Bozzetti, M.

Canavero, Flavio

Serra, R.

English

Serra R.

Bozzetti M.

CANAVERO, Flavio

PORTO@iris (Publications Open Repository TOrino - Politecnico di Torino)

05 August 2020POLITECNICO DI TORINORepository ISTITUZIONALEMisleading Issues that Came Up when Calibrating the Alenia Aeronautica Reverberation Chamber / Serra R.; BozzettiM.; Canavero F.G.. - STAMPA. - (2009), pp. 913-916. ((Intervento presentato al convegno International Conference onElectromagnetics in Advanced Applications (ICEAA 2009) tenutosi a Torino (Italy) nel Sept. 14-18, 2009.OriginalMisleading Issues that Came Up when Calibrating the Alenia Aeronautica Reverberation ChamberPublisher:PublishedDOI:10.1109/ICEAA.2009.5297325Terms of use:openAccessPublisher copyright(Article begins on next page)This article is made available under terms and conditions as specified in the  corresponding bibliographic description inthe repositoryAvailability:This version is available at: 11583/2280659 since:IEEEMisleading Issues that Came Up when Calibratingthe Alenia Aeronautica Reverberation ChamberR. Serra∗ †, M. Bozzetti‡ and F. G. Canavero∗Abstract — In this paper we present two mislead-ing issues that masked the correct considerationof the lowest useable frequency when applying theIEC 61000-4-21 international standard to the Ale-nia Aeronautica reverberation chamber. Analysis ofresults showed some contradictions between theoryand practical experience of RCs. Particularly, theseissues were found to be the number of frequencypoints and the harmonic distortion produced by theamplifiers.1 IntroductionWhen a RC is thought to be used for testing, itneeds to undergo a calibration procedure. The cal-ibration (or, better said: validation, in up-datedlexicon) is mainly focused on determining the low-est useable frequency (LUF) and other character-ization parameters. Important criteria to do so isgiven by statistical models [1, 2, 3]. Nevertheless,from the operational point of view, using theoreticaldistribution functions to determine whether a RC isuseable as a test facility is not viable when homo-geneous test conditions and standardization mustbe assured. As known, standards like [4] establisha performance-based decision criteria, without anyreference to statistical distributions. Applying therequirements and using the procedures introducedin [4] a performance-based description of RCs canbe realized by means of a field uniformity measure-ment. However, some precautions need to be takenwhen performing such measurements.Alenia Aeronautica SpA has recently put intooperation an experimental reverberation chamber(RC) prototype as part of its High Intensity Radi-ated Fields Ground Test Center located at Torino-Caselle, Italy. A feasibility research program hasbeen conducted into the use of this technology toperform testing in small platforms for aircrafts.An intensive characterization of the chamber wasundertaken. We will address in the present pa-per some issues that came up when characteriz-ing the Alenia Aeronautica Reverberation Cham-ber (AARC). Even though all the requirements in[4] were met, the first results were not consistentwith other evaluations performed and with whatis reported in other RC measurements. These is-sues are specifically reported to be the number of∗Dipartimento di Elettronica, Politecnico di Torino,C.so Duca degli Abruzzi 24, 10129 Torino, Italy, e-mail: {ramiro.serra,falvio.canavero}@polito.it, tel.:+39 011 564 4181, fax: +39 011 5644099.†Thales Netherlands, Hengelo, The Netherlands.‡Alenia Aeronautica SpA, Strada Malanghero, 10072Caselle, Italy, e-mail: mbozzetti@alenia.it, tel.: +39 011996 0526.frequency points and the harmonic distortion pro-duced by the amplifiers.2 The Alenia Aeronautica ReverberationChamber PrototypeThe prototype RC shown in Fig. 1 has inner di-mensions of 3.83 × 3.83 × 3.04 m (height), givinga total internal volume of approximately 44.6 m3.It features several geometrical details such as oneaccess door of 1.48 × 2.10 m; two access panels of0.35 × 0.35 m; two honeycomb ducts for ventila-tion of 0.25 × 0.25 m. One access panel is used asa feed-through panel, and the other one for mount-ing the stirrer motor drive unit. The chamber wallsare made of zinc-galvanized steel, welded.Figure 1: AARC prototype. Inside: the “Z-fold” stirrer,a logperiodic excitation antenna, a conical dipole receivingantenna, the field probe and a dummy EUT.The vertical “Z-fold” stirrer measures 2.5 × 1.1×1.2 m. The distance from the lowest paddle edge tothe RC floor is 0.2 m, and from the topmost paddleedge to the ceiling, 0.35 m. The stirrer was built ac-cording to the generally accepted design principlesavailable at the time of the prototype construction’sstart, i.e.: the stirrer should be electrically large atthe LUF and the overall stirrer structure must notbe rotationally symmetric [4]. Measurements de-scribed in this paper were performed using mode-tuning techniques, thus under static conditions.3 Lowest Useable FrequencyReverberation chambers are band-limited testequipments. The lowest useable frequency (LUF,fLUF ) is commonly understood to be the frequencyfrom which on a RC meets basic operational re-quirements. Such a value, however, depends on thechosen criterion and field-related quantity of prac-tical interest and generally does not show a clearthreshold characteristic (see [7, §2.3.7]).978-1-4244-3386-5/09/$25.00 ©2009 IEEE913Some empirical definitions can be found for theLUF, coming from practical experience. It is gen-erally accepted that the LUF in a chamber is closeto one or both of the following definitions [4]: 1)the LUF is approximately 3. . .6 times the cutoff fre-quency fc of the fundamental mode of a cavity withthe same dimensions as the RC under investigation;2) the LUF is the frequency at which 60 . . . 100modes within an ideal cavity of the same size asthe RC are excited and at least 1.5 modes/MHz arepresent. The AARC has its first (TM110) resonanceat 55.4 MHz. The LUF as defined in [4] results infLUF = 166 . . . 332 MHz when the first criteria isused and in fLUF = 160 . . . 200 MHz, when the sec-ond one is used. The frequency at which at least1.5 modes per MHz is present results in 192.3 MHz.Some theoretical models attempt to predict theLUF analytically. In [5], for example, an expressionfor the LUF is derived based on the chamber modedensity. In [6] instead, a thermodynamic approachhas been used and an approximation for the LUFwas deduced by matching the coherence volume ofa quasimonochromatic blackbody radiator with theworking volume of a RC. Theoretical approxima-tions as defined in [5] and [6] are fLUF = 459.4MHz and fLUF = 590.0 MHz, respectively.Considering both the empirical and theoreti-cal approaches, the predicted LUF for the AARCranges from 166 to 590 MHz. It is true that thesevalues are only intended to provide an estimatefor the order of magnitude of fLUF , rather than asharp value. But such a broad frequency span wit-nesses some still unclear issues regarding the use ofthe LUF as a functional threshold. Anyway, con-sensus in defining the LUF was somehow reachedby measuring field uniformity. Even though thiskind of measurement resembles pretty much to ane-choic chamber calibration, and thus are originallythought to a completely different test method, isthe winning indicator and is the main criteria usedin the standards such as [4].In this sense, the LUF becomes finally definedas the lowest frequency at which a specified fielduniformity can be achieved over a defined volume.This definition is much more stringent than the pre-vious ones, since it involves measurements withinthe chamber and forces the user to think about thedesired measurement uncertainties and confidenceintervals to be obtained for a given number of stir-rer steps. It is therefore of a great utility to have aunified consensus on how to define the LUF. Nev-ertheless, there are still some unclear issues in itspractical definition that can lead to deceptive orconfusing conclusions.4 Field UniformityThe lowest useable frequency from which a RC canbe used is mainly determined by the size and shapeof the chamber and the effectiveness of the stirrer.A procedure for knowing a RC’s LUF is describedin [4].For the calibration, the fields must be recordedat eight positions within the working volume (itscorner points). Field uniformity must be testedat 45 logarithmically spaced frequencies over thefirst decade, after only 20 frequencies per decadeare required. Subsequently, the standard deviation(deviation between the eight positions in space) iscalculated for the field components. For acceptablemode-stirring, the standard deviations should laybelow a tolerance level defined in [4], knowing alsothat three frequencies per octave may exceed thelimits by no more than 1 dB.The field uniformity measurement as describedabove was performed in the AARC. The “volumeof uniform field” has dimensions of 2.8 × 1.5 × 1.4m. Figure 2 shows the field uniformity in terms ofthe standard deviations σξ (ξ = x, y, z and total)and the IEC limit. It can be seen that a LUF ofabout fLUF ≈ 258 MHz was found, which agreeswith the general estimations of section 3.Figure 2: Field uniformity σξ measurements at AARC.Nevertheless, it is to be noticed that the num-ber of frequency points in Fig. 2 is not the onerequired in [4]. In fact, more than 230 logarith-mically spaced frequencies were considered in thefirst decade. The reason for this decision will beexplained in the next section, where some caveatsfor the calibration process as described in [4] willbe addressed and explained.5 Caveats for CalibrationSome precautions need to be taken when perform-ing field uniformity measurements. We will addressin the present section some misleading issues thatcame up when characterizing the AARC, specifi-cally about the number of frequency points andthe harmonic distortion produced by the amplifiers.914Even though all the requirements were met, the firstresults were not satisfactory.Figure 3: Field uniformity σξ measurements with few fre-quency points.Figure 3 shows the field uniformity that was mea-sured the first time that the calibration process wasapplied. The LUF was not found since the only twopoints exceeding the IEC limit are not in the sameoctave and do not overpass the limit by more than1 dB.Further measurements were performed startingfrom 30 MHz and for the first decade. In this way,the required 45 frequency points would be concen-trated in the first decade, and the probability ofknowing the actual LUF would increase. Figure 4shows this measurement.Figure 4: Field uniformity σξ measurements obtained at 45frequency points in the first decade by considering a startingfrequency fs = 30 MHz.As it can be seen from Fig. 4, the measured LUFis approximately fLUF ≈ 100 MHz. It means thatfield uniformity was reached with only 11 modespresent. Even though this fact could be theoret-ically probable, it is obviously practically impos-sible, considering the widely-accepted criteria thatat least 60 modes should be present. It is true thatsome works report on the fact that special cham-bers like the VIRC can achieve acceptable rever-beration conditions with approximately 40 modes[8], but this is still far from the 11 modes foundfor the AARC. However, as discussed in [7, §2.2.7],11 ideally well-stirred modes (i.e. statistically inde-pendent, identically distributed with no one dom-inating) could be enough to be able to apply thecentral limit theorem and thus, obtaining the de-sired statistical behavior.Theory and practice seem to disagree when look-ing at these measurements. It is then crucialto highlight that several statistical indicators (i.e.field uniformity, stirring ratio, power deviation tothe mean, autocorrelation coefficient, etc.) canguide us to different conclusions and the only crite-ria to be used in order to understand that “some-thing is going wrong” is just based on practical ex-perience.5.1 Frequency pointsThe standard deviation curves as defined by [4]have a “noise-like” shape. It is clear then, that be-tween two consecutive measurement points it wouldbe quite difficult to predict whether that measure-ment would have exceeded or not the IEC limit. Inorder to investigate this fact, a new measurementwas defined. The idea is to choose three frequencybands: flow = 70 . . . 110 MHz, fmid = 160 . . . 200MHz and fhigh = 490 . . . 510 MHz. The frequencypoints were uniformly spaced in each band every1 MHz. Figure 5 shows the field uniformity mea-sured for this experiment. It can be seen how theaspect of the field uniformity graph significantlychanges when choosing more frequency points. Atflow, many or most of the points exceed the limit,at fhigh none of the points does it, while at fmidsome of them overpass the limit. The idea of deter-mining the exact LUF is not completely straightfor-ward, and thus other ways of characterizing a RCshould be applied if it is necessary to more thor-oughly understand these facts.Figure 5: Field uniformity σξ measurements for three dif-ferent frequency bands.If we assume that σξ would immediately exceedthe limit before fmid, the LUF would be fLUF ≈160 MHz. A more coherent result with respect tothe general accepted estimations. Nevertheless, itstill results in a somehow too optimistic LUF (lessthan three times the cut-off frequency).9155.2 HarmonicsThe IEC 61000-4-21 international standard has arequirement over the amplifiers to be used in RCcalibration and measurements, that is [4, §7]:“Theharmonics and distortion produced by the poweramplifier shall be at a level less than or equal to15 dB below carrier level.”.Before initiating with the calibration in theAARC, this requirement was checked and found outthat the level of the harmonics were never morethan 22 dB below the fundamental, thus largelycompliant with the IEC requirement. Nevertheless,it is known that due to the filtering property ofcavities, even when the distortion can be relativelylow when measuring it directly from the amplifierto the spectrum analyzer, the situation drasticallychanges inside the chamber. It would amplify thefrequencies close to the natural resonances and re-duce those that are not. Figure 6 shows the har-monic contribution inside the chamber, for four fre-quencies and for different output power levels of thesignal generator. It can be seen that for an outputpower of 0 dBm (the level used in the previous mea-surements, and the level at which the validation ofthe IEC requirement was done), the harmonic con-tribution is larger than the accepted in [4].Figure 6: Harmonic contribution inside the chamber forfour different frequencies and three output power levels ofthe signal generator.The presence of important harmonic contributionwill affect especially the electric field probe, dueto its inherent wide-band nature. All frequenciespresent in the cavity will be measured by the probe,providing potentially misleading results. Further-more, this effect is more influent at low frequen-cies (where the characterization is focussed), sincea larger number of frequencies lay inside the wide-band probe.Having learned the effect of the number of fre-quency points and the presence of harmonic distor-tion on the research of the LUF, a measurementwas defined with the signal generator at an outputlevel where the contribution of the harmonics wasbelow 30 dB the level of the fundamental inside thechamber, cf. Fig. 6, and with more points to betaken. The result was already shown in Fig. 2.6 ConclusionsMisleading issues that came up during the AARCcalibration process such as the influence of the num-ber of frequency points and the presence of har-monics (even within the standard limits) on thedetermination of the LUF according to [4] were ad-dressed.Table 1 sums up the different LUFs that werefound performing different calibration processes,with and without caring about these factors, i.e.the number of frequency points and the harmonicdistortion.Few points Many pointsHarmonics IEC 100 MHz 160 MHzHarmonics reduced 110 MHz 258 MHzTable 1: The field uniformity test is highly sensitive to thenumber of frequency points and the presence of harmonics(even if compliant to the standard).AcknowledgmentsThe authors wish to thank E. Carluccio (AleniaAeronautica) who developed the acquisition andcontrol software. Particular thanks to B. Demoulin(University of Lille) and P. Besnier (IETR-INSA,Rennes) for helpful comments and discussions.References[1] J. G. Kostas, B. Boverie: “Statistical model for a mode-stirred chamber”, IEEE Trans. on EMC, vol. 33, pp.366-370, 1991.[2] T. H. Lehman: “A statistical theory of electromagneticfields in complex cavities”, EMP Int. Note 494, 1993.[3] D. Hill: “Plane Wave Integral Representation for Fieldsin Reverberation Chambers”, IEEE Trans. on EMC,vol. 40, pp. 209-217, 1998.[4] CISPR/A and IEC SC 77B: IEC 61000-4-21 EMC -Part 4-21: Testing and Measurement Techniques - Re-verberation Chamber Test Methods, International stan-dard, August 2003.[5] L. R. Arnaut: “Operation of Electromagnetic Rever-beration Chambers With Wave Diffractors at RelativelyLow Frequencies”, IEEE Trans. on EMC, vol. 43, no. 4,pp. 637-653, November 2001.[6] —–: “Compound Exponential Distributions for Un-dermoded Reverberation Chambers”, IEEE Trans. onEMC, vol. 44, no. 3, pp. 442-457, August 2002[7] R. Serra: “Introduction of Randomness in Determinis-tic, Physically-Consistent Descriptions of ReverberationChambers and Experimental Verification”, PhD Disser-tation, Politecnico di Torino, Turin, Italy, 2009.[8] F. B. Leferink: “High Field in a large volume: the intrin-sic reverberation chamber”, IEEE Int. Symp. on EMC,vol. 1, pp. 24-27, 1998.916

Misleading Issues that Came Up when Calibrating the Alenia Aeronautica Reverberation Chamber

R. Serra

M. Bozzetti

F. G. Canavero

Crossref

Misleading issues that came up when calibrating the Alenia Aeronautica reverberation chamber

PORTO Publications Open Repository TOrino

Misleading Issues that Came Up when Calibrating
the Alenia Aeronautica Reverberation Chamber
R. Serra∗ †, M. Bozzetti‡ and F. G. Canavero∗
Abstract — In this paper we present two mislead-
ing issues that masked the correct consideration
of the lowest useable frequency when applying the
IEC 61000-4-21 international standard to the Ale-
nia Aeronautica reverberation chamber. Analysis of
results showed some contradictions between theory
and practical experience of RCs. Particularly, these
issues were found to be the number of frequency
points and the harmonic distortion produced by the
amplifiers.
1 Introduction
When a RC is thought to be used for testing, it
needs to undergo a calibration procedure. The cal-
ibration (or, better said: validation, in up-dated
lexicon) is mainly focused on determining the low-
est useable frequency (LUF) and other character-
ization parameters. Important criteria to do so is
given by statistical models [1, 2, 3]. Nevertheless,
from the operational point of view, using theoretical
distribution functions to determine whether a RC is
useable as a test facility is not viable when homo-
geneous test conditions and standardization must
be assured. As known, standards like [4] establish
a performance-based decision criteria, without any
reference to statistical distributions. Applying the
requirements and using the procedures introduced
in [4] a performance-based description of RCs can
be realized by means of a field uniformity measure-
ment. However, some precautions need to be taken
when performing such measurements.
Alenia Aeronautica SpA has recently put into
operation an experimental reverberation chamber
(RC) prototype as part of its High Intensity Radi-
ated Fields Ground Test Center located at Torino-
Caselle, Italy. A feasibility research program has
been conducted into the use of this technology to
perform testing in small platforms for aircrafts.
An intensive characterization of the chamber was
undertaken. We will address in the present pa-
per some issues that came up when characteriz-
ing the Alenia Aeronautica Reverberation Cham-
ber (AARC). Even though all the requirements in
[4] were met, the first results were not consistent
with other evaluations performed and with what
is reported in other RC measurements. These is-
sues are specifically reported to be the number of
∗Dipartimento di Elettronica, Politecnico di Torino,
C.so Duca degli Abruzzi 24, 10129 Torino, Italy, e-
mail: {ramiro.serra,falvio.canavero}@polito.it, tel.:
+39 011 564 4181, fax: +39 011 5644099.
†Thales Netherlands, Hengelo, The Netherlands.
‡Alenia Aeronautica SpA, Strada Malanghero, 10072
Caselle, Italy, e-mail: mbozzetti@alenia.it, tel.: +39 011
996 0526.
frequency points and the harmonic distortion pro-
duced by the amplifiers.
2 The Alenia Aeronautica Reverberation
Chamber Prototype
The prototype RC shown in Fig. 1 has inner di-
mensions of 3.83 × 3.83 × 3.04 m (height), giving
a total internal volume of approximately 44.6 m3.
It features several geometrical details such as one
access door of 1.48 × 2.10 m; two access panels of
0.35 × 0.35 m; two honeycomb ducts for ventila-
tion of 0.25 × 0.25 m. One access panel is used as
a feed-through panel, and the other one for mount-
ing the stirrer motor drive unit. The chamber walls
are made of zinc-galvanized steel, welded.
Figure 1: AARC prototype. Inside: the “Z-fold” stirrer,
a logperiodic excitation antenna, a conical dipole receiving
antenna, the field probe and a dummy EUT.
The vertical “Z-fold” stirrer measures 2.5 × 1.1×
1.2 m. The distance from the lowest paddle edge to
the RC floor is 0.2 m, and from the topmost paddle
edge to the ceiling, 0.35 m. The stirrer was built ac-
cording to the generally accepted design principles
available at the time of the prototype construction’s
start, i.e.: the stirrer should be electrically large at
the LUF and the overall stirrer structure must not
be rotationally symmetric [4]. Measurements de-
scribed in this paper were performed using mode-
tuning techniques, thus under static conditions.
3 Lowest Useable Frequency
Reverberation chambers are band-limited test
equipments. The lowest useable frequency (LUF,
fLUF ) is commonly understood to be the frequency
from which on a RC meets basic operational re-
quirements. Such a value, however, depends on the
chosen criterion and field-related quantity of prac-
tical interest and generally does not show a clear
threshold characteristic (see [7, §2.3.7]).
978-1-4244-3386-5/09/$25.00 ©2009 IEEE
913
Some empirical definitions can be found for the
LUF, coming from practical experience. It is gen-
erally accepted that the LUF in a chamber is close
to one or both of the following definitions [4]: 1)
the LUF is approximately 3. . .6 times the cutoff fre-
quency fc of the fundamental mode of a cavity with
the same dimensions as the RC under investigation;
2) the LUF is the frequency at which 60 . . . 100
modes within an ideal cavity of the same size as
the RC are excited and at least 1.5 modes/MHz are
present. The AARC has its first (TM110) resonance
at 55.4 MHz. The LUF as defined in [4] results in
fLUF = 166 . . . 332 MHz when the first criteria is
used and in fLUF = 160 . . . 200 MHz, when the sec-
ond one is used. The frequency at which at least
1.5 modes per MHz is present results in 192.3 MHz.
Some theoretical models attempt to predict the
LUF analytically. In [5], for example, an expression
for the LUF is derived based on the chamber mode
density. In [6] instead, a thermodynamic approach
has been used and an approximation for the LUF
was deduced by matching the coherence volume of
a quasimonochromatic blackbody radiator with the
working volume of a RC. Theoretical approxima-
tions as defined in [5] and [6] are fLUF = 459.4
MHz and fLUF = 590.0 MHz, respectively.
Considering both the empirical and theoreti-
cal approaches, the predicted LUF for the AARC
ranges from 166 to 590 MHz. It is true that these
values are only intended to provide an estimate
for the order of magnitude of fLUF , rather than a
sharp value. But such a broad frequency span wit-
nesses some still unclear issues regarding the use of
the LUF as a functional threshold. Anyway, con-
sensus in defining the LUF was somehow reached
by measuring field uniformity. Even though this
kind of measurement resembles pretty much to ane-
choic chamber calibration, and thus are originally
thought to a completely different test method, is
the winning indicator and is the main criteria used
in the standards such as [4].
In this sense, the LUF becomes finally defined
as the lowest frequency at which a specified field
uniformity can be achieved over a defined volume.
This definition is much more stringent than the pre-
vious ones, since it involves measurements within
the chamber and forces the user to think about the
desired measurement uncertainties and confidence
intervals to be obtained for a given number of stir-
rer steps. It is therefore of a great utility to have a
unified consensus on how to define the LUF. Nev-
ertheless, there are still some unclear issues in its
practical definition that can lead to deceptive or
confusing conclusions.
4 Field Uniformity
The lowest useable frequency from which a RC can
be used is mainly determined by the size and shape
of the chamber and the effectiveness of the stirrer.
A procedure for knowing a RC’s LUF is described
in [4].
For the calibration, the fields must be recorded
at eight positions within the working volume (its
corner points). Field uniformity must be tested
at 45 logarithmically spaced frequencies over the
first decade, after only 20 frequencies per decade
are required. Subsequently, the standard deviation
(deviation between the eight positions in space) is
calculated for the field components. For acceptable
mode-stirring, the standard deviations should lay
below a tolerance level defined in [4], knowing also
that three frequencies per octave may exceed the
limits by no more than 1 dB.
The field uniformity measurement as described
above was performed in the AARC. The “volume
of uniform field” has dimensions of 2.8 × 1.5 × 1.4
m. Figure 2 shows the field uniformity in terms of
the standard deviations σξ (ξ = x, y, z and total)
and the IEC limit. It can be seen that a LUF of
about fLUF ≈ 258 MHz was found, which agrees
with the general estimations of section 3.
Figure 2: Field uniformity σξ measurements at AARC.
Nevertheless, it is to be noticed that the num-
ber of frequency points in Fig. 2 is not the one
required in [4]. In fact, more than 230 logarith-
mically spaced frequencies were considered in the
first decade. The reason for this decision will be
explained in the next section, where some caveats
for the calibration process as described in [4] will
be addressed and explained.
5 Caveats for Calibration
Some precautions need to be taken when perform-
ing field uniformity measurements. We will address
in the present section some misleading issues that
came up when characterizing the AARC, specifi-
cally about the number of frequency points and
the harmonic distortion produced by the amplifiers.
914
Even though all the requirements were met, the first
results were not satisfactory.
Figure 3: Field uniformity σξ measurements with few fre-
quency points.
Figure 3 shows the field uniformity that was mea-
sured the first time that the calibration process was
applied. The LUF was not found since the only two
points exceeding the IEC limit are not in the same
octave and do not overpass the limit by more than
1 dB.
Further measurements were performed starting
from 30 MHz and for the first decade. In this way,
the required 45 frequency points would be concen-
trated in the first decade, and the probability of
knowing the actual LUF would increase. Figure 4
shows this measurement.
Figure 4: Field uniformity σξ measurements obtained at 45
frequency points in the first decade by considering a starting
frequency fs = 30 MHz.
As it can be seen from Fig. 4, the measured LUF
is approximately fLUF ≈ 100 MHz. It means that
field uniformity was reached with only 11 modes
present. Even though this fact could be theoret-
ically probable, it is obviously practically impos-
sible, considering the widely-accepted criteria that
at least 60 modes should be present. It is true that
some works report on the fact that special cham-
bers like the VIRC can achieve acceptable rever-
beration conditions with approximately 40 modes
[8], but this is still far from the 11 modes found
for the AARC. However, as discussed in [7, §2.2.7],
11 ideally well-stirred modes (i.e. statistically inde-
pendent, identically distributed with no one dom-
inating) could be enough to be able to apply the
central limit theorem and thus, obtaining the de-
sired statistical behavior.
Theory and practice seem to disagree when look-
ing at these measurements. It is then crucial
to highlight that several statistical indicators (i.e.
field uniformity, stirring ratio, power deviation to
the mean, autocorrelation coefficient, etc.) can
guide us to different conclusions and the only crite-
ria to be used in order to understand that “some-
thing is going wrong” is just based on practical ex-
perience.
5.1 Frequency points
The standard deviation curves as defined by [4]
have a “noise-like” shape. It is clear then, that be-
tween two consecutive measurement points it would
be quite difficult to predict whether that measure-
ment would have exceeded or not the IEC limit. In
order to investigate this fact, a new measurement
was defined. The idea is to choose three frequency
bands: flow = 70 . . . 110 MHz, fmid = 160 . . . 200
MHz and fhigh = 490 . . . 510 MHz. The frequency
points were uniformly spaced in each band every
1 MHz. Figure 5 shows the field uniformity mea-
sured for this experiment. It can be seen how the
aspect of the field uniformity graph significantly
changes when choosing more frequency points. At
flow, many or most of the points exceed the limit,
at fhigh none of the points does it, while at fmid
some of them overpass the limit. The idea of deter-
mining the exact LUF is not completely straightfor-
ward, and thus other ways of characterizing a RC
should be applied if it is necessary to more thor-
oughly understand these facts.
Figure 5: Field uniformity σξ measurements for three dif-
ferent frequency bands.
If we assume that σξ would immediately exceed
the limit before fmid, the LUF would be fLUF ≈
160 MHz. A more coherent result with respect to
the general accepted estimations. Nevertheless, it
still results in a somehow too optimistic LUF (less
than three times the cut-off frequency).
915
5.2 Harmonics
The IEC 61000-4-21 international standard has a
requirement over the amplifiers to be used in RC
calibration and measurements, that is [4, §7]:“The
harmonics and distortion produced by the power
amplifier shall be at a level less than or equal to
15 dB below carrier level.”.
Before initiating with the calibration in the
AARC, this requirement was checked and found out
that the level of the harmonics were never more
than 22 dB below the fundamental, thus largely
compliant with the IEC requirement. Nevertheless,
it is known that due to the filtering property of
cavities, even when the distortion can be relatively
low when measuring it directly from the amplifier
to the spectrum analyzer, the situation drastically
changes inside the chamber. It would amplify the
frequencies close to the natural resonances and re-
duce those that are not. Figure 6 shows the har-
monic contribution inside the chamber, for four fre-
quencies and for different output power levels of the
signal generator. It can be seen that for an output
power of 0 dBm (the level used in the previous mea-
surements, and the level at which the validation of
the IEC requirement was done), the harmonic con-
tribution is larger than the accepted in [4].
Figure 6: Harmonic contribution inside the chamber for
four different frequencies and three output power levels of
the signal generator.
The presence of important harmonic contribution
will affect especially the electric field probe, due
to its inherent wide-band nature. All frequencies
present in the cavity will be measured by the probe,
providing potentially misleading results. Further-
more, this effect is more influent at low frequen-
cies (where the characterization is focussed), since
a larger number of frequencies lay inside the wide-
band probe.
Having learned the effect of the number of fre-
quency points and the presence of harmonic distor-
tion on the research of the LUF, a measurement
was defined with the signal generator at an output
level where the contribution of the harmonics was
below 30 dB the level of the fundamental inside the
chamber, cf. Fig. 6, and with more points to be
taken. The result was already shown in Fig. 2.
6 Conclusions
Misleading issues that came up during the AARC
calibration process such as the influence of the num-
ber of frequency points and the presence of har-
monics (even within the standard limits) on the
determination of the LUF according to [4] were ad-
dressed.
Table 1 sums up the different LUFs that were
found performing different calibration processes,
with and without caring about these factors, i.e.
the number of frequency points and the harmonic
distortion.
Few points Many points
Harmonics IEC 100 MHz 160 MHz
Harmonics reduced 110 MHz 258 MHz
Table 1: The field uniformity test is highly sensitive to the
number of frequency points and the presence of harmonics
(even if compliant to the standard).
Acknowledgments
The authors wish to thank E. Carluccio (Alenia
Aeronautica) who developed the acquisition and
control software. Particular thanks to B. Demoulin
(University of Lille) and P. Besnier (IETR-INSA,
Rennes) for helpful comments and discussions.
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A statistical theory of electromagnetic ﬁelds in complex cavities”,

Arnaut: “Operation of Electromagnetic Reverberation Chambers With Wave Diﬀractors at Relatively Low Frequencies”,

Exponential Distributions for Undermoded Reverberation Chambers”,

IEC SC 77B: IEC 61000-4-21 EMC -Part 4-21: Testing and Measurement Techniques - Reverberation Chamber Test Methods, International standard,

Introduction of Randomness in Deterministic, Physically-Consistent Descriptions of Reverberation Chambers and Experimental Veriﬁcation”, PhD Dissertation, Politecnico di

Leferink: “High Field in a large volume: the intrinsic reverberation chamber”,

Plane Wave Integral Representation for Fields in Reverberation Chambers”,

Statistical model for a modestirred chamber”,

https://iris.polito.it/retrieve/handle/11583/2280659/51666/reverb.pdf

Misleading Issues that Came Up when Calibrating the Alenia Aeronautica Reverberation Chamber

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