This presentation was shown during a 'Quaestiones Disputatae' during the virtual 'International Symposium on Electromagnetic Compatibility' (EMC Europe) in September 2020. Question 1 was 'Are (properly designed) curved objects placed inside a RC the responsible for a better RC performance?'. The debaters were Guillaume Andrieu and Valter Mariani Primiani. The debate was moderated by Ramiro Serra. Question 2 dealt with 'Is there a real distinction between the so-called chaotic chambers and the more traditional reverberation chambers?'. This question was debated by Mathias Magdowski and Olivier Legrand. This second debate was moderated by Gabriele Gradoni.

1. Is there a real distinction between the so-called chaotic chambers
and the more traditional reverberation chambers?
Mathias Magdowski
Chair for Electromagnetic Compatibility
Institute for Medical Engineering
Otto von Guericke University Magdeburg, Germany
September 24, 2020

2. Definitions Chaotic Chambers Traditional Chambers Conclusion
Reverberation chambers
Source: Hans Georg Krauthäuser, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=15785481

3. Definitions Chaotic Chambers Traditional Chambers Conclusion
Chaoticity
Source: By Catslash - Own work, Public Domain, https://commons.wikimedia.org/w/index.php?curid=10404903

4. Definitions Chaotic Chambers Traditional Chambers Conclusion
Chaoticity
▸ deterministic nonlinear system

5. Definitions Chaotic Chambers Traditional Chambers Conclusion
Chaoticity
▸ deterministic nonlinear system
▸ highly sensitive to initial conditions (butterfly effect)

6. Definitions Chaotic Chambers Traditional Chambers Conclusion
Chaoticity
▸ deterministic nonlinear system
▸ highly sensitive to initial conditions (butterfly effect)
▸ random states of disorder and irregularities

7. Definitions Chaotic Chambers Traditional Chambers Conclusion
Chaoticity
▸ deterministic nonlinear system
▸ highly sensitive to initial conditions (butterfly effect)
▸ random states of disorder and irregularities
▸ non-periodicity, strange attractors

8. Definitions Chaotic Chambers Traditional Chambers Conclusion
Chaoticity
▸ deterministic nonlinear system
▸ highly sensitive to initial conditions (butterfly effect)
▸ random states of disorder and irregularities
▸ non-periodicity, strange attractors
▸ constant feedback loops, repetition, self-similarity, fractals, and self-organization

9. Definitions Chaotic Chambers Traditional Chambers Conclusion
Chaoticity
Edward Lorenz:
“Chaos: When the present
determines the future, but the
approximate present does not
approximately determine the
future.”
Source: https:
//en.wikipedia.org/w/index.php?curid=8932424

10. Definitions Chaotic Chambers Traditional Chambers Conclusion
Billard
Source: Wikimedia Commons, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=57028

11. Definitions Chaotic Chambers Traditional Chambers Conclusion
Bingo
Source: Nina Garman (BilliTheCat), https://pixabay.com/de/vectors/grafik-bingo-trommel-bingo-4067697/

12. Definitions Chaotic Chambers Traditional Chambers Conclusion
Flipper
Source: Clker-Free-Vector-Images, https://pixabay.com/de/vectors/flipper-pin-maschine-jahrgang-296568/

13. Definitions Chaotic Chambers Traditional Chambers Conclusion
Turbulence
Source: C. Fukushima and J. Westerweel, Technical University of Delft, The Netherlands, CC BY 3.0,
https://commons.wikimedia.org/w/index.php?curid=3082535

14. Definitions Chaotic Chambers Traditional Chambers Conclusion
Chua’s circuit
+
−
OPA
290
1
290
R1
GND
L1
I_L1(Z)
C2
U_C2(Y)
U_C1(X)
C1
D1
R2
D2
R
2
3
Source: Public Domain, https://commons.wikimedia.org/w/index.php?curid=4320592

15. Definitions Chaotic Chambers Traditional Chambers Conclusion
Chua’s circuit
V(V2)
-6V -5V -4V -3V -2V -1V 0V 1V 2V 3V 4V 5V 6V
-1.2V
-1.0V
-0.8V
-0.6V
-0.4V
-0.2V
0.0V
0.2V
0.4V
0.6V
0.8V
1.0V
1.2V
V(v1)
Source: Chua’s circuit – a chaos generator, https://juho-eric.blogspot.com/2011/12/ltspice-simulation-of-chuas-circuit.html

16. Definitions Chaotic Chambers Traditional Chambers Conclusion
Sound example
First voltage:
Play
Second voltage:
Play

17. Definitions Chaotic Chambers Traditional Chambers Conclusion
Highly symmetrical structure broken by diffractorsFig. 4. Cumulative NNSD and number variance for the first 571 modes of the cavity with one half-sphere and two caps shown in Fig. 5. The results obtained
are very close to those expected for a chaotic cavity in the universal regime.
Fig. 5. Left: Probability density of the x-component of the electric field for the 230th mode at 1.03 GHz of the cavity shown in the insert (Gaussian fit in
red). Right: colour map of the same component in three orthogonal planes. The results for the other components are similar.
The Fig. 5 shows a typical mode of the chaotic RC and the corresponding amplitude distribution for the x-component of
the electric field. As stressed in [12], such statistics are spoilt when the field close to the walls is taken into account. Thus,
we performed the analysis by excluding a zone λ/4 wide at the boundaries. Its spectral statistics being given by GOE, the
Source: J.-B. Gros, O. Legrand, F. Mortessagne, et al., “Universal behaviour of a wave chaos based electromagnetic reverberation chamber,” Wave
Motion, vol. 51, no. 4, pp. 664–672, 2014, Innovations in Wave Modelling, issn: 0165-2125. doi:
https://doi.org/10.1016/j.wavemoti.2013.09.006. [Online]. Available:
http://www.sciencedirect.com/science/article/pii/S0165212513001583, Fig. 5

18. Definitions Chaotic Chambers Traditional Chambers Conclusion
Highly symmetrical structure broken by diffractors
Source: K. Selemani, J.-B. Gros, E. Richalot, et al., “Comparison of reverberation chamber shapes inspired from chaotic cavities,” IEEE Transactions
on Electromagnetic Compatibility, vol. 57, no. 1, pp. 3–11, Feb. 2015, issn: 0018-9375. doi: 10.1109/TEMC.2014.2313355, Fig. 2

19. Definitions Chaotic Chambers Traditional Chambers Conclusion
Highly symmetrical structure broken by diffractors
Figure 1: Left: RC made chaotic through the introduc-
tion of 3 half-spheres. Right: Conventional RC. The small
the trans
cels the
widths Γ
obtained
tems (se
a more r
width sh
tion 5 of
In th
indicate
ductivity
Source: J.-B. Gros, U. Kuhl, O. Legrand, et al., “Statistics of the electromagnetic response of a chaotic reverberation chamber,” Advanced
Electromagnetics, vol. 4, no. 2, pp. 38–43, Nov. 2015. doi: 10.7716/aem.v4i2.271, Fig. 1

20. Definitions Chaotic Chambers Traditional Chambers Conclusion
Highly symmetrical structure broken by diffractors
Source: K. Selemani, E. Richalot, O. Legrand, et al., “Energy localization effects within a reverberation chamber and their reduction in chaotic
geometries,” IEEE Transactions on Electromagnetic Compatibility, vol. 59, no. 2, pp. 325–333, Apr. 2017, issn: 0018-9375. doi:
10.1109/TEMC.2016.2617322, Fig. 3

21. Definitions Chaotic Chambers Traditional Chambers Conclusion
Highly symmetrical structure broken by diffractors
calculations of the response.
Mt
een an at-
ng a wide
hysics [1],
d-wave op-
ss of wave
uch a vari-
ism which
ior. Since
ectromag-
t used ex-
erties have
h
l w
movable
hemisphere
(rm)
patch 1
patch 2
FIG. 1. (color online) Lossy parallelepipedic reverberation
chamber with length l=0.985 m, width w=0.785 m, and height
h=0.995 m. It is made chaotic through the introduction of a
Source: J.-B. Gros, U. Kuhl, O. Legrand, et al., “Lossy chaotic electromagnetic reverberation chambers: Universal statistical behavior of the vectorial
field,” Phys. Rev. E, vol. 93, p. 032 108, 3 Mar. 2016. doi: 10.1103/PhysRevE.93.032108. [Online]. Available:
https://link.aps.org/doi/10.1103/PhysRevE.93.032108, Fig. 1

22. Definitions Chaotic Chambers Traditional Chambers Conclusion
Highly symmetrical structure broken by diffractors
Source: L. Bastianelli, F. Moglie, V. M. Primiani, et al., “Reverberation chambers deformed by spherical diffractors,” in International Symposium on
Electromagnetic Compatibility (EMC EUROPE), Angers, France: IEEE, Sep. 2017, p. 5. doi: 10.1109/EMCEurope.2017.8094735, Fig. 2

23. Definitions Chaotic Chambers Traditional Chambers Conclusion
Complex shaped objects
Source: Hans Georg Krauthäuser, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=15785481

24. Definitions Chaotic Chambers Traditional Chambers Conclusion
Complex shaped equipment
Source: High Frequency Engineering Group at the Department of Electrical Engineering & Electronics of the University of Liverpool, United Kingdom

25. Definitions Chaotic Chambers Traditional Chambers Conclusion
Complex shaped antennas and cables
Source: Elektrotechnisches Institut, Technische Universität Dresden, Germany

26. Definitions Chaotic Chambers Traditional Chambers Conclusion
Conclusion
Maxwell’s equations are linear:
▸ fixed electromagnetic boundary condition → fixed solution of the field
distribution

27. Definitions Chaotic Chambers Traditional Chambers Conclusion
Conclusion
Maxwell’s equations are linear:
▸ fixed electromagnetic boundary condition → fixed solution of the field
distribution
▸ no “self-stirring” of the field

28. Definitions Chaotic Chambers Traditional Chambers Conclusion
Conclusion
Maxwell’s equations are linear:
▸ fixed electromagnetic boundary condition → fixed solution of the field
distribution
▸ no “self-stirring” of the field
Harmonic excitation:
▸ initial condition?

29. Definitions Chaotic Chambers Traditional Chambers Conclusion
Conclusion
Maxwell’s equations are linear:
▸ fixed electromagnetic boundary condition → fixed solution of the field
distribution
▸ no “self-stirring” of the field
Harmonic excitation:
▸ initial condition?
▸ butterfly effect?

30. Definitions Chaotic Chambers Traditional Chambers Conclusion
Conclusion
Is there a real distinction between the so-called chaotic chambers and the more
traditional reverberation chambers?

31. Definitions Chaotic Chambers Traditional Chambers Conclusion
Conclusion
Is there a real distinction between the so-called chaotic chambers and the more
traditional reverberation chambers?
Probably not.

32. Definitions Chaotic Chambers Traditional Chambers Conclusion
But wait!

33. Definitions Chaotic Chambers Traditional Chambers Conclusion
But wait!
Source: F. B. J. Leferink, D. Boerle, F. A. Sogtoen, et al., “In-situ emi measurements using a vibrating intrinsic reverberation chamber,” in 14th
International Symposium and Technical Exhibition on Electromagnetic Compatibility, Paper ID: 122R5, Zurich, Switzerland, Feb. 2001, p. 6, Fig. 6

34. Definitions Chaotic Chambers Traditional Chambers Conclusion
Thanks for your attention!
Are there questions?

35. Definitions Chaotic Chambers Traditional Chambers Conclusion
Effects of field probe movement
Source: L. Bastianelli, V. M. Primiani, and F. Moglie, “Analysis of field probe perturbation in a mode stirred reverberation chamber,” in IEEE
Symposium on Electromagnetic Compatibility and Signal Integrity, Santa Clara, CA, USA: IEEE, Mar. 2015, pp. 197–202, isbn: 978-1-4799-1993-2.
doi: 10.1109/EMCSI.2015.7107685, Fig. 6

36. Definitions Chaotic Chambers Traditional Chambers Conclusion
Effects of mechanical percussions
0 100 200 300 400
−55
−50
−45
−40
−35
−30
−25
−20
−15
Leaving
Knock 1
Knock 2
Knock 3
Knock 4
Outer door Entering
time [s]
Amplitude[dBm]
Step
Source: G. Zimmer, R. Geise, and B. Neubauer, “Einfluss mechanischer Umgebungseffekte auf Messungen in Modenverwirbelungskammern,” in emv
– Internationale Fachmesse und Kongress für Elektromagnetische Verträglichkeit, H. Garbe, Ed., Düsseldorf: Apprimus Verlag, Aachen, Feb. 2016,
pp. 157–164, isbn: 978-3-86359-396-4, Fig. 4 (translated)