Robust, Precise, Fast - Chose Two for Radiated EMC Measurements!

Semi-anechoic chambers Reverberation chambers Conversion of results Generic EUT Summary
Robust, Precise, Fast
Chose Two for Radiated EMC Measurements!
Dr.-Ing. Mathias Magdowski
Chair for Electromagnetic Compatibility
Institute for Medical Engineering
Otto von Guericke University Magdeburg, Germany
February 27, 2024
License: cb CC BY 4.0 (Attribution, ShareAlike)
Mathias Magdowski Robust, Precise, Fast – Chose Two! 2024-02-27 1 / 40

Motivation

Motivation
Ensuring electromagnetic compatibility:
▶ Will there be a radiated disturbance or interference?

Don’t be that kind of test engineer!
Source: https://imgflip.com/i/8h538q

Fundamental questions
What is a good measurand for emission?
▶ field strength in V
m (in a certain distance)
▶ power flux density in W
m2 (in a certain distance)
▶ total radiated power W (independent of the distance)

Fundamental questions
What is a good measurand for emission?
▶ field strength in V
m (in a certain distance)
▶ power flux density in W
m2 (in a certain distance)
▶ total radiated power W (independent of the distance)
In which environment is the measurement performed?
▶ reflection-free environment
▶ environment with reflections
▶ highly reflective environment

Overview
Measurements in semi-anechoic chambers
Measurements in reverberation chambers
Conversion of results
Emission measurements with a generic EUT
Summary

Simple idea of a semi-anechoic chamber
Figure: Schematic measurement setup in a semi-anechoic chamber (top view)

Practical semi-anechoic chamber
Figure: Semi-anechoic chamber with 10 m measurement distance in Magdeburg

Measurand
What you would like to measure:
▶ radiated field strength in the far field
▶ maximum over all directions for all frequencies

Measurand
▶ radiated field strength in the far field
▶ maximum over all directions for all frequencies
What you actually measure:
▶ radiated field strength at a certain distance
▶ maximum over each sampled direction for each measured frequency
▶ radiation upwards (and downwards) is neglected

Overview
Summary

Simple idea of a reverberation chamber
Figure: Schematic setup of a reverberation chamber (top view)

Practical reverberation chamber
Figure: Large reverberation chamber in Magdeburg

Think about it!
Source: https://imgflip.com/i/6sa6a6

How to stir the field?
Changes of the electromagnetic boundary conditions:
▶ mechanical stirrer(s)
▶ moving walls
▶ relocating the antenna(s)
▶ switching between several antennas

How to stir the field?
Changes of the electromagnetic boundary conditions:
▶ mechanical stirrer(s)
▶ moving walls
▶ relocating the antenna(s)
▶ switching between several antennas
Narrow band frequency changes:
▶ only for immunity testing

Vibrating intrinsic reverberation chamber
(a) Demonstration with neon tubes (b) In-situ test on a ship
Source: Prof. Leferink, University of Twente and THALES, Netherlands

Oscillating wall stirrer
Figure: Reverberation chamber with an oscillating wall stirrer at the Laboratory of
Electromagnetic Compatibility, School of Mechanical Engineering, Southeast University,
Nanjing, China
Source: https://dx.doi.org/10.1109/TEMC.2020.2983981

Statistical properties of the field
Homogeneity:
▶ uniformity over the space
▶ free placement of the EUT in the working volume

Homogeneity:
Isotropy:
▶ uniformity in all directions
▶ orientation of the EUT does not matter

Homogeneity:
Isotropy:
▶ uniformity in all directions
▶ orientation of the EUT does not matter
Validity:
▶ only in the working volume
▶ minimum distance to the walls > λ
4

Change my mind!
Source: https://imgflip.com/i/6sa4e8

Measurand
▶ total radiated power for all frequencies

Measurand
▶ total radiated power for each measured frequency
▶ but falsified by the statistical uncertainty of the measurement
▶ Background: remaining field inhomogeneity, limited sample size

Measurand
▶ total radiated power for each measured frequency
▶ but falsified by the statistical uncertainty of the measurement
▶ Background: remaining field inhomogeneity, limited sample size
For what limits exist:
▶ maximum radiated field strength at a certain distance

Overview
Summary

Electrical size of an equipment under test
a
Definition as k · a:
k: wave number, k = 2πf
c = 2π
λ
a: radius of the smallest sphere surrounding the
EUT

Electrical size of an equipment under test
a
Definition as k · a:
k: wave number, k = 2πf
c = 2π
λ
a: radius of the smallest sphere surrounding the
EUT
Questions:
▶ What belongs to the EUT (case, cables, . . . )?
▶ Which cable length has to be considered?

Electrical small EUTs
Condition: k · a ≤ 1
Figure: Radiation pattern of a small dipole (Source: Wikipedia)

Electrical large EUTs
Condition: k · a > 1
Figure: Radiation pattern (planar cut) of a practical EUT (Source: Magnus Höijer, FOI)

The higher the frequency, the larger the problem!
Source: https://imgflip.com/i/6sagu4

Directivity
Definition:
D(ϑ, φ) =
Φ(ϑ, φ)
Prad/4π
(1)
▶ Φ is the power density radiated per solid angle
▶ Prad is the total radiated power
▶ Prad/4π is the average radiated power
Maximum directivity Dmax:
▶ Directivity in the main beam direction
▶ electrically short dipole: Dmax = 3/2 = 1.76 dBi
▶ electrically large EUT: Dmax ≈ 10 = 10 dBi

Free space or fully anechoic room (FAR)
Relationship between power and field strength:
E2
max = Dmax
η0
4πr2
Prad (2)
▶ η0 is the free space impedance
▶ r is the distance
▶ derivation with the help of a short electric dipole
▶ valid in the far field

Half space or semi-anechoic chamber (SAC)
Relationship between power and field strength:
E2
max = Dmax
η0
4πr2
Prad g2
max (3)
▶ gmax is an additional geometry factor
▶ value range between 0 and 2
▶ consideration of the reflection at the ground plane
▶ interference of the direct and the reflected wave

How to estimate or model the directivity?
“Statistical Analysis of the Correlation
of Emission Limits for Established and
Alternative Test Sites”
by Hans Georg Krauthäuser
published in the IEEE Transactions on
EMC, vol. 53, no. 4, Nov. 2011
https://ieeexplore.ieee.org/
document/5715864/
IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 53, NO. 4, NOVEMBER 2011 863
Statistical Analysis of the Correlation of Emission
Limits for Established and Alternative Test Sites
Hans Georg Krauthäuser, Member, IEEE
Abstract—This paper discusses the correlation of radiated emis-
sion measurements on open area test sites, in TEM waveguides,
fully anechoic rooms and reverberation chambers. Distributions
of all essential factors have been derived and mean and quantile
values are given. Influence of polarization mismatch and directivity
is discussed. Based on the analysis of uncertainties, an alternative
data treatment on open area test sites and in fully anechoic cham-
bers is proposed. A statistical link has been established between
the spherical wave expansion model and the array of point sources
model of directivity.
Index Terms—Directivity, fully anechoic room (FAR), gigahertz
transverse electromagnetic (GTEM), open area test sites (OATS),
polarization mismatch, radiated emission limits, reverberation
chamber (RC), unintentional emitters.
I. INTRODUCTION
HISTORICALLY, emission limits have been developed for
measurements on open area test sites (OATS). In order
to be independent of weather conditions and to reduce ambient
noise, most OATS-like emission measurements are nowadays
done in semianechoic chambers (SAC). No distinction between
OATS and SAC will be made within this paper. Alternative
methods claim to have advantages regarding one or more of
the aspects: speed, costs, reliability, frequency range, and ap-
proximation of reality. These alternative methods include the
reverberation chamber (RC) method and the TEM waveguide
method that are already covered by international standards, e.g.,
[1], [2], and also the fully anechoic room (FAR) method for
which an international standard is in development [3].
This paper will not address the validity of these claims. In-
stead, it focuses on the correlation of the physical quantities
measured by the methods in the case of unintentional radiators.
The analysis is strongly based on the discussion of the statistical
properties of the quantities involved.
Also, this paper will not address the intrinsic uncertainties of
the measurement methods itself. This study is focused on uncer-
tainties of the prediction of a measurement result for a certain
measurement site based on the (supposedly correct) measure-
ment results from another site.
Understanding the directivity patterns for electrically large
sources turns out to be a key topic for the application of alter-
Manuscript received September 15, 2010; revised December 6, 2010;
accepted December 21, 2010. Date of publication February 17, 2011; date
of current version November 18, 2011. Review of this manuscript was arranged
by Department Editor H. Garbe
H. G. Krauthäuser is with the TU Dresden 01069 Dresden, Germany (e-mail:
hgk@ieee.org).
Digital Object Identifier 10.1109/TEMC.2010.2102764
native radiated emission and immunity measurement methods
and is already addressed in various papers, e.g., [4]–[15].
A second important quantity for the correlation of uninten-
tional emissions is the polarization mismatch factor μ.
A. Directivity
Directivity D is defined as the ratio of the radiated power per
unit solid angle Θ(θ, φ) in direction (θ, φ) and the average radi-
ated power 1/(4π) ·
2π
0
π
0 Θ(φ, θ) sin θdθdφ = 1/(4π)·PT ,
D(φ, θ) =
4π · Θ(φ, θ)
PT
(1)
where PT is the total radiated power. Most often, one is not
interested in the whole radiation pattern, but in the maximum
of the directivity Dmax which is the directivity of the largest
radiation:
Dmax =
4π · max [Θ(φ, θ)]
PT
. (2)
It is clear that a measured value of Dmax depends on the
angular sampling. The true value is only achieved for very fine
angular resolution on the whole surface of a sphere surrounding
the source region. In this paper, a sampling of the complete
surface of a sphere is denoted as a 3D scan or a 3D case. In
contrast to this 3D case, a 1D case will also be investigated.
The 1D case describes a situation where the samples are located
along a great circle of the sphere surrounding the sources. An
intermediate case occurs in the context of OATS measurements.
Directivity models for unintentional radiators are discussed
in Section III.
B. Polarization Mismatch
The polarization mismatch factor μ ∈ [0, 1] is the fraction of
the measured power to the emitted power in a certain direction
μ(θ, φ) =
Pmeasured(θ, φ)
Pradiated(θ, φ)
. (3)
Linearly polarized antennas are used on OATS or in FAR to
pick up equipment under test (EUT) radiation. Measurements
are done in horizontal and vertical polarizations. For uninten-
tional emitters, having emissions with uniformly distributed po-
larization angles, none of the orientations of the receiving an-
tenna will completely pick up all radiated power. Thus, also
the maximum of both measurements is an uncertain quantity (a
random variable, RV).
The influence of this additional source of uncertainty has been
neglected until now. It will be addressed in Section II-A.
0018-9375/$26.00 © 2011 IEEE

Conversion SAC to RC w. r. t. f for a = 0.75 m and r = 10 m
107
108
109
1010
0
2
4
6
8
10
12
14
Frequency, f in Hz
Conversion
factor
E
2
max
P
rad
in
V
2
W
m
2
95. percentile
average
50. percentile
5. percentile
https://octav.onl/corr_OATS_RC

Conversion FAR to RC w. r. t. f for a = 0.75 m and r = 3 m
107
108
109
1010
0
5
10
15
20
25
Frequency, f in Hz
Conversion
factor
E
2
max
P
rad
in
V
2
W
m
2
95. percentile
average
50. percentile
5. percentile
https://octav.onl/corr_FAR_RC_f

Conversion between FAR and RC with respect to ka for r = 10 m
10−1
100
101
102
103
0
0.5
1
1.5
2
2.5
3
Product of wavenumber and EUT size, ka
Conversion
factor
E
2
max
P
rad
in
V
2
W
m
2
95. percentile
average
50. percentile
5. percentile
https://octav.onl/corr_FAR_RC

Which type of measurement would you like to have?

Environment: deterministic

EUT: random

EUT: random
Environment: random

EUT: random
Environment: random
EUT: deterministic

Overview
Summary

(a) in the reverberation chamber (b) in the semi-anechoic chamber
Figure: Utilized equipment under test (Source: Matthias Hirte, OVGU)

200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1 000
55
60
65
70
75
Frequency in MHz
Field
strength
in
dB
µV
m Measurement in the semi-anechoic chamber
Measurement in the reverberation chamber
Figure: Comparison of the emission measurement in different environments, directivity = 1
(Source: Matthias Hirte, OVGU)

200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1 000
55
60
65
70
75
Frequency in MHz
Field
strength
in
dB
µV
m 10◦ steps
90◦ steps
Figure: Comparison of the emission measurement for different turntable steps (Source:
Matthias Hirte, OVGU)

Overview
Summary

Catch my radiation, if you can!
Source: https://imgflip.com/i/6sae2q

There is a solution, wait, not.
Source: https://imgflip.com/i/6sahm3

All good things are never together.
robust
precise fast

robust
precise fast
reverberation
chamber

robust
precise fast
reverberation
chamber
semi-anechoic
chamber
(full sampling)

robust
precise fast
reverberation
chamber
semi-anechoic
chamber
(full sampling)
semi-anechoic chamber
(undersampling for known radiators)

robust
precise fast
reverberation
chamber
semi-anechoic
chamber
(full sampling)
semi-anechoic chamber
(undersampling for known radiators)
perfect
test

Source: https://twitter.com/MarkusRidderbu8/status/
1523708966039351297
Thank you very much for
your attention!
Are there any questions?

Robust, Precise, Fast - Chose Two for Radiated EMC Measurements!

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