CN112464602A

CN112464602A - High-frequency SPICE model establishment method for multi-resonance-point resistor and inductor

Info

Publication number: CN112464602A
Application number: CN202011410609.8A
Authority: CN
Inventors: 杜平安; 潘泽宇; 聂宝林; 李景钦; 韩润; 张宇; 刘颖
Original assignee: University of Electronic Science and Technology of China
Current assignee: University of Electronic Science and Technology of China
Priority date: 2020-12-03
Filing date: 2020-12-03
Publication date: 2021-03-09
Anticipated expiration: 2040-12-03
Also published as: CN112464602B

Abstract

The invention discloses a method for establishing a high-frequency SPICE model of a multi-resonance-point resistor and an inductor, which is applied to the field of modeling and simulation of electronic components and aims at solving the problem that the actual high-frequency models of the multi-resonance-point inductor and the multi-resonance-point resistor cannot be accurately established in the prior art; firstly, testing by an impedance analyzer to obtain amplitude-frequency data and phase-frequency data of an impedance curve of a resistor or an inductor of a model to be established; then establishing an equivalent circuit model according to the obtained amplitude-frequency data and phase-frequency data; obtaining an amplitude-frequency expression of impedance according to the established equivalent circuit model; according to the amplitude-frequency data, the phase-frequency data and the amplitude-frequency expression, performing nonlinear fitting based on a least square method and a particle swarm intelligent optimization algorithm; calculating circuit parameters of the equivalent circuit model; and finally, packaging the circuit parameters and the corresponding equivalent circuit model into an SPICE model.

Description

High-frequency SPICE model establishment method for multi-resonance-point resistor and inductor

Technical Field

The invention belongs to the field of modeling simulation of electronic components, and particularly relates to a high-frequency SPICE model establishing technology for a multi-resonance-point resistor and an inductor.

Background

Resistors and inductors are widely used as basic passive electronic components in various electronic devices. The Resistor (Resistor) is a current limiting element, and after the Resistor is connected in the circuit, the resistance of the Resistor is fixed, generally two pins, which can limit the current passing through the branch connected with the Resistor. Actual devices such as bulbs, heating wires, resistors, etc. may be represented as resistances. The main physical characteristic of the resistor is that the electric energy is changed into heat energy, and the resistor can also be called as an energy consumption element, and the electric current generates internal energy through the energy consumption element. The resistor generally plays a role in voltage division and shunt in the circuit. For signals, both ac and dc signals may pass through resistors. An Inductor (Inductor) is a component that can convert electrical energy into magnetic energy and store the magnetic energy. The inductor is similar in structure to a transformer, but has only one winding. The inductor has a certain inductance value which only impedes the change of the current. If the inductor is in a state where no current is passing, it will try to block the current from flowing through it when the circuit is closed; if the inductor is in a state of passing current, the inductor will try to keep the current unchanged when the circuit is disconnected. The inductor is also called choke, reactor, dynamic reactor. The inductor has the functions of flow resistance, tuning and frequency selection, signal screening, noise filtering, current stabilization, electromagnetic wave interference suppression and the like.

In electromagnetic compatibility, inductors are also often used for filtering to reduce the effect of electromagnetic interference on sensitive devices, resistors can be used to limit the amount of current, and the like. In the process of performing electromagnetic compatibility simulation, SI, PI and other circuit simulation and field circuit collaborative simulation, the high-frequency characteristics of actual resistance and inductance need to be considered, and at this time, the existing high-frequency parasitic parameters of the high-frequency characteristics often need to be noticed, and a corresponding high-frequency model is established. The resistor usually presents a resistance at a low frequency, presents an inductance again as the frequency increases, then presents a capacitance again, and presents a resonance point at the junction of the capacitive area and the inductive area, so that the commonly used resistor high-frequency equivalent circuit model is that an equivalent RL is connected in series and then connected in parallel with a C, as shown in figure 2. The inductor usually appears inductive at low frequency, gradually appears capacitive as the frequency increases, and a resonance point appears at the boundary of the inductive and capacitive areas, and a common inductor high-frequency equivalent circuit model is also shown in fig. 2. The impedance curve of a single resonance point resistance is shown in fig. 3, and the impedance curve of a single resonance point inductance is shown in fig. 4.

However, in practical engineering applications, there are some practical inductors and resistors, impedance characteristics of the inductors and resistors are not only single resonance points, as shown in fig. 5, the equivalent RL series C parallel model of 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 proper equivalent circuit model is available to reflect the impedance characteristics of the resistance and the inductance of the multiple resonance points, no proper method for establishing the resistance and the inductance of the multiple resonance points exists, and the model parameter solving capability is very limited, the high-frequency model of the inductance and the resistance of the multiple resonance points is difficult to be established quickly and accurately. 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 calling of circuit simulation software and the transmission of model data are inconvenient. Comparing files: the power converter conducted electromagnetic interference modeling research [ D ]. tianjin university, 2012, and bin, etc. is modeling an inductor with multiple resonance points, but the modeling method is relatively blind, the accuracy of the established model is low, linear display is adopted, it can be seen from the comparison graph of the modeling impedance curve that the relative error of the impedance amplitude of part of the low impedance frequency point is extremely large, the true credible frequency range of the model is only 1KHz to 1MHz, the applicable frequency width is small, and the phase error comparison is not performed.

Disclosure of Invention

In order to solve the technical problems, the invention provides a high-frequency SPICE model establishment method of multi-resonance-point resistance and inductance, and the model accuracy of circuit simulation such as electromagnetic compatibility of the model is improved.

The technical scheme adopted by the invention is as follows: a method for establishing a high-frequency SPICE model of multi-resonance-point resistance and inductance comprises the following steps:

s1, testing through an impedance analyzer to obtain amplitude-frequency data and phase-frequency data of an impedance curve of the resistance or the inductance of the model to be established;

s2, establishing an equivalent circuit model according to the amplitude-frequency data and the phase-frequency data in the step S1;

s3, obtaining an amplitude-frequency expression of the impedance according to the equivalent circuit model established in the step S2;

s4, according to the amplitude-frequency data and the phase-frequency data in the step S1 and the amplitude-frequency expression in the step S3, performing nonlinear fitting based on a least square method and a particle swarm intelligent optimization algorithm; calculating circuit parameters of the equivalent circuit model;

and S5, packaging the circuit parameters and the corresponding equivalent circuit model into a SPICE model.

Step S2 determines R of equivalent circuit model according to capacitive segment existing in impedance curve_i-L_i-C_iThe number of layers in parallel connection is indicated by subscript i, i is more than or equal to 1, R_i、L_i、C_iRespectively showing the resistance, the inductance and the capacitance of the ith layer in series connection.

The equivalent circuit model of step S2 further includes parallel R₀-L₀And (3) a layer.

The equivalent circuit model of step S2 further includes parallel R_xAnd (3) a layer.

Step S4 includes the following substeps:

s41, initializing parameters, including: the method comprises the following steps of (1) counting the number N of groups, the number d of equivalent circuit parameters, the maximum iteration number ger, a local group updating coefficient p2, the local updating iteration number ger2, the iteration termination precision rsk, 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 parameter range of each equivalent circuit, and randomly generating an initial velocity matrix V in the value range of the variation velocity of the parameters of the equivalent circuit; 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: the individual history optimal solution is a matrix xm, the population history optimal solution is a vector ym, the vector of the fitness function value when the solution is xm is fxm, the fitness function value when the solution is ym is fym, and the current iteration time t is 0;

s44, calculating the fitness function value of each individual solution in the population solution matrix;

s45, re-determining fxm, fym, xm and ym according to the optimal fitness function value of each solution calculated in the step S44;

s46, updating the population solution matrix X and the population velocity matrix V according to the fxm, fym, xm and ym redetermined in the step S5;

s47, updating the population solution matrix X and the population speed matrix V based on the step S46, and repeating the steps S44-S45 to obtain new fxm, fym, xm and ym;

s48, if at least one of the following conditions is met, outputting equivalent circuit parameters; otherwise, return to step S46:

1) whether the fym redetermined in step S45 reaches the iteration termination accuracy rsk;

2) the maximum number of iterations ger is reached.

Step S48 further includes, before returning to step S46: and judging whether the local population initialization condition is met, specifically judging whether the current iteration number t can be evenly divided by the ger2, if so, performing local population solution initialization, and if not, returning to the step S46.

The local population solution initialization is specifically as follows: and carrying out random value taking on the individual solutions of the first N × p2 rows of the population solution matrix within the value range of each parameter.

The invention has the beneficial effects that: the method realizes the accurate modeling of the high-frequency model of the multi-resonance-point resistor and the inductor, and has high impedance characteristic accuracy, thereby improving the model accuracy of circuit simulation such as electromagnetic compatibility of the model. The high-frequency resistor or inductor model is packaged into an SPICE model file, so that the circuit simulation software is convenient to use. The nonlinear equivalent circuit parameter curve fitting algorithm based on the least square method and the particle swarm optimization algorithm can quickly, accurately and effectively calculate the global optimal fitting result in the value range of undetermined parameters of the high-frequency model of the multi-resonance-point resistor and the inductor, so that a quick and effective means is provided for calculating the equivalent circuit parameters of the high-frequency model modeling of the multi-resonance-point capacitor, the fitting speed is extremely high, the impedance phase and amplitude of the multi-resonance resistor and the inductor high-frequency model are more accurately corresponded, the average relative error is optimal, and the recommended parameter value range is provided, so that the value range of the equivalent circuit parameters is more targeted, and the problem that the parameter value range is too large to cause a large sea needle or the parameter value range is too small to contain the optimal solution is solved. The high-frequency equivalent circuit general model of the actual resistance and the inductance constructed in the invention can well reflect the multi-resonance phenomenon of the actual resistance and the inductance, and the model parameters can be solved by the fitting algorithm in the invention to obtain a good solution.

Drawings

FIG. 1 is a main flow diagram of the present invention;

FIG. 2 is a schematic diagram of an equivalent RL series C parallel model of a resistor or an inductor;

FIG. 3 is a graph of the impedance of a single resonance point resistance;

FIG. 4 is a graph of the impedance of a single resonance point inductor;

FIG. 5 is a graph of impedance curves for an actual multi-resonance point inductor;

FIG. 6 is a generalized model of an equivalent circuit of a resistor and an inductor according to the present invention;

FIG. 7 shows a practical inductor with 2R layers according to an embodiment of the present invention_i-L_i-C_iAn inductance high-frequency equivalent circuit model of the structure;

FIG. 8 is a flowchart of a non-linear equivalent circuit parameter curve fitting algorithm with local population initialization based on a least square method and a particle swarm optimization algorithm according to an embodiment of the present invention;

fig. 9 is a comparison diagram of an impedance curve corresponding to an equivalent circuit parameter calculated from a 47uH actual inductance according to an embodiment of the present invention and an actually measured impedance curve;

wherein, fig. 9(a) is a comparison graph of fitting and actual measurement of an impedance amplitude-frequency curve; FIG. 9(b) is a comparison graph of the fit and measured impedance phase frequency curve;

fig. 10 is a circuit model diagram of impedance simulation performed by introducing CST circuit simulation software into a SPICE model of a 47uH multiple resonance point inductor according to an embodiment of the present invention;

fig. 11 is a comparison graph of impedance simulation and actual measurement of an established high-frequency SPICE model of a 47uH multi-resonance-point capacitor according to an embodiment of the present invention;

wherein, fig. 11(a) is a comparison graph of simulation amplitude-frequency curve result and actual measurement amplitude-frequency curve, and fig. 11(b) is a comparison graph of simulation phase-frequency curve result and actual measurement phase-frequency curve;

fig. 12 is an impedance curve diagram of a 10 Ω multiple resonance point resistor according to an embodiment of the present invention;

fig. 13 is a comparison diagram of an impedance curve corresponding to an equivalent circuit parameter calculated by a certain 10 Ω resistance and an actually measured impedance curve according to the embodiment of the present invention;

wherein, fig. 13(a) is a comparison graph of fitting and actual measurement of an impedance amplitude-frequency curve; fig. 13(b) is a comparison graph of the fitting of the impedance phase frequency curve and the actual measurement.

Detailed Description

In order to facilitate the 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 resistor and inductor includes the steps of:

step 1, obtaining impedance amplitude-frequency curve data and impedance phase-frequency curve data of a resistor or an inductor to be modeled, specifically: an impedance curve of an actual 47uH inductor is measured by an impedance analyzer, the measurement range is 40 Hz-110 MHz, the number of measurement points is 801 points, logarithmic frequency sweep is performed in a frequency sweep mode, the measured result is shown in figure 5, and an ASCII file containing amplitude frequency data and phase frequency data is derived.

Step 2, obtaining the impedance curve characteristic of the object to be modeled according to the step 1, and determining a suitable high-frequency equivalent circuit model, specifically: fig. 6 shows a generalized model of a high-frequency equivalent circuit of an actual resistor and inductor according to the present invention. According to the impedance curve characteristic of the 47uH inductor in fig. 5, it can be known that the impedance is sequentially changed with the increase of the frequency in the range of 40Hz to 110MHz, such as resistive (the impedance hardly changes with the increase of the frequency), inductive (the impedance amplitude increases), capacitive (the impedance amplitude decreases), inductive and capacitive, so that there are 2 capacitive segments, and therefore, the equivalent circuit model of the 47uH actual inductor is determined to have 2 layers of R_i-L_i-C_iThe inductance high frequency equivalent circuit model of the structure is shown in fig. 7.

And 3, obtaining an amplitude-frequency expression of the impedance according to the high-frequency equivalent circuit model determined in the step 2: determining an impedance amplitude-frequency expression taking the equivalent circuit parameter as an undetermined coefficient according to the equivalent circuit model of fig. 7 as follows:

Z₀＝R₀+j·2πf·L₀

Z_Rx＝R_x

M(f)＝|Z(f)|

wherein R is₀、L₀、R₁、L₁、C₁、R₂、L₂、C₂、R_xThe equivalent circuit model parameters (solving parameters), f is frequency (independent variable), and Z is₀Representing R at a frequency value f₀-L₀Impedance of the layer, Z₁Representing layer 1R at a frequency value f_i-L_i-C_iImpedance of (Z)₂Representing layer 2R at a frequency value f_i-L_i-C_iImpedance of (Z)_RxRepresents R_xThe impedance of the layer, Z being the total impedance of the entire equivalent circuit model, m (f) representing the impedance magnitude as a function of frequency, and Z (f) representing the impedance as a function of frequency.

And 4, carrying out nonlinear fitting based on a least square method and a particle swarm intelligent optimization algorithm, calculating equivalent circuit parameters, and obtaining an impedance amplitude-frequency curve comparison graph and an impedance phase-frequency curve comparison graph corresponding to fitting data and actual data: and (3) according to the impedance data in the step (1) and the amplitude-frequency expression determined in the step (3), writing a nonlinear fitting program based on a least square method and a particle swarm intelligent optimization algorithm by using matlab, calculating an impedance result corresponding to a corresponding equivalent circuit parameter, and obtaining an amplitude curve comparison graph and a phase curve comparison graph comparing the fitting result with the impedance data obtained in the step (1).

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. 8.

Step S4-1, initializing the overall setting parameters: the population number N, N is 200000; the number d of equivalent circuit parameters is 9; the maximum number of iterations ger, which is 30; the local population update coefficient p2, p2 is 0.85; local update iteration number ger2, ger2 ═ 15; iteration termination precision rsk, which is 1 e-8; value range x of each equivalent circuit parameter_{j lim}＝[x_{j min},x_{j max}](j ═ 1,2,3, …,9), (where x is_{j min}、x_{j max}Lower boundary value and upper boundary representing jth equivalent circuit parameter), and the value range v of the change speed of each equivalent circuit parameter_{j lim}＝[v_{j min},v_{j max}](j＝1,2,3,…,9) (wherein, v_{j min},v_{j max}A lower boundary value and an upper boundary value indicating a change speed of the jth equivalent circuit parameter).

If x_{j lim}(j-1, 2,3, …, d) corresponds to

x_1lim＝[R_0min,R_0max],x_2lim＝[L_0min,L_0max]，

x_3lim＝[R_1min,R_1max],x_4lim＝[L_1min,L_1max],x_5lim＝[C_1min,C_1max],...,x_8lim＝[C_2min,C_2max]，

x_9lim＝[R_{x min},R_{x max}]，

X is then_{j lim}The boundary of (j ═ 1,2,3, …,9) can be selected by the following method:

for x_1limThe values of (a) can be obtained in the following manner,

since the modeling object is an inductance-type element, x can be taken_1min＝0，x_1max＝|Z_f0|*(1+s₂)，(0≤s₂1) or less, wherein | Z_f0L is the minimum frequency f of the low-frequency resistive area₀The impedance magnitude of (d);

from the impedance amplitude-frequency curve shown in fig. 9, the corresponding impedance amplitude at the minimum frequency f0 is found, and | Z is obtained_f0If 0.2419827, x is preferable_1lim＝[0,0.245]。

For x_2limThe values of (a) can be obtained in the following manner,

L′₀＝|Z_f01|/(2πf₀₁)

wherein f is₀₁Is a certain frequency in the middle of the first inductive section, where_f01L is f₀₁The magnitude of the corresponding impedance is such that,

calculating to obtain L'₁＝43.5835e-6，

If the modeling object is an inductance-type element, x can be taken_2min＝L′₀*(1-s₃)，(0≤s₃≤1)，x_2max＝L′₀*(1+s₄)，(0≤s₄≤1)，

Thus, can take x_2lim＝[40e-6,45e-6]。

For x_(3b)limThe values of (b ═ 1,2) can be obtained by,

x_(3b)min＝0，x_(3b)max＝|Z_fb|*(1+s_k)，(b＝1,2)，(0≤s_kless than or equal to 1) for each layer R_i、L_i、C_iR in (1)_iValue range of resistance (wherein | Z)_fbI is the impedance magnitude at the resonance point of the b-th impedance minimum);

from the impedance amplitude-frequency curve shown in FIG. 9, | Z is obtained_f1216.8765, without | Z_f2L, and thus x can be taken_5lim＝[0,220]，x_8lim＝[0,0]。

For x_(3b+2)limThe values of (b ═ 1,2) can be obtained by,

can take x_(3b+2)min＝0，x_(3b+2)max＝C′₁*(1+s_k2)，(b＝1,2)，(0≤s_k2≤1)，C′₁The following can be obtained by the following method,

c 'since the modeling object is an inductance-type element, the first inductance appears first and the first capacitance appears later'₁Can be obtained by the following formula:

C′₁＝C′_1r-l-c＝1/[(2πf₁)²L′₀]

wherein f is₁The frequency at the first maximum resonance point,

solving to obtain C'₁5.3211e-12, so x is preferable_5lim＝[0,10e-12]，x_8lim＝[0,10e-12]。

For x_(3b+1)limThe values of (b ═ 1,2) can be obtained by,

can take x_(3b+1)min＝0，x_(3b+1)max＝L′₁*(1+s_k3)，(b＝1,2)，(0≤s_k3Less than or equal to 1), x can be taken out because the last section is capacitive_7lim＝[0,0]L of wherein'₁The following can be obtained by the following method,

since the modeling object is an inductance-type element, then

L″₁＝1/[(2πf₁)²C′₁]＝1/[(2πf₁)²C′_1r-l-c]

Calculate to obtain L₁＝1.1962e-6，

L″′₁＝|Z_f21|/(2πf₂₁)

Wherein f is₂₁At a certain frequency in the middle of the second inductive section of the inductive device, where_f21L is f₂₁A corresponding impedance magnitude;

calculated L'₁＝7.836e-6，

Then L 'is calculated'₁＝max(L″₁，L″′₁) 7.836e-6, so x is preferable_4lim＝[0,10e-6]，x_7lim＝[0,0]。

For x_9limThe value of (A) can be obtained by the following method,

from the impedance amplitude-frequency curve shown in FIG. 9, | Z is obtained_max41618.77 ≈ 41.6e3, so x may be taken_9lim＝[41.6e3,4160e3]。

To sum up x_{j lim}(j ═ 1,2,3, …,9), i.e., x_1lim＝[0,0.245]，x_2lim＝[40e-6,45e-6]，x_3lim＝[0,220]，x_4lim＝[0,10e-6]，x_5lim＝[0,10e-12]，x_6lim＝[0,0]，x_7lim＝[0,0]，x_8lim＝[0,10e-12]，x_9lim＝[41.6e3,4160e3]。

Wherein v is_{j lim}Can select

(j ═ 1,2,3, …,9), and a is 10.

Step S4-2, generating an initial population solution matrix and an initial population speed matrix, and setting more than or equal to 0 initial solutions: within each equivalent circuit parameter range x_{j lim}＝[x_{j min},x_{j max}](j is 1,2,3, …,9) randomly generating an initial population solution matrix X, and obtaining a value range v of the variation speed of the equivalent circuit parameter_{j lim}＝[v_{j min},v_{j max}]And (j ═ 1,2,3, …,9) randomly generating an initial velocity matrix. Both matrices are N200000 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 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. And then, assigning q row vectors in the generated initial population solution matrix X as the desired set initial value solution (q is a non-negative integer). In this embodiment, q is 0, i.e., an initial value solution is not 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.)

Step S4-3, initializing optimal parameters: the matrix xm is an individual historical optimal solution (including N200000 rows, d 9 columns, each row representing all the optimal values of the historical equivalent circuit parameters of the individual), the vector ym is a population historical optimal solution (including d 9 items, each item representing the corresponding value of the equivalent circuit parameters), 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, the optimal fitness function value is the population historical optimal), and the iteration number t is 0.

Step S4-4, calculating the fitness function value of each individual solution in the population solution matrix: from the 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 value rs corresponding to the solution (parameter value of the equivalent circuit to be determined) of each individual in the population_lgTo obtain the current values ofThe fitness function vector fx (containing N terms, representing the current fitness function value of each individual) corresponding to the individual,

M_lg(f_k)＝log₁₀(M(f_k))

M_lgk＝log₁₀(M_k)

wherein f is_kRepresenting k-th frequency data, k being 1,2,3 …, m (wherein m being 801), in the impedance amplitude frequency data obtained in the step 1; m (f)_k) Denotes the result of step 3 is f_kIs an amplitude-frequency expression of an independent variable; m_kRepresenting the kth impedance amplitude value data in the impedance amplitude-frequency data obtained in the step 1; ylg denotes the actual impedance data M_kAnd 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); rslg is an extended mathematical quantity of the sum of the squares of errors of the common logarithms of the dependent variables, the effect approximating the sum of the squares of errors of the logarithms of the dependent variables. Minimizing rslg to be optimal corresponds to ylg being minimized to be optimal (in this case, the least squares method of the common logarithm of the fit), thus minimizing rs_lgThe minimum is optimally equivalent to an extension of the least squares method.

Step 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 fxm according to the optimal fitness function value of each solution calculated in the step S4-4.

Step S4-6, updating a population solution matrix, a population speed matrix: updating each element V in the population velocity matrix V, V_kjThe updating is performed in the following manner.

v′_kj＝wv_kj+c₁rand₁(xm_kj-x_kj)+c₂rand₂(ym_j-x_kj),(1≤k≤N,1≤j≤d)

Where w is the inertial weight, c₁、c₂For acceleration factor, rand₁And rand₂Is a random number between 0 and 1 generated at random each time, wherein w is 0.8, c₁＝c₂＝1，N＝200000，d＝9。v_kjElements, x, representing the kth row and jth column of the population velocity matrix V_kjThe elements, xm, representing the kth row and jth column of the population solution matrix X_kjThe k row and j column elements, ym, of the optimal solution matrix xm of the population history_jThe jth element of the population history optimal solution vector ym is represented.

V 'for each new element'_kjAnd (3) carrying out boundary limiting treatment: v 'if'_kjExceeding v_{j lim}＝[v_{j min},v_{j max}](j is more than or equal to 1 and less than or equal to 9), and taking the distance v'_kjThe nearest boundary limit is taken as v ″)_kjV 'if in the value range'_kjDirectly as v ″)_kj。

Then, each element X of the population solution matrix X, X is updated_kjThe 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 is 200000, d is 9.

For each new element x'_kjAnd (3) carrying out boundary limiting treatment: x'_kjExceeding x_{j lim}＝[x_{j min},x_{j max}](j is more than or equal to 1 and less than or equal to 9), and taking the distance x 'out of the corresponding value range'_kjThe nearest boundary limit is x ″)_kjX 'if in the value range'_kjDirectly as x ″)_kj. Thereby forming a new X' matrix X ″_kj。

Then all elements v ″', are added_kj(k ═ 1,2,3, …, N), (j ═ 1,2,3, …, d), constitute the updated population velocity matrix V; all elements x ″)_kj(k ═ 1,2,3, …, N), (j ═ 1,2,3, …, d), constitutes the updated population solution matrix X, where N ═ 200000 and d ═ 9.

Step 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 time t by 1.

Step S4-8, judging whether the output condition is reached: and judging whether the population history optimal fitness function value fym reaches the iteration termination precision rsk to be 1e-8 or not and whether the iteration time t reaches the germax iteration time to be 30 or not. If the population history optimal fitness function value fym does not reach the iteration termination precision rsk-8 and the iteration number t does not reach ger-30 maximum iteration number, then step S4-8-1 is executed next; and if the historical optimal fitness function value fym reaches the iteration termination precision rsk-1 e-8 or the iteration number t reaches ger-30 maximum iteration number, executing step S4-9.

Step S4-8-1, judging whether the local population initialization condition is met: it is determined whether t can be divisible by ger 2-15, and if so, step S4-8-2 is executed, and if not, the process returns to step S4-6 again to restart the loop.

Step S4-8-2, local population solution initialization is carried out: local initialization of the population solution matrix X is performed and then returns to step S4-6 to loop again. The local population solution initialization method is to randomly take values in the value range of each parameter for the individual solution (row vector) of the first N × p2 row 170000 rows of the population solution matrix.

And 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. Takes 179.455350 seconds, i.e. fym ═ rs is calculated_lg＝0.014833219513785，

ym(1)＝0.245000000000000＝R0，

ym(2)＝4.382358953254640e-05＝L0,

ym(3)＝220＝R1,

ym(4)＝3.841944051624469e-06＝L1,

ym(5)＝1.537085966318994e-12＝C1,

ym(6)＝0＝R2,

ym(7)＝0＝L2,

ym(8)＝3.754792781933755e-12＝C2,

ym(9)＝4.463100854579426e+04＝Rx。

Wherein f is_kRepresenting k-th frequency data in the impedance amplitude frequency data obtained in the step 1, wherein k is 1,2,3 …, m, and m is 801; m (f)_k) Denotes the result of step 3 is f_kIs an independent variable amplitude-frequency expression; m_kRepresenting the kth impedance amplitude value data in the impedance amplitude-frequency data obtained in the step 1; y represents actual impedance data M_kWith M (f) calculated by high frequency equivalent circuit parameters_k) The sum of the squares of the errors between; rs is an extended mathematical quantity of the sum of squares of errors, and is not taken as an optimal evaluation index in the algorithm, but is taken as a reference index for consideration, because rs is taken as the optimal index, a large number error of high impedance easily occurs to overwhelm a small number error of a low impedance part, so that the problem that the relative error of the low impedance part is large is caused, and the calculation result is that rs is 1.847227197131390e + 02.

A comparison graph of the impedance curve corresponding to the calculated equivalent circuit parameter and the measured impedance is shown in fig. 9, in which fig. 9(a) is a comparison graph of fitting of the impedance amplitude frequency curve and the measured impedance, and fig. 9(b) is a comparison graph of fitting of the impedance phase frequency curve and the 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.

Step 5, compiling the obtained equivalent circuit parameters and the corresponding equivalent circuit model into an SPICE model according to the SPICE grammar rule, 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 the fitted equivalent circuit parameters into a corresponding SPICE model according to the equivalent circuit, wherein the SPICE model comprises the following contents:

substituting the contents of the SPICE model into the CST DS to perform circuit impedance simulation, wherein an impedance simulation circuit model diagram is shown in FIG. 10, and an impedance simulation result and an actually measured comparison diagram of the SPICE model are obtained, as shown in FIG. 11, wherein FIG. 11(a) is an impedance amplitude-frequency curve comparison diagram, and FIG. 11(b) is an impedance phase-frequency curve comparison diagram. The comparison result of the impedance simulation result of the SPICE model and the actual measurement result obtained here illustrates that after the equivalent circuit parameters obtained in the last step and the corresponding equivalent circuit model are packaged into the SPICE model, the accuracy of the built equivalent circuit model is not reduced, and the good matching degree of the impedance curve indicates that no error exists 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.

Now, the method of the present invention is adopted to model a certain 10 ohm resistor, the impedance curve is shown in fig. 12, the modeling steps are basically the same as the steps of establishing the 47uH inductor in the previous embodiment, and important process data occurring in the process of completing modeling are as follows:

since there are 2 capacitive segments, the equivalent circuit model shown in fig. 7 is also taken.

The parameters are set to N200000, p2 0.8, d 9, ger 30, rsk 1e-8, and ger2 10.

The parameter boundary selecting method in the invention is adopted to obtain the parameter boundary of x_1lim＝[9.9,11]，x_2lim＝[0,80e-9]，x_3lim＝[2.6,4]，x_4lim＝[0,150e-9]，x_5lim＝[0,300e-12]，x_6lim＝[0,0]，x_7lim＝[0,0]，x_8lim＝[0,300e-12]，x_9lim＝[119,119e2]。

The method adopts a nonlinear equivalent circuit parameter curve fitting algorithm based on a least square method and a particle swarm intelligent optimization algorithm to calculate equivalent circuit parameters, takes 177.874294 seconds to calculate,

fym＝rs_lg＝0.017113478343242

ym(1)＝R0＝10.035768974755150

ym(2)＝L0＝7.560356871276895e-08

ym(3)＝R1＝2.600000000000000

ym(4)＝L1＝9.016140738376952e-08

ym(5)＝C1＝6.661758370444966e-11

ym(6)＝R2＝0

ym(7)＝L2＝0

ym(8)＝C2＝1.220877193734597e-10

ym(9)＝Rx＝11900

rs＝2.594834727831832

a comparison graph of the impedance curve corresponding to the calculated equivalent circuit parameters and the actually measured impedance is shown in fig. 13, wherein fig. 13(a) is a comparison graph of fitting of an impedance amplitude-frequency curve and actually measured impedance, and fig. 13(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 then packaging the equivalent circuit parameters into a SPICE model according to the determined equivalent circuit schematic diagram, thereby completing the modeling of the high-frequency SPICE model with 10-ohm resistance as shown in FIG. 12. Since the process of packaging the equivalent circuit parameters into the SPICE model does not affect the model precision, the method can be directly demonstrated through the graph 13 that the technical method is also suitable for modeling the multi-resonance-point resistor, the modeling precision is also high, and the modeling speed is also fast.

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

1. A method for establishing a high-frequency SPICE model of a multi-resonance-point resistor and inductor is characterized by comprising the following steps:

2. The method for building the high-frequency SPICE model of the resistance and the inductance of the multiple resonance points as claimed in claim 1, wherein the step S2 is to determine the R of the equivalent circuit model according to the capacitive segment existing in the impedance curve_i-L_i-C_iThe number of layers in parallel connection is indicated by subscript i, i is more than or equal to 1, R_i、L_i、C_iRespectively showing the resistance, the inductance and the capacitance of the ith layer in series connection.

3. The method as claimed in claim 2, wherein the equivalent circuit model of step S2 further includes R connected in parallel₀-L₀And (3) a layer.

4. The method as claimed in claim 3, wherein the equivalent circuit model of step S2 further includes R connected in parallel_xAnd (3) a layer.

5. The method for building the high-frequency SPICE model of the resistance and the inductance with multiple resonance points as claimed in claim 4, wherein the step S4 comprises the following sub-steps:

2) the maximum number of iterations ger is reached.

6. The method as claimed in claim 5, wherein step S48 further comprises, before returning to step S46: and judging whether the local population initialization condition is met, specifically judging whether the current iteration number t can be evenly divided by the ger2, if so, performing local population solution initialization, and if not, returning to the step S46.

7. The method for establishing the high-frequency SPICE model of the multi-resonance-point resistor and inductor according to claim 6, wherein the initialization of the local population solution is specifically as follows: and carrying out random value taking on the individual solutions of the first N × p2 rows of the population solution matrix within the value range of each parameter.