CN108470104A - Equivalent circuit parameter Modeling Calculation method for impedance analyzer - Google Patents
Equivalent circuit parameter Modeling Calculation method for impedance analyzer Download PDFInfo
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- CN108470104A CN108470104A CN201810238511.5A CN201810238511A CN108470104A CN 108470104 A CN108470104 A CN 108470104A CN 201810238511 A CN201810238511 A CN 201810238511A CN 108470104 A CN108470104 A CN 108470104A
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- equivalent circuit
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/30—Circuit design
- G06F30/36—Circuit design at the analogue level
- G06F30/367—Design verification, e.g. using simulation, simulation program with integrated circuit emphasis [SPICE], direct methods or relaxation methods
Abstract
The present invention relates to a kind of equivalent circuit parameter Modeling Calculation methods for impedance analyzer, including：1) frequency range is selected, multiple Frequency points are selected in frequency range and measures the impedance value of these Frequency points in a manner of log series model；2) equivalent-circuit model is selected：3) function of its impedance about component parameters is calculated according to selected model；4) impedance value that step 1) measures is substituted into respectively in the function that step 3) calculates gained, simultaneous inconsistent equation group；5) complex field least-squares estimation formula is utilized to calculate the normal equation of inconsistent equation group；6) it utilizes numerical algorithm to solve estimation equation, obtains the parameter of equivalent circuit.The present invention carries out modeling analysis to the equivalent circuit that multiple element forms, and calculates equivalent circuit parameter using the testing impedance data of different frequency point；By the least square curve fitting algorithm of complex field, equivalent circuit parameter is calculated, to achieve the purpose that modeling analysis.
Description
Technical field
The invention belongs to electronic surveying field, especially a kind of equivalent circuit parameter Modeling Calculations for impedance analyzer
Method.
Background technology
Existing impedance measurement technique is the real part and imaginary part for measuring impedance respectively by hardware circuit, then with resistance-electricity
The form of the series connection (or in parallel) of (or capacitance) is felt to characterize the impedance under specific frequency point.
But when measurement frequency is higher, the parasitism that can not describe to generate on component with this parameter characterization form is joined
Number；Or when measured piece has complex internal composed structure, which can not also describe the practical impedance characteristic of measured piece.
Invention content
The technical problem to be solved by the present invention is to：A kind of equivalent circuit parameter Modeling Calculation for impedance analyzer is provided
Method, the impedance value measured in multiple Frequency points using measured piece calculate equivalent circuit parameter.
The technical solution adopted by the present invention to solve the technical problems is：A kind of equivalent circuit for impedance analyzer is joined
Number Modeling Calculation method, includes the following steps：
1) frequency range is selected, multiple Frequency points are selected in frequency range and measures these frequencies in a manner of log series model
The impedance value of point；The impedance measurement of multi-frequency point is carried out, frequency range is bigger, points are the more then better；
2) equivalent-circuit model is selected：Such as MODEL C,
3) model selected according to step 2) calculates function of its impedance about component parameters；
4) impedance value that step 1) measures is substituted into respectively in the function that step 3) calculates gained, simultaneous inconsistent equation group；
5) complex field least-squares estimation formula is utilized to calculate the normal equation of inconsistent equation group；The solution of normal equation is former lance
The least squares sense solution of shield equation group, then normal equation also known as estimate equation；
6) it utilizes numerical algorithm to solve estimation equation, obtains the parameter of equivalent circuit.
Furtherly, the invention also includes steps 7), make impedance-frequency by the equivalent circuit parameter that step 6) is calculated
Matched curve, and with experiment curv compare；If fitting result mismatches, assert that the selected model of step 2) is not suitable for
Equivalent measured piece, an alternative model simultaneously repeat step 4) to step 7).
The invention has the advantages that solving defect present in background technology, to the equivalent electricity of multiple element composition
Road carries out modeling analysis, and calculates equivalent circuit parameter using the testing impedance data of different frequency point；Most by complex field
Small two multiply curve fitting algorithm, and equivalent circuit parameter is calculated, to achieve the purpose that modeling analysis；The present invention can be used as one
The effective means that kind parasitic parameter measures and black box measures.
Description of the drawings
Present invention will be further explained below with reference to the attached drawings and examples.
Fig. 1 is a kind of typical equivalent circuit；
Fig. 2-Fig. 8 is seven kinds of common equivalent circuits.
Specific implementation mode
Presently in connection with attached drawing and preferred embodiment, the present invention is described in further detail.These attached drawings are simplified
Schematic diagram, the basic structure of the invention will be illustrated schematically only, therefore it only shows the composition relevant to the invention.
Shown in FIG. 1 is that one kind carrying out modeling analysis by taking typical circuit as an example：
First, the foundation of equivalent circuit mathematical model, circuit, founding mathematical models are as follows as shown in figure：
For ith measurement data (0≤i≤n, n are the number of measurement point), have：
For ith measurement point, wiFor its angular frequency, RiAnd XiRespectively it measures the real part and imaginary part of gained impedance.
(1-2) and (1-3) formula denominator of dividing out can be obtained：
R1-Riwi 2R1 2C1 2=Ri (1-4)
j[wi 3L1R1 2C1 2-Xiwi 2R1 2C1 2+wi(L1-R1 2C1)]=jXi (1-5)
(1-4) is added with (1-5) both members：
R1-R1 2C1 2(Riwi 2+jXiwi 2)+jwi 3(L1R1 2C1 2)+jwi(L1-R1 2C1)=Ri+jXi
=Zi (1-6)
Write as matrix form：
Further it is written as：
AK=B (1-8)
A, K, B are multifactor matrix.
Then, pass through least square solution inconsistent equation group；
For formula (1-8), the estimation formulas of the least square method in complex field need to be used to solve K.
Estimation formulas is write：
According to formula (1-7), obtained in conjunction with estimation formulas：
By both members with divided by wi 3It is calculated with simplifying：
Formula (2-3) is to calculate the estimation equation of circuit model parameters shown in figure one.
R is can be obtained with Numerical Methods Solve formula (2-3)1、L1、C1。
Fig. 2-Fig. 8 is 7 kinds of circuit common models, their parameter Estimation equation inference is as follows：
Model A is shown in Fig. 2 (Inductor with high corecoss)
By the admittance function of modelSimultaneous inconsistent equation group：
Calculating is substituted into according to complex field least-squares estimation formula and abbreviation obtains its and estimates equation：
Model B is shown in Fig. 3 (Inductor Resistor)
By the admittance function of modelSimultaneous inconsistent equation group：
Calculating is substituted into according to complex field least-squares estimation formula and abbreviation obtains its and estimates equation：
MODEL C is shown in Fig. 4 (High-value resistor)
By the impedance function of modelSimultaneous inconsistent equation group：
Calculating is substituted into according to complex field least-squares estimation formula and abbreviation obtains its and estimates equation：
Model D is shown in Fig. 5 (Capacitor)
By the impedance function of modelSimultaneous inconsistent equation group：
Calculating is substituted into according to complex field least-squares estimation formula and abbreviation obtains its and estimates equation：
Model E is shown in Fig. 6 (Resonator)
By the admittance function of modelSimultaneous inconsistent equation group：
Calculating is substituted into according to complex field least-squares estimation formula and abbreviation obtains its and estimates equation：
Model F is shown in Fig. 7 (Inductor with ESR)
By the impedance function of modelSimultaneous inconsistent equation group：
Calculating is substituted into according to complex field least-squares estimation formula and abbreviation obtains its and estimates equation：
Model G is shown in Fig. 8 (Capacitor)
By the impedance function of modelSimultaneous inconsistent equation group：
Calculating is substituted into according to complex field least-squares estimation formula and abbreviation obtains its and estimates equation：
The specific implementation mode of the only present invention described in description above, various illustrations are not to the reality of the present invention
Matter Composition of contents limits, and person of an ordinary skill in the technical field can be to described in the past specific after having read specification
Embodiment is made an amendment or is deformed, without departing from the spirit and scope of invention.
Claims (4)
1. a kind of equivalent circuit parameter Modeling Calculation method for impedance analyzer, it is characterised in that include the following steps：
1) frequency range is selected, multiple Frequency points are selected in frequency range and measures these Frequency points in a manner of log series model
Impedance value；
2) equivalent-circuit model is selected；
3) model selected according to step 2) calculates function of its impedance about component parameters；
4) impedance value that step 1) measures is substituted into respectively in the function that step 3) calculates gained, simultaneous inconsistent equation group；
5) complex field least-squares estimation formula is utilized to calculate the normal equation of inconsistent equation group；
6) it utilizes numerical algorithm to solve normal equation, obtains the parameter of equivalent circuit.
2. being used for the equivalent circuit parameter Modeling Calculation method of impedance analyzer as described in claim 1, it is characterised in that：Also
Including step 7), make the matched curve of impedance-frequency by the equivalent circuit parameter that step 6) is calculated, and with experiment curv pair
Than；If fitting result mismatches, assert that the selected model of step 2) is not suitable for equivalent measured piece, an optionally model and repetition
Step 4) is to step 7).
3. being used for the equivalent circuit parameter Modeling Calculation method of impedance analyzer as described in claim 1, it is characterised in that：Institute
The solution for stating normal equation in step 5) is the solution of inconsistent equation group least square, and normal equation is also estimation equation.
4. being used for the equivalent circuit parameter Modeling Calculation method of impedance analyzer as described in claim 1, it is characterised in that：Institute
Stating step 2) electrical equivalent model is：
Or
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110542794A (en) * | 2019-08-28 | 2019-12-06 | 华南理工大学 | Equivalent circuit impedance measurement method and device based on constraint optimization problem |
| CN112464602A (en) * | 2020-12-03 | 2021-03-09 | 电子科技大学 | High-frequency SPICE model establishment method for multi-resonance-point resistor and inductor |
| GB2618861A (en) * | 2021-09-02 | 2023-11-22 | Qmax Test Equipments Pvt Ltd | Portable nodal impedance analyser |
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| US20070276642A1 (en) * | 2004-04-30 | 2007-11-29 | Austriamicrosystems Ag | Process For Producing A High-Frequency Equivalent Circuit Diagram For Electronic Components |
| CN101692109A (en) * | 2009-10-13 | 2010-04-07 | 清华大学 | Impedance measurement method based on system discrimination |
| CN104679959A (en) * | 2015-03-12 | 2015-06-03 | 华北电力大学（保定） | Modeling method for broadband equivalent circuit of 1,000kV extra-high-voltage capacitive voltage divider |
| CN106021811A (en) * | 2016-06-08 | 2016-10-12 | 福州大学 | Determination method for broadband complex magnetic conductivity of magnetic material |
| WO2018032713A1 (en) * | 2016-08-16 | 2018-02-22 | 南京展芯通讯科技有限公司 | Field effect transistor small-signal equivalent circuit model having channel advanced parasitic element |
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Patent Citations (5)
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| US20070276642A1 (en) * | 2004-04-30 | 2007-11-29 | Austriamicrosystems Ag | Process For Producing A High-Frequency Equivalent Circuit Diagram For Electronic Components |
| CN101692109A (en) * | 2009-10-13 | 2010-04-07 | 清华大学 | Impedance measurement method based on system discrimination |
| CN104679959A (en) * | 2015-03-12 | 2015-06-03 | 华北电力大学（保定） | Modeling method for broadband equivalent circuit of 1,000kV extra-high-voltage capacitive voltage divider |
| CN106021811A (en) * | 2016-06-08 | 2016-10-12 | 福州大学 | Determination method for broadband complex magnetic conductivity of magnetic material |
| WO2018032713A1 (en) * | 2016-08-16 | 2018-02-22 | 南京展芯通讯科技有限公司 | Field effect transistor small-signal equivalent circuit model having channel advanced parasitic element |
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110542794A (en) * | 2019-08-28 | 2019-12-06 | 华南理工大学 | Equivalent circuit impedance measurement method and device based on constraint optimization problem |
| CN112464602A (en) * | 2020-12-03 | 2021-03-09 | 电子科技大学 | High-frequency SPICE model establishment method for multi-resonance-point resistor and inductor |
| GB2618861A (en) * | 2021-09-02 | 2023-11-22 | Qmax Test Equipments Pvt Ltd | Portable nodal impedance analyser |
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