1. Equivalent source corresponding to radiated field of EMC filter components September 16, Sanâa ZANGUI

2. Outline
Introduction
Aims
Equivalent model
Mutual inductance
Validation
Measurement method
Summary
Questions

3. Power electronic system
Introduction
In Power electronic
=> Noises
By conduction
By radiation
Low pass filter => reduce conducted noises (HF)
Power electronic system
Filter
Motor
Magnitude (dB)
Low pass filter
Frequency

4. The self-parasitics of components
Introduction
1MHz
30MHz
Mutuals inductances
Frequency
Magnitude (dB)
The self-parasitics of components 1 2 Cy DM
EPC
EPR L
ESR
ESL M 3
Magnetic Coupling Analysis (Low voltage/ high current)
Near-field Approximation
- Distance between components<< wavelength λ
- Maximum frequency (100MHz) => λmax= 3meters
Parasitic parameters and EMC Filter Performances:
- Self-parasitic
- Filter components coupling

5. Aims
Taking into account the effects of parasitic parameters in the first step of designer a filter
Equivalent Model Components :
Model the magnetic near-field produced by filter components
Take into account the near electromagnetic environment
Integrated in an electrical circuit software
Compute Coupling Effects
Using the equivalent model of components
According to their geometric placement.

6. Equivalent model ( Multipolar expansion)
3D EM fields : multipolar expansion
The field is computed outside the sphere that contains the equivalent source.
n=1 m=0 (dipole)
n=2 m=0 (quadrupole)

7. Equivalent model ( Equivalent model)
The expression of the magnetic field :
Qnm are functions of H
Computing H by using 3D numerical model or measurement
n: degree, m: azimuthal order, Ynm : The spherical harmonics functions
Qnm are parameters which need to be identified => equivalent model of the radiated field component

8. Mutual inductance Using the equivalent radiated field source model.
The spheres which contain each of the sources don’t intersect
The expression of the mutual inductance is:
The coefficients of the multipolar expansion of sources 1 and 2 must be expressed in the same reference => translation.

9. Computing method
Component 1
Component 2
H1 field by numerical modeling or measurement
H2 field by numerical modeling or measurement
Q1nm Computation
Q2nm Computation
Equivalent model 1
Equivalent model 2
Rotation + translation in the reference1 of Q2nm => Q’2nm
Computation of the mutual inductance M in function of Q1nm and Q’2nm
The translation is based on the
“Addition Theorem for Vector Spherical Harmonics”

10. Numerical modeling H field by FEM method(Flux3D®)
To result this case :
- Flux3D => 2000 unknows
- Multipolar expansion :
For n=Nmax=3 =>15unknows
For n=Nmax=5 => 35unknows
Infinite box
Sphere of validity
Element to modeling
Normal component of H => Qnm => equivalent model => mutual inductance

11. Validation (case 1)
Our result was compared to the numerical result computed by FEM(Flux3D cedrat).
Two loops, C1 and C2 with a radius “Rspire” of 10 cm, separated by r
At r =0.2m the error is greater for Nmax=3 than Nmax=5
Relative error (%)
Mutual inductance(H)

12. Validation (case 2) For the same previous loops C1 and C2
For a rotation of 45° around the y axis of the loop C2
The results are similar to the previous case
Mutual inductance(H)
Relative error (%)

13. Measurement method Coefficient of coupling K
Relation valid : L1. > 10*R (R : resistance of coil)
This method will be used : measure K in function of the distance between 2 identical loops
K: coefficient of coupling,
M: mutual inductance,
VS: input voltage, VE : output voltage.

14. Summary The method is validated :
Using multipolar expansion => equivalent model of the radiated field of components.
Using the equivalent model to compute the coupling (Mutual inductance) between components.
Apply this method to more complex components.
Measurement system that measures Qnm components .
Couple this method with Partial Element Equivalent Circuit (PEEC)=> filter modeling including all coupling (track/track, components/components, components/track).
The cylindrical harmonics can be considered for modeling components such as capacitors or cables.
Provide component libraries including models of coupling between power electronic components.

15. Questions