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Experimental Modeling of CM Chokes
This chapter treats an experimental modeling method of CM chokes used in EMI filters. This method involves the build of a choke model through impedance measurements, which are frequency domain small-signal analysis in essence. Under real working conditions, the large signal performances of the choke will be affected due to saturation effects in magnetic material. However, the small signal modeling approach is still widely used as the first step for EMI filter design, since they can reveal many important physic insights of the filter or components such as CM filtering inductance, DM filtering inductance as well as the parasitic capacitances and other HF effects.
In the following parts, the existing models of CM chokes will first be reviewed. Next, the IRFA fitting method will be presented before introducing the proposed HF equivalent circuit model for CM chokes. A simple parameter extraction procedure is described by an example and experimental validations are given at the end to show the effectiveness of the proposed model and the extraction algorithm.
HF Equivalent Circuits of CM Chokes
Brief Review of Existing Models
Figure 2.1(a) illustrates the electric symbol of a CM choke, which is the simplest form for representation and is hardly used in simulations. During the past decades, many physic-based and measurement-based models are studied. For the reasons stated in the first chapter, measurement-based models relying on black-box are not covered in this section but only equivalent circuit models are discussed. A commonly used equivalent circuit for CM chokes is given in Figure 2.1(b). It is a coarse model since it does not consider the frequency dependent losses of the choke due to the characteristics of magnetic core and winding losses. Moreover, the parasitic capacitances network is not sufficient to fully represent the electrostatic behavior of the component. Indeed, note that three independent voltages (V13, V24, V34) can be established between the terminals of the component, and three independent capacitances are thereby necessary to completely describe the electric energy stored in the component [41]. In common practice, the parameters of such models are determined from measured data on several frequency points, so it will not provide high accuracy on a wide frequency band.
In [33], a more sophisticated equivalent circuit model is proposed for CM chokes [see Figure 2.1(c)] and its parameters are extracted by optimization with genetic algorithms. This equivalent circuit allows a high modeling accuracy over the HF resonances. However, the LF part accuracy is really poor as it can be seen from the validation results given in [33] .Besides, it does not provide any clear physic interpretations for the elements in the model so that it remains somehow a black-box model for designers. Though the parameters of the model are extracted through an optimization process instead of manual trials, using heuristic methods such as 50 genetic algorithms requires relatively long time for searching the results and may suffer from convergence problems.
Equivalent Circuit Model for CM Chokes with More Physical Meanings
Model Structure and Parameter Extraction
Recently, a HF equivalent circuit model for CM chokes with more physic meanings has been reported in [30] [see Figure 2.2(a)]. This symmetrical structure consists in a special case of a 2-winding transformer equivalent circuit [41]. The main elements in this model are:
η : transformation ratio that is assumed to be unity;
Z1: leakage impedance including frequency-variant winding resistance Rw(f), leakage inductance Ll(f) due to skin and proximity effects of the winding wire [see Figure 2.2(b)]
Z2: magnetizing impedance including the frequency-dependent inductance and magnetic core losses |see Figure 2.2(c)].
To extract these equivalent circuit parameters, five specific impedance measurements are performed, as presented in Figure 2.3. Table 2.1 summarizes the correspondences between these measurements and the parameters that can be determined.
The extraction procedure consists in observations on the variation of the measured impedances, while some typical frequency responses are identified to extract the searched parameters. For example, 20 dB/dec. and -20 dB/dec. slopes symbolize an inductance and a capacitance respectively. The resonance frequency can also be used to determine the parasitic capacitance through the well-known formula (2.1)
where fres denotes the resonance frequency, L the inductance and Cpara the parasitic capacitance. Regarding the determination of impedances Z1 and Z2, some manual adjustments on the parameters are necessary to further improve the accuracy of the results. Once these parameters are determined, the large frequency band behavior of the CM choke can be accurately modeled by the obtained equivalent circuit.
Limits of Application
Though the previous HF equivalent circuit model can effectively describe the behavior of a CM choke, this model and its parameter extraction procedure can still be improved for the following reasons:
a. The choice of the circuit topology is based on observations. For example, the admittance Y2 = (Z2)-1 in Figure 2.2(c) contains:
One pole at origin: the branch of L2;
One stable real pole: the branch of R2, RC2, C2 and R2¢ ;
One pure imaginary pole-pair: the branch of L2¢ and C2¢ .
In fact, choosing such circuit topology through observations requires a lot of experience, making this model less accessible to novice designers. Therefore, a clear and systematic procedure is needed for synthesizing the equivalent circuit. b. Manual tweaking on the parameters are needed in [30] to achieve a high accuracy. As a result of numerous trial/error iterations, this procedure becomes complex and time-consuming. Therefore, a computer-aided procedure seems
more attractive for practical applications.
Introduction to the Developed Modeling Method
In consideration with the previous necessities, the HF equivalent circuit model for CM chokes proposed in [30] will be improved so that its circuit topology can be determined systematically. Besides, the parameters of the model will be extracted by a numerical method called Iterative Rational Function Approximation (IRFA). Using an unfixed topology coupled with IRFA algorithm, the equivalent circuits can be generated automatically, based on well-chosen impedance measurements. With decent treatment, the obtained equivalent circuit allows to have a good accuracy over a wide frequency range.
For better understanding, the IRFA method will be presented at first step and the improved HF equivalent circuit model will be introduced subsequently.
Table of contents :
Abstract
Résumé
General Introduction
Scope of the Work
Organization of the Dissertation
Chapter 1. Introduction
1.1 EMI in Power Electronics
1.1.1 EMI Sources in Power Electronics
1.1.2 EMC Standards and Conducted EMI Measurements
1.2 Power Line EMI Filters
1.2.1 Overview
1.2.2 Passive EMI Filters
1.2.3 Technologies for Passive EMI Filters
1.2.4 Design of Planar EMI Filters
1.3 Modeling of Planar EMI Filters
1.3.1 Global View of the Modeling Issue
1.3.2 Experimental Modeling Methods
1.3.3 Analytical Methods
1.4 Conclusion
Chapter 2. Experimental Modeling of CM Chokes
2.1 HF Equivalent Circuits of CM Chokes
2.1.1 Brief Review of Existing Models
2.1.2 Equivalent Circuit Model for CM Chokes with More Physical Meanings
2.1.3 Introduction to the Developed Modeling Method
2.2 Iterative Rational Function Approximation Approach
2.2.1 Reminder on Rational Functions
2.2.2 Rational Function Approximation
2.2.3 Introduction of Iterative Rational Function Approximation Method
2.3 IRFA Adapted Equivalent Circuit Synthesis
2.3.1 Foster Expansion General Expression
2.3.2 General Topology and Terms d and e·s
2.3.3 Real Pole-Residue Terms
2.3.4 Complex Pole-Residue Pair Terms
2.4 Complete Identification Process
2.4.1 Improved HF Equivalent Circuit Model
2.4.2 General Parameter Extraction Procedure
2.4.3 Application Example
2.5 Experimental Validations
2.5.1 Impedance Measurements and Sensitivity Analysis
2.5.2 Insertion Loss Measurements
2.6 Discussion
2.7 Conclusion
Chapter 3. Analytical Modeling of Parasitic Capacitances of Planar Components
3.1 Review of Analytical Methods for Parasitic Capacitances Modeling
3.1.1 Plate Capacitance Formula and Other Empirical Formulas
3.1.2 Conformal Mapping
3.2 Electric Field Decomposition Method
3.2.1 Overview of EFD Method
3.2.2 Field-Based Stray Capacitance Modeling
3.3 Parasitic Capacitance Analysis of Planar Components based on EFD
3.3.1 Basic Structures
3.3.2 Configuration of PCB Structure with Six Conductors
3.3.3 Numerical Validation
3.3.4 Configuration of PCB structure with Eight Conductors
3.4 Influence of Ferrite Core
3.4.1 Permittivity of Ferrite Core
3.4.2 Perfect Electric Conductor
3.4.3 Transformation Technique for Handling Floating PEC Core
3.4.4 Combination of EFD Method and Transformation Technique
3.5 Energy Approach
3.5.1 Derivation of Self-parasitic Capacitance
3.5.2 Calculation of Electric Energy in a Single Port Component
3.5.3 Procedure for Calculating the Parasitic Capacitances of Planar CM Chokes
3.6 Applications
3.6.1 Planar Inductor without Ferrite Core
3.6.2 Planar Inductor with Ferrite Core
3.6.3 Planar CM Choke with Ferrite Core
3.7 Discussion
3.8 Conclusion
Chapter 4. Modeling of Parasitic Elements of Planar CM Choke via Multilayered Green’s Function
4.1 Green’s Function Theory
4.1.1 Introduction to Green’s Function
4.1.2 2D Green’s Function for Homogenous Space
4.2 Parasitic Capacitance Calculation Using Multilayered Green’s Function
4.2.1 Declaration of Problem: PCB Structure with Ferrite Core
4.2.2 Multilayered Green’s Function for Rectangular Region
4.2.3 Numerical Stability of the Green’s Function
4.2.4 Moment Method for Calculating the Capacitance Matrix
4.2.5 Numerical Validation
4.2.6 Applications on Planar Components
4.2.7 Discussion
4.3 Static Leakage Inductance Calculation Using Multilayered Green’s Function
4.3.1 Energy Base Method for Calculating Static Leakage Inductance
4.3.2 Review of Existing Methods
4.3.3 Multilayered Green’s Function in Magnetostatic
4.3.4 Application on Planar CM Choke with FPC Leakage Layer
4.3.5 Discussion
4.4 Conclusion
Chapter 5. Designs of Planar Components for EMI Filters
5.1 Improved Parasitic Capacitance Cancellation with Planar Components
5.1.1 Overview of Parasitic Capacitance Cancellation Techniques
5.1.2 Improved Parasitic Capacitance Cancellation for Planar DM Chokes
5.1.3 Experimental Validations
5.1.4 Discussion
5.2 Toroid-EQ Mixed Structured CM Choke
5.2.1 Review of Integration Techniques of CM and DM Chokes
5.2.2 Design of the Toroid-EQ CM Choke
5.2.3 Experimental Validations and Discussion
5.2.4 Discussion
5.3 Conclusion
Conclusion and Perspectives
Appendix
Appendix I. Householder Transformation
Appendix II. Derivation of (2.16)-(2.17)
Appendix III. Derivation of Eq.(3.5)
III.1 Elliptic Integral of the First Kind
III.2 Demonstration of (3.4) and (3.5)
Appendix IV. Derivation of (3.45)
Appendix V. Derivation of Multilayered Green’s Function for Electrostatic
V.1 General Solution by Separation of Variable
V.2 Derivation of (4.16)-(4.19)
Appendix VI. Derivation of Multilayered Green’s Function for Magnetostatic
References
Remerciements
