Calculation of conversion factors for the RVC method in accordance with CISPR 16-4-5

Introduction Validation Emission measurement Conversion of results
Calculation of conversion factors for the RVC method
in accordance with CISPR 16-4-5
Dr.-Ing. Mathias Magdowski
Chair for Electromagnetic Compatibility
Institute for Medical Engineering
Otto von Guericke University Magdeburg, Germany
June 29, 2023
License: cb CC BY 4.0 (Attribution, ShareAlike)
Mathias Magdowski Conversion factors for RVCs 2023-06-29 1 / 31

Overview
What is a reverberation chamber?
How to validate the proper operation?
How to measure emission?
How to apply the CISPR-16-4-5?

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

Practical reverberation chamber
Figure: Large reverberation chamber in Magdeburg

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

Overview

Chamber field uniformity and loading validation
Goal:
▶ verification of a sufficiently small field inhomogeneity in the working volume
▶ determination of the lowest usable frequency (LUF)
▶ for the empty and maximum loaded chamber

Chamber field uniformity and loading validation
Goal:
▶ verification of a sufficiently small field inhomogeneity in the working volume
▶ determination of the lowest usable frequency (LUF)
▶ for the empty and maximum loaded chamber
Maximum chamber loading verification:
▶ simulate the chamber loading by the EUT
▶ using a sufficient amount of absorbers
▶ EUT loading ≤ maximum loading

Evaluation for each receiving antenna location:
Net input power (for each stirrer position):
PInput = PFwd − PRev (1)

Average input power:
PInput = PInput NTuner
(2)

(2)
Average received power:
PAveRec = ⟨PRec⟩NTuner
(3)

(2)
Average received power:
PAveRec = ⟨PRec⟩NTuner
(3)
Maximum received power:
PMaxRec = ⌈PRec⌉NTuner
(4)

Evaluation
For the empty and maximum
loaded chamber:
Antenna validation factor:
AVF =

PAveRec
PInput

8 positions
(5)
Insertion loss:
IL =

PMaxRec
PInput

8 positions
(6)

Evaluation
For the empty and maximum
loaded chamber:
Antenna validation factor:
AVF =

PAveRec
PInput

8 positions
(5)
Insertion loss:
IL =

PMaxRec
PInput

8 positions
(6)
For the chamber loaded with the
EUT:
Chamber validation factor:
CVF =

PAveRec
PInput

p positions
(7)
Chamber loading factor:
CLF =
CVF
AVF
(8)

Overview

Radiated emission measurement
Based on the measurement of the
average received power:
Prad =
ηTX · PAveRec
CVF
(9)
Advantages:
▶ lower statistical uncertainty when
using averages
▶ influence of the EUT validation
only, empty chamber validation
does not matter

Radiated emission measurement
average received power:
Prad =
ηTX · PAveRec
CVF
(9)
Advantages:
▶ lower statistical uncertainty when
using averages
▶ influence of the EUT validation
only, empty chamber validation
does not matter
maximum received power:
Prad =
ηTX · PMaxRec
CLF · IL
(10)
Advantages:
▶ better signal-to-noise ratio for
weak emitters close to noise floor
▶ easy to use the maximum hold
(or peak hold) function of the
measuring instrument

Further discussion on radiated emission measurements
“Monte Carlo Simulation of the
Statistical Uncertainty of Emission
Measurements in an Ideal
Reverberation Chamber”
by Mathias Magdowski and Ralf Vick
published at the EMC Europe 2017 in
Angers/France
https://ieeexplore.ieee.org/
document/8094737
Monte Carlo Simulation of the Statistical
Uncertainty of Emission Measurements
in an Ideal Reverberation Chamber
Mathias Magdowski and Ralf Vick
Chair for Electromagnetic Compatibility
Otto von Guericke University
Magdeburg, Germany
Email: mathias.magdowski@ovgu.de
Abstract—This paper describes the results of a Monte Carlo
simulation to quantify the statistical uncertainty of emission
measurements in the scope of electromagnetic compatibility in a
reverberation chamber. Such a measurement can be performed
based on the average or maximum received power at the
reference antenna. Depending on whether value is measured,
different parameters as the chamber validation factor CVF, the
chamber loading factor CLF or the insertion loss IL are needed
to calculate the total radiated power of a device under test. Each
parameter as well as the measurement itself features its own
statistical uncertainty, which are combined into a joint statistical
uncertainty of the total radiated power, which is analyzed in this
paper.
I. INTRODUCTION
A reverberation chamber (or mode-stirred chamber) is an
alternative test environment for radiated immunity tests and
emissions measurements in the scope of electromagnetic
compatibility. It consists of a shielded room that forms an
electromagnetic cavity resonator and a rotating metallic object
(known as the mode stirrer) to change the boundary conditions
and to obtain a statistically homogenous and isotropic field.
Reverberation chambers are rather popular for immunity
testing [1, Annex D], as their high quality factor allows to
reach high field strengths with only low input powers.
The utilization for emission measurements [1, Annex E]
is unfortunately not that prevalent, as the measured quantity
is the total radiated power of some device under test (DUT)
that cannot be easily compared with standard limits, which are
usually given in terms of a maximum emitted field strength
in a certain distance. A conversion between both quantities
would be possible, if the maximum directivity of the device
under test is known, which is usually not the case.
One solution of this problem is to model the maximum
directivity of a generic device under test as a function of the
frequency and its size [1, Annex E.8]. A more sophisticated
model including the statistical distribution and uncertainty of
the directivity and the conversion of emission limits is given
in [2].
Another solution is to establish conversion factors between
different test environments on an empirical basis as described
in [3]. For a correct application of radiated emission limits, also
the uncertainty of each test environment has to be known. While
such uncertainties are quite well known for the established
test environments like open area test sites or semi-anechoic
chambers, no plausible values are available for reverberation
chambers. The goal of this paper is to determine this uncertainty
for emission measurements.
Section II repeats and summarizes the standard procedure
of emission measurements in reverberation chambers. The
assumptions and simplifications of the utilized simulation
model are given in Sec. III. The following Sections IV, V
and VI contain the probability density functions, cumulative
distribution functions and percentiles of the quantities of
interest, respectively. The main conclusions are summarized in
Sec. VII.
II. MEASUREMENT OF THE TOTAL RADIATED POWER
The total radiated power of any device under test can be
calculated from [1, Eq. (E.1)]
Prad =
PAveRec · ηTx
CVF
(1)
in terms of the average received power PAveRec or from [1,
Eq. (E.2)]
Prad =
PMaxRec · ηTx
CLF · IL
(2)
in terms of the maximum received power PMaxRec. The
efficiency of the transmitting antenna used during the chamber
validation is denoted with ηTx.
The chamber validation factor
CVF =

PAveRec
PInput

Np
(3)
and the chamber loading factor
CLF =
CVF
AVF
(4)
are both determined from the validation of the chamber
performance with the DUT in place [1, Eqs. (B.11) and (B.12)],
where PAveRec is the average received power at the reference
antenna and PInput is the average input power into the chamber,
978-1-5386-0689-6/17/$31.00 © 2017 IEEE

Overview

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
(11)
▶ 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 (12)
▶ 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 (13)
▶ 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://octave-online.net/bucket~Lk6YAigoBeuKfmDvu2sWDr

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://octave-online.net/bucket~MovSav14VA5nnoHKoo7s3A

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://octave-online.net/bucket~NWBmAdyjm8aqLKaBRMNbzS

Which type of measurement would you like to have?

Environment: deterministic

EUT: random

EUT: random
Environment: random

EUT: random
Environment: random
EUT: deterministic

Back to a more fundamental question
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)

Back to a more fundamental question
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

Thank you very much for your attention!
Are there any questions?

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