CN115422499A - Coupling matrix extraction method and device based on rational fitting and matrix transformation - Google Patents
Coupling matrix extraction method and device based on rational fitting and matrix transformation Download PDFInfo
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Abstract
The method can accurately extract the coupling matrix corresponding to the current tuning state from the actual measurement or simulation S parameters of a filter, does not depend on the selection of an initial value, and is high in calculation speed.
Description
Technical Field
The application relates to a coupling matrix extraction method, in particular to a coupling matrix extraction method and device based on rational fitting and matrix transformation.
Background
Unlike wired communication, wireless communication is performed 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 in suppressing interfering signals in wireless communication systems. Currently, with the continuous development of mobile communication technology, the popularization of technologies such as internet of things and unmanned driving, the demand of various microwave and millimeter wave filters will continuously increase.
A key problem in designing and manufacturing filters is that their electrical characteristics are sensitive to physical dimensional errors or to variations in material parameters, and even small perturbations in the dimensions of a resonator shift its resonant frequency from within the passband to outside the passband, causing the filter characteristics to deviate substantially from the target response. A filter typically has tens of physical parameters and design variables, and if the measured or simulated filter response does not meet the design criteria, it is difficult to directly determine which units need to be tuned. However, the production process of the filter inevitably has errors, so that accurate debugging at the later stage of the process is indispensable. The traditional solution relies on the technician to determine how to adjust the individual tuning elements based on accumulated experience through observation of the measured responses, which is very challenging, tedious and burdensome, and therefore costly to debug manually.
In order to realize the mechanized automatic debugging of the filter and reduce the production cost, a method for deducing how to debug the filter according to the current filter measurement response is needed, the core technology of the method is circuit model parameter extraction, and the coupling matrix is a universal circuit model for describing various types of filters. The extracted coupling matrix corresponding to the current tuning state is compared with the coupling matrix in the ideal state of the filter to find out the elements with larger difference, and then the filter can be quickly determined to be further debugged according to the corresponding relation between the elements of the coupling matrix 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.
The coupling matrix extraction mainly comprises two categories, namely an optimization method and an analysis method. The optimization method is to try to modify the element values of the coupling matrix through various optimization algorithms on the basis of an initial coupling matrix, so that the difference between the response of the coupling matrix and the measured/simulated S parameters is minimized. Whether the optimization algorithm succeeds or not depends on the selection of the initial value, the optimization algorithm is easy to converge to a local optimal solution to influence the accuracy of an extraction result, and the other limitation of the optimization algorithm is that the matrix extraction speed is low due to large calculation amount to influence the debugging efficiency.
The existing method for analyzing and extracting the coupling matrix simplifies an actual filter model to different degrees, neglects various actual factors, for example, a port transmission line can introduce phase shift which changes along with frequency change, a resonator and a coupling structure can generate power loss, the loss degree of each unit is different, parasitic coupling exists in a filter network, and other factors, so that the precision is poor when the actual filter coupling matrix is extracted, the actual filter is difficult to assist in debugging, and particularly, the high-order filter is difficult to debug.
Disclosure of Invention
Aiming at the problem that the algorithm for analyzing and extracting the coupling matrix is difficult to accurately extract the coupling matrix of the actual filter in the prior art, the application provides a coupling matrix extraction method and electronic equipment based on rational fitting and matrix transformation.
In a first aspect, the application provides a coupling matrix extraction method based on rational fitting and matrix transformation, including the following steps:
step1: acquiring multiple groups of original scattering parameter matrixes of a filter at multiple sampling frequency points respectively
Wherein S is 11 Is the reflection coefficient of the first port of the filter, S 12 Is the inverse transmission coefficient of said filter, S 21 Is the forward transmission coefficient, S, of the filter 22 Is the reflection coefficient of the second port of the filter;
step2: converting the initial scattering parameter matrix S from a physical band-pass domain to a normalized low-pass domain to obtain a low-pass domain scattering parameter matrix
Step3: respectively performing rational fitting on the reflection coefficient of each port in the low-pass domain scattering parameter matrix S ', wherein the order of the rational formula is higher than that of the filter, converting the obtained fitted rational formula into a zero-pole form, calculating the loading phase of the port and the phase shift introduced by the transmission line and changed along with the frequency change by adopting the zero-pole with the distance from the origin greater than the distance threshold, and removing the phase shift from the low-pass domain scattering parameter matrix S ' to obtain the scattering parameter matrix S ' after phase correctionParameter matrix
Step4: converting the scattering parameter matrix S' after phase correction into an admittance parameter matrix
The reference impedance of all ports in the conversion process is 1 ohm;
step5: fitting the elements of the admittance parameter matrix Y using a set of rational equations sharing poles, the number of shared poles being equal to the order of the filter, wherein Y 11 And Y 22 Is in the form of a partial fraction, and Y 12 And Y 21 Is limited to be equal to the number of transmission zeros of the filter, and for Y 12 And Y 21 The fitting data of (2) is weighted, and the smaller the modulus value is, the larger the data weight is;
step6: converting the fitting rational expression of the admittance parameter matrix Y into a pole-residue form, and constructing a transverse coupling matrix M and a capacitance matrix C according to the pole and the residue;
step7: and carrying out a series of basic matrix transformation on the transverse coupling matrix M and the capacitance matrix C to obtain a target coupling matrix corresponding to the actual coupling structure form of the filter.
In one possible implementation form of the method,
the Step3 specifically includes:
the reflection coefficient S of the ith port in the scattering parameter matrix S' in the low-pass domain is measured i ' i Rational formulation is performed according to the following formula (1):
wherein i is taken in {1,2}Value r k And p k Are the kth residue and kth pole, z, respectively k Is the kth zero, d is a constant term, s = j ω, ω is the low-pass angular frequency, j is an imaginary unit, m is a positive integer;
according to the distance from each pole-zero to the origin on the complex plane, rewriting the form of the pole-zero in the formula (1) into the following formula (2);
wherein z is 1 ～z nz Nz zeros, p, respectively, at distances from the origin on the complex plane greater than a distance threshold 1 ～p np Np poles whose distances from the origin on the complex plane are greater than a distance threshold, respectively;
calculating the phase factor alpha of the ith port according to the following formula (3) i ；
Calculating the loading phase of the ith port and the phase shift theta introduced by the transmission line and changed along with the frequency change according to the following formula (4) i (s)；
θ i (s)＝arg(α i )/2 (4)
A phase-shift matrix D is constructed,
removing the phase shift theta of the ith port in the low-pass domain scattering parameter matrix S' by the following formula (5) i (s) obtaining a phase corrected scattering parameter matrix
S”＝DSD (5)
The Step4 specifically comprises the following steps:
through the lower partThe scattering parameter matrix S' after phase correction is converted into an admittance parameter matrix by the formula (6)
The reference impedance of all ports in the conversion process is 1 ohm;
Y＝(I-S”)(I+S”) -1 ＝(I+S”) -1 (I-S”) (6)
wherein I is an identity matrix;
the Step5 specifically comprises the following steps:
performing rational fitting on each element of the admittance parameter matrix Y by the following equation (7):
wherein, the first and the second end of the pipe are connected with each other,
d 11 ,d 22 coefficient to be solved for rational fitting, a k The pole of the fitting basis function, N is the order of the filter, and nfz is the number of transmission zeros;
determine the
d 11 ,d 22 Obtaining a target fitting rational formula based on the formula (7);
converting the target fitting rational into a pole-residue form according to the following formula (8):
wherein p is k Fitting a rationally shared pole to the target,
is Y pq Corresponding to pole p k The residue of (1), pq is combined in {11, 12, 2}1, 22} value, K 11 And K 22 Are each Y 11 And Y 22 Constant terms of rational formulae;
the Step6 specifically includes:
constructing a transverse coupling matrix M with the size of (N + 2) × (N + 2) according to the poles and the residue in the formula (8), wherein the non-zero elements in the transverse matrix M are calculated in the following way:
M 11 ＝K 11 /j，M N+2,N+2 ＝K 22 /j；
and for k =1,2,. N, there are:
M k+1，k+1 ＝jp k ,
if it is
Then
If it is
Then
A capacitance matrix C is constructed which has a size of (N + 2) × (N + 2) and is in the form of a diagonal matrix, and for each diagonal element of the capacitance matrix C, 1 is left except for the first and last ones which are 0.
In a possible implementation manner, in Step1, a plurality of groups of original scattering parameter matrices S of the filter at a plurality of sampling frequency points are obtained by measuring a real object of the filter or simulating a model of the filter, and a sampling frequency range of the measurement or simulation covers a pass band of the filter and resonance frequencies of all relevant resonance modes, where the number of the sampling frequency points is not less than 20.
In a possible implementation, in Step2, according to the formula ω = f 0 /B*(f/f 0 –f 0 Band-pass-low-pass frequencies represented by/f)A mapping relation, wherein the initial scattering parameter matrix S is converted from a physical band-pass domain to a normalized low-pass domain;
wherein f is 0 Is the center frequency of the filter, B is the bandwidth of the filter, and f is the physical frequency.
In a possible implementation manner, in Step3, m is 1 or 2, and the distance threshold is a value in a range from 2 to 5.
In one possible implementation manner, in Step4, the calculation method of each element of the admittance parameter matrix Y is as follows:
in one possible implementation manner, in Step5, a in formula (7) is first adopted k Optionally selecting a set of initial values, and constructing a fitting equation (9) in the following form to solve the coefficient to be solved of rational fitting
d 11 ,d 22 ：
Wherein the data of each frequency point corresponds to one line of the fitting equation (9),
Y pq is a diagonal matrix of size Ns x Ns, Y pq Has a value of Y for the u-th diagonal element pq (s u )，
y pq Is sizeVector of Ns x 1, y pq Has the u-th element value of Y pq (s u )，
W 12 Is a diagonal matrix of size Ns x Ns, W 12 Has a value of the u-th diagonal element of
pq combinations were taken in {11, 12, 21, 22}, u =1,2,3.. Ns;
A 1 is a matrix of size Ns x (N + 1), ns being the number of said sampling frequency points, A 1 The u-th row of elements of (1):
A 2 is a matrix of size Ns N, A 2 The u-th row of elements of (1):
A 3 is a matrix of size Ns x (nfz + 1), A 3 The u-th row of elements of (1):
c 11 ，c 12 ，c 22 and
the four vectors contain the coefficients to be solved for equation (7), where:
wherein the pp combinations take values in {11, 22 };
solving from the fitting equation (9)
The pole a of the fitted basis function is updated as follows k The position of (c):
construction matrix
All eigenvalues of the matrix are solved as poles a of the new fitted basis functions k Where A is a diagonal matrix of size NxN, and the diagonal elements of A are poles a k The original position, b is an N × 1 vector and each element is 1;
fitting the poles a of the basis functions k And after the position of the target object is updated, reconstructing a rational fitting equation in the form of a fitting equation (9), and iteratively solving in the manner until the rational fitting process converges to obtain the target rational.
In one possible implementation, in Step5, when the pole a is calculated twice in succession k Is less than a first set threshold, or vector
Is less than a second set threshold, the established rational fitting process is determined to converge.
In a possible implementation manner, in Step7, the basic matrix transformation includes a node scale transformation, a row and column superposition transformation, and a rotation transformation.
In a second aspect, the present application provides an electronic device, comprising:
a memory for storing a plurality of data files to be transmitted,
a processor connected to the memory, an
Instructions stored in the memory and executable by the processor;
wherein the processor, when executing the instructions, implements the method of the first aspect.
Compared with the coupling matrix extraction method based on optimization, the coupling matrix extraction method based on the optimization does not depend on the selection of the initial value, the calculation speed is high, and the coupling matrix extraction at one time can be completed within seconds. The method can be used for assisting debugging personnel in debugging the microwave millimeter wave filter, and can also be combined with a debugging machine to realize the mechanical automatic debugging of the filter.
Drawings
To more clearly illustrate the technical solutions of the embodiments of the present application, the drawings of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description only relate to some embodiments of the present application and are not limiting to the present application.
Fig. 1 is a flowchart of a method according to an embodiment of the present application.
Fig. 2 is a filter picture according to an embodiment of the present disclosure.
Fig. 3 is a plot of the measured S-parameter amplitude for the filter of fig. 2 in one tuning state.
Fig. 4 is a coupling matrix corresponding to the filter shown in fig. 2, which is obtained by using the coupling matrix extraction method provided in the embodiment of the present application.
Fig. 5 is a capacitance matrix corresponding to the filter shown in fig. 2, which is obtained by using the coupling matrix extraction method provided in the embodiment of the present application.
Fig. 6 is a filter picture according to another embodiment of the present application.
Fig. 7 is a plot of the measured S-parameter amplitude of the filter of fig. 6 in one tuning state.
Fig. 8 is a coupling matrix corresponding to the filter shown in fig. 6, which is obtained by using the coupling matrix extraction method provided in the embodiment of the present application.
Fig. 9 is a capacitance matrix corresponding to the filter shown in fig. 6 obtained by using the coupling matrix extraction method provided in the embodiment of the present application.
Fig. 10 is a schematic process diagram for assisting filter debugging according to an embodiment of the present application.
Detailed Description
In order to make the objects, 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 drawings of the embodiments of the present application. It should be apparent that the described embodiments are only some of the embodiments of the present application, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the described embodiments of the application without any invasive task, are within the scope of protection of the application. It is understood that some of the techniques of the various embodiments described herein may be substituted for or combined with each other without conflict.
In the description of the present application and claims, the terms "first", "second", and the like, if any, are used solely to distinguish one from another as described, and not necessarily in any sequential or technical sense. Thus, an object defined as "first," "second," etc. may explicitly or implicitly include one or more of the object.
Reference throughout this specification to "one embodiment" or "some embodiments," or the like, means that a particular feature, structure, or characteristic described in connection with the embodiment is included in one or more embodiments of the present application. Thus, appearances of the phrases "in one embodiment," "in some embodiments," "in other embodiments," or the like, in various places throughout this specification are not necessarily all referring to the same embodiment, but rather "one or more but not all embodiments" unless specifically stated otherwise.
In order to facilitate the reader to better understand the technical solutions of the embodiments of the present application, the following description first introduces related terms and concepts.
1) S parameter
The scattering parameter is an electrical parameter that can be directly measured in the microwave and millimeter wave frequency band, and the parameter represents the reflection or transmission coefficient between each port of a network.
2) Y parameter
The short-circuit admittance parameter is one of the parameters commonly used for describing the microwave network, and the parameter characterizes the self-admittance of each port and the mutual admittance between the ports. Given the reference impedance of each port of the network, the Y parameter can be converted from the S parameter.
3) Rational type
Rational expressions are univariate expressions whose numerators and denominators are all polynomials. Rational formulae have different forms, common forms include polynomial division forms, pole-zero forms and partial fraction forms.
4) Vector fitting method
A calculation method of rational fitting can directly obtain a pole-residue form of a rational.
5) Coupled resonant network
Passive networks, which may have one to more ports, are formed by coupling a plurality of resonators together in a particular topology, typically used to construct microwave filters, power splitting combiners, matching networks, and the like.
6) Coupling matrix
A matrix model for describing a coupled resonant network, the elements of the coupling matrix usually have a definite correspondence with the physical elements of the filter: each diagonal element corresponds to a resonant mode, the values of the diagonal elements being associated with the resonant mode, and each off-diagonal element corresponds to a normalized coupling coefficient.
7) Capacitor matrix
Another matrix model generated along with the coupling matrix, which together with the coupling matrix functions to describe the circuit model of the filter, requires a capacitance matrix for calculating the coupling matrix response.
8) Transverse coupling matrix
In a special form of the coupling matrix, the first column of the first row and the last column of the last row are non-zero elements, and the central part is a diagonal matrix. The transverse matrix can be constructed directly from the poles and residuals of the Y-parameter polynomial. Other forms of coupling matrices are obtained by applying an equivalent transformation to the transverse coupling matrix.
A coupling matrix extraction method based on rational fitting and matrix transformation according to an embodiment of the present application is described below with reference to fig. 1, and the method includes the following steps:
step1: obtaining a plurality of groups of original scattering parameter matrixes of a filter at a plurality of sampling frequency points respectively
Wherein S is 11 Is the reflection coefficient of the first port of the filter, S 12 Is the inverse transmission coefficient of the filter, S 21 Is the forward transmission coefficient, S, of the filter 22 Is the reflection coefficient of the second port of the filter.
In some embodiments, the multiple sets of original scattering parameter matrices S may be obtained by performing measurements on the filter entities.
In other embodiments, a model of the filter may be simulated to obtain the plurality of sets of raw scattering parameter matrix S.
In Step1, the measured or simulated sampling frequency range preferably covers the pass band 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.
Step2: converting the initial scattering parameter matrix S from the physical band-pass domain to the normalized low-pass domain to obtain a low-pass domain scattering parameter matrix
Wherein, S' 11 And S 11 Corresponding to S' 12 And S 12 Corresponding to S' 21 And S 21 Corresponding to, S' 22 And S 22 And (7) corresponding.
Specifically, the formula ω = f may be expressed 0 /B*(f/f 0 –f 0 Band-pass-low-pass of/f)And (3) frequency mapping relation, namely converting the initial scattering parameter matrix S from a physical band-pass domain to a normalized low-pass domain to obtain the scattering parameter matrix S' of the low-pass domain. Wherein, 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.
The band-pass-low-pass frequency transform establishes a one-to-one correspondence between the physical frequency f and the normalized low-pass angular frequency ω. The frequency conversion is characterized in that the upper and lower passband edge frequencies of the band-pass filter can be respectively mapped to-1 and 1rad/s, and the center frequency f 0 Mapped to 0rad/s, corresponding to the origin of the complex plane.
In Step2, the low-pass angular frequency ω is further converted to a complex frequency s = j ω, which will be the argument of the fitted rational equations in Step3 and Step5 described below.
Step3: the reflection coefficient S 'of the ith port in the low-pass domain scattering parameter matrix S' ii Rational fitting was performed according to the following formula (1):
wherein i is taken as 1,2, i is taken as 1 and 2 respectively, so that the reflection coefficient S ' of the 1 st port in the low-pass domain scattering parameter matrix S ' can be obtained ' 11 And reflection coefficient S 'of 2 nd port' 22 Fitting is carried out according to the formula (1) and the fitting is converted into a zero pole form according to the formula.
In the above formula (1), r k And p k Are the kth residue and kth pole, z, respectively k Is the kth zero; m is a positive integer and represents the number of poles-zero which is more than the order of the filter, and m can be 1 or 2 generally, namely, rational formulas which are slightly higher than the order of the filter are used for respectively fitting the reflection coefficients of all the ports; d is a constant term; s is the complex frequency, in particular s = j ω, where ω is the low-pass angular frequency already described above and j is the imaginary unit.
The pole-zero form in the above equation (1) can be written as the form of the following equation (2) according to the distance of each pole-zero to the origin on the complex plane;
wherein z is 1 ～z nz Nz zeros, p, respectively, at distances from the origin on the complex plane greater than a distance threshold 1 ～p np Respectively np poles at a distance from the origin in the complex plane greater than a distance threshold, it is clear that nz and np are integers.
Specifically, the pole-zero can be classified into two categories according to the distance of the pole-zero from the origin on the complex plane, i.e., the module value of the pole-zero. The first type of zero-pole is close to the origin, namely is less than or equal to a set distance threshold, is a zero-pole generated by resonance and has a large influence on amplitude response; the second type of pole-zero is far away from the origin, which is larger than a set distance threshold, and the pole-zero is generated by the port transmission line, has small influence on amplitude response, and mainly introduces a phase shift which changes along with frequency change. The distance threshold for distinguishing the two types of pole-zero points is preferably in the range of 2-5.
In the above pole-zero expression, equation (2), z nz+1 ～z N+m And p np+1 ～p N+m Is a pole zero of the first type, and z 1 ～z nz And p 1 ～p zp Poles-zero of the second kind, which together with a constant term d form a phase factor α i 。
It is to be understood that the second equal sign of equation (1) is the pole-zero form, and equation (2) further rewrites the pole-zero form in equation (1) to estimate the port phase with the pole-zero farther from the origin for the convenience of discussion.
Then, the phase factor α of the ith port is calculated according to the following equation (3) i ；
As already mentioned above, i is in {12, so that the phase factor α of the 1 st port can be obtained according to the equation (3) 1 And phase factor alpha of 2 nd port 2 。
The loading phase of the ith port and the phase shift introduced by the transmission line as a function of frequency may be determined by a phase factor α i The phase of (2) is calculated, and the specific calculation method is as follows:
the loading phase of the ith port and the phase shift θ introduced by the transmission line as a function of frequency can be calculated by the following equation (4) i (s)；
θ i (s)＝arg(α i )/2 (4)
As mentioned above, i takes the value of {1,2}, so that the loading phase of the 1 st port and the phase shift θ induced by the transmission line and varying with the frequency can be obtained according to equation (4) 1 (s) and the loading phase of the 2 nd port and the phase shift θ introduced by the transmission line as a function of frequency 2 (s)。
When the loading phases of the two ports and the transmission line phases are calculated according to the steps, a phase shift matrix D is constructed,
at this time, the loading phase and the transmission line phase can be removed from the low-pass domain scattering parameter matrix S', and the specific method for removing is as follows:
the phase shift of each port in the low-pass scattering parameter matrix S' is removed by the following equation (5) (i.e., the above-mentioned θ) 1 (s) and θ 2 (s)) to obtain a phase corrected scattering parameter matrix
Wherein, S " 11 And S' 11 Corresponding, S " 12 And S' 12 Corresponding, S " 21 And S' 21 Corresponding, S " 22 And S' 22 And (7) corresponding.
S”＝DSD (5)
As mentioned above, S "is a scattering parameter matrix after phase correction, S is an original scattering parameter matrix obtained by measurement or simulation, and D is a constructed phase shift matrix.
As can be seen from the above, in Step3, the present embodiment utilizes the rational expression containing N + m poles and zeros to reflect the coefficients of each port, i.e., the diagonal elements S of the S parameter matrix ii And respectively performing rational fitting, wherein N is the order of the filter, and m can be 1 or 2 generally, namely, respectively fitting the reflection coefficient of each port by using a rational formula slightly higher than the order of the filter. More specifically, the present embodiment uses a vector fitting method to complete rational formula fitting, obtain a pole-residue form of the rational formula, and then convert the pole-residue form of the rational formula into a zero-pole form.
Step4: converting the scattering parameter matrix S' after phase correction into an admittance parameter matrix by the formula (6)
The reference impedance of all ports in the conversion process is 1 ohm;
Y＝(I-S”)(I+S”) -1 ＝(I+S”) -1 (I-S”) (6)
wherein, I is a unit matrix; s "has been described above as a phase corrected scattering parameter matrix.
By expanding the above formula (6), the specific calculation formulas of each element in the admittance parameter matrix Y are respectively:
step5: each element in the admittance parameter matrix Y is fitted with a rational formula (7) (it is readily apparent that the right part of the equality sign of formula (7) is a set of rational formulas sharing poles):
wherein the content of the first and second substances,
coefficients to be solved for rational fitting (in particular, d) 11 And d 22 Are each Y 11 And Y 22 Constant term of molecular rational formula), a) k N is the order of the filter, and nfz is the number of transmission zeros, for the poles of the fitting basis function. The meaning of S has been explained above for complex frequencies, in particular S = j ω.
Determine the
A target fitting rational equation based on equation (7) is obtained.
Specifically, when the admittance parameter matrix Y is fitted by equation (7), a in equation (7) may be first obtained k A set of initial values is arbitrarily selected, and a fitting equation (9) in the following form is constructed to solve coefficients to be solved for rational fitting
d 11 ,d 22 ：
Wherein, the data of each frequency point corresponds to one line of the fitting equation (9), since for Y 11 、Y 12 (Y 21 ＝Y 12 ) And Y 22 Fitting is performed simultaneously, so that the fitting equation (9) has 3Ns rows in total, and Ns is the number of sampling frequency points (i.e. the number of sampling frequency points).
Y pq Is a diagonal matrix of size Ns x Ns, Y pq Has a value of Y as the u-th diagonal element pq (s u )；
y pq Is a vector of size Ns x 1, y pq Has the u-th element value of Y pq (s u )；
W 12 Is a diagonal matrix of size Ns x Ns, W 12 Has a value of the u-th diagonal element of
Wherein, the pq combination takes values in {11, 12, 21, 22}, namely, the pq combination takes 11, 12, 21 and 22 respectively; u =1,2,3... Ns, i.e. u takes a value in {1,2,3 \8230; \8230ns };
A 1 the matrix is Ns (N + 1), wherein Ns is the number of sampling frequency points, and N is the order of the filter; a. The 1 The u-th row of elements of (1):
A 2 is a matrix of size Ns N, A 2 The u-th row of elements of (1):
A 3 is a matrix of size Ns × (nfz + 1), where nfz is the number of transmission zeros, as already mentioned above; a. The 3 The u-th row of elements of (1):
c 11 ，c 12 ，c 22 and
the four vectors contain the coefficients to be solved for equation (7) above, where:
the pp combination takes values in {11, 22}, and in the three formulas, the superscript T represents the transpose of the matrix.
Solving from the fitting equation (9)
The pole a of the fitted basis function is then updated as follows k The position of (2):
first, a matrix is constructed
All eigenvalues of the matrix are solved as poles a of the new fitted basis functions k Where A is a diagonal matrix of size N, with diagonal elements being poles a k The original position, b is an N × 1 vector and each element is 1, and the superscript T represents the transposition of the matrix; as already mentioned above, N is the order of the filter.
Fitting the poles a of the basis functions k After the position of (3) is updated, a rational fit equation in the form of a fit equation (9) is reconstructed, and iterative solution is performed in this manner until the rational fit process converges, thereby obtaining a target fit rational.
The above-mentioned "convergence" is judged according to
Pole a close to zero vector, or calculated twice in succession k Is kept substantially unchanged, e.g. when the tenth pole a is calculated k And the pole a calculated at the ninth time k Of the position ofWhen the difference is smaller than the set threshold, the rational formula fitting process is considered to be converged, and the target fitting rational formula is obtained.
The target fitting rational is converted into the form of pole-residue according to the following equation (8):
wherein p is k For the poles shared in the target rational,
is Y pq Corresponding to pole p k The pq combination takes the value in {11, 12, 21, 22}, K 11 And K 22 Are each Y 11 And Y 22 Constant terms of rational expressions.
Step6: constructing a transverse coupling matrix M with the size of (N + 2) × (N + 2) according to the poles and the residue in the above formula (8), wherein the non-zero elements in the transverse matrix M are calculated in a mode of:
M 11 ＝K 11 /j，M N+2,N+2 ＝K 22 /j；
and for k =1,2,3 \8230, N, all have:
M k+1，k+1 ＝jp k ,
if it is
Then
If it is
Then
Wherein M is tv Elements representing the ith row and the vth column of the transverse coupling matrix M, e.g. M N+2，k Representing a transverse couplingCombining the elements of the N +2 th row and the k column in the matrix M; as mentioned above, j is the unit of imaginary number and N is the order of the filter.
While constructing the above-described lateral coupling matrix M, a capacitance matrix C having a size of (N + 2) × (N + 2) and in the form of a diagonal matrix is also constructed, for each diagonal element of which 1 is left except for the first and last ones being 0.
Step7: the transverse coupling matrix M and the capacitance matrix C are transformed into a form corresponding to the actual filter coupling structure.
Starting from the constructed initial transverse coupling matrix M and the initial capacitance matrix C, a series of basic matrix transformations are carried out to obtain a target coupling matrix corresponding to the actual coupling structure form of the filter.
In Step7, the basic matrix transformation includes a node scale transformation, a row-column superposition transformation, and a rotation transformation. Wherein:
the node scale transformation comprises the following steps: multiplying all elements of an e-th row and an e-th column of the coupling matrix and the capacitor matrix by a nonzero constant alpha at the same time, wherein e takes a value in {1,2,3 \ 8230; \8230; (N + 2) };
the row-column superposition transformation comprises the following steps: adding beta times of an e-th row of the coupling matrix M and the capacitance matrix C to a g-th row, and adding beta times of an e-th column to the g-th column, wherein g takes values in {1,2, 3' \ 8230; \ 8230; N +2 }; as mentioned above, e takes a value in {1,2,3 \8230, 8230and N +2 };
the rotational transformation includes: multiplying the coupling matrix and the capacitance matrix by a rotation matrix R and a transpose R of the rotation matrix R respectively T . I.e. M' = R T MR,C'＝R T CR。
The fundamental matrix transform includes three types: node scale transformation, row and column superposition transformation and rotation transformation. Transforming the transverse coupling matrix into the coupling matrix of the target structure requires applying a series of fundamental matrix transformations, which generally include multiple steps of node scaling, row-column superposition transformation, and rotation transformation. It can be understood by those skilled in the art that the specific basic transformation sequence is determined by the target coupling matrix structure, and the transformation sequence required by different target coupling matrix structures is different, so that the specific transformation process cannot be uniformly given. For example, the two coupling matrices in fig. 4 and 8 are obtained from the transverse matrices respectively by different transformation orders.
Various fundamental matrix transformations affect the structure and elemental values of the coupling matrix and the capacitance matrix, but do not change the response of the coupling matrix. The kind and order of the elementary matrix transformations implemented will vary for different coupling structures.
Furthermore, an embodiment of the present application further provides an electronic device (for example, a PC), including: a memory, a processor coupled to the memory, instructions stored in the memory and executable by the processor; the processor executes the instructions to implement the coupling matrix extraction method.
Referring to fig. 2, fig. 2 is a first filter provided in an embodiment of the present application, wherein an S-parameter amplitude curve measured in one tuning state of the first filter is shown as scattered data points in fig. 3. The coupling matrix and the capacitance matrix corresponding to the first filter obtained by using the above coupling matrix extraction method are respectively shown in fig. 4 and 5, and the S parameter amplitude responses of the extracted coupling matrix and capacitance matrix are shown by solid lines in fig. 3.
Referring again to fig. 6, fig. 6 is a second filter provided in another embodiment of the present application, wherein the measured S-parameter amplitude curve in one tuning state of the second filter is shown as scattered data points in fig. 7. The coupling matrix and the capacitance matrix corresponding to the second filter obtained by the above coupling matrix extraction method are shown in fig. 8 and 9, respectively, and the S-parameter amplitude responses of the extracted coupling matrix and capacitance matrix are shown in fig. 7 by solid lines.
The coupling matrix extraction method provided by the embodiment of the application can be applied to computer-aided debugging of single-passband and multi-passband microwave and millimeter wave filters, can be combined with simulation software to guide engineers to design the filters, can assist debugging personnel to debug actual filters, and can also be matched with a machine to realize automatic debugging of the filters.
Referring to fig. 10, fig. 10 is a flowchart illustrating a coupling matrix extraction method for computer-aided debugging and mechanized automatic debugging based on rational fitting and matrix transformation according to an embodiment of the present application.
Claims (10)
1. A coupling matrix extraction method based on rational fitting and matrix transformation is characterized by comprising the following steps:
step1: acquiring multiple groups of original scattering parameter matrixes of a filter at multiple sampling frequency points respectively
Wherein S is 11 Is the reflection coefficient of the first port of the filter, S 12 Is the inverse transmission coefficient of said filter, S 21 Is the forward transmission coefficient, S, of the filter 22 Is the reflection coefficient of the second port of the filter;
step2: converting the initial scattering parameter matrix S from a physical band-pass domain to a normalized low-pass domain to obtain a low-pass domain scattering parameter matrix
Step3: respectively performing rational fitting on the reflection coefficient of each port in the scattering parameter matrix S ' of the low pass domain, wherein the order of the rational formula is higher than that of the filter, converting the obtained fitted rational formula into a zero pole form, calculating the loading phase of the port and the phase shift introduced by the transmission line and changed along with the frequency change by adopting the zero pole with the distance from the origin greater than the distance threshold, and removing the phase shift from the scattering parameter matrix S ' of the low pass domain to obtain the scattering parameter matrix S ' after phase correction
Step4: subjecting the phases to phase transformationConverting scattering parameter matrix S' after bit correction into admittance parameter matrix
The reference impedance of all ports in the conversion process is 1 ohm;
step5: fitting the elements of the admittance parameter matrix Y using a set of rational equations sharing poles, the number of shared poles being equal to the order of the filter, wherein Y is 11 And Y 22 Is in the form of a partial fraction, and Y 12 And Y 21 Is limited to be equal to the number of filter transmission zeros, and for Y 12 And Y 21 The fitting data of (3) is weighted, and the data with smaller modulus value has larger weight;
step6: converting the fitting rational expression of the admittance parameter matrix Y into a pole-residue form, and constructing a transverse coupling matrix M and a capacitance matrix C according to the pole and the residue;
step7: and carrying out a series of basic matrix transformation on the transverse coupling matrix M and the capacitance matrix C to obtain a target coupling matrix corresponding to the actual coupling structure form of the filter.
2. The coupling matrix extraction method of claim 1,
the Step3 specifically comprises the following steps:
reflecting coefficient S 'of ith port in the low-pass domain scattering parameter matrix S' ii Rational fitting was performed according to the following formula (1):
wherein i takes the value of {1,2}, r k And p k Respectively the kth residue and the kth pole, z k Is the kth zero, d is a constant term, s = j ω, ω is the low-pass angular frequency, j is the imaginary unit, m is a positive integer;
according to the distance from each zero pole to the origin on the complex plane, rewriting the zero pole form in the formula (1) into the following formula (2);
wherein z is 1 ～z nz Nz zeros, p, respectively, at distances from the origin on the complex plane greater than a distance threshold 1 ～p np Np poles whose distances from the origin on the complex plane are greater than a distance threshold, respectively;
calculating the phase factor alpha of the ith port according to the following formula (3) i ；
Calculating the loading phase of the ith port and the phase shift theta introduced by the transmission line and changed along with the frequency change by the following formula (4) i (s)；
θ i (s)＝arg(α i )/2 (4)
A phase-shift matrix D is constructed,
removing the phase shift theta of the ith port in the scattering parameter matrix S' in the low-pass domain by the following formula (5) i (s) obtaining a scattering parameter matrix after phase correction
S”＝DSD (5)
The Step4 specifically comprises the following steps:
converting the phase-corrected scattering parameter matrix S' into an admittance parameter matrix by the following formula (6)
The reference impedance of all ports in the conversion process is 1 ohm;
Y＝(I-S”)(I+S”) -1 ＝(I+S”) -1 (I-S”) (6)
wherein, I is a unit matrix;
the Step5 specifically comprises the following steps:
performing rational fitting on each element of the admittance parameter matrix Y by the following equation (7):
wherein the content of the first and second substances,
d 11 ,d 22 coefficient to be solved for rational fitting, 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;
determine the
d 11 ,d 22 Obtaining a target fitting rational formula based on the formula (7);
converting the target fitting rational into a pole-residue form according to the following formula (8):
wherein p is k Fitting a rationally shared pole to the target,
is Y pq Corresponding to pole p k The pq combination takes the value in {11, 12, 21, 22}, K 11 And K 22 Are each Y 11 And Y 22 Constant term of rational equation；
The Step6 specifically comprises the following steps:
constructing a transverse coupling matrix M with the size of (N + 2) × (N + 2) according to the poles and the residue in the formula (8), wherein the non-zero elements in the transverse matrix M are calculated in the following way:
M 11 ＝K 11 /j，M N+2,N+2 ＝K 22 /j；
and for k =1,2, \8230;, N, there are:
M k+1，k+1 ＝jp k ,
if it is
Then
If it is
Then
A capacitance matrix C is constructed which has a size of (N + 2) × (N + 2) and is in the form of a diagonal matrix, and for each diagonal element of the capacitance matrix C, 1 is provided except for the first and last ones which are 0.
3. The method for extracting the coupling matrix according to claim 1 or 2, wherein in Step1, a plurality of sets of original scattering parameter matrixes S of the filter at a plurality of sampling frequency points are obtained by measuring an object of the filter or simulating a model of the filter, and the measured or simulated sampling frequency range covers a pass band of the filter and resonance frequencies of all relevant resonance modes, and the number of the sampling frequency points is not less than 20.
4. The coupling matrix extraction method according to claim 1 or 2, characterized in thatIn Step2, according to the formula ω = f 0 /B*(f/f 0 –f 0 A band-pass-low-pass frequency mapping relation represented by/f), and converting the initial scattering parameter matrix S from a physical band-pass domain to a normalized low-pass domain;
wherein, f 0 Is the center frequency of the filter, B is the bandwidth of the filter, and f is the physical frequency.
5. The method according to claim 2, wherein in Step3, m is 1 or 2, and the distance threshold value is a value in a range of 2 to 5.
6. The method of claim 2, wherein in Step4, each element of the admittance parameter matrix Y is calculated as follows:
7. the method of extracting a coupling matrix according to claim 2, wherein Step5 is preceded by a in equation (7) k A set of initial values is arbitrarily selected, and a fitting equation (9) in the following form is constructed to solve coefficients to be solved for rational fitting
d 11 ,d 22 ：
Wherein the data of each frequency point corresponds to one line of the fitting equation (9),
Y pq is a diagonal matrix of size Ns x Ns, Y pq Has a value of Y as the u-th diagonal element pq (s u )，
y pq Is a vector of size Ns x 1, y pq Has the u-th element value of Y pq (s u )，
W 12 Is a diagonal matrix of size Ns x Ns, W 12 Has a value of the u-th diagonal element of
pq combination is valued in {11, 12, 21, 22}, u =1,2,3 \8230; 8230; ns;
A 1 is a matrix of size Ns x (N + 1), ns being the number of said sampling frequency points, A 1 The u-th row of elements of (1):
A 2 is a matrix of size Ns x N, A 2 The u-th row of elements of (1):
A 3 is a matrix of size Ns x (nfz + 1), A 3 The u-th row of elements of (1):
c 11 ，c 12 ，c 22 and
the four vectors include the coefficients to be found for equation (7), where:
wherein the pp combination takes values in {11, 22 };
solving from the fitting equation (9)
Updating the pole a of the fitting basis function in the following way k The position of (2):
construction matrix
All eigenvalues of the matrix are solved as poles a of the new fitted basis functions k Where A is a diagonal matrix of size NxN, and the diagonal elements of A are poles a k The original position, b is an N × 1 vector and each element is 1;
fitting the poles a of the basis functions k After the position of (2) is updated, a rational fitting equation in the form of a fitting equation (9) is reconstructed, and iterative solution is carried out in such a way until the rational fitting process converges, thus obtaining the target rational.
8. The method of claim 7, wherein in Step5, when the sequence is continuous, the method further comprisesPole a calculated twice in sequence k Is less than a first set threshold, or vector
Is less than a second set threshold, the established rational fitting process is determined to converge.
9. The method of claim 1 or 2, wherein in Step7, the basic matrix transformation comprises a node scale transformation, a row-column superposition transformation, and a rotation transformation.
10. An electronic device, comprising:
a memory for storing a plurality of data to be transmitted,
a processor connected to said memory, an
Instructions stored in the memory and executable by the processor;
wherein the processor, when executing the instructions, implements the method of any of claims 1 to 9.
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