Pulsed Excitation of Reverberation Chambers

Work package 5 of the Doctoral Network NEPIT (Network for Evaluation of Propagation and Interference Training) deals with pulsed excitation of reverberation chambers, transient field distributions, experimental and simulative approaches.

The objective is to development appropiate models to predict the average and maximum field strength amplitude and its time derivative that will act onto a certain device under test in a reverberation chamber (RC), via simulation of transient fields inside the working volume and close to the (planar) boundaries of a RC, and validation via measurements and experiment in three reverberation chambers of different size (tiny, small, large w.r.t. wavelength).

The expected results are efficient field simulation methods based on plane-wave approaches or raytracing methods and the statistic distributions of field quantities of general validity for the time and frequency domain and different loading conditions. The corresponding doctoral candidate shall be trained in statistical field distribution in reverberant environments.

In this brief talk, some existing full-wave simulations as well as their corresponding challenges are discussed. The advantages of a plane wave integral representation of the field are shown, also for the analysis of transmission line coupling. The talk closes with a general discussion and an outlook with ideas for future work.

1. Full-wave SimulationsPlane Wave Integral RepresentationTransmission Line CouplingDiscussion and Outlook
Pulsed Excitation of Reverberation Chambers
Mathias Magdowski
Otto von Guericke University Magdeburg
Faculty of Electrical Engineering and Information Technology
Chair of Electromagnetic Compatibility
24. September 2024
License:c bCC BY 4.0 (Attribution, share alike)

2. Full-wave SimulationsPlane Wave Integral RepresentationTransmission Line CouplingDiscussion and Outlook
Motivation
Source:https://imgflip.com/i/6sa4e8

3. Full-wave SimulationsPlane Wave Integral RepresentationTransmission Line CouplingDiscussion and Outlook
Overview
Full-wave Simulations
Plane Wave Integral Representation
Transmission Line Coupling
Discussion and Outlook

4. Full-wave SimulationsPlane Wave Integral RepresentationTransmission Line CouplingDiscussion and Outlook
Method of Moments
H. G. Krauthäuser and J. B. Nitsch,
Elektromagnetische Verträglichkeit EMV 2002, ser. 10. Internationale Fachmesse und Kongress für Elektromagnetische Verträglichkeit,
ISBN 3-8007-2684-X, Düsseldorf: VDE Verlag, Apr. 2002, pp. 363–374

5. Full-wave SimulationsPlane Wave Integral RepresentationTransmission Line CouplingDiscussion and Outlook
Method of Moments
Parameters of this study:
Simulation frequency:200MHz
System of equations:13 000unknowns
Stirrer positions:72positions or5
◦
steps
Computer:
Challenges:
▶700minsimulation time per stirrer position (15minin pCONCEPT)
▶no reliable results with infinite conductivity of the chamber walls
▶wall conductivity has to be lowered from7.7×10
6S
m
to10
3S
m
to10
4S
m
to achieve
practical quality factors
▶numerical problems and unphysical results (field strength vs. conductivity)

6. Full-wave SimulationsPlane Wave Integral RepresentationTransmission Line CouplingDiscussion and Outlook
Method of Moments
Parameters of this study:
Simulation frequency:200MHz
System of equations:13 000unknowns
Stirrer positions:72positions or5
◦
steps
Computer:
Challenges:
▶700minsimulation time per stirrer position (15minin pCONCEPT)
▶no reliable results with infinite conductivity of the chamber walls
▶wall conductivity has to be lowered from7.7×10
6S
m
to10
3S
m
to10
4S
m
to achieve
practical quality factors
▶numerical problems and unphysical results (field strength vs. conductivity)

7. Full-wave SimulationsPlane Wave Integral RepresentationTransmission Line CouplingDiscussion and Outlook
Finite Differences in Time Domain
(a) 91.6MHz (b) 1.2GHz
F. Petit,
le domaine temporel,”

8. Full-wave SimulationsPlane Wave Integral RepresentationTransmission Line CouplingDiscussion and Outlook
Finite Differences in Time Domain
Problems associated with FDTD itself:
▶spatial discretization of objects inside the chamber
▶numerical dispersion resulting from the discretization of Maxwell’s equations by the
Yee scheme
▶adaption of mesh adapted to the wavelengths
▶numerical errors for non-uniform meshes (e.g. for the stirrer)
Inclusion of losses:
1.
2.
simulation to measured results in the post-processing)

9. Full-wave SimulationsPlane Wave Integral RepresentationTransmission Line CouplingDiscussion and Outlook
Finite Differences in Time Domain
Problems associated with FDTD itself:
▶spatial discretization of objects inside the chamber
▶numerical dispersion resulting from the discretization of Maxwell’s equations by the
Yee scheme
▶adaption of mesh adapted to the wavelengths
▶numerical errors for non-uniform meshes (e.g. for the stirrer)
Inclusion of losses:
1.
2.
simulation to measured results in the post-processing)

10. Full-wave SimulationsPlane Wave Integral RepresentationTransmission Line CouplingDiscussion and Outlook
Transmission-Line Matrix Method
(a)(b)(c)
J. Clegg, A. C. Marvin, J. F. Dawson,et al., IEEE Transactions on
Electromagnetic Compatibility, vol. 47, no. 4, pp. 824–832, Nov. 2005

11. Full-wave SimulationsPlane Wave Integral RepresentationTransmission Line CouplingDiscussion and Outlook
Transmission-Line Matrix Method
Challenges:
▶chamber wall reflection coefficient of−0.99
▶Q factor of800to2000in the frequency range200MHzto600MHz
▶simulation time of50minfor one stirrer position (42hfor full turn)
▶longer simulation time for finer mesh size or a reflection closer to unity
Idea for optimization:
▶optimize the stirrer design in free space with plane wave excitation
▶simulation time reduced by a factor of1500

12. Full-wave SimulationsPlane Wave Integral RepresentationTransmission Line CouplingDiscussion and Outlook
Transmission-Line Matrix Method
Challenges:
▶chamber wall reflection coefficient of−0.99
▶Q factor of800to2000in the frequency range200MHzto600MHz
▶simulation time of50minfor one stirrer position (42hfor full turn)
▶longer simulation time for finer mesh size or a reflection closer to unity
Idea for optimization:
▶optimize the stirrer design in free space with plane wave excitation
▶simulation time reduced by a factor of1500

13. Full-wave SimulationsPlane Wave Integral RepresentationTransmission Line CouplingDiscussion and Outlook
Finite Element Method
(a)(b)
G. Orjubin, E. Richalot, O. Picon,et al.,
obtained by fem,”IEEE Transactions on Electromagnetic Compatibility, vol. 49, no. 4, pp. 762–771, Nov. 2007, ISSN: 1558-187X.
DOI:10.1109/TEMC.2007.908266

14. Full-wave SimulationsPlane Wave Integral RepresentationTransmission Line CouplingDiscussion and Outlook
Finite Element Method
Challenges:
▶singular eigenproblem for perfect electrically conducting walls
▶increased complexity for realistic modeling of wall and material losses
▶poor performance for fictitious air losses
▶adaptive mesh technique for spurious solutions removal
Software packages:
▶Ansys HFSS (commercial)
▶PyFemax (open source)
▶COMSOL Multiphysics, prior FEMLAB (commercial)

15. Full-wave SimulationsPlane Wave Integral RepresentationTransmission Line CouplingDiscussion and Outlook
Finite Element Method
Challenges:
▶singular eigenproblem for perfect electrically conducting walls
▶increased complexity for realistic modeling of wall and material losses
▶poor performance for fictitious air losses
▶adaptive mesh technique for spurious solutions removal
Software packages:
▶Ansys HFSS (commercial)
▶PyFemax (open source)
▶COMSOL Multiphysics, prior FEMLAB (commercial)

16. Full-wave SimulationsPlane Wave Integral RepresentationTransmission Line CouplingDiscussion and Outlook
It is and remains a challenge!
Source:https://imgflip.com/i/94ht47andhttps://imgflip.com/i/94htdy

17. Full-wave SimulationsPlane Wave Integral RepresentationTransmission Line CouplingDiscussion and Outlook
It is and remains a challenge!
Source:https://imgflip.com/i/94ht47andhttps://imgflip.com/i/94htdy

18. Full-wave SimulationsPlane Wave Integral RepresentationTransmission Line CouplingDiscussion and Outlook
Plane Wave Integral Representation

19. Full-wave SimulationsPlane Wave Integral RepresentationTransmission Line CouplingDiscussion and Outlook
Plane Wave Integral Representationchamber
stirrer
receiving- or
transmitting
antenna
test item
working
volume
cable
D. A. Hill, IEEE Transactions on Electromagnetic
Compatibility, vol. 40, no. 3, pp. 209–217, Aug. 1998, ISSN: 0018-9375. DOI:10.1109/15.709418

20. Full-wave SimulationsPlane Wave Integral RepresentationTransmission Line CouplingDiscussion and Outlook
Single Plane WavexyzkEφϑ
(a)kˆφ
ˆ
ϑEα (b)
ϑ:
φ:
α:
(c)
Figure: kand the polarization of the electric fieldEin spherical
coordinates.

21. Full-wave SimulationsPlane Wave Integral RepresentationTransmission Line CouplingDiscussion and Outlook
Numerical Monte Carlo Simulation of the Stochastic Field
Chamber constant:
E
2
0=
QP
ωεV
=
D
|E|
2
E
Q:
P:
ω:
ε:
V:
Field strength normalization viaE=
E0/
√
Nfor every wave:
▶for comparable results with different numbers of waves
▶factor of 2 is due to the reflection of the waves at the plane

22. Full-wave SimulationsPlane Wave Integral RepresentationTransmission Line CouplingDiscussion and Outlook
Numerical Monte Carlo Simulation of the Stochastic Field
Chamber constant:
E
2
0=
QP
ωεV
=
D
|E|
2
E
Q:
P:
ω:
ε:
V:
Field strength normalization viaE=
E0/
√
Nfor every wave:
▶for comparable results with different numbers of waves
▶factor of 2 is due to the reflection of the waves at the plane

23. Full-wave SimulationsPlane Wave Integral RepresentationTransmission Line CouplingDiscussion and Outlook
Distribution of the Angles for the Monte Carlo Approach
Direction of the wave vectors:
goal:
problem:
solution:
Summary of chosen distributions:
polar angle: ϑ→arccos(U(−1,1))
azimuth angle: φ→U(0,2π)
angle of polarization:α→U(0, π)
phase angle: β→U(0,2π)

24. Full-wave SimulationsPlane Wave Integral RepresentationTransmission Line CouplingDiscussion and Outlook
Distribution of the Angles for the Monte Carlo Approach
Direction of the wave vectors:
goal:
problem:
solution:
Summary of chosen distributions:
polar angle: ϑ→arccos(U(−1,1))
azimuth angle: φ→U(0,2π)
angle of polarization:α→U(0, π)
phase angle: β→U(0,2π)

25. Full-wave SimulationsPlane Wave Integral RepresentationTransmission Line CouplingDiscussion and Outlook
Utilization for Pulsed Carriers in Time Domain
Assumption:
▶reverberation chamber is a sphere
▶volume:V=
4
3
πr
3
▶surface area:S= 4πr
2
Average transit time:
ttransit=
2r
c0
(1)
c0: velocity of light
A. Manicke and H. G. Krauthäuser,
im Zeitbereich,” emv – Internationale Fachmesse und Kongress für Elektromagnetische Verträglichkeit, H. Garbe, Ed., Düsseldorf:
VDE Verlag, Feb. 2012, ISBN: 978-3-8007-3405-4

26. Full-wave SimulationsPlane Wave Integral RepresentationTransmission Line CouplingDiscussion and Outlook
Utilization for Pulsed Carriers in Time Domain
Assumption:
▶reverberation chamber is a sphere
▶volume:V=
4
3
πr
3
▶surface area:S= 4πr
2
Average transit time:
ttransit=
2r
c0
(1)
c0: velocity of light
A. Manicke and H. G. Krauthäuser,
im Zeitbereich,” emv – Internationale Fachmesse und Kongress für Elektromagnetische Verträglichkeit, H. Garbe, Ed., Düsseldorf:
VDE Verlag, Feb. 2012, ISBN: 978-3-8007-3405-4

27. Full-wave SimulationsPlane Wave Integral RepresentationTransmission Line CouplingDiscussion and Outlook
Utilization for Pulsed Carriers in Time Domain
Occurrence condition for the waves:
an(t) =h
`
t−tstart−(n−1)·ttransit
´
−h
`
t−tend−(n−1)·ttransit
´
(2)
n:
tstartandtend:
Amplitude of then-th wave:
En=E1·Γ
n−1
(3)
E1:
Γ:
A. Manicke and H. G. Krauthäuser,
im Zeitbereich,” emv – Internationale Fachmesse und Kongress für Elektromagnetische Verträglichkeit, H. Garbe, Ed., Düsseldorf:
VDE Verlag, Feb. 2012, ISBN: 978-3-8007-3405-4

28. Full-wave SimulationsPlane Wave Integral RepresentationTransmission Line CouplingDiscussion and Outlook
Utilization for Pulsed Carriers in Time Domain
Occurrence condition for the waves:
an(t) =h
`
t−tstart−(n−1)·ttransit
´
−h
`
t−tend−(n−1)·ttransit
´
(2)
n:
tstartandtend:
Amplitude of then-th wave:
En=E1·Γ
n−1
(3)
E1:
Γ:
A. Manicke and H. G. Krauthäuser,
im Zeitbereich,” emv – Internationale Fachmesse und Kongress für Elektromagnetische Verträglichkeit, H. Garbe, Ed., Düsseldorf:
VDE Verlag, Feb. 2012, ISBN: 978-3-8007-3405-4

29. Full-wave SimulationsPlane Wave Integral RepresentationTransmission Line CouplingDiscussion and Outlook
Utilization for Pulsed Carriers in Time Domain
Relation to the quality factor:
Q=
2πr
λ·(1−Γ)
(4)
λ: wavelength
E. Amador,
réverbérante électromagnétique,”
https://theses.hal.science/tel- 00652164v1
Q=
4πV
λS
D
(1− |Γ|
2
·cosθ
E (5)
θ: incident angles of plane waves
D. A. Hill, IEEE Transactions on Electromagnetic
Compatibility, vol. 38, no. 4, pp. 591–592, Nov. 1996, ISSN: 1558-187X. DOI:10.1109/15.544314

30. Full-wave SimulationsPlane Wave Integral RepresentationTransmission Line CouplingDiscussion and Outlook
Utilization for Pulsed Carriers in Time Domain
Maximum sum of the field strength:
Emax(t) =E1·
Γ
j
t
transit
t
k
+1
−1
Γ−1
(6)
Maximum sum of the field strength in the steady state:
Emax(∞) =
E1
1−Γ
(7)
Normalization of the field strength in the chamber at different times:
Enorm(t) =E(t)·
√
Γ−1
q
Γ
j
t
transit
t
k
+1
−1
(8)

31. Full-wave SimulationsPlane Wave Integral RepresentationTransmission Line CouplingDiscussion and Outlook
Utilization for Pulsed Carriers in Time Domain
Maximum sum of the field strength:
Emax(t) =E1·
Γ
j
t
transit
t
k
+1
−1
Γ−1
(6)
Maximum sum of the field strength in the steady state:
Emax(∞) =
E1
1−Γ
(7)
Normalization of the field strength in the chamber at different times:
Enorm(t) =E(t)·
√
Γ−1
q
Γ
j
t
transit
t
k
+1
−1
(8)

32. Full-wave SimulationsPlane Wave Integral RepresentationTransmission Line CouplingDiscussion and Outlook
Utilization for Pulsed Carriers in Time Domain
Maximum sum of the field strength:
Emax(t) =E1·
Γ
j
t
transit
t
k
+1
−1
Γ−1
(6)
Maximum sum of the field strength in the steady state:
Emax(∞) =
E1
1−Γ
(7)
Normalization of the field strength in the chamber at different times:
Enorm(t) =E(t)·
√
Γ−1
q
Γ
j
t
transit
t
k
+1
−1
(8)

33. Full-wave SimulationsPlane Wave Integral RepresentationTransmission Line CouplingDiscussion and Outlook
Simulation Parameters
(half) chamber size: r= 2.25m
Transit time: ttransit= 1.5ns
Frequency: f= 1GHz
Reflection factor: Γ = 0.1to0.999
Pulse start: tstart= 0µs
Pulse end: tend= 15µs
Simulation time: 30µs
Number of waves: N= 1001
Number of individual simulations:250

34. Full-wave SimulationsPlane Wave Integral RepresentationTransmission Line CouplingDiscussion and Outlook
Comparison of Results 0 5 10 15 20 25
time in micro seconds
50
45
40
35
30
25
20
15
10
power in dBm
power over time
measurement
TDPW
A. Manicke and H. G. Krauthäuser,
im Zeitbereich,” emv – Internationale Fachmesse und Kongress für Elektromagnetische Verträglichkeit, H. Garbe, Ed., Düsseldorf:
VDE Verlag, Feb. 2012, ISBN: 978-3-8007-3405-4

35. Full-wave SimulationsPlane Wave Integral RepresentationTransmission Line CouplingDiscussion and Outlook
Comparison of Results0 100 200 300 400 500 600 700
no of measurement
0.0
0.2
0.4
0.6
0.8
1.0
normalized power
maximum transient to steady state power - measurement
Pmax
Psteady 0 50 100 150 200 250
no of simulation
0.0
0.2
0.4
0.6
0.8
1.0
normalized power
maximum transient to steady state power - simulation
Pmax
Psteady
Figure:
to the absolute maximum of the power, sorted by ascending maximum
A. Manicke and H. G. Krauthäuser,
im Zeitbereich,” emv – Internationale Fachmesse und Kongress für Elektromagnetische Verträglichkeit, H. Garbe, Ed., Düsseldorf:
VDE Verlag, Feb. 2012, ISBN: 978-3-8007-3405-4

36. Full-wave SimulationsPlane Wave Integral RepresentationTransmission Line CouplingDiscussion and Outlook
Transmission Line Coupling

37. Full-wave SimulationsPlane Wave Integral RepresentationTransmission Line CouplingDiscussion and Outlook
Exemplary Examined Three-Wire NetworkR1uR1Node 1R3uR3Node 4R2uR2Node 330
◦
Node 2ujuncLine 1Line 2Line 3xyz
M. Magdowski and R. Vick,
Proceedings of the Joint International Symposium on Electromagnetic Compatibility and Asia-Pacific International Symposium on
Electromagnetic Compatibility, Sapporo, Japan: IEICE & IEEE, Jun. 2019, pp. 383–386, ISBN: 978-4-8855-2322-9. DOI:
10.23919/EMCTokyo.2019.8893805

38. Full-wave SimulationsPlane Wave Integral RepresentationTransmission Line CouplingDiscussion and Outlook
Equivalent Circuit Model of the Exemplary Examined NetworkR1uR1Ut,1L1Utan,1,1L1Utan,1,2C1C1C1R2uR2Ut,2L2Utan,2,1L2Utan,2,2C2C2C2L3Utan,3,1L3Utan,3,2Ut,3R3uR3C3C3C3Ut,4ujunc

39. Full-wave SimulationsPlane Wave Integral RepresentationTransmission Line CouplingDiscussion and Outlook
Parameters of the Transmission Line Network and the Incident Plane Wave
Line lengths:
l1= 40cm l2= 30cm l3= 50cm (9)
Wire radii:
r0,1= 0.6mm r0,2= 0.5mm r0,3= 0.4mm (10)
Characteristic impedances and chosen load resistances:
Zc,1= 210.2 Ω Zc,2= 221.1 Ω Zc,3= 234.5 Ω (11)
R1= 210.2 Ω R2= 442.2 Ω R3= 117.3 Ω (12)

40. Full-wave SimulationsPlane Wave Integral RepresentationTransmission Line CouplingDiscussion and Outlook
Parameters of the Transmission Line Network and the Incident Plane Wave
Line lengths:
l1= 40cm l2= 30cm l3= 50cm (9)
Wire radii:
r0,1= 0.6mm r0,2= 0.5mm r0,3= 0.4mm (10)
Characteristic impedances and chosen load resistances:
Zc,1= 210.2 Ω Zc,2= 221.1 Ω Zc,3= 234.5 Ω (11)
R1= 210.2 Ω R2= 442.2 Ω R3= 117.3 Ω (12)

41. Full-wave SimulationsPlane Wave Integral RepresentationTransmission Line CouplingDiscussion and Outlook
Parameters of the Transmission Line Network and the Incident Plane Wave
Line lengths:
l1= 40cm l2= 30cm l3= 50cm (9)
Wire radii:
r0,1= 0.6mm r0,2= 0.5mm r0,3= 0.4mm (10)
Characteristic impedances and chosen load resistances:
Zc,1= 210.2 Ω Zc,2= 221.1 Ω Zc,3= 234.5 Ω (11)
R1= 210.2 Ω R2= 442.2 Ω R3= 117.3 Ω (12)

42. Full-wave SimulationsPlane Wave Integral RepresentationTransmission Line CouplingDiscussion and Outlook
Single Sine Pulse as the Time Function of the Incident Plane Wave00.20.40.60.811.21.41.61.822.22.42.62.83−1−0.500.51Time,t(inns)Electric field strength,E(in
kV
m
)

43. Full-wave SimulationsPlane Wave Integral RepresentationTransmission Line CouplingDiscussion and Outlook
Excitation in the Direction of Line 10123456789101112−20−15−10−5051015Time,t(inns)Coupled voltage,u(t)(inV)via BLT eq. & IFFT:uR1uR2uR3ujuncvia network model:uR1uR2uR3ujunc

44. Full-wave SimulationsPlane Wave Integral RepresentationTransmission Line CouplingDiscussion and Outlook
Simulation with Non-Linear LoadingR2
(a)R2 (b)R2 (c)
Figure: R2at
the beginning of line 2

45. Full-wave SimulationsPlane Wave Integral RepresentationTransmission Line CouplingDiscussion and Outlook
Coupled VoltageuR1at the Beginning of Line 10123456789101112−10−50510Time,t(inns)Coupled voltage,u(t)(inV)linear loadsforward diodereverse diodeanti-parallel diodes

46. Full-wave SimulationsPlane Wave Integral RepresentationTransmission Line CouplingDiscussion and Outlook
Coupled VoltageuR2at the Beginning of Line 20123456789101112−15−10−50510Time,t(inns)Coupled voltage,u(t)(inV)linear loadsforward diodereverse diodeanti-parallel diodes

47. Full-wave SimulationsPlane Wave Integral RepresentationTransmission Line CouplingDiscussion and Outlook
Coupled VoltageuR3at the End of Line 30123456789101112−6−4−202468Time,t(inns)Coupled voltage,u(t)(inV)linear loadsforward diodereverse diodeanti-parallel diodes

48. Full-wave SimulationsPlane Wave Integral RepresentationTransmission Line CouplingDiscussion and Outlook
Discussion and Outlook

49. Full-wave SimulationsPlane Wave Integral RepresentationTransmission Line CouplingDiscussion and Outlook
Discussion and Outlook
Parameter studies:
▶different quality factors and loading conditions
▶different pulse lengths
Open questions:
▶(fast) continuous stirring
▶coupling to objects (e. g. transmission lines)
▶chamber geometry and boundary fields
▶correlated field distributions
▶emission measurements with modulated signals

50. Full-wave SimulationsPlane Wave Integral RepresentationTransmission Line CouplingDiscussion and Outlook
Discussion and Outlook
Parameter studies:
▶different quality factors and loading conditions
▶different pulse lengths
Open questions:
▶(fast) continuous stirring
▶coupling to objects (e. g. transmission lines)
▶chamber geometry and boundary fields
▶correlated field distributions
▶emission measurements with modulated signals

51. Full-wave SimulationsPlane Wave Integral RepresentationTransmission Line CouplingDiscussion and Outlook
https://twitter.com/MarkusRidderbu8/status/1523708966039351297
Thank you for your attention!
What questions are still open?