EMC’14/Tokyo
16A1-A3
Influence of Reverberation Chamber Loading
on Extreme Field Strength
Robert Vogt-Ardatjew1, Stefan van de Beek1, Frank Leferink1,2
1
2
University of Twente
Enschede, The Netherlands
r.a.vogtardatjew@utwente.nl
Thales Nederland B.V.
Hengelo, The Netherlands
Frank.Leferink@utwente.nl
Abstract— Electronic equipment is often susceptible to the
maximum field strength instead of the average field strength.
The difficulty of finding the absolutely maximal field strength
inside a reverberation chamber arises from the troublesome link
between the statistical and deterministic approach. The
established theoretical models propose interesting solutions to
this problem but require more experimental verification.
This paper focuses on the experiments utilizing a Vibrating
Intrinsic Reverberation Chamber (VIRC) as a tool allowing for
extended real-life field analysis. The randomness of movement of
flexible walls of a VIRC is exploited by conducting long, 1 hour
measurements. Statistical analysis of the data is conducted to
evaluate the maximal and average, and their ratio for different
chamber loads and quality factors.
Keywords— reverberation chamber, enclosed environments, field
strength, Q-factor
[4]. The general Q-factor is measured as an average of the
composite Q-factors of many stirrer positions. It is related to
the average power received by an antenna, therefore it is also
related the average field intensity in any point in that cavity.
With lowering the Q by opening apertures or putting
absorbers in the chamber, the bandwidths of modes become
larger, which can make the mode stirring more effective [5].
On the other hand, if the absorbers are approximated by
perfectly lossy objects or apertures, some of those modes
would cease to exist and the performance of the chamber
degrades [6]. Because both factors affect the extreme field
strengths, this tradeoff has become the main research goal of
this paper. In previous work, [7], [3] it has been shown that
the Q-factor does not influence the relation between the
maximal and average field strengths, however, our new
presented method allows to verify this theory by conducting
such measurements with greater accuracy [8]. The average
and maximal field strength behaviors have been observed, and
their ratio analyzed as a function of the chamber loading in 20
subsequent, 1-hour measurement steps, delivering 3.6 million
samples per each measurement.
I. INTRODUCTION
A very important and useful tool for the analytical
representation of fields inside a reverberation chamber is the
Plane Wave Integral [1]. It states that the field intensity in any
point is a sum of many incoming independent waves with
random amplitudes, phases, and polarizations. A very good
agreement with theory can be reached by taking an arbitrary
number of incoming waves. However, the total amount of
incoming waves inside a real cavity is unknown. Additionally,
due to the randomness of wave parameters and their
assumption of independence leads to inaccurate estimation of
the absolute maximal field strength value. Unlike the nearaverage region, the estimation of the maximal field shows
strong dependence on the amount of incoming waves, or
modes, included in calculation. Due to the decreasing
probability of reaching extremely high field intensity,
statistical approach partially solves this issue by describing the
fields within a certain confidence level, but this solution lacks
the definitive limit. Even though recent publications, e.g. [2],
provide tools to estimate this value in quite an accurate way,
the risk of exceeding it remains. Analytical attempts to link
the statistical behavior to deterministic results have been
reported [3] and deliver a tempting hypothesis for the
experimental approach.
In real enclosures, the electromagnetic energy can be
dissipated in many ways, e.g. through imperfectly conducting
walls, aperture leakage, lossy medium or objects. These can
be reverberation chambers dedicated for Electromagnetic
Compatibility (EMC) testing, airplane fuselage or house
interiors. Enclosures are often described using the composite
quality factor (Q) as a general estimator of the cavity losses
Copyright 2014 IEICE
II. MEASUREMENT SETUP
The measurement setup is the same as the one introduced in
[8]. It utilizes the Vibrating Intrinsic Reverberation Chamber
(VIRC) [9] (1.5 m x 1.2 m x 1 m), which allows obtaining
many independent samples by conducting long, in this case 1
hour, measurements. This is exploited by using the
unpredictable character of flexible walls, similar to the walls
of a tent, pulled by 2 DC motors, as opposed to periodic
behavior of a regular reverberation chamber with a
mechanical stirrer. The matter of its usability for such unique
measurements is discussed in [8]. However, unlike in the
referenced setup, in this work only single extreme values are
taken into account, thus the issue of repeatability of the
recorded samples does not impair the experiment.
Furthermore, all the measurements presented in this paper
were conducted in a similar manner so a relative comparison
between them is justified.
The layout of the antennas is presented in Table 1. The
transmitting discone antenna [10] was connected directly to a
RF generator. The highly directional double-ridged guide horn
antenna was placed on an empty cardboard box, in the blind
spot of the discone antenna and directed at the most moving
wall to minimize the line of sight and influence of any
unstirred components. The signal received by the horn
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EMC’14/Tokyo
16A1-A3
antenna was being transmitted to a fast logarithmic detector
with 70 dB dynamic range [11], similar to the one used in [12].
The envelope of the time varying electric field was being
recorded by a 14-bit Data Acquisition System (DAQ),
connected further to a PC. All measurements were conducted
using 1 GHz frequency. The setup was automated by a
LabVIEW program. Because finding very high field peaks
was the objective of the measurement, the generator output
power was set to a value that created a safety margin in the
upper linear region of the detector. This margin was never
crossed during the actual measurements.
The DAQ was recording samples with the frequency of
1 kHz and sending the data to the PC, where it was stored.
The recording took 1 hour, which is 3.6 million samples per
each measurement. The whole experiment consisted of 20
such measurement steps, resulting in 20 hours’ worth of saved
data. Because the sampling rate is exaggerated w.r.t. the speed
of change of the recorded envelope, not all of the samples
yield useful information. It is, however, necessary for
removing the quantisation error by applying a low-pass filter.
For the purpose of further processing and analysis, every 10th
sample is taken from the filtered signal, meaning that
effective sampling frequency is 100 Hz.
The goal of the experiment was the analysis of observed
field strength changes as a function of the Q-factor. The Q
was therefore being changed by increasing the amount of
absorber in the chamber. This was done in 10 unique steps,
starting with empty chamber and ending with loading the
chamber with a whole block of the absorber. The steps are
listed in Table 1. Every step was then repeated for the sake of
result verification, giving 20 sets of data. Introducing internal
losses was chosen instead of creating apertures in the VIRC
because of lack of interference coming from the outside world.
Such interference was proven to be highly harmful for the
measurement due to the broadband character of the receiver.
Fig. 1. Average power decay curve used for the Q-factor measurement of the
empty chamber
III. Q-FACTOR MEASUREMENT
The Q-factor was measured for every step by using the
decrement method [13]. In the decrement method, when the
cavity is in a steady state, filled with electromagnetic energy,
the input is suddenly disconnected and the dissipation of
energy from the cavity is analyzed in time domain. Such a
maneuver was implemented by modulating the amplitude of
the input signal with a square wave with rise- and fall-times
much smaller than the decay time. The slope of the
exponential power decay, averaged over many stirrer positions,
is then related to the composite Q-factor of the chamber. The
example power decay curve of the empty VIRC is shown in
Fig. 1. Note that if the natural logarithmic scale is used, the
decay curve becomes linear. Although the samples for
maximal and average field strength analysis were recorded for
1 h per measurement step, the average Q-factor was measured
over about 20 second period, to limit the overall measurement
time. In [8] it is shown that the average value measurements
converge much faster to the expected values than the maximal
ones, thus even during such a short average Q measurement,
the possible error is not significant.
Copyright 2014 IEICE
686
IV. DATA ANALYSIS
From the data recorded during every measurement step,
the average and maximal values were extracted. Under the
assumption of statistical isotropicity inside the reverberation
chamber [9], the power received by the directional antenna
was translated to the E field intensity in a point, where an
isotropic antenna would be placed instead. The
maximum-to-average (max/avg) E field ratio, expressed in
dB, is the universal, relative value that is the main result of
the experiment. Because the maximal obtainable values lie in
the tail of the theoretical Rayleigh distribution [14], the
probability of their occurrence becomes very low. Even
under the assumption that the absolute maximal field is a
finite number, it is unproven that it was actually reached
during the 1 h measurement. Moreover, the max/avg ratio is
greatly affected by the maximal values, which can lead to a
significant spread of the results. For example, a single, very
high peak might occur during the measurement, leading to a
sudden rise of the max/avg. Apart from showing the absolute
maximal field strength changes during the long
measurements, this paper focuses on finding any relative
changes of the max/avg under different loads. In order to
make the latter comparisons more clear, a certain number N
of highest value samples were removed from the calculations.
Such an operation is similar to limiting theoretical probability
distributions with a confidence interval and can effectively
lower the spread of results. It is important to note that the
results after the elimination process do not represent the real,
measured fields, but are done only for the sake of relative
comparison between each other. In the presented setup,
single high peaks consist of 5-10 samples above the average
value. Therefore, the data analysis was conducted after
eliminating N={0, 10, 50} extreme samples. The behavior of
maximal and average values after the elimination, as a
function of the measured Q-factor, is shown in Fig. 2 and 3
respectively. It can be observed that even after elimination of
50 extreme samples the changes in the average values are
negligible. In case of maximal values, these changes become
more significant, meaning that the extreme values are very
rare. The measured Q-factor values along with corresponding
max/avg ratios for all measurement steps is contained in
EMC’14/Tokyo
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Table 1. The same max/avg results plotted as a function of Q
are presented in Fig. 4. Additionally, the histograms of the
obtained data, for N=0, was compared to the theoretical
Rayleigh distribution. It was qualitatively observed that the
resemblance is high for every case of the chamber load.
Example histograms with theoretical Rayleigh curves, for
loads consisting of 1 pyramid and 6 pieces are shown in
Fig. 5 and 6, proving proper field stirring under the given
conditions.
Fig. 5. Histogram of the data recorded in the chamber loaded with 1 pyramid,
compared to the normalized, theoretical Rayleigh curve
Fig. 2. Average field strength as a function of the Q factor for different
number of eliminated extreme samples
Fig. 6. Histogram of the data recorded in the chamber loaded with 6 pieces of
absorber, compared to the normalized, theoretical Rayleigh curve
Fig. 3. Maximum field strength as a function of the Q factor for different
number of eliminated extreme samples
Fig. 4. Maximum-to-average ratio as a function of the Q factor for different
number of eliminated extreme samples
Copyright 2014 IEICE
V. CONCLUSIONS
The number of recorded independent samples is unknown
and repetition rate is likely to be high, although creation of
new, independent positions in the VIRC is possible even after
a very long measurement time, as opposed to a regular RC.
Such an approach can therefore be successfully used to search
for single maximal values with very long, e.g. 1 hour or longer
measurements.
The observed changes in the maximum-to-average ratio in
loaded chambers are not significant even when the Q-factor is
lowered by 80% w.r.t. the empty chamber value. The maximal
observed ratio in this case was around 12 dB. In case of heavy
loads, i.e. when the Q-factor becomes smaller than 20% of the
empty chamber value, the observed maximum-to-average
ratio gradually decreases. The smallest max/avg ratio was
obtained for the smallest Q, when the chamber was loaded
with all 6 pieces of the cut absorber. One possible explanation
is that a large amount of material put inside the chamber
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TABLE I
Performed measurement steps with corresponding results
Empty
Setup
Q
Total
Ratio
[dB]
N=10
Ratio
[dB]
N=50
Ratio
[dB]
2037
11.8
11.6
11.1
Layout
impairs its stirring efficiency, thus lowering the number of
potentially obtainable independent samples, therefore leading
to underestimation of the maximal field strength [15].
However, the mechanism of this phenomenon has not been
analyzed in detail and requires further research.
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2026
11.5
11.3
11.0
1029
12.6
11.4
10.7
976
12.0
11.1
10.7
616
12.5
11.4
11.0
[4]
624
12.3
11.8
11.0
[5]
418
11.9
10.6
9.9
[6]
411
12.3
11.3
10.7
416
12.6
10.9
10.3
2 halves, spikes
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[7]
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Copyright 2014 IEICE
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