CN112464601B - Method for establishing high-frequency SPICE model of multi-resonance-point capacitor - Google Patents
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Abstract
The invention discloses a method for establishing a high-frequency SPICE model of a multi-resonance-point capacitor, which is applied to the field of electronic component modeling and aims at solving the problem that the prior art cannot well solve the modeling problem of the high-frequency model of the multi-resonance-point capacitor; and obtaining impedance data of the capacitor; then determining a high-frequency equivalent circuit model according to the impedance curve of the step S1; secondly, obtaining an amplitude-frequency expression of impedance according to the high-frequency equivalent circuit model; then, according to impedance data of the capacitor and an amplitude-frequency expression, solving by adopting a least square method and a particle swarm intelligent optimization algorithm to obtain an optimal equivalent circuit parameter; and finally, compiling the equivalent circuit parameters into a corresponding SPICE model according to the equivalent circuit.
Description
Technical Field
The invention belongs to the field of electronic component modeling, and particularly relates to a high-frequency SPICE model establishing technology.
Background
The capacitor is widely applied to various electronic products as a passive electronic device, and plays an important role in circuits such as tuning, bypassing, coupling, filtering and the like. For example, a tuning circuit of a transistor radio is used, and a coupling circuit, a bypass circuit, and the like of a color television set are also required.
In electromagnetic compatibility, capacitance is also often used for filtering to reduce the effect of electromagnetic interference on sensitive devices. The high-frequency characteristics of the actual capacitor need to be considered in performing electromagnetic compatibility simulation, SI, PI and other circuit simulation and field circuit collaborative simulation, and at the moment, the existing high-frequency parasitic parameters of the capacitor need to be noticed frequently, and a corresponding high-frequency model is established. The capacitance is usually capacitive at low frequency, inductive at high frequency, and a resonance point appears at the boundary between the capacitive and inductive areas, so the commonly used capacitance high frequency equivalent circuit model is an equivalent RLC series model, as shown in fig. 2. The equivalent RLC series model can reflect the impedance characteristic of capacitive and inductive and a resonance point, which is shown in fig. 3. Nowadays, a high-frequency model of the capacitance is established, an RLC series model is often used, and corresponding RLC equivalent circuit parameters are obtained through data fitting and the like.
However, in practical engineering applications, there are many practical capacitors, and their impedance characteristics have multiple resonance points, as shown in fig. 4, the equivalent RLC series model shown in fig. 2 cannot be used for modeling, otherwise, large errors occur at high frequency when circuit simulation calculations such as electromagnetic compatibility simulation are performed.
Because no suitable equivalent circuit model is available at present to represent the impedance characteristics of the capacitance at multiple resonance points, it is difficult to establish a high-frequency model of the capacitance at multiple resonance points. If the models are established by some hard methods, the problems of complex method, low model precision, no physical significance and the like often exist, and the modeling of the high-frequency model of the multi-resonance-point capacitor cannot be well solved. In addition, the existing high-frequency equivalent circuit model is often in an equivalent circuit form and is not packaged into a model file, so that the circuit simulation software is inconvenient to call and transmit model data.
The prior art has the following problems:
1. the actual high-frequency model of the multi-resonance-point capacitor cannot be accurately established;
2. the high-frequency model is not packaged into a model file, so that the use is inconvenient;
3. the established model has narrow applicable frequency range and model parameters have no actual physical significance;
4. the existing equivalent circuit parameter nonlinear fitting method has the defects of difficult solving, slow speed and poor solving effect when the optimal equivalent circuit parameters of the complex circuit model are solved.
Disclosure of Invention
In order to solve the technical problems, the invention provides a method for establishing a high-frequency SPICE model of a multi-resonance-point capacitor, which realizes the accurate modeling of the high-frequency model of the multi-resonance-point capacitor and has high impedance characteristic accuracy, thereby improving the model accuracy of circuit simulation such as electromagnetic compatibility of the model.
The technical scheme adopted by the invention is as follows: a method for establishing a high-frequency SPICE model of a multi-resonance-point capacitor comprises the following steps:
s1, measuring an impedance curve of a capacitor through an impedance analyzer; and obtaining impedance data of the capacitor;
s2, determining a high-frequency equivalent circuit model according to the impedance curve in the step S1;
s3, obtaining an amplitude-frequency expression of the impedance according to the high-frequency equivalent circuit model in the step S2;
s4, solving by adopting a least square method and a particle swarm intelligent optimization algorithm according to impedance data of the capacitor and the amplitude-frequency expression to obtain the optimal equivalent circuit parameter;
and S5, compiling the equivalent circuit parameters into a corresponding SPICE model according to the equivalent circuit.
Step S1 impedance data includes amplitude-frequency data and phase-frequency data.
The step S2 specifically comprises the following steps: and obtaining the frequency M of capacitive appearance according to the impedance curve characteristics, and determining that the equivalent circuit model of the capacitor is an M-layer parallel structure capacitance high-frequency equivalent circuit model.
The solving process of the step S4 comprises the following steps:
s41, initializing parameters, wherein the parameters comprise: the number of the groups N, the number of the equivalent circuit parameters d, the maximum iteration times ger, the iteration termination precision, the value range of each equivalent circuit parameter and the value range of the change speed of each equivalent circuit parameter;
s42, randomly generating an initial population solution matrix X in the value range of each equivalent circuit parameter, and randomly generating an initial velocity matrix V in the value range of the variation velocity of each equivalent circuit parameter;
each row of data of the population solution matrix X represents all equivalent circuit parameter values obtained by corresponding population individuals, and each element in the row is the value of the corresponding equivalent circuit parameter; each row of data of the population velocity matrix V represents the value variation of all equivalent circuit parameters of corresponding population individuals, and each element in the row is the value variation of the corresponding equivalent circuit parameter;
s43, initializing optimal parameters, including: a matrix xm representing an individual historical optimal solution, a vector ym representing a population historical optimal solution, a vector fxm representing a fitness function value when the solution is xm, a fitness function value fym representing when the solution is ym, and the iteration number t =0;
s44, calculating the fitness function value of each individual solution in the population solution matrix: from the input impedance data matrix [ f, M, P ]]Solving a fitness function rs corresponding to the solution of each individual in the population lg So as to obtain fitness function vectors fx corresponding to each current individual; f. m and P are respectively a column vector, a corresponding frequency, an impedance amplitude and an impedance phase of M rows;
s45, generating the optimal parameters corresponding to the initial solution matrix: based on the optimal fitness function values of the respective solutions calculated in step S44, re-determining an individual historical optimal fitness function value vector fxm, a population historical optimal fitness function value fym, and population historical optimal solution vectors ym corresponding to population individual historical optimal solution matrixes xm and fym corresponding to fxm;
s46, updating a population solution matrix and a population speed matrix;
s47, calculating a fitness function value of each individual solution in the population solution matrix, and updating optimal parameters: returning to the step S44, calculating the fitness function value of each individual solution in the population matrix again, then updating the optimal parameters again according to the step S45, and increasing the iteration times t by 1;
s48, judging whether the output condition is met: if the population history optimal fitness function value fym does not reach the iteration termination precision and the iteration time t does not reach the maximum iteration time ger, returning to the step S46; otherwise, executing step S49;
and S49, finally obtaining the solution of each individual, namely the optimal equivalent circuit parameter.
The invention has the beneficial effects that: the method realizes accurate modeling of the high-frequency model of the multi-resonance-point capacitor, and has high impedance characteristic accuracy, thereby improving the model accuracy of circuit simulation such as electromagnetic compatibility of the model; the invention encapsulates the high frequency model into SPICE model file, thereby facilitating the use of circuit simulation software; the nonlinear equivalent circuit parameter curve fitting algorithm based on the least square method and the particle swarm intelligent optimization algorithm can quickly, accurately and effectively calculate the global optimal fitting result in the parameter value range, thereby providing a quick and effective means for calculating the equivalent circuit parameters of the high-frequency model modeling of the multi-resonance-point capacitor, and the fitting speed is extremely high;
the nonlinear equivalent circuit parameter curve fitting algorithm based on the least square method and the particle swarm intelligent optimization algorithm has the advantages that as the logarithm (common logarithm) of the impedance amplitude is selected as the optimal evaluation index of the least square extension, the error rate of the equivalent circuit parameter which is equivalent to solution is minimum, so that the precision of the impedance detail is considered, and the problem that the error of the decimal is submerged by the error of the decimal is prevented;
the nonlinear equivalent circuit parameter curve fitting algorithm based on the least square method and the particle swarm intelligent optimization algorithm can set an initial solution, a limited parameter range of the solution and the speed and a method for selecting the parameter value range of the suggested capacitance equivalent circuit model, so that the optimization of equivalent circuit parameters is more targeted;
the nonlinear equivalent circuit parameter curve fitting algorithm based on the least square method and the particle swarm intelligent optimization algorithm has 2 different random numbers in each element of the solution matrix when the solution matrix is updated every time, so that the solution matrix with N rows and d columns has N x d x 2 random numbers when the solution matrix with N rows and d columns is updated every time, all positions in the element change path can be searched, and the global optimization capability is greatly exerted;
the general model of the actual capacitance high-frequency equivalent circuit constructed by the invention can well reflect the multi-resonance phenomenon of the actual capacitance, and the model has actual physical significance.
Drawings
FIG. 1 is a main flow diagram of the present invention;
FIG. 2 is a schematic diagram of an equivalent RLC series model of a capacitor;
FIG. 3 is a graph of impedance curves for a practical single resonance point capacitance;
FIG. 4 is a graph of impedance of an actual capacitor measured according to an embodiment of the present invention;
FIG. 5 is a generalized model of a capacitive high-frequency equivalent circuit according to the present invention;
fig. 6 is a high-frequency equivalent circuit model of a capacitor with a 3-layer parallel structure of a certain actual capacitor provided in an embodiment of the present invention;
FIG. 7 is a flowchart of a nonlinear equivalent circuit parameter curve fitting algorithm based on a least square method and a particle swarm optimization algorithm provided by the embodiment of the invention;
fig. 8 is a comparison diagram of an impedance curve corresponding to the calculated equivalent circuit parameter and an actually measured impedance curve according to the embodiment of the present invention;
wherein, fig. 8 (a) is a comparison graph of fitting and actual measurement of impedance amplitude-frequency curve, and fig. 8 (b) is a comparison graph of fitting and actual measurement of impedance phase-frequency curve;
FIG. 9 is SPICE model contents of the multi-resonance-point capacitor established according to the embodiment of the present invention;
fig. 10 is a circuit model diagram of impedance simulation performed by introducing CST circuit simulation software into the SPICE model of the multi-resonance-point capacitor according to the embodiment of the present invention;
fig. 11 is an impedance simulation and actual measurement comparison diagram of the high-frequency SPICE model of the multi-resonance-point capacitor established according to the embodiment of the present invention;
fig. 11 (a) is a comparison graph of a simulation amplitude-frequency curve result and an actual measurement amplitude-frequency curve, and fig. 11 (b) is a comparison graph of a simulation phase-frequency curve result and an actual measurement phase-frequency curve.
Detailed Description
In order to facilitate understanding of the technical contents of the present invention by those skilled in the art, the present invention will be further explained with reference to the accompanying drawings.
As shown in fig. 1, a method for establishing a high-frequency SPICE model of a multi-resonance-point capacitor includes the steps of:
Since each layer has too high impedance with increasing frequency due to the inductance, a low impedance path needs to be restarted for impedance reduction, which needs to be realized by the capacitance of a new layer (if the inductance is directly appeared, the path cannot be passed). Each layer firstly shows capacitance and then shows inductance, and shows resistance at the turning point, so that the number of parallel layers can be determined by the capacitive section.
for example, for the general model of fig. 5, the corresponding impedance amplitude-frequency expression is obtained as follows:
the impedance expression of the kth layer is formula (1), where k =1,2, 3.. N;
the impedance expression of fig. 5 is formula (2):
the general impedance amplitude-frequency expression corresponding to fig. 5 is formula (3):
M(f)＝|Z(f)| (3)
in the formulae (1), (2) and (3), f is an independent variable, Z k Is the impedance of the k-th layer, Z is the total impedance of FIG. 5, R k ，L k ，C k The values of resistance, inductance, and capacitance in the kth layer, respectively.
Determining an impedance amplitude-frequency expression taking the equivalent circuit parameter as an undetermined coefficient according to the equivalent circuit model of fig. 6 as follows:
M(f)＝|Z(f)| (5)
wherein R is 1 、L 1 、C 1 、R 2 、L 2 、C 2 、R 3 、L 3 、C 3 The equivalent circuit model parameters (solution parameters) are equal to f, the frequency (independent variable), the impedance is Z, and the impedance amplitude is expressed by M (f) in a function of the frequency.
The nonlinear equivalent circuit parameter curve fitting algorithm based on the least square method and the particle swarm intelligent optimization algorithm is concretely as follows. The flow chart is shown in fig. 7.
S4-1, initializing total setting parameters, namely the number of the population N =200000, the number of the equivalent circuit parameters d =9, the maximum iteration number ger =30, the iteration termination precision rsk =1e-8, and the value range x of each equivalent circuit parameter jlim ＝[x jmin ,x jmax ](j＝1,2,3,…,9)，x jmin 、x jmax Respectively showing the lower boundary value and the upper boundary of the jth equivalent circuit parameter, and the value range v of the change speed of each equivalent circuit parameter jlim ＝[v jmin ,v jmax ](j＝1,2,3,…,9)，v jmin ,v jmax Respectively representing the lower boundary value and the upper boundary value of the jth equivalent circuit parameter change speed.
If x jlim (j =1,2,3, \ 8230;, 9) corresponds to
x 1lim ＝[R 1min ,R 1max ],x 2lim ＝[L 1min ,L 1max ],x 3lim ＝[C 1min ,C 1max ],...,x 9lim ＝[C 3min ,C 3max ]，
Then x jlim The boundary of (j =1,2,3, \ 8230;, 9) may take the following parameters: x is a radical of a fluorine atom (3b-2)min ＝0，x (3b-2)max ＝|Z b |*(1+s k )，(b＝1,2,3)，(0≤s k Less than or equal to 1), is the value range of each layer resistance, | Z b And | is the impedance magnitude at the resonance point of the b-th impedance minimum.
Obtaining | Z from impedance data 1 |＝4.781228，|Z 2 | =57.20618, without | Z 3 L, thus calculating x 1lim ＝[0,5]，x 4lim ＝[0,60]，x 7lim ＝[0,0]。
C′ 1 ＝1/(2πf 0 |Z 0 |)，
Wherein f is 0 A frequency before the first resonance point, where 0 L is f 0 Corresponding impedance magnitude
Calculating to obtain C' 1 ＝787.983e-12。
x 3min ＝C′ 1 *(1-s 1 )，x 3max ＝C′ 1 *(1+s 2 )，(0≤s 1 ≤1,0≤s 2 ≤1)
Thus taking x 3lim ＝[750e-12,800e-12]。
L′ 1 ＝1/[(2πf 1 ) 2 C′ 1 ]，f 1 At the frequency of the first resonance point
Calculating to obtain L' 1 ＝6.8734e-6。
x (3b-1)min ＝0，x (3b-1)max ＝L′ 1 *(1+s 3 ) (generally 0. Ltoreq. S) 3 ≤1)，(b＝1,2,3)
Thus taking x 2lim ＝[0,7.5e-6]，x 5lim ＝[0,7.5e-6]，x 8lim ＝[0,7.5e-6]。
C′ 2 ＝1/[(2πf 2 ) 2 L′ 1 ]Wherein f is 2 At the frequency of the second resonance point
Calculating to obtain C' 2 ＝5.095e-12。
x (3b)min ＝0，x (3b)max ＝C′ 2 *(1+s 4 ) (generally 0. Ltoreq. S) 4 ≤1)，(b＝2,3)，
Thus taking x 6lim ＝[0,6e-12]，x 9lim ＝[0,6e-12]。
To sum up x jlim (j =1,2,3, \ 8230;, 9), which is x 1lim ＝[0,5]，x 2lim ＝[0,7.5e-6]，x 3lim ＝[750e-12,800e-12]，x 4lim ＝[0,60]，x 5lim ＝[0,7.5e-6]，x 6lim ＝[0,6e-12]，x 7lim ＝[0,0]，x 8lim ＝[0,7.5e-6]，x 9lim ＝[0,6e-12]。
And v is jlim Is convenient to use
(j =1,2,3, \8230;, 9), and a is 10.
S4-2, generating an initial population solution matrix and an initial population speed matrix, and setting a small number of initial solutions in each equivalent circuit parameter range x jlim ＝[x jmin ,x jmax ](j =1,2,3, \8230;, 9) randomly generating an initial population solution matrix X in a value range v of the variation speed of the equivalent circuit parameters jlim ＝[v jmin ,v jmax ](j =1,2,3, \ 8230;, 9) randomly generates an initial velocity matrix. Both matrices are N =200000 rows and d =9 columns. Each row of data of the population solution matrix X represents all equivalent circuit parameter values obtained by corresponding population individuals, and each element in the row is the corresponding equivalent circuit parameterA value; each row of data of the population velocity matrix V represents the value variation of all equivalent circuit parameters of corresponding population individuals, and each element in the row represents the value variation of the corresponding equivalent circuit parameter. Then, q row vectors in the generated initial population solution matrix X are assigned to the desired initial value solutions (q is a non-negative integer), in this embodiment, q =0, that is, none of the initial value solutions is set. (if repeated operation can take the calculation result obtained last time as an initial value solution, so that inheritance of good solution can be realized, and the solution can be better and better in the next time.)
S4-3, initializing optimal parameters: the matrix xm is an individual historical optimal solution (including N =200000 rows and d =9 columns, each row represents all equivalent circuit parameter values of the individual optimal historical optimal), the vector ym is a population historical optimal solution (including d =9 items, each item represents a corresponding equivalent circuit parameter value), fxm is a vector of fitness function values when the solution is xm (including N items, representing the historical optimal fitness function values of each individual), fym is a fitness function value when the solution is ym (1 item, representing the optimal fitness function value of the population historical optimal), and the iteration number t =0.
S4-4, calculating the fitness function value of each individual solution in the population solution matrix: from the input impedance data matrix [ f, M, P ]]F, M and P are column vectors of M rows respectively, corresponding to frequency, impedance amplitude and impedance phase, and solving a fitness function rs corresponding to a solution (undetermined equivalent circuit parameter value) of each individual in the population lg To obtain a fitness function vector fx (containing N terms, representing the current fitness function value of each individual) corresponding to each individual at present,
M lg (f k )＝log 10 (M(f k ))
M lgk ＝log 10 (M k )
wherein f is k K =1,2,3 \ 8230in impedance amplitude frequency data obtained in step 1, (wherein m = 801); m (f) k ) Denotes the result of step 3 is f k Is an amplitude-frequency expression of an independent variable; m is a group of k Representing the kth impedance amplitude value data in the impedance amplitude-frequency data obtained in the step 1; y is lg Representing actual impedance data M k And M (f) calculated by the parameters of the undetermined high-frequency equivalent circuit k ) The sum of squared errors between the common logarithms of (c); rs lg Is an extended mathematical quantity of the sum of the squared errors of the common logarithms of the dependent variables, and the effect is similar to the sum of the squared errors of the logarithms of the dependent variables. Make rs lg The minimum to the optimum is equivalent to y lg The minimum is optimal (in this case least squares of the common logarithm of the fit), thus making rs lg The minimum is optimally equivalent to an extension of the least squares method.
S4-5, generating the optimal parameters corresponding to the initial solution matrix: and re-determining the individual history optimal fitness function value vector fxm, the population history optimal fitness function value fym and the population history optimal solution vector ym corresponding to the population individual history optimal solution matrix xm and fym corresponding to the individual history optimal solution vector fxm and the population history optimal solution vector ym corresponding to the population history optimal solution matrix fym which are calculated in the step S4-4.
Step S4-6, updating a population solution matrix, wherein the population speed matrix is as follows: updating each element V in the population velocity matrix V, V kj The updating is performed in the following manner.
v′ kj ＝wv kj +c 1 rand 1 (xm kj -x kj )+c 2 rand 2 (ym j -x kj ),(1≤k≤N,1≤j≤d)
Where w is the inertial weight, c 1 、c 2 For acceleration factor, rand 1 And rand 2 To calculate a single v 'at a time' kj Random numbers between 0 and 1 are randomly regenerated by the elements. Wherein w =0.8,c is taken 1 ＝c 2 =1,n =200000,d =9. Wherein v is kj Elements, x, representing the kth row and jth column of the population velocity matrix V kj Elements, xm, representing the kth row, jth column of the population solution matrix X kj The k row and j column elements, ym, of the optimal solution matrix xm of the population history j The jth element of the population history optimal solution vector ym is represented.
V 'for each new element' kj And (3) carrying out boundary limiting treatment: v 'if' kj Exceeding v jlim ＝[v jmin ,v jmax ](j is more than or equal to 1 and less than or equal to 9), and taking the distance v' kj Let the nearest boundary value be v ″) kj V 'if the number is within the value range' kj Directly as v' kj 。
Then, each element X of the population solution matrix X, X is updated kj The updating is performed in the following manner.
x′ kj ＝x kj +v″ kj ,(k＝1,2,3,…,N),(j＝1,2,3,…,d)
Wherein N =200000, d =9.
For each new element x' kj And (3) carrying out boundary limiting treatment: x' kj Exceeding x jlim ＝[x jmin ,x jmax ] (1≤j≤9) Taking the distance x 'out of the corresponding value range' kj Taking the nearest boundary limit as x ″) kj X 'if in the value range' kj Directly as x ″) kj . Thereby forming a new X' matrix X ″ kj ；
Then all elements v ″', are added kj (k =1,2,3, \8230;, N), (j =1,2,3, \8230;, d), constituting an updated population velocity matrix V; all elements x ″) kj (k =1,2,3, \8230;, N), (j =1,2,3, \8230;, d), constituting an updated population solution matrix X, where N =200000, d =9.
S4-7, calculating the fitness function value of each individual solution in the population solution matrix, and updating the optimal parameters: and (4) calculating the fitness function value of each individual solution in the population matrix again according to the step S4-4, updating the optimal parameters again according to the step S4-5, and increasing the iteration times t by 1.
S4-8, judging whether an output condition is reached: and if the population history optimal fitness function value fym does not reach the iteration termination precision rsk =1e-5 and the iteration time t does not reach ger =30 maximum iteration time, repeating the steps S4-6 and S4-7 until the population history optimal fitness function value fym reaches the iteration termination precision rsk =1e-8 or the iteration time t reaches ger =30 maximum iteration time.
S4-9, outputting the equivalent circuit parameter fitting result: the fitted optimal equivalent circuit parameter vector is ym, and the fitness function value when the optimal equivalent circuit parameter vector is fym. The time is 94.256268 seconds
fym＝rs lg ＝0.01420800777564,
ym(1)＝5＝R1,
ym(2)＝6.97888839234103e-6＝L1,
ym(3)＝7.660348222373256e-10＝C1,
ym(4)＝59.749359838926239＝R2,
ym(5)＝5.932947578354753e-6＝L2,
ym(6)＝1.206748444999840e-12＝C2,
ym(7)＝0＝R3,
ym(8)＝2.475743448581526e-8＝L3,
ym(9)＝3.591637605725691e-12＝C3。
Wherein f is k K =1,2,3 \ 8230in impedance amplitude frequency data obtained in step 1, wherein m =801; m (f) k ) Denotes the result obtained in step S3 is f k Is an independent variable amplitude-frequency expression; m k Representing the kth impedance amplitude value data in the impedance amplitude-frequency data obtained in the step 1; y represents actual impedance data M k With M (f) calculated by high frequency equivalent circuit parameters k ) The sum of squared errors between; rs is the extended mathematical quantity of the sum of squared errors. Calculated rs =2.170112502692959e +4.
A comparison graph of the impedance curve corresponding to the calculated equivalent circuit parameters and the actually measured impedance is shown in fig. 8, wherein fig. 8 (a) is a comparison graph of fitting of an impedance amplitude-frequency curve and actually measured impedance, and fig. 8 (b) is a comparison graph of fitting of an impedance phase-frequency curve and actually measured impedance; it can be seen that the impedance curve fitting and the actually measured comparison graph herein illustrate that the solved equivalent circuit parameters of the modeling and the impedance characteristics reflected by the corresponding equivalent model are very consistent with the reality, which directly illustrates that the modeling precision of the finally established equivalent circuit model is very high.
And 5, generating an SPICE model, substituting the SPICE model into simulation software for simulation, and obtaining an impedance amplitude-frequency curve comparison graph and an impedance phase-frequency curve comparison graph between the impedance of the SPICE model and the actually measured impedance: writing a corresponding SPICE model according to the fitted equivalent circuit parameters and the equivalent circuit, wherein the content of the SPICE model is shown in figure 9 and substituted into CST DS for circuit impedance simulation, and an impedance simulation circuit model diagram is shown in figure 10, so that an impedance simulation result and an actually measured comparison diagram of the SPICE model are obtained, as shown in figure 11, wherein figure 11 (a) is an impedance amplitude-frequency curve comparison diagram, and figure 11 (b) is an impedance phase-frequency curve comparison diagram; the comparison result of the impedance simulation result and the actual measurement result of the SPICE model obtained here illustrates that after the equivalent circuit parameters and the corresponding equivalent circuit model obtained in the previous step are packaged into the SPICE model, the precision of the built equivalent circuit model is not reduced, and the impedance curve has good coincidence degree, which indicates that no error occurs in the packaging process. The formed SPICE model is a high-frequency SPICE model of a multi-resonance-point capacitor which is finally used, and the impedance curve coincidence degree is good, so that the modeled model is consistent with the reality. The impedance curve is the most important electrical parameter of the passive device (resistance, capacitance and inductance), and the more the impedance curve is matched with the reality, the higher the description precision is, and the wider the matching frequency width is, the wider the applicable frequency range of the model is.
It will be appreciated by those of ordinary skill in the art that the embodiments described herein are intended to assist the reader in understanding the principles of the invention and are to be construed as being without limitation to such specifically recited embodiments and examples. Various modifications and alterations to this invention will become apparent to those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the claims of the present invention.
Claims (6)
1. A method for establishing a high-frequency SPICE model of a multi-resonance-point capacitor is characterized by comprising the following steps:
s1, measuring an impedance curve of a capacitor through an impedance analyzer; and obtaining impedance data of the capacitor;
s2, determining a high-frequency equivalent circuit model according to the impedance curve in the step S1;
s3, obtaining an amplitude-frequency expression of the impedance according to the high-frequency equivalent circuit model in the step S2;
s4, solving by adopting a least square method and a particle swarm intelligent optimization algorithm according to impedance data of the capacitor and the amplitude-frequency expression to obtain the optimal equivalent circuit parameter; the solving process of the step S4 is as follows:
s41, initializing parameters, wherein the parameters comprise: the number of the groups N, the number of the equivalent circuit parameters d, the maximum iteration times ger, the iteration termination precision, the value range of each equivalent circuit parameter and the value range of the change speed of each equivalent circuit parameter;
s42, randomly generating an initial population solution matrix X in the value range of each equivalent circuit parameter, and randomly generating an initial velocity matrix V in the value range of the variation velocity of each equivalent circuit parameter;
each row of data of the population solution matrix X represents all equivalent circuit parameter values obtained by corresponding population individuals, and each element in the row is the value of the corresponding equivalent circuit parameter; each row of data of the population velocity matrix V represents the value variation of all equivalent circuit parameters of corresponding population individuals, and each element in the row is the value variation of the corresponding equivalent circuit parameter;
s43, initializing optimal parameters, including: a matrix xm representing an individual historical optimal solution, a vector ym representing a population historical optimal solution, a vector fxm representing a fitness function value when the solution is xm, a fitness function value fym representing when the solution is ym, and the iteration number t =0;
s44, countingCalculating the optimal fitness function value of each individual solution in the population solution matrix: from the input impedance data matrix f, M, P]Solving a fitness function rs corresponding to the solution of each individual in the population lg So as to obtain fitness function vectors fx corresponding to each current individual; f. m and P are column vectors of M rows respectively, and correspond to frequency, impedance amplitude and impedance phase;
s45, generating the optimal parameters corresponding to the initial solution matrix: based on the optimal fitness function values of the respective solutions calculated in step S44, re-determining an individual historical optimal fitness function value vector fxm, a population historical optimal fitness function value fym, and population historical optimal solution vectors ym corresponding to population individual historical optimal solution matrixes xm and fym corresponding to fxm;
s46, updating a population solution matrix and a population speed matrix;
s47, calculating a fitness function value of each individual solution in the population solution matrix, and updating the optimal parameters: returning to the step S44, calculating the fitness function value of each individual solution in the population matrix again, then updating the optimal parameters again according to the step S45, and increasing the iteration times t by 1;
s48, judging whether the output condition is met: if the historical optimal fitness function value fym of the population does not reach the iteration termination precision and the iteration times t does not reach the maximum iteration times ger, returning to the step S46; otherwise, executing step S49;
s49, finally obtaining the solution of each individual, namely the optimal equivalent circuit parameter;
and S5, compiling the equivalent circuit parameters into a corresponding SPICE model according to the equivalent circuit.
2. The method for establishing the high-frequency SPICE model of the multi-resonance-point capacitor as claimed in claim 1, wherein the impedance data in step S1 comprises amplitude frequency data and phase frequency data.
3. The method for establishing the high-frequency SPICE model of the multi-resonance-point capacitor as claimed in claim 1, wherein the step S2 is specifically as follows: and obtaining the frequency M of capacitive appearance according to the impedance curve characteristics, and determining that the equivalent circuit model of the capacitor is an M-layer parallel structure capacitance high-frequency equivalent circuit model.
4. The method for building the high-frequency SPICE model of the multi-resonance-point capacitor as claimed in claim 1, wherein the step S4 is to make the fitness function rs lg The minimum value of the impedance is the optimum, and the logarithm of the impedance amplitude is specifically selected as the optimum evaluation index of the least square extension.
5. The method for establishing the high-frequency SPICE model of the multi-resonance-point capacitor according to claim 1, wherein the elements in the population velocity matrix are updated in step S46 by adopting the following formula:
v' kj ＝wv kj +c 1 rand 1 (xm kj -x kj )+c 2 rand 2 (ym j -x kj ),(1≤k≤N,1≤j≤d)
where w is the inertial weight, c 1 、c 2 For acceleration factor, rand 1 And rand 2 To calculate a single v 'at a time' kj Random number between 0 and 1, v, of random regeneration of elements kj Elements, x, representing the kth row and jth column of the population velocity matrix V kj The elements, xm, representing the kth row and jth column of the population solution matrix X kj The k row and j column elements, ym, of the optimal solution matrix xm of the population history j The jth element of the population history optimal solution vector ym is represented, N represents the row number of the population speed matrix, and d represents the column number of the population speed matrix.
6. The method for building a high-frequency SPICE model of a multi-resonance-point capacitor according to claim 5, wherein step S46 is implemented by updating elements in a population solution matrix according to the following formula:
x' kj ＝x kj +v″ kj ,(k＝1,2,3,…,N),(j＝1,2,3,…,d)
for each v' kj And (3) carrying out boundary limiting treatment: v 'if' kj Exceeding v jlim ＝[v jmin ,v jmax ]Outside the corresponding range of values of the first and second,then take distance v' kj The nearest boundary limit is designated as v ″) kj V 'if the number is within the value range' kj Directly as v ″) kj ；
Wherein, x' kj And (4) representing the elements of the kth row and the jth column after the updating of the population solution matrix X.
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