CN115544933A - Capacitor equivalent circuit modeling method - Google Patents
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Abstract
The invention provides a capacitor equivalent circuit modeling method, which comprises the following steps: adding impedance functions of a resistor-capacitor network containing a coefficient to be determined, the resistor-inductor network and the resistor-inductor-capacitor parallel resonance network to form a capacitor impedance function; respectively presetting initial values of the undetermined coefficients based on parameters of the capacitor and impedance test data; fitting the capacitor impedance function and the impedance test data; adjusting the initial value of the undetermined coefficient if necessary according to the range of the fitting error until the fitting error meets the end condition, and determining the coefficient of the impedance function; and selecting a target resistance-capacitance network and a resistance-inductance network from the candidate network type set, and generating a capacitor equivalent circuit model by using the coefficient of the impedance function. The invention can flexibly and efficiently obtain various high-precision equivalent circuit models of various capacitors, can ensure the passivity and the realizability of the equivalent circuit and various elements, and is convenient for computer programming to realize process automation.
Description
Technical Field
The invention relates to the technical field of electronic circuits, in particular to a capacitor equivalent circuit modeling method.
Background
In recent years, with the rapid improvement of the function and performance requirements of users on electronic devices, the trend of development of electronic technologies towards high speed and high frequency is more and more obvious, and Power Integrity (PI), signal Integrity (SI) and electromagnetic compatibility (EMC) become problems to be mainly solved by hardware circuit design engineers, and are also important application fields of passive components such as capacitors, inductors, magnetic beads and resistors. In these application fields, EDA (electronic design automation) technology becomes indispensable. The working state and performance parameters of the electronic circuit can be accurately and rapidly simulated by using proper EDA software, so that the hardware debugging period is shortened, and the product development cost is reduced. The equivalent circuit model capable of accurately reflecting the performance of the actual element is one of the precondition for the EDA software to play the greatest role, and particularly for a complex high-speed digital circuit, compared with a frequency domain model of the element, the efficiency of time domain simulation can be remarkably improved by using the equivalent circuit model. Therefore, leading electronic component manufacturers place great importance on providing circuit design engineers with accurate component performance parameter data and equivalent circuit models, which are usually provided in the form of SPICE-compatible format files or EDA software component libraries.
In particular to capacitors, the most common basic equivalent circuit is a CRL series circuit consisting of one each of capacitive (C), resistive (R), inductive (L) elements. The basic equivalent circuit has a larger error compared with the actual performance of the components, and particularly cannot reflect the condition that the series equivalent resistance (ESR) of the actual capacitor is obviously increased and/or decreased along with the increase of the frequency. In order to improve the accuracy of the equivalent circuit, more C, R and L elements are required to form a more complex network. The classic basic RC and RL network types are Foster I, foster II, cauer I and Cauer II type networks, respectively.
To obtain an accurate equivalent circuit model for a capacitor, the prior art typically first selects a certain type of RC, RL or RLC network and corresponding order (equal to the sum of the number of C and L elements), and obtains the value of each C, R, L element by minimizing the error (evaluation) function of the impedance of the selected network and the measured impedance data of the capacitor to determine a complete equivalent circuit model. Typically, as disclosed in patent 1JP4507421B2 (JP 2002259482A, TW544604B, US7266485B2, WO2002068972A 1), any one of an RC circuit, an RL circuit, and an RCL circuit formed by connecting the RC circuit and the RL circuit in series is selected, and the value of each C, R, L element in the circuit is determined by minimizing the error (evaluation) function of the complex impedance of the circuit at any set of sampling frequencies and the corresponding capacitor complex impedance data. The RC and RL circuits can be Foster I, foster II, cauer I and Cauer II type RC and RL circuits. Also as in patent 2JP5475563B2 (JP 2010136335A, US 8527256) the C-elements and part of the R-elements of a substantially equivalent circuit of a MLCC (multilayer chip capacitor) are replaced by more complex RC series-parallel networks, the remaining L-elements and part of the R-elements are replaced by RL series-parallel networks, and part of them are associated with their physical meaning (e.g. mutual capacitance, mutual inductance, etc.). In both of the above patent 1 and patent 2, the impedance of the equivalent circuit and the impedance data of the capacitor test are directly fitted by a numerical optimization method to obtain the values of each element of the equivalent circuit. The method has the problems that because the circuit structure and the corresponding impedance calculation are complex, the order of the circuit is not convenient to increase or decrease so as to improve the fitting precision or reduce the complexity of the circuit according to actual needs, and the method is also not beneficial to realizing higher automation through computer programming. Meanwhile, the setting rule of the initial value of each element in the modeling method is complex, slow convergence of fitting iteration is easy to occur, and the modeling efficiency is reduced. Furthermore, the equivalent circuit structure and its physical meaning adopted by patent 2 for MLCCs may not be applicable to other kinds of inductors. Patent 3CN104246777B provides an equivalent circuit modeling method capable of reflecting a capacitor when a dc bias voltage is applied, wherein basic equivalent circuits when the dc bias voltage is zero are Foster I, foster II type RC and RL circuits and RLC parallel or series resonance circuits, but does not disclose how to determine the order and element values of a specific equivalent circuit.
Besides the modeling method, a more general Passive macro model building (Passive macro modeling) method is also provided. Fitting the battery impedance characteristic data to obtain an impedance function as in patent 4CN114065681A, wherein the impedance function is a complex function in the form of a pole and a residue; and obtaining an equivalent circuit model according to the determined equivalent replacement logic according to the properties of the poles and the residue. The method is suitable for different types of components and has strong universality, but the method cannot ensure that the values (resistance value, inductance value and capacitance) of all RLC elements of an equivalent circuit are positive numbers, so that the application range of the method is limited. First, even if the entire equivalent circuit is passive, the negative RLC element values cause these elements to lose their own passivity and are physically impossible to implement; for some fields or simulation software, negative RLC element values may also cause instability in time domain simulation.
Disclosure of Invention
The invention aims to provide a capacitor equivalent circuit modeling method to solve the problems that in the prior art, the order and the network type of an equivalent circuit are difficult to flexibly change according to actual needs, computer programming is inconvenient to realize process automation, the types and the structures of applicable capacitors are not wide enough, or an RLC element has a negative value.
The invention provides a capacitor equivalent circuit modeling method, wherein the equivalent circuit is composed of R (resistance), C (capacitance) and L (inductance) elements, and the method comprises the following steps:
adding impedance functions of an RC network, an RL network and an RLC parallel resonance network containing a coefficient to be determined to form a capacitor impedance function;
respectively presetting initial values of the undetermined coefficients based on parameters of the capacitor and impedance test data;
fitting the capacitor impedance function and the impedance test data;
adjusting the initial value of the undetermined coefficient if necessary according to the range of the fitting error until the fitting error meets the end condition, and determining the coefficient of the impedance function;
and selecting a target RC network and a target RL network from the candidate network type set, and generating a capacitor equivalent circuit model by using the coefficients of the impedance function.
Further, in a complex frequency domain (s-domain), the RC network impedance function with the coefficient to be determined is represented by:
The expression of the RL network impedance function containing the coefficient to be determined is as follows:
The expression of the RLC parallel resonance network impedance function containing undetermined coefficients is as follows:
Further, the initial value presetting method of the undetermined coefficient comprises the following steps:
dividing the impedance test angular frequency range by taking the self-resonance angular frequency of the capacitor as a boundary, and recording a low frequency band and a high frequency band as a first frequency interval and a second frequency interval respectively;
generating a first geometric progression based on a first common ratio in the first frequency interval;
generating a second geometric series based on a second common ratio in the second frequency interval;
and acquiring the central angular frequency of the part with larger or non-monotonous change of the capacitor impedance or resistance curve curvature in the second frequency interval.
And sequentially presetting initial values of undetermined coefficients of impedance functions of the RC network, the RL network and the RLC parallel resonant network according to a fixed rule based on the first equal-ratio sequence, the second equal-ratio sequence and the central angular frequency respectively in combination with the nominal capacity of the capacitor, the self-resonant angular frequency and corresponding impedance test data.
Further, the method of the fitting process includes:
and fitting by using a nonlinear least square method so that the relative error between the capacitor impedance function value and the modulus and the real part of the impedance test data is smaller than a preset error threshold value.
Further, the method for adjusting the initial value of the undetermined coefficient includes:
adjusting the value range of the first geometric progression and the first common ratio;
adjusting the value range of the second geometric series and the second common ratio;
adjusting the number and location of the center angular frequencies.
Further, the set of candidate network types includes:
one of Foster I, foster II, cauer I and Cauer II types, or a mixture of two or more of the network types.
Drawings
FIG. 1 is a flow chart of a method of modeling a capacitor equivalent circuit of the present invention;
FIG. 2 is a schematic diagram of typical impedance frequency characteristics of various types of capacitors;
FIG. 3 is an impedance frequency characteristic curve obtained by testing and fitting a 1nF stacked chip capacitor in an embodiment of the present invention;
fig. 4 is a fitting error of the impedance frequency characteristic of the 1nF stacked chip capacitor in the embodiment of the present invention.
Fig. 5 shows various types of RC sub-networks of the equivalent circuit model of the 1nF stacked chip capacitor in the embodiment of the present invention.
Fig. 6 is a diagram of various types of RL sub-networks of a 1nF stacked chip capacitor equivalent circuit model in an embodiment of the present invention.
Fig. 7 is an RLC parallel resonant sub-network of the 1nF stacked chip capacitor equivalent circuit model in an embodiment of the present invention.
Detailed Description
In order to make the purpose, technical solution and advantages of the present invention more clearly apparent, the present invention is further described in detail below with reference to the accompanying drawings and embodiments, and it is obvious that the embodiments described below are part of the embodiments of the present invention, and are used for illustrating the present invention only, but not for limiting the scope of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In one embodiment, as shown in fig. 1, there is provided a capacitor equivalent circuit modeling method for obtaining a passive network composed of R, C, and L elements, comprising the steps of:
s11, adding impedance functions of an RC network, an RL network and an RLC parallel resonance network containing undetermined coefficients to form a capacitor impedance function;
where the general form of the impedance or admittance function of any passive network consisting of R, L, C elements is:
wherein s = j ω is the complex frequency; p(s) and Q(s) are respectively an n-order numerator polynomial and an m-order denominator polynomial, | n-m |, is less than or equal to 1; a is i ,b k More than or equal to 0 are respectively the coefficients of polynomials P(s) and Q(s); the formula (1) is expressed as follows by partial development:
in the formula p k And r k The poles of F(s) and the corresponding residue, k 1 s+k 0 Is the remainder, k 1 ,k 0 Not less than 0; according to the network passivity and stability requirements, p k ≤0；
The expression of the RC network impedance function containing the undetermined coefficient is as follows:
in the formula p 1,k ≤0，r 1,k >0，k 0 ≥0；|Z RC |,R RC Is not less than 0 and all decrease with increasing omega, and X RC <0；
The expression of the impedance function of the RL network containing the coefficient to be determined is as follows:
wherein p is 2,k <0，c k >0，k 1 ≥0；|Z RL |,R RL Is not less than 0 and all increases with omega, and X RL >0；
The expression of the RLC parallel resonance network impedance function containing undetermined coefficients is as follows:
wherein d is k >0，e 1,k >0，e 0,k >0；|Z RLC,k |,R RLC,k Not less than 0 and all increase and decrease with increasing omega, and X RLC,k Monotonically decreasing with ω and being 0 at the respective resonant frequency.
In general, the typical impedance-angular frequency characteristic of a capacitor is shown in fig. 2, where: the place where the reactance X =0 is called self-resonance angular frequency omega sr ；ω<ω sr When X<0, exhibiting capacitive behavior; omega>ω sr When X>0, appearing as perceptual; the resistance R is usually at omega sr The vicinity takes a minimum value. Recording the start angular frequency and the end angular frequency of the impedance test data as omega in sequence 1 And omega 2 At ω sr Testing impedance for angular frequency range omega 1 ≤ω<ω 2 Divided into a first frequency interval omega 1 ≤ω<ω sr And a second frequency interval omega sr <ω≤ω 2 . According to the above RC, RL and RLCThe characteristics of the parallel resonant network, the impedance-angular frequency characteristics of the capacitor in the first frequency interval and the second frequency interval may be fitted with RC and RL networks, respectively, while the part of the capacitor impedance-angular frequency characteristic curve with a larger curvature (including non-monotonic variation) in the second frequency interval may be fitted with the RLC parallel resonant network.
In the step, the impedance function of the capacitor is decomposed into the sum of the impedance functions of RC, RL and RLC parallel resonance sub-networks, so that the constraint on respective coefficients is increased, the negative value RLC elements appearing in the universal complex function fitting and equivalent circuit replacement are fundamentally avoided, and the passivity and the realizability of the equivalent circuit and each element can be ensured.
S12, respectively presetting initial values of the undetermined coefficients based on the parameters of the capacitor and the impedance test data;
according to the impedance-angular frequency characteristics of each sub-network and the angular frequency range fitted by the impedance-angular frequency characteristics, presetting initial values of each undetermined coefficient of the impedance function of the sub-network according to the following method:
for the RC network, a first common ratio alpha is set in a first frequency interval>0, generating a first series of equal ratios ω 1,k (ii) a A preset initial value p 1,k ＝-ω 1,k ，r 1,k ＝ω 1,k R 1,k ，k 0 ＝R 0 Wherein R is 1,k For capacitors at omega 1,k Resistance of (d), R 0 Is the minimum value of the resistance; at p is 1,k And r 1,k Adding 0 and 1/C respectively n In which C is n Is the nominal capacity of the capacitor;
for RL network, a second common ratio β is set in a second frequency interval>0, generating a second equal-ratio sequence omega 2,k (ii) a A preset initial value p 2,k ＝-ω 2,k ，c k ＝R 2,k ，
Wherein R is 2,k For capacitors at omega 2,k The resistance of (d);
for an RLC parallel resonant network, a capacitor impedance or resistance curve is acquired over a second frequency intervalThe central angular frequency at large or non-monotonic variation of the curvature is noted as ω 0,k Preset initial value
Wherein R is 0,k For capacitors at omega 0,k The resistance of (c).
This step is a specific method for presetting the initial value of the waiting coefficient of the impedance function of each sub-network. Because each sub-network impedance function is a partial fractional or first/second order rational function expansion in the same form, the initial value of the corresponding coefficient only depends on the parameter of the capacitor and the impedance test data, and the setting rule is fixed, the realization of computer programming is easy, manual intervention can be greatly reduced or even completely avoided, and higher modeling efficiency and automation degree can be realized.
S13, fitting the capacitor impedance function and the impedance test data;
the objective function of the fit is set to be the relative error of the modulus and real part of the capacitor impedance function and the impedance test data, i.e. | | Z mod |-|Z mea ||/|Z mea I and R mod -R mea |/R mea And fitting by a nonlinear least square method while making the objective function smaller than a preset threshold. Since the impedance is complex, the variation range of the modulus and its real part (resistance) and imaginary part (reactance) can reach several orders of magnitude, and in order to obtain a more accurate fitting result in a wider angular frequency range, it is necessary to make the relative error of two independent components of the impedance smaller than a preset threshold value at the same time. The specific fitting process can be realized by adopting corresponding algorithms of common commercial or open-source scientific computing software.
And S14, adjusting the initial value of the undetermined coefficient if necessary according to the range of the fitting error until the fitting error meets the end condition, and obtaining the coefficient of the impedance function.
The method for adjusting the initial value of the undetermined coefficient comprises one or more of the following steps:
adjusting the first geometric progression ω 1,k And the first common ratio alpha;
adjusting the second geometric progression ω 2,k And the second common ratio beta;
adjusting the central angular frequency ω 0,k Number and location of the cells.
The order of the impedance functions of the RC, RL and RLC parallel resonant networks can be respectively changed by adjusting the parameters, so that the impedance functions can be flexibly set according to the requirement of fitting precision or the complexity limit of an equivalent circuit. Generally, fitting error can be reduced within a certain range by decreasing α and β, thereby increasing the number of poles and the order.
And S15, selecting a target RC network and a target RL network from the candidate network type set, and generating a capacitor equivalent circuit model by using the coefficient of the impedance function.
For RC, RL networks, the set of candidate network types includes: one of Foster I, foster II, cauer I and Cauer II types, or a mixture of two or more of them network types. The values of the respective elements can be obtained by classical network synthesis methods.
For an RLC parallel resonant network, the element values are calculated according to the following formula:
R 3,k ＝d k /e 1,k ，L 3,k ＝d k /e 0,k ，C 3,k ＝1/d k 。 (6)
in another embodiment, the capacitor equivalent circuit modeling method may be extended to fit admittance test data to a corresponding function, and the corresponding function form and initial value settings of the fitting variables may be obtained according to a dual rule of the circuit network.
In one specific embodiment, the impedance frequency characteristic of a certain type of stacked chip capacitor with a nominal capacity of 1nF is shown in solid line in fig. 3. The initial values of the coefficients to be determined for the impedance functions of the various sub-networks are set as follows:
RC network: alpha is taken to be 5.012 1,k ＝[0,-6.2832×10 6 ,-3.1491×10 7 ,-1.5783×10 8 ]，r 1,k ＝[1×10 9 ,1.1615×10 7 ,2.4082×10 7 ,5.9308×10 7 ]，k 0 ＝0.2408；
The RL network: beta is taken to be 10,p 2,k ＝-4.042×10 9 ，c k ＝0.2236，k 1 ＝6.6399×10 -10 ；
RLC parallel resonant network: d k ＝[4.123×10 9 ,3.1555×10 10 ,9.09×10 10 ,1.4918×10 11 ]，e 0,k ＝[6.2094×10 19 ,4.7524×10 20 ,1.369×10 21 ,2.2468×10 21 ]，e 1,k ＝[5.2859×10 9 ,2.895×10 9 ,9.3905×10 9 ,7.7497×10 9 ]。
After fitting treatment by a nonlinear least square method, the following coefficients are obtained:
RC network: p is a radical of 1,k ＝[0,-1.7929×10 7 ,-1.6913×10 9 ,-2.3105×10 8 ]，r 1,k ＝[1.0758×10 9 ,3.8342×10 7 ,2.7471×10 8 ,5.9274×10 7 ]，k 0 =0.14131, i.e.:
conversion to a rational function is:
RL network: p is a radical of 2,k ＝-3.9421×10 11 ，c k ＝182.82，k 1 ＝3.7336×10 -18 Namely:
conversion to a rational function is:
RLC parallel resonant network: d k ＝[8.0973×10 8 ,8.9189×10 10 ,1.513×10 11 ,5.5647×10 10 ]，e 0,k ＝[6.0642×10 19 ,4.7709×10 20 ,1.5239×10 21 ,2.2527×10 21 ]，e 1,k ＝[3.1904×10 9 ,9.4024×10 9 ,2.4382×10 10 ,5.0575×10 9 ]Namely:
the fitting time can be controlled within 5 seconds; the fitted model impedance frequency characteristic curve is shown by a dotted line in fig. 3; the fit error is within 5%, as shown in fig. 4.
And the RC and RL networks of Foster I, foster II, cauer I and Cauer II types can be respectively obtained by using a classical network synthesis method. For example, an RC network of Foster type I is readily obtained from a partial fractal expansion of equation (7), as shown in FIG. 5 (a), where:
C 0 ＝1/(1.0758×10 9 )＝9.2957×10 -10 ，
R inf ＝k 0 ＝0.14131，
C k ＝1/r 1,k ＝[2.6081×10 -8 ,3.6402×10 -9 ,1.6871×10 -8 ]，
R k ＝-r 1,k /p 1,k ＝[2.1386,0.16242,0.25655]。
taking reciprocal of the formula (8) to obtain admittance function Y of the RC network RC (s) reacting Y RC The Foster type II RC network is easily obtained by partial development of (s)/s as shown in FIG. 5 (b). Will Z RC (s) developing at s = ∞ in a continuous fraction manner, so that a Cauer type I RC network can be obtained, as shown in fig. 5 (c); will Z RC (s) develop at s =0 in successive fractions, and a Cauer type II RC network can be obtained, as shown in fig. 5 (d). RL networks of the types Foster I, foster II, cauer I and Cauer II are similarly obtainable according to formula (9) or (10), as shown in FIG. 6.
The values of the elements of the RLC parallel resonant network can be calculated according to equations (11) and (6), as shown in fig. 7, where:
R 3,k ＝[0.2538,9.4858,6.2053,11.003]，
L 3,k ＝[1.3353×10 -11 ,1.8694×10 -10 ,9.9288×10 -11 ,2.4703×10 -11 ]，
C 3,k ＝[1.235×10 -9 ,1.1212×10 -11 ,6.6094×10 -12 ,1.797×10 -11 ]，
connecting any one of the types of RC network (fig. 5 (a) - (d)), RL network (fig. 6 (a) - (d)) and RLC parallel resonance network (fig. 7) in series is a complete equivalent circuit model of the laminated chip capacitor of the model.
The invention provides a capacitor equivalent circuit modeling method, which comprises the following steps: adding impedance functions of a resistor-capacitor network containing a coefficient to be determined, the resistor-inductor network and the resistor-inductor-capacitor parallel resonance network to form a capacitor impedance function; respectively presetting initial values of the undetermined coefficients based on parameters of the capacitor and impedance test data; fitting the capacitor impedance function and the impedance test data; adjusting the initial value of the undetermined coefficient if necessary according to the range of the fitting error until the fitting error meets the end condition, and determining the coefficient of the impedance function; and selecting a target resistance-capacitance network and a resistance-inductance network from the candidate network type set, and generating a capacitor equivalent circuit model by using the coefficient of the impedance function.
The invention has the following advantages:
1. different from the prior art that the network type and the order are firstly determined and then circuit element values are directly fitted, the method firstly fits the impedance or the coefficient of the impedance function of the RC, RL and RLC parallel resonance networks, and then selects the network type to obtain the final equivalent circuit and the element values thereof through network synthesis. The method used in the present invention has a wider general applicability since any RC and RL impedance or admittance function is used, independent of the kind and structure of the capacitor.
2. Hair brushThe order of the RC and RL impedance or admittance functions used for the fitting may be varied by changing the first series of equal ratios ω 1,k Second equal-ratio series omega 2,k The value range, the first common ratio alpha and the second common ratio beta are adjusted, so that the value range, the first common ratio alpha and the second common ratio beta can be flexibly set according to the fitting precision requirement or the complexity limitation of an equivalent circuit. Generally, fitting error can be reduced within a certain range by decreasing α and β, thereby increasing the number of poles and the order.
3. Except that the order can be conveniently adjusted, the fitting functions are respectively partial or first-order/second-order rational function expansion in the same form, the rule of initial value setting of the corresponding coefficient is fixed, the modeling process is easy to realize by computer programming, manual intervention can be greatly reduced or even completely avoided, and therefore higher modeling efficiency and automation degree can be realized.
4. The invention can obtain various types of circuit networks with completely equivalent impedance and admittance frequency characteristics, the network types can be flexibly selected or combined according to actual requirements, and the conversion process can be efficiently realized by simple computer programming.
5. The invention decomposes the fitting impedance function into the sum of the impedance functions of the RC, RL and RLC parallel resonance networks, avoids the negative value RLC elements appearing in the fitting of universal complex function and the replacement of equivalent circuit, and can ensure the passivity and the realizability of the equivalent circuit and each element.
The embodiments in the present specification are described in a progressive manner, and all the embodiments are directly referred to the same or similar parts, and each embodiment is mainly described as different from the other embodiments. In particular, for the system embodiment, since it is substantially similar to the method embodiment, the description is simple, and for the relevant points, reference may be made to the partial description of the method embodiment. It should be noted that, the technical features of the embodiments may be arbitrarily combined, and for the sake of brevity, all possible combinations of the technical features in the embodiments are not described, but should be considered as the scope of the present specification as long as there is no contradiction between the combinations of the technical features.
The above-mentioned embodiments only express some preferred embodiments of the present application, and the description thereof is more specific and detailed, but not construed as limiting the scope of the invention. It should be noted that, for those skilled in the art, various modifications and substitutions can be made without departing from the technical principle of the present invention, and these should be construed as the protection scope of the present application. Therefore, the protection scope of the present patent shall be subject to the protection scope of the claims.
Claims (6)
1. A capacitor equivalent circuit modeling method, wherein the equivalent circuit is composed of R (resistance), C (capacitance), and L (inductance) elements, the method comprising:
adding impedance functions of an RC network, an RL network and an RLC parallel resonance network containing a coefficient to be determined to form a capacitor impedance function;
respectively presetting initial values of the undetermined coefficients based on parameters of the capacitor and impedance test data;
fitting the capacitor impedance function and the impedance test data;
adjusting the initial value of the undetermined coefficient if necessary according to the range of the fitting error until the fitting error meets the end condition, and determining the coefficient of the impedance function;
and selecting a target RC network and a target RL network from the candidate network type set, and generating a capacitor equivalent circuit model by using the coefficients of the impedance function.
2. The method of claim 1, wherein in the complex frequency domain (s-domain), the RC network impedance function with the coefficient to be determined is represented by:
The expression of the RL network impedance function containing the coefficient to be determined is as follows:
The expression of the RLC parallel resonance network impedance function containing undetermined coefficients is as follows:
3. The method as claimed in claim 2, wherein the method for presetting the initial value of the undetermined coefficient comprises:
dividing the impedance test angular frequency range by taking the self-resonance angular frequency of the capacitor as a boundary, and recording a low frequency band and a high frequency band as a first frequency interval and a second frequency interval respectively;
generating a first geometric progression based on a first common ratio in the first frequency interval;
generating a second geometric progression based on a second common ratio in the second frequency interval;
and acquiring the central angular frequency of the part with larger or non-monotonic change of the capacitor impedance or resistance curve curvature in the second frequency interval.
And presetting initial values of impedance function undetermined coefficients of the RC network, the RL network and the RLC parallel resonance network in sequence according to a fixed rule based on the first equal-ratio sequence, the second equal-ratio sequence and the central angular frequency respectively in combination with the nominal capacity of the capacitor, the self-resonance angular frequency and corresponding impedance test data.
4. The method of claim 1, wherein the fitting process comprises:
and fitting by using a nonlinear least square method so that the relative error between the capacitor impedance function value and the modulus and the real part of the impedance test data is smaller than a preset threshold value.
5. The method of claim 3, wherein the method of adjusting the initial value of the pending coefficient comprises:
adjusting the value range of the first geometric series and the first common ratio;
adjusting the value range of the second geometric series and the second common ratio;
adjusting the number and location of the center angular frequencies.
6. The method of claim 1, wherein the set of candidate network types comprises:
one of Foster I, foster II, cauerI and CauerII types, or a mixed type of two or more network types therein.
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| CN117517792A (en) * | 2023-10-31 | 2024-02-06 | 盐城工学院 | Automatic capacity detection device and detection method for new energy capacitor |
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2022
- 2022-10-10 CN CN202211233496.8A patent/CN115544933A/en active Pending
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117517792A (en) * | 2023-10-31 | 2024-02-06 | 盐城工学院 | Automatic capacity detection device and detection method for new energy capacitor |
| CN117517792B (en) * | 2023-10-31 | 2024-06-07 | 盐城工学院 | Automatic capacity detection device and detection method for new energy capacitor |
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