \(u = 1, 2, 3,\cdots, N_s\), that is, \(u\) takes values in \(\{1, 2, 3,\cdots, N_s\}\).

[0171] A 1 is a matrix of size \(N_s\times(N + 1)\). As mentioned above, \(N_s\) is the number of sampling frequency points and \(N\) is the order of the filter; the \(u\)-th row elements of \(A\) 1 are:

[0172]

[0173] A 2 is a matrix of size \(N_s\times N\), and the \(u\)-th row elements of \(A\) 2 are:

[0174]

[0175] A 3 is a matrix of size \(N_s\times(n_{fz}+1)\). As mentioned above, \(n_{fz}\) is the number of transmission zeros; the \(u\)-th row elements of \(A\) 3 are:

[0176]

[0177] c 11 , \(c\) 12 , \(c\) 22 and the four vectors contain the coefficients to be solved in the above formula (7), where:

[0178]

[0179]

[0180]

[0181] the \(pp\) combination takes values in \(\{11, 22\}\). In the above three formulas, the superscript \(T\) represents the transpose of the matrix.

[0182] After solving \(\hat{\mathbf{c}}\) from the above fitting equation (9), the position of the pole \(a\) of the fitting basis function is updated in the following way: First, construct the matrix k of

[0183] First, construct the matrix Find all the eigenvalues of the matrix as the poles \(a\) of the new fitting basis functions k where \(A\) is a diagonal matrix of size \(N\times N\) with the diagonal elements being the poles \(a\) k original position, \(b\) is an \(N\times1\) vector with all elements being \(1\), and the superscript \(T\) represents the transpose of the matrix; as mentioned above, \(N\) is the order of the filter.

[0184] The poles \(a\) of the fitting basis functions k After updating the positions of the poles \(a\), reconstruct the rational fitting equation in the form of fitting equation (9), and iterate to solve in this way until the rational fitting process converges, thus obtaining the target fitting rational expression.

[0185] The judgment basis for the above "convergence" is is close to the zero vector, or the positions of the poles \(a\) calculated successively twice are basically unchanged. For example, when the difference between the position of the pole \(a\) calculated for the tenth time k and the position of the pole \(a\) calculated for the ninth time k is less than the set threshold, it can be considered that the above rational fitting process converges and the target fitting rational expression is obtained. k Convert the target fitting rational expression into the pole-residue form according to the following formula (8):

[0186] where \(p\)

[0187]

[0188] is the shared pole in the target rational expression, k is the residue corresponding to the pole \(p\) is \(Y\) pq corresponding to the pole \(p\) k and the \(pq\) combination takes values in \(\{11, 12, 21, 22\}\), \(K\) 11 and \(K\) 22 are the constant terms of the rational expressions of \(Y\) 11 and \(Y\) 22 respectively.

[0189] Step 6: Construct a transverse coupling matrix \(M\) of size \((N + 2)\times(N + 2)\) according to the poles and residues in the above formula (8), and the calculation method of the non-zero elements in the transverse matrix \(M\) is as follows:

[0190] \(M\) 11 = \(K\) 11 / j, \(M\) N+2,N+2 = \(K\) 22 / j;

[0191] And for \(k = 1, 2, 3\cdots N\), there are:

[0192] \(M\) k+1，k+1 = \(jp\)k ,

[0193] If then

[0194] If then

[0195] wherein, M tv represents the element in the t-th row and v-th column of the transverse coupling matrix M. For example, M N+2，k represents the element in the (N + 2)-th row and k-th column of the transverse coupling matrix M; as mentioned above, j is the imaginary unit and N is the order of the filter.

[0196] While constructing the above transverse coupling matrix M, a capacitance matrix C of size (N + 2)×(N + 2) in the form of a diagonal matrix is also constructed. For each diagonal element of the capacitance matrix C, except the first and the last being 0, the rest are all 1.

[0197] Step 7: Transform the transverse coupling matrix M and the capacitance matrix C into the form corresponding to the actual filter coupling structure.

[0198] Starting from the constructed initial transverse coupling matrix M and initial capacitance matrix C, a series of basic matrix transformations are implemented to obtain the target coupling matrix corresponding to the actual coupling structure form of the filter.

[0199] In this Step 7, the above basic matrix transformations include node scaling transformation, row-column superposition transformation, and rotation transformation. Among them:

[0200] The node scaling transformation includes: multiplying all elements in the e-th row and e-th column of the coupling matrix and the capacitance matrix by a non-zero constant α, where e takes values in {1, 2, 3... N + 2};

[0201] The row-column superposition transformation includes: adding β times of the e-th row of the coupling matrix M and the capacitance matrix C to the g-th row, and adding β times of the e-th column to the g-th column, where g takes values in {1, 2, 3... N + 2}; as mentioned above, e takes values in {1, 2, 3... N + 2};

[0202] The rotation transformation includes: multiplying the coupling matrix and the capacitance matrix by the rotation matrix R and the transpose R T of the rotation matrix R before and after respectively. That is, M' = R T MR, C' = R T CR.

[0203] There are three basic matrix transformations: node scaling transformation, row-column superposition transformation, and rotation transformation. To transform a transverse coupling matrix into the coupling matrix of the target structure, a series of basic matrix transformations need to be applied. This series of basic transformations generally includes multiple node scaling transformations, row-column superposition transformations, and rotation transformation steps. Those of ordinary skill in the art can understand that the specific order of basic transformations is determined by the target coupling matrix structure. Different target coupling matrix structures require different transformation orders, so the specific transformation process cannot be uniformly given. For example Figure 4 and Figure 8 the two coupling matrices in are obtained from the transverse matrix through different transformation orders respectively.

[0204] Various basic matrix transformations affect the structure and element values of the coupling matrix and the capacitance matrix, but do not change the response of the coupling matrix. For different coupling structures, the types and orders of the basic matrix transformations implemented will be different.

[0205] Moreover, the embodiment of the present application also provides an electronic device (such as a PC), and the electronic device includes: a memory, a processor connected to the memory, and instructions stored in the memory and executable by the processor; wherein, when the processor executes the foregoing instructions, the above-mentioned coupling matrix extraction method is implemented.

[0206] Please refer to Figure 2 , Figure 2 which is the first filter provided by an embodiment of the present application. The S-parameter magnitude curve measured under one tuning state of the first filter is as shown by the scattered data points in Figure 3 . The coupling matrix and capacitance matrix corresponding to the first filter obtained by using the above coupling matrix extraction method are respectively as shown in Figure 4 and Figure 5 shown, and the S-parameter magnitude responses of the extracted coupling matrix and capacitance matrix are as shown by the solid line in Figure 3 .

[0207] Please refer to again Figure 6 , Figure 6 which is the second filter provided by another embodiment of the present application. The S-parameter magnitude curve measured under one tuning state of the second filter is as shown by the scattered data points in Figure 7 . The coupling matrix and capacitance matrix corresponding to the second filter obtained by using the above coupling matrix extraction method are respectively as shown in Figure 8 and Figure 9 shown, and the S-parameter magnitude responses of the extracted coupling matrix and capacitance matrix are as shown by the solid line in Figure 7 .

[0208] The coupling matrix extraction method provided by the embodiments of the present application can be applied to the computer-aided debugging of single-band and multi-band microwave and millimeter-wave filters. It can be combined with simulation software to guide engineers in filter design, assist debuggers in debugging actual filters, and cooperate with machines to achieve automatic filter debugging.

[0209] Please refer to Figure 10 , Figure 10 which is a flowchart of a coupling matrix extraction method based on rational fitting and matrix transformation for computer-aided debugging and mechanized automatic debugging provided by an embodiment of the present application.

Claims

1. A method for extracting a coupling matrix based on rational fitting and matrix transformation, characterized in that, it includes the following steps: Step1: Obtain multiple groups of original scattering parameter matrices of the filter at multiple sampling frequency points Among them, S 11 is the reflection coefficient of the first port of the filter, and S 12 is the reverse transmission coefficient of the filter, and S 21 is the forward transmission coefficient of the filter, and S 22 is the reflection coefficient of the second port of the filter; Step 2: Transform the original scattering parameter matrix S from the physical band - pass domain to the normalized low - pass domain to obtain the low - pass domain scattering parameter matrix Step 3: Perform rational fitting on the reflection coefficients of each port in the low-pass domain scattering parameter matrix S' respectively. The order of the rational expression used is higher than the order of the filter. Convert the obtained fitted rational expression into the form of zeros and poles. Calculate the loading phase of the port and the phase shift introduced by the transmission line that varies with frequency using the zeros and poles whose distance from the origin is greater than the distance threshold, and remove this phase shift from the low-pass domain scattering parameter matrix S' to obtain the phase-corrected scattering parameter matrix Step 4: Convert the phase-corrected scattering parameter matrix S” into admittance parameter matrix The reference impedance of all ports during the conversion is 1 ohm; Step 5: Use a set of rational expressions with shared poles to fit the elements of the admittance parameter matrix Y, and the number of shared poles is equal to the order of the filter, where Y 11 and Y 22 are fitted in the form of partial fractions, while Y 12 and Y 21 are fitted such that the numerator polynomials of the rational expressions are restricted to be equal to the number of transmission zeros of the filter, and weights are applied to the fitting data of Y 12 and Y 21 ; the smaller the magnitude of the data, the greater the weight Step 6: Convert the fitting rational formula of the admittance parameter matrix Y into the pole-residue form, and construct the transverse coupling matrix M and the capacitance matrix C according to the poles and residues; Step 7: Perform a series of basic matrix transformations on the transverse coupling matrix M and the capacitance matrix C to obtain the target coupling matrix corresponding to the actual coupling structure form of the filter; wherein, the specific content of the Step4 includes: Convert the phase-corrected scattering parameter matrix S” into an admittance parameter matrix using the following equation (6). The reference impedance of all ports is 1 ohm during the conversion process. Y = (I - S”)(I + S”) -1 = (I + S”) -1 (I - S”) (6) where I is the identity matrix.

2. The coupling matrix extraction method according to claim 1, characterized in that, the specific content of the Step3 includes: The reflection coefficient S′ of the i-th port in the low-pass domain scattering parameter matrix S' ii is subjected to rational approximation according to the following formula (1): where \(i\) takes values in \(\{1, 2\}\), \(r\) k and \(p\) k are the \(k\)-th residue and the \(k\)-th pole respectively, \(z\) k is the \(k\)-th zero, \(d\) is the constant term, \(s = j\omega\), \(\omega\) is the low-pass angular frequency, \(j\) is the imaginary unit, and \(m\) is a positive integer; According to the distances from each zero-pole to the origin in the complex plane, rewrite the zero-pole form in formula (1) into the following formula (2); Among them, z 1 ~z nz are respectively nz zeros whose distances to the origin in the complex plane are greater than the distance threshold, and p 1 ~p np are respectively np poles whose distances to the origin in the complex plane are greater than the distance threshold; Calculate the phase factor α of the i-th port according to the following formula (3) i ; The loading phase of the i-th port and the phase shift θ(s) introduced by the transmission line that varies with frequency are calculated by the following formula (4). i (s); θ i (s) = arg(α i ) / 2(4) Construct the phase shift matrix D, Remove the phase shift θ of the i-th port in the low-pass domain scattering parameter matrix S' through the following formula (5) i (s) to obtain the phase-corrected scattering parameter matrix S” = DSD(5) the specific content of the Step5 includes: Perform rational fitting on each element of the admittance parameter matrix Y through the following formula (7): wherein, d 11 ,d 22 are coefficients to be determined for rational fitting, a k are poles of the fitting basis function, N is the order of the filter, and nfz is the number of transmission zeros; Determine d 11 ,d 22 , and obtain the target fitting rational expression based on Equation (7); Convert the target fitting rational formula into the pole-residue form according to the following formula (8): Among them, p k is the pole shared by the target fitting rational expression, is Y pq corresponding to the residue of the pole p k and the pq combination takes values in {11, 12, 21, 22}, K 11 and K 22 are the constant terms of the rational expressions of Y 11 and Y 22 respectively; the specific content of the Step6 includes: Construct a transverse coupling matrix M of size (N + 2)×(N + 2) according to the poles and residues in formula (8), and the calculation method of the non-zero elements in the transverse coupling matrix M is: M 11 = K 11 / j, M N+2,N+2 = K 22 / j; and for k = 1, 2,..., N, there is: M k+1，k+1 = jp k , If then If then Construct a capacitance matrix C of size (N + 2)×(N + 2) and in the form of a diagonal matrix. For each diagonal element of the capacitance matrix C, except the first and the last one are 0, the rest are all 1.

3. The coupling matrix extraction method according to claim 1 or 2, characterized in that, in the Step1, by measuring the physical object of the filter or simulating the model of the filter, multiple groups of original scattering parameter matrices S of the filter at multiple sampling frequency points are obtained, and the sampling frequency range of the measurement or simulation covers the passband of the filter and the resonance frequencies of all relevant resonance modes, and the number of sampling frequency points is not less than 20.

4. The coupling matrix extraction method according to claim 1 or 2, characterized in that, In the said Step 2, according to the band-pass to low-pass frequency mapping relationship expressed by ω = f 0 / B*(f / f 0 – f 0 / f), the original scattering parameter matrix S is transformed from the physical band-pass domain to the normalized low-pass domain; where f 0 is the center frequency of the filter, B is the bandwidth of the filter, and f is the physical frequency.

5. The coupling matrix extraction method according to claim 2, characterized in that, in the Step3, m is 1 or 2, and the distance threshold is taken within the range of 2 to 5.

6. The coupling matrix extraction method according to claim 2, characterized in that, in the Step4, the calculation method of each element of the admittance parameter matrix Y is as follows:

7. The coupling matrix extraction method according to claim 2, characterized in that, In the said Step 5, first, for a in formula (7) k arbitrarily select a set of initial values, and construct a fitting equation (9) in the following form to solve the coefficients to be determined for rational expression fitting d 11 , d 22 : wherein, the data of each frequency point corresponds to one row of the fitting equation (9), Ypq is a diagonal matrix of size Ns×Ns, and the value of the u-th diagonal element of Ypq is Y pq (s u ) y pq is a vector of size Ns×1, and the pq u-th element value of y pq (s u ) W 12 is a diagonal matrix of size Ns×Ns, and the 12 u-th diagonal element value of W the pq combination takes values in {11, 12, 21, 22}, u = 1, 2, 3......Ns; A 1 is a matrix of size Ns×(N + 1), where Ns is the number of said sampling frequency points, and A 1 The elements of the u-th row of are: A 2 is a matrix of size Ns×N, and the 2 u-th row elements of A are: A 3 is a matrix of size Ns×(nfz + 1), where A 3 The u-th row elements of are: c 11 ,c 12 ,c 22 and four vectors contain the coefficients to be determined in the formula (7), where: wherein, the pp combination takes values in {11, 22}; Solve from the fitting equation (9) Update the position of the pole a of the fitting basis function in the following manner k : Construct a matrix Find all the eigenvalues of the matrix as the poles a of the new fitting basis function k where A is a diagonal matrix of size N×N, and the diagonal elements of A are the poles a k original position, b is an N×1 vector and all its elements are 1; The poles a of the fitting basis function k After the position is updated, a rational fitting equation in the form of the fitting equation (9) is re-established, and the iterative solution is performed in this way until the rational fitting process converges, so as to obtain the target fitting rational expression.

8. The coupling matrix extraction method according to claim 7, characterized in that, In the said Step 5, when the difference in the positions of the pole a k calculated successively twice is less than the first set threshold value, or the length of the vector is less than the second set threshold value, it is determined that the rational expression fitting process formed converges.

9. The coupling matrix extraction method according to claim 1 or 2, characterized in that, In the Step 7, the basic matrix transformation includes node scale transformation, row-column superposition transformation, and rotation transformation.

10. An electronic device, characterized in that, comprising: a memory, a processor connected to the memory, and instructions stored in the memory and executable by the processor; wherein, when the processor executes the instructions, the method according to any one of claims 1 to 9 is implemented.

Images