CN116205185A - MMIC passive device equivalent circuit model parameter extraction method based on gray wolf algorithm - Google Patents

MMIC passive device equivalent circuit model parameter extraction method based on gray wolf algorithm Download PDF

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CN116205185A
CN116205185A CN202310278530.1A CN202310278530A CN116205185A CN 116205185 A CN116205185 A CN 116205185A CN 202310278530 A CN202310278530 A CN 202310278530A CN 116205185 A CN116205185 A CN 116205185A
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刘海文
宋泽人
王思栋
田洪亮
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Xian Jiaotong University
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Abstract

The invention discloses a method for extracting parameters of an MMIC passive device equivalent circuit model based on a gray wolf algorithm, which comprises the following steps: determining an equivalent circuit model and parameters of the MMIC passive device according to the type of the MMIC passive device; iteratively updating parameters in the equivalent circuit model by using a gray wolf algorithm; calculating a model fitted scattering parameter according to the equivalent circuit model based on the updated parameters; calculating an error value between the scattering parameter fitted by the model and the scattering parameter of the device obtained by testing by using an error function; judging whether the error value is smaller than or equal to the error threshold value, if so, completing the extraction of the equivalent circuit model parameters of the MMIC passive device, otherwise, performing iterative updating again; the method and formula analysis based on the method do not need to perform equivalent circuit model parameter calculation, the extraction difficulty is not increased due to the complexity increase of the topology structure of the equivalent circuit model, the extraction speed is higher, secondary fitting is not needed, and the fitting precision is high.

Description

MMIC passive device equivalent circuit model parameter extraction method based on gray wolf algorithm
Technical Field
The invention belongs to the technical field of semiconductors and integrated circuits, and particularly relates to a parameter extraction method for an MMIC passive device equivalent circuit model based on a gray wolf algorithm.
Background
MMICs, monolithic microwave integrated circuits, are passive and active devices fabricated by a series of semiconductor processes on a semi-insulating semiconductor substrate and connected together to form functional circuits such as low noise amplifiers, power amplifiers. Among them, passive devices are an important class of MMIC devices, including resistors, capacitors, inductors, matching networks, resonators, filters, etc., and play a very important role in MMIC design.
With the continuous development of communication technology and the increasingly wide application of MMIC, the research on the equivalent circuit model of MMIC passive devices is also more in depth. And the equivalent circuit model of the MMIC passive device plays an important role in the design of MMIC. However, with the continuous development of the requirements of high-frequency applications, the topology structure of the equivalent circuit model of the device is quite complex due to the non-ideal effects such as high-frequency parasitic effects. Therefore, it is very difficult to quickly and accurately extract the parameter values of the equivalent circuit model and build an accurate equivalent circuit model of the device, which can greatly hinder the design of the MMIC by computer simulation and improve the working performance of the MMIC. The modeling of MMIC passive device equivalent circuits has become an important and hot spot in research in the semiconductor and integrated circuit fields.
The traditional MMIC passive device equivalent circuit model parameter extraction method is complex and complicated, and requires a great deal of time, substances and labor cost. The traditional extraction method generally measures scattering parameters of passive devices and then reversely deduces equivalent circuit model parameters by using a formula. The difficulty of reversely pushing out the parameters of the equivalent circuit model by using a formula is also rapidly increased because the topological structure of the built equivalent circuit model of the device is more and more complex. In addition, because the extraction complexity is often reduced by using approximate conditions in the extraction calculation process, the scattering parameters simulated by the MMIC passive device equivalent circuit model extracted by the traditional method are usually different from the scattering parameters obtained by testing, so that the parameters of the MMIC passive device equivalent circuit model are required to be optimized secondarily, and the scattering parameters simulated by the MMIC passive device equivalent circuit model are consistent with the scattering parameters obtained by testing. Therefore, the method for extracting the parameters of the equivalent circuit model of the MMIC passive device has very important significance.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a method for extracting parameters of an MMIC passive device equivalent circuit model based on a gray wolf algorithm, so that the parameters of the MMIC passive device equivalent circuit model can be extracted rapidly, accurately and conveniently.
In order to achieve the above purpose, the technical scheme adopted by the invention is as follows: the MMIC passive device equivalent circuit model parameter extraction method based on the wolf algorithm comprises the following steps:
s1, determining an equivalent circuit model according to the type of an MMIC passive device;
s2, setting parameters of an MMIC passive device equivalent circuit model;
s3, setting parameters of a wolf algorithm, including the population scale and the maximum iteration number of the wolf;
s4, constructing an error function and setting an error threshold;
s5, the position of each wolf group in the wolf algorithm corresponds to parameters in a group of MMIC passive device equivalent circuit models, and the position of each wolf group is updated according to the principle of the wolf algorithm;
s6, substituting the updated MMIC passive device equivalent circuit model parameters corresponding to each wolf group individual position into the MMIC passive device equivalent circuit model, and calculating corresponding model fitting scattering parameters;
s7, calculating error values corresponding to the individual positions of each wolf group according to the scattering parameters of each group of model fitting and the scattering parameters of the devices obtained through testing by utilizing an error function, finding out the individual positions of the wolf group corresponding to the minimum error value, and determining the equivalent circuit model parameters of the MMIC passive devices corresponding to the error values as the final equivalent circuit model parameters of the MMIC passive devices extracted by the iteration of the round;
and S8, judging whether the minimum error value of the iteration of the round is smaller than or equal to an error threshold value, and when the minimum error value of the iteration of the round is smaller than or equal to the error threshold value, considering that the extraction of the equivalent circuit model parameters of the MMIC passive device is completed, otherwise, returning to S5 to perform iterative updating again.
The device type is resistor, capacitor, inductor, resonator, matching network, filter or transformer.
Setting parameters of an equivalent circuit model of the MMIC passive device comprises setting initial values and changing ranges thereof; the initial values are set randomly or over a smaller range of variation.
Error function Error is constructed to describe the difference between the scattering parameters of the model fit and the scattering parameters of the device obtained by the test, and is as follows:
Figure BDA0004137237110000031
wherein ,
Figure BDA0004137237110000032
representing parameter variable values in an MMIC passive device equivalent circuit model, m is the number of parameters in the MMIC passive device equivalent circuit model, N is the sampled frequency point number, omega i For the angular frequency at the ith frequency bin, < >>
Figure BDA0004137237110000033
and />
Figure BDA0004137237110000034
Scattering parameters fitted to the model S 11 (ω i ) mea 、S 12 (ω i ) mea 、S 21 (ω i ) mea and S22 (ω i ) mea Is the scattering parameter of the device obtained by the test.
And S6, calculating admittance parameters of the model fitting by adopting an indefinite admittance matrix method, and converting the admittance parameters into scattering parameters to obtain the scattering parameters of the model fitting.
In any at least one step from S5 to S8, judging whether the current iteration number is larger than or equal to the maximum iteration number, and considering that the extraction of the equivalent circuit model parameters of the MMIC passive device is completed when the current iteration number is larger than or equal to the maximum iteration number.
The Error threshold determination principle is as follows:
Error threshold＝1-GOF
the GOF is a preset fitting degree value.
In S5, during the current iteration, the wolf with the smallest corresponding error function value of the first three positions in all iterations before the current iteration is set as alpha, beta and delta, then the positions of each individual in the wolf group are updated respectively,
first, the distance between each wolf population and alpha, beta and delta in the previous iteration is calculated
Figure BDA0004137237110000041
The calculation formula is as follows: />
Figure BDA0004137237110000042
Where t represents the current number of iterations,
Figure BDA0004137237110000043
is a random vector +.>
Figure BDA0004137237110000044
r 1 Is [0,1 ]]Random number between->
Figure BDA0004137237110000045
Is the position vector of alpha, beta and delta, < >>
Figure BDA0004137237110000046
Is the position orientation of one individual in the wolf populationAn amount of;
then for each individual position of the wolf
Figure BDA0004137237110000047
Updating, wherein the updating formula is as follows:
Figure BDA0004137237110000048
Figure BDA0004137237110000049
wherein
Figure BDA00041372371100000410
Figure BDA00041372371100000411
Gradually decreasing from 2 to 0 as the number of iterations increases, r 2 Is [0,1 ]]Random numbers in between.
Compared with the prior art, the invention has at least the following beneficial effects: compared with the traditional MMIC passive device equivalent circuit model parameter extraction method without the need of carrying out equivalent circuit model parameter calculation and formula analysis, the extraction difficulty is not increased due to the increase of the complexity of the topology structure of the equivalent circuit model, and the extraction speed is higher; according to the MMIC passive device equivalent circuit model parameter extraction method, the optimal solution of the model parameter is found based on the gray wolf algorithm, so that secondary fitting is not needed, and the model fitting precision is high.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings that are needed in the embodiments will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
Fig. 1 is a schematic flow chart of an equivalent circuit model parameter extraction method of an MMIC passive device based on a wolf algorithm provided by an embodiment of the invention.
Fig. 2 is a spiral inductor equivalent circuit model provided in an embodiment of the present invention.
FIG. 3a shows a spiral inductance scattering parameter S obtained by testing according to an embodiment of the present invention 11 Scattering parameters S fitted to the model 11 Comparing the result graphs.
FIG. 3b shows a spiral inductance scattering parameter S obtained by testing according to an embodiment of the present invention 12 Scattering parameters S fitted to the model 12 Comparing the result graphs.
FIG. 3c shows a spiral inductance scattering parameter S obtained by testing according to an embodiment of the present invention 21 Scattering parameters S fitted to the model 21 Comparing the result graphs.
FIG. 3d shows a spiral inductance scattering parameter S obtained by testing according to an embodiment of the present invention 22 Scattering parameters S fitted to the model 22 Comparing the result graphs.
Fig. 4 is an equivalent circuit model of a MIM capacitor according to an embodiment of the present invention.
FIG. 5a shows a MIM capacitor scattering parameter S obtained by testing according to an embodiment of the present invention 11 The resulting map is compared with the scattering parameter S11 fitted by the model.
Fig. 5b is a graph of the comparison of the MIM capacitor scattering parameter S12 obtained by the test and the scattering parameter S12 obtained by the model fitting according to the present invention.
Fig. 5c is a graph of a comparison of a MIM capacitor scattering parameter S21 obtained by testing and a model-fitted scattering parameter S21 according to an embodiment of the present invention.
Fig. 5d is a graph of a comparison of a MIM capacitor scattering parameter S22 obtained by testing and a model-fitted scattering parameter S22 according to an embodiment of the present invention.
Detailed Description
In order to further explain the technical means and the effects adopted by the invention to achieve the preset aim, the invention provides a method for extracting parameters of an equivalent circuit model of an MMIC passive device based on a Grey wolf algorithm in detail by combining the drawings and the specific embodiments.
The foregoing and other features, aspects, and advantages of the present invention will become more apparent from the following detailed description of the preferred embodiments when taken in conjunction with the accompanying drawings. The technical means and effects adopted by the present invention to achieve the intended purpose can be more deeply and specifically understood through the description of the specific embodiments, however, the attached drawings are provided for reference and description only, and are not intended to limit the technical scheme of the present invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The invention provides a method for extracting parameters of an MMIC passive device equivalent circuit model based on a gray wolf algorithm, which refers to figure 1 and comprises the following steps:
s1, determining an equivalent circuit model according to the type of an MMIC passive device;
s2, setting parameters of an MMIC passive device equivalent circuit model;
s3, setting parameters of a wolf algorithm, including the population scale and the maximum iteration number of the wolf;
s4, constructing an error function and setting an error threshold;
s5, the position of each wolf group is corresponding to parameters in a group of MMIC passive device equivalent circuit model, and the position of each wolf group is updated according to the gray wolf algorithm principle;
s6, substituting the updated MMIC passive device equivalent circuit model parameters corresponding to each wolf group individual position into the MMIC passive device equivalent circuit model, and calculating corresponding model fitting scattering parameters;
s7, calculating error values corresponding to the individual positions of each wolf group according to the scattering parameters of each group of model fitting and the scattering parameters of the devices obtained through testing by utilizing an error function, finding out the individual positions of the wolf group corresponding to the minimum error value, and determining the equivalent circuit model parameters of the MMIC passive devices corresponding to the error values as the final equivalent circuit model parameters of the MMIC passive devices extracted by the iteration of the round;
s8, judging whether the minimum error value of the iteration of the round is smaller than or equal to an error threshold value, and when the minimum error value of the iteration of the round is smaller than or equal to the error threshold value, considering that the extraction of the equivalent circuit model parameters of the MMIC passive device is completed, otherwise, returning to the step S5 to perform iteration updating again.
Embodiment one:
the method is described in detail below by taking the extraction of the spiral inductor equivalent circuit model parameters by using the Fu-Linked process as an example.
S1, determining an equivalent circuit model according to the type of an MMIC passive device;
in the step, a chip test probe station (Cascade M150) and a vector network analyzer (Si meter 3672B-Ceyear) are used for testing spiral inductors adopting a Fulian process, and scattering parameter test data in a frequency range of 1-30GHz are obtained. The spiral inductance equivalent circuit model parameter extraction will be performed using scattering parameter test data from 31 frequency points 1GHz apart from 1-30 GHz.
The device type has been determined to be a spiral inductance according to the present embodiment, and the spiral inductance equivalent circuit model used is shown in fig. 2.
R 2 -C 2 The parallel network is used for representing the substrate coupling effect at high frequency, L s R is the spiral inductance value s Is the series resistance of the spiral inductor, which is mainly due to the skin effect. In cascade L s And parasitic resistance R s One R is connected in series with the branch 1 -L 1 And the parallel network is used for representing skin effect and proximity effect at high frequency. C (C) ox1 、C ox2 R is the capacitance between the spiral inductor and the substrate sub1 and Rsub2 ，C sub1 and Csub2 Substrate loss and substrate capacitance, respectively.
S2, setting parameters of an MMIC passive device equivalent circuit model;
in this step, R 2 Is set to a variation range of 0 to 1000 omega, C 2 Is set to a range of 0-100fF, L s Is set to 0-10nH, R s Is set to a variation range of 0 to 20Ω, R 1 Is set to a range of 0 to 1000 omega, L 1 Is set to 0-5nH, C ox1 and Cox2 Is set to 0-1pF, R sub1 and Rsub2 Is set to a variation range of 0 to 3000 omega, C sub1 and Csub2 The respective ranges of variation are set to 0-10pF.
All initial values of the spiral inductance equivalent circuit model parameters are randomly set in the set change range.
As an alternative embodiment, the set point may be empirically taken over a smaller range of variation of the spiral inductance equivalent circuit model parameters.
S3, setting parameters of a wolf algorithm, including the population scale and the maximum iteration number of the wolf;
in this step, the wolf group size is set to 30 and the maximum number of iterations is set to 5000.
S4, constructing an error function and setting an error threshold;
in this step, the Error function Error used is as follows:
Figure BDA0004137237110000081
wherein ,
Figure BDA0004137237110000082
representing the parameter variable value in the spiral inductance equivalent circuit model, m is the parameter quantity in the spiral inductance equivalent circuit model, N is the sampled frequency point number, omega i For the angular frequency at the ith frequency point,
Figure BDA0004137237110000083
Figure BDA0004137237110000084
and />
Figure BDA0004137237110000085
Scattering parameters fitted to the model S 11 (ω i ) mea 、S 12 (ω i ) mea 、S 21 (ω i ) mea and S22 (ω i ) mea Is the scattering parameter of the spiral inductance obtained by the test.
The preset fit is 98% and therefore the error threshold is set to 0.02.
S5, the position of each wolf group is corresponding to parameters in a group of MMIC passive device equivalent circuit model, and the position of each wolf group is updated according to the gray wolf algorithm principle;
during the current iteration, the first three positions in all iterations before the current iteration are set to be α, β, and δ, where the first three positions have the smallest corresponding error function value.
The location of each individual in the wolf population is then updated separately.
First, the distance between each wolf population and alpha, beta and delta in the previous iteration is calculated
Figure BDA0004137237110000086
The calculation formula is as follows:
Figure BDA0004137237110000087
/>
where t represents the current number of iterations,
Figure BDA0004137237110000088
is a random vector +.>
Figure BDA0004137237110000089
r 1 Is [0,1 ]]Random number between->
Figure BDA0004137237110000091
Is the position vector of alpha, beta and delta, < >>
Figure BDA0004137237110000092
Is the position vector of one of the individuals in the wolf population.
Then for each individual position of the wolf
Figure BDA0004137237110000093
Updating, wherein the updating formula is as follows:
Figure BDA0004137237110000094
Figure BDA0004137237110000095
wherein
Figure BDA0004137237110000096
Figure BDA0004137237110000097
Gradually decreasing from 2 to 0 as the number of iterations increases, r 2 Is [0,1 ]]Random numbers in between.
S6, substituting the updated MMIC passive device equivalent circuit model parameters corresponding to each wolf group individual position into the MMIC passive device equivalent circuit model, and calculating corresponding model fitting scattering parameters;
in the step, the parameters in the updated equivalent circuit model are utilized, an indefinite admittance matrix method is adopted to calculate admittance parameters (Y parameters) fitted by the spiral inductance equivalent circuit model, and then the admittance parameters (Y parameters) are converted into scattering parameters (S parameters), so that the scattering parameters (S parameters) fitted by the spiral inductance equivalent circuit model can be obtained through calculation by utilizing the updated parameters.
In this embodiment, the indefinite admittance matrix method and the mutual conversion between admittance parameters (Y parameters) and scattering parameters (S parameters) are common methods in the art, and will not be described herein.
S7, calculating error values corresponding to the individual positions of each wolf group according to the scattering parameters of each group of model fitting and the scattering parameters of the devices obtained through testing by utilizing an error function, finding out the individual positions of the wolf group corresponding to the minimum error value, and determining the equivalent circuit model parameters of the MMIC passive devices corresponding to the error values as the final equivalent circuit model parameters of the MMIC passive devices extracted by the iteration of the round;
in this step, an error formula in step S4 is used, and according to the scattering parameter fitted by each group of spiral inductance equivalent circuit model and the scattering parameter of the device obtained through testing in this embodiment, the error value of each wolf group is calculated, the position of the wolf group corresponding to the minimum error value is found, and the corresponding spiral inductance equivalent circuit model parameter is determined to be the final spiral inductance equivalent circuit model parameter extracted by this round of iteration.
S8, judging whether the minimum error value of the iteration of the round is smaller than or equal to an error threshold value, and when the minimum error value of the iteration of the round is smaller than or equal to the error threshold value, considering that the extraction of the equivalent circuit model parameters of the MMIC passive device is completed, otherwise, returning to the step S5 to perform iteration updating again.
In this step, in each iteration, it is determined whether the minimum error value calculated in step S7 is smaller than the error threshold, and when the minimum error value is smaller than the error threshold, the extraction of the spiral inductance equivalent circuit model parameters is considered to be completed, otherwise, the process returns to step S5 to perform iterative updating again.
In this step, in each iteration, after the minimum error value calculated in step S7 is greater than or equal to the error threshold, before returning to step S5, it is determined whether the current total iteration number is less than or equal to the maximum iteration number, and the current total iteration number is greater than the maximum iteration number, so as to stop the process of extracting the parameters of the spiral inductor equivalent circuit model, so as to prevent the extraction time from being too long, otherwise, continuing to return to step S5 to perform iterative updating again.
On a CPU i7-11700K main frequency 4.6GHz and memory 32GB computer, after 50 seconds and 4235 iterations, the Error value error=0.0181 is smaller than the Error threshold value 0.02, and the spiral inductance equivalent circuit model parameter extraction is considered to be completed.
The extraction results of the spiral inductor equivalent circuit model parameters in this embodiment are shown in table 1.
TABLE 1 spiral inductance equivalent circuit parameter extraction results
Equivalent parameters Parameter value Equivalent parameters Parameter value
R s (Ω) 0.44196 C ox1 (fF) 75.8615
L s (pH) 445.2077 C ox2 (fF) 466.2510
R 1 (Ω) 239.3563 C sub1 (pF) 9.3744
L 1 (pH) 766.0255 C sub2 (fF) 995.2748
R 2 (Ω) 358.4155 R sub1 (Ω) 324.4506
C 2 (fF) 0.2045 R sub2 (Ω) 1348.3840
And combining the spiral inductance equivalent circuit model parameter extraction result with the spiral inductance model topological structure adopted in the embodiment to obtain the model fitting scattering parameter.
The comparison of the spiral inductance scattering parameters obtained by the test and the scattering parameters fitted by the model in this example is shown in fig. 3a, 3b, 3c and 3 d.
Embodiment two:
the method is further described below by taking the parameter extraction of the equivalent circuit model of the MIM capacitor by using the Fulian technology as an example, so as to better understand the parameter extraction method of the equivalent circuit model of the MMIC passive device based on the Grey wolf algorithm.
S1, determining an equivalent circuit model according to the type of an MMIC passive device;
in the step, a chip test probe station (Cascade M150) and a vector network analyzer (Si meter 3672B-Ceyear) are used for testing MIM capacitors adopting the Fulian technology, so that scattering parameter test data in the frequency range of 1-30GHz are obtained. The MIM capacitor equivalent circuit model parameter extraction will be performed using scattering parameter test data from 31 frequency points 1GHz apart from 1-30 GHz.
In this step, the device type has been determined to be a MIM capacitor according to the present embodiment, and the MIM capacitor equivalent circuit model used is shown in fig. 4.
R s1 and Rs2 Is a series resistor connected in series with two ends of the capacitor L 1 and L2 R is a series inductance connected in series with two ends of a capacitor l C is leakage current of dielectric layer of MIM capacitor 0 Is MIM capacitance. R is R sub1 and Rsub2 ，C sub1 and Csub2 Substrate loss and substrate capacitance, respectively.
S2, setting parameters of an MMIC passive device equivalent circuit model;
in this step, R s1 and Rs2 Is set to a range of 0 to 20Ω, L 1 and L2 Is set to a pH of 0-20, R l Is set to a variation range of 0 to 2000 omega, C 0 Is set to a variation range of 0-50pF. R is R sub1 and Rsub2 Is set to a variation range of 0 to 5000 omega, C sub1 and Csub2 Is set to a range of 0-100fF.
All the initial values of the parameters of the equivalent circuit model of the MIM capacitor are randomly set in the set variation range.
S3, setting parameters of a wolf algorithm, including the population scale and the maximum iteration number of the wolf;
in this step, the wolf group size is set to 30 and the maximum number of iterations is set to 3000.
S4, constructing an error function and setting an error threshold;
Figure BDA0004137237110000121
wherein ,
Figure BDA0004137237110000122
representing the parameter variable value in the MIM capacitor equivalent circuit model, m is the parameter quantity in the MIM capacitor equivalent circuit model, N is the sampled frequency point number, omega i For the angular frequency at the ith frequency point,
Figure BDA0004137237110000123
and />
Figure BDA0004137237110000124
Scattering parameters fitted to the model S 11 (ω i ) mea 、S 12 (ω i ) mea 、S 21 (ω i ) mea and S22 (ω i ) mea Is the scattering parameter of the MIM capacitor obtained by the test.
The preset fit is 98% and therefore the error threshold is set to 0.02.
S5, the position of each wolf group is corresponding to parameters in a group of MMIC passive device equivalent circuit model, and the position of each wolf group is updated according to the gray wolf algorithm principle;
during the current iteration, the first three positions in all iterations before the current iteration are set to be α, β, and δ, where the first three positions have the smallest corresponding error function value.
The location of each individual in the wolf population is then updated separately.
First, the distance between each wolf population and alpha, beta and delta in the previous iteration is calculated
Figure BDA0004137237110000125
The calculation formula is as follows:
Figure BDA0004137237110000126
where t represents the current number of iterations,
Figure BDA0004137237110000127
is a random vector +.>
Figure BDA0004137237110000128
r 1 Is [0,1 ]]Random number between->
Figure BDA0004137237110000129
Is the position vector of alpha, beta and delta, < >>
Figure BDA00041372371100001210
Is the position vector of one of the individuals in the wolf population.
Then for each individual position of the wolf
Figure BDA00041372371100001211
Updating, wherein the updating formula is as follows:
Figure BDA00041372371100001212
Figure BDA00041372371100001213
wherein
Figure BDA0004137237110000131
Figure BDA0004137237110000132
Gradually decreasing from 2 to 0 as the number of iterations increases, r 2 Is [0,1 ]]Random numbers in between.
S6, substituting the updated MMIC passive device equivalent circuit model parameters corresponding to each wolf group individual position into the MMIC passive device equivalent circuit model, and calculating corresponding model fitting scattering parameters;
in this step, the parameters in the updated equivalent circuit model are used to calculate the admittance parameters (Y parameters) fitted by the MIM capacitor equivalent circuit model by adopting an indefinite admittance matrix method, and then the admittance parameters (Y parameters) are converted into scattering parameters (S parameters), so that the scattering parameters (S parameters) fitted by the MIM capacitor equivalent circuit model can be obtained by calculating the updated parameters.
In this embodiment, the indefinite admittance matrix method and the mutual conversion between admittance parameters (Y parameters) and scattering parameters (S parameters) are common methods in the art, and will not be described herein.
S7, calculating error values corresponding to the individual positions of each wolf group according to the scattering parameters of each group of model fitting and the scattering parameters of the devices obtained through testing by utilizing an error function, finding out the individual positions of the wolf group corresponding to the minimum error value, and determining the equivalent circuit model parameters of the MMIC passive devices corresponding to the error values as the final equivalent circuit model parameters of the MMIC passive devices extracted by the iteration of the round;
in this step, the error formula in step S4 is used, and according to the scattering parameter fitted by each group of MIM capacitor equivalent circuit model and the scattering parameter of the device obtained by testing in this embodiment, the error value of each wolf-group unit is calculated, and the position of the wolf-group unit corresponding to the minimum error value is found, and the corresponding MIM capacitor equivalent circuit model parameter is determined to be the final MIM capacitor equivalent circuit model parameter extracted by the present iteration.
S8, judging whether the minimum error value of the iteration of the round is smaller than or equal to an error threshold value, and when the minimum error value of the iteration of the round is smaller than or equal to the error threshold value, considering that the extraction of the equivalent circuit model parameters of the MMIC passive device is completed, otherwise, returning to the step S5 to perform iteration updating again.
In this step, in each iteration, it is determined whether the minimum error value calculated in step S7 is smaller than the error threshold, and when the minimum error value is smaller than the error threshold, the MIM capacitor equivalent circuit model parameter extraction is considered to be completed, otherwise, the process returns to step S5 to perform iterative updating again.
In this step, in each iteration, after the minimum error value calculated in step S7 is greater than or equal to the error threshold, before returning to step S5, it is determined whether the current total iteration number is less than or equal to the maximum iteration number, and the current total iteration number is greater than the maximum iteration number, so as to stop the MIM capacitor equivalent circuit model parameter extraction process, so as to prevent the extraction time from being too long, otherwise, continuing to return to step S5 to perform iterative updating again.
On a CPU i7-11700K main frequency 4.6GHz and memory 32GB computer, after 20 seconds of calculation time and 1547 iterations, the Error value error=0.0072 is smaller than the Error threshold value 0.02, and the MIM capacitance equivalent circuit model parameter extraction is considered to be completed.
TABLE 2 MIM capacitor equivalent circuit parameter extraction results
Equivalent parameters Parameter value Equivalent parameters Parameter value
R s1 (Ω) 1.2934 C sub1 (fF) 38.5027
R s2 (Ω) 2.0221 C sub2 (fF) 30.2530
L 1 (pH) 1.4465 R sub1 (Ω) 1489.0691
L 2 (pH) 2.4168 R sub2 (Ω) 1299.4452
C 0 (pF) 11.8414 R l (Ω) 400.7953
And combining the MIM capacitor equivalent circuit model parameter extraction result with the MIM capacitor model topological structure adopted in the embodiment to obtain the model fitting scattering parameter.
The comparison of the MIM capacitor scattering parameters obtained by the test and the scattering parameters fitted by the model in this example is shown in fig. 5a, 5b, 5c and 5 d.
Therefore, the method for extracting the equivalent circuit model parameters of the MMIC passive device based on the gray-wolf algorithm is a suitable, rapid, accurate, convenient and direct method for extracting the equivalent circuit model parameters of the MMIC passive device.
According to the method for extracting the parameters of the MMIC passive device equivalent circuit model based on the gray wolf algorithm, disclosed by the invention, a method and formula analysis for calculating the parameters of the equivalent circuit model are not needed, the extraction difficulty is not increased due to the increase of the complexity of the topological structure of the equivalent circuit model, the extraction speed is higher, secondary fitting is not needed, and the model fitting precision is high.
The principles and embodiments of the present invention have been described in detail with reference to specific examples, which are provided to facilitate understanding of the method and core ideas of the present invention; also, it is within the scope of the present invention to be modified by those of ordinary skill in the art in light of the present teachings. In view of the foregoing, this description should not be construed as limiting the invention.

Claims (8)

1. The MMIC passive device equivalent circuit model parameter extraction method based on the gray wolf algorithm is characterized by comprising the following steps of:
s1, determining an equivalent circuit model according to the type of an MMIC passive device;
s2, setting parameters of an MMIC passive device equivalent circuit model;
s3, setting parameters of a wolf algorithm, including the population scale and the maximum iteration number of the wolf;
s4, constructing an error function and setting an error threshold;
s5, the position of each wolf group in the wolf algorithm corresponds to parameters in a group of MMIC passive device equivalent circuit models, and the position of each wolf group is updated according to the principle of the wolf algorithm;
s6, substituting the updated MMIC passive device equivalent circuit model parameters corresponding to each wolf group individual position into the MMIC passive device equivalent circuit model, and calculating corresponding model fitting scattering parameters;
s7, calculating error values corresponding to the individual positions of each wolf group according to the scattering parameters of each group of model fitting and the scattering parameters of the devices obtained through testing by utilizing an error function, finding out the individual positions of the wolf group corresponding to the minimum error value, and determining the equivalent circuit model parameters of the MMIC passive devices corresponding to the error values as the final equivalent circuit model parameters of the MMIC passive devices extracted by the iteration of the round;
and S8, judging whether the minimum error value of the iteration of the round is smaller than or equal to an error threshold value, and when the minimum error value of the iteration of the round is smaller than or equal to the error threshold value, considering that the extraction of the equivalent circuit model parameters of the MMIC passive device is completed, otherwise, returning to S5 to perform iterative updating again.
2. The method for extracting parameters of equivalent circuit model of MMIC passive device based on the gray wolf algorithm according to claim 1, wherein the device type is resistor, capacitor, inductor, resonator, matching network, filter or transformer.
3. The method for extracting parameters of the equivalent circuit model of the MMIC passive device based on the gray wolf algorithm as claimed in claim 1, wherein the setting of the parameters of the equivalent circuit model of the MMIC passive device comprises setting an initial value and a variation range thereof; the initial values are set randomly or over a smaller range of variation.
4. The method for extracting parameters of an equivalent circuit model of an MMIC passive component based on the gray wolf algorithm as set forth in claim 1, wherein an Error function Error is constructed for describing the difference between the scattering parameters of the model fitting and the scattering parameters of the component obtained by the test, the Error function Error being as follows:
Figure FDA0004137237100000021
wherein ,
Figure FDA0004137237100000022
representing parameter variable values in an MMIC passive device equivalent circuit model, m is the number of parameters in the MMIC passive device equivalent circuit model, N is the sampled frequency point number, omega i For the angular frequency at the ith frequency bin, < >>
Figure FDA0004137237100000023
and />
Figure FDA0004137237100000024
Scattering parameters fitted to the model S 11 (ω i ) mea 、S 12 (ω i ) mea 、S 21 (ω i ) mea and S22 (ω i ) mea Is the scattering parameter of the device obtained by the test.
5. The method for extracting parameters of the equivalent circuit model of the MMIC passive component based on the gray wolf algorithm as claimed in claim 1, wherein the method is characterized in that an indefinite admittance matrix method is adopted in S6 to calculate admittance parameters of model fitting, and then the admittance parameters are converted into scattering parameters to obtain the scattering parameters of model fitting.
6. The method for extracting parameters of an equivalent circuit model of an MMIC passive component based on the gray wolf algorithm according to claim 1, wherein in any one of the steps S5 to S8, it is judged whether the current iteration number is greater than or equal to the maximum iteration number, and when the current iteration number is greater than or equal to the maximum iteration number, the extraction of the equivalent circuit model parameters of the MMIC passive component is considered to be completed.
7. The method for extracting parameters of the equivalent circuit model of the MMIC passive component based on the gray wolf algorithm as set forth in claim 1, wherein the Error threshold value Error threshold determination principle is as follows:
Error threshold＝1-GOF
the GOF is a preset fitting degree value.
8. The method for extracting parameters of MMIC passive component equivalent circuit model based on the gray wolf algorithm as set forth in claim 1, wherein in S5, during the current iteration, the wolf with the smallest corresponding error function value of the first three positions in all iterations before the current iteration is set as alpha, beta and delta, then the positions of each individual in the wolf group are updated respectively,
first, the distance between each wolf population and alpha, beta and delta in the previous iteration is calculated
Figure FDA0004137237100000031
The calculation formula is as follows:
Figure FDA0004137237100000032
where t represents the current number of iterations,
Figure FDA0004137237100000033
is a random vector +.>
Figure FDA0004137237100000034
r 1 Is [0,1 ]]Random number between->
Figure FDA0004137237100000035
Is the position vector of alpha, beta and delta, < >>
Figure FDA0004137237100000036
Is a position vector of one of the individuals in the gray wolf population;
then for each individual position of the wolf
Figure FDA0004137237100000037
Updating, wherein the updating formula is as follows:
Figure FDA0004137237100000038
Figure FDA0004137237100000039
wherein
Figure FDA00041372371000000310
Figure FDA00041372371000000311
Gradually decreasing from 2 to 0 as the number of iterations increases, r 2 Is [0,1 ]]Random numbers in between. />
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