A Proposed Method for Quantifying Uncertainty in RF Immunity Testing Due to EUT Presence

Progress In Electromagnetics Research B, Vol. 29, 175–190, 2011
A PROPOSED METHOD FOR QUANTIFYING UNCER-
TAINTY IN RF IMMUNITY TESTING DUE TO EUT
PRESENCE
E. Pa´ez, C. Tremola, and M. Azpu´rua
Instituto de Ingenier´ıa, Venezuela
Abstract—Throughout the performance of a RF immunity test
according IEC 61000-4-3 there are several factors that should be taken
into account to ensure the quality and to estimate the uncertainty
associated to the results. One phenomenon that should be considered
to calculate uncertainty is the disturbing effect produced by the
EUT over the electric field generated within the calibrated uniform
field area; nevertheless the mentioned effect is not easily quantifiable
because the measuring process using additional antennas or field probes
inside the semianechoic chamber could also alter the electric field
distribution. An experimental method for quantifying the mentioned
uncertainty contribution is presented. The method is based upon
the fact that antenna-EUT coupling and reflection effects could
be measured through changes in the input impedance of the field
generation antenna. A validation procedure for the proposed method is
also described. Hence, a relationship between the reflection coefficient
at the antenna input port and the electric field strength is derived. The
uncertainty contribution is calculated through the maximum relative
change in the E-field intensity magnitude for the frequency range of
80–1000MHz, considering the worst case for several EUT positions.
1. INTRODUCTION
In the execution of a RF immunity test according IEC 61000-4-3
inside a semianechoic chamber, the enclosure of the equipment under
test (EUT) and other metallic parts can be coupled to the field
generation antenna [1, 2], especially when the distance between EUT
and the antenna is 3m or less. This coupling implies changes in
Received 8 February 2011, Accepted 24 March 2011, Scheduled 30 March 2011
Corresponding author: Marco A. Azpurua (bazpurua@fii.gob.ve).

176 Pa´ez, Tremola, and Azpu´rua
the imaginary part of antenna input impedance, and consequently, it
changes the reflected and transmitted electromagnetic energy in the
antenna port. The reflected electromagnetic energy over the EUT
back to the transmit antenna also affect the magnitude of the electric
field intensity applied to the EUT, that’s the reason why, changes
in the real part to the antenna input impedance are produced [3, 4].
Both, antenna-EUT coupling and reflected energy back to the transmit
antenna, are represented in changes of the antenna input impedance
and therefore introduce uncertainty in the magnitude of the electric
field intensity effectively applied over the uniform field area (UFA) [5].
Changes in the total input impedance of transmit antenna implies
relatively more o less reflected and transmitted power with respect to
the data collected during the field calibration of the UFA according
IEC 61000-4-3. This data is actually used during the test to generate
the necessary power in the transmit antenna port to achieve a certain
test severity level required by IEC 61000-4-3.
This document proposes a method to measure the uncertainty
in the electric field magnitude over the UFA introduced due to EUT
presence. The method is based on the direct measurement of antenna
input impedance with and without presence of EUT over different
position within the UFA defined by IEC 61000-4-3. Then the variation
of the electric field magnitude is calculated in order to obtain the
uncertainty contribution.
The main issues to measure directly the variations of the electric
field within the UFA are: diffraction effects due to EUT presence would
disturb the measured field, and that the use of measuring antennas or
probes would alter the field distribution in the UFA.
All methods previously reported [2, 5] do not take into count the
uncertainty due to dimensions of the EUT and the position over the
test plane.
2. THEORETICAL JUSTIFICATION
In real antennas part of the energy applied to the input port is
dissipated as heat due to finite conductive effects, and other portion
of the energy is reflected back to the line due to impedance mismatch
and the rest is radiated. It all depends on the relationship between line
impedance and the antenna characteristic impedance. The real part of
antenna impedance is called “Antenna Resistance” and the imaginary
part “Antenna Reactance” [7]. The Antenna Resistance is the sum
of radiation resistance and loss resistance. The radiation resistance
is associated with the electromagnetic energy that is radiated into
free space and the loss resistance is associated with the energy that

Progress In Electromagnetics Research B, Vol. 29, 2011 177
is lost or dissipated as heat. The antenna reactance by definition
does not produce any radiated energy and depends on its size in
relation to the wavelength. This reactance could be quite influenced
by mutual coupling with nearby objects [8, 9]. These facts should be
considered when performing tests according IEC 61000-4-3, because
the interaction EUT-Antenna affects the antenna impedance, and in
consequence the magnitude of the E-field is generated in the UFA.
2.1. RF Immunity Test According the IEC 61000-4-3
Standard
The IEC 61000-4-3 standard is applicable to the immunity
requirements of electrical and electronic equipment to radiated
electromagnetic fields. It establishes test levels and the required test
procedures. This requires radiated RF field generated by an antenna
in a shielded anechoic enclosure using a precalibrated field, swept from
80MHz to 1000MHz with the step size not exceeding 1% previous
frequency and dwell time sufficient to allow the equipment under test
(EUT) to respond [10]. As shown in the Figure 1, the equipment under
test is placed on the 0.8m high wooden table (for table top devices)
with its front face in the same plane as the UFA that was previously
calibrated. Both the antenna position and the uniform area are fixed
Figure 1. Example of a suitable setup for RF immunity testing [10].

178 Pa´ez, Tremola, and Azpu´rua
with respect to the chamber. The standard requires at least 1m of
connected cable length to be exposed to the field, and recommends the
use of ferrite chokes to decouple longer cables. The equipment under
test is rotated on the table so that each of its four sides, and the top
and bottom if it may be used in any orientation, face the antenna in
turn, and are coplanar with the uniform area. For each orientation, two
sweeps are performed across the frequency range, one in each antenna
polarization. Severity levels are unmodulated and have to be 1, 3 or
10V/m. The actual applied signals are modulated to 80% with a 1 kHz
sine wave.
2.2. Uncertainty for RF Immunity Testing
The measurement is done over the hypothetical test field strength
(without an EUT) within the UFA selected according to the field
calibration process. To calculate the uncertainty budget for RF
Immunity test, it should be taken into account several technical
contributions, such as, field probe linearity, field probe anisotropy,
field probe frequency interpolation error, power amplifier short and
long term stability, power amplifier compression, stability and drift of
signal generator, antenna location and absorber placement, mismatch
between power meters and directional couplers, mismatch between
antenna and power amplifiers, and the coupling between antenna and
EUT [11].
While it is true that each laboratory have to select the most
important contribution components to be included in their uncertainty
budget calculation, on the basis of its particular circumstances, it is
also a fact that there are some common elements in the uncertainty
budgets for RF immunity test according IEC 61000-4-3 that have been
reported. Some examples of uncertainty budgets for RF immunity test
according IEC 61000-4-3 could be found in [5, 6, 11]. In all of them, it
is considered that the influence of the EUT-Antenna interaction plays
an important role and in consequence it should be determined. What
is still not well defined is a method to simultaneously quantify the
uncertainties due to EUT-Antenna coupling and reflections due to the
EUT presence in the UFA.
2.3. Method Previously Reported
According to [2] “Uncertainties of immunity measurement” —
Schaffner Guide, three methods are exposed to calculate the
uncertainties due to antenna-EUT coupling: the antenna-antenna
coupling method, the antenna-image coupling method and the
antenna-ground plane coupling method.

Progress In Electromagnetics Research B, Vol. 29, 2011 179
(a) (b)
Figure 2. Geometry of modeled coupling. (a) Free Space. (b)
Simulation of EUT-antenna coupling [2].
2.3.1. Antenna-Antenna Coupling Method
This method assumes that in many situations the EUT acts as a
secondary coupled antenna, and computes the electric field strength
on the UFA produced by an 80MHz tuned, half-wave dipole with
and without (free space) a similar shorted dipole placed 3m away in
parallel, as its shown in Figure 2. The source antenna was supplied
from a 50Ω voltage source. To compute the electromagnetic fields,
was used Numerical Electromagnetic Code and specific codes based on
method of moments [12].
This method is by no means representative of the phenomenon of
interaction EUT-antenna during a RF immunity test. The limitations
of this method are: it is just a numerical calculation of a very
simplified model of the phenomena that did not take into account the
effect of the reflections from the EUT nor the coupling between the
source antenna and shielded room (anechoic chamber), the calculation
of the coupling only occurs at the lowest frequency and the field
generating antennas recommended by the IEC 61000-4-3 standard are
Biconical antenna, Log-periodic antenna, Horn antenna and double
ridge waveguide antenna while in the simulation it was used a half-
wave dipole which is not recommended for this type of test, the position
of the coupled dipole never was varied to know how this parameters
change.
2.3.2. Antenna-Image Coupling Method
This method is also based upon numerical calculation of the electric
field intensity that intends to model the antenna-EUT coupling
phenomena using an 80MHz tuned half-wave dipole placed 3m from a
conducting metal sheet of infinite extent. Then the fields are calculated
on UFA produced by the tuned half-wave dipole with and without
the conductive ground plane of infinite extend. In this situation the

180 Pa´ez, Tremola, and Azpu´rua
coupling occurs between the source antenna and its image in the metal
sheet, this image being located 6m from the source antenna. Although
the image is 3m further away than the coupled antenna in the previous
method, the current in the image is identical to that in the source
antenna. In this case, it was also used Numerical Electromagnetic
Code. The component of the total field that lies in the plane of the
sheet is zero (boundary condition), but it is the field due to the source
antenna that is of interest not the total field created by the source and
its image [12].
In the same way as the Antenna-Antenna Coupling Method, the
Antenna-Image Coupling Method is not appropriate to predict and
measure the effect of the EUT presence in neither the field uniformity
nor its magnitude. It should be noticed that both Antenna-Antenna
Coupling Method and the Antenna-Image Coupling Method leads to
different results.
2.3.3. Antenna-Ground Plane Coupling Method
A 90MHz tuned, half-wave dipole with balun was measured over the
frequency range 80–200MHz over a ground plane on an open area
test site. The antenna was first placed 4m above the ground plane
and oriented in vertical polarization to simulate the free-space (empty
chamber) situation. It is known that there is only small coupling to
the ground plane in this situation. It was then mounted 3m above the
ground plane in horizontal polarization to simulate the presence of a
large metal EUT as is shown in — see Figure 3.
(a) (b)
Figure 3. Geometry of antenna-ground plane experimental method.
(a) Free space. (b) Simulation of EUT-antenna coupling [2].
Fairly obviously, fields cannot be measured, and as an alternative
the change in the antenna input current amplitude was determined.
Since the 50Ω source was the same for both orientations it was only
necessary to measure the antenna input impedance, Zin, with a VNA.

Progress In Electromagnetics Research B, Vol. 29, 2011 181
From the measured values of Zin = Rin+jXin in the two arrangements
it is possible to determine the change in antenna current in decibels.
Since the field from the source is directly proportional to the current
this gives the change in electric field in decibels.
The problems with this method are: first of all an “infinite”
ground plane is not a good representation of an EUT because the
maximum EUT size is restricted by the UFA, so the coupling and
reflection effects are not whatsoever equal, and once again the source
antenna used is not the recommended one by the standard to perform
the RF immunity test.
2.4. The Proposed Method
This method is based upon the fact that the electric field distribution
over UFA is perturbed due to changes in the antenna input impedance
caused by the presence of the EUT and its position within the UFA,
making this E-field variation an uncertainty contribution component
that should be quantified. Considering that the EUT could be placed
anywhere within the 1.5 × 1.5m UFA and that the signal frequency
is swept from 80MHz to 1GHz, the changes in the antenna input
impedance caused by the variation in reflection coefficient depends on
the EUT position and the particular electromagnetic behavior of the
test arrangement for a specific frequency.
The IEC 61000-4-3 standard establishes the procedure to calibrate
field uniformity over the UFA [8]. Basically, the entire plane is
subdivided in nine 0.5 × 0.5m zones, forming a 16 point grid over
which the field probe measures the electric field. Hence a conductive
reflective plate (0.7mm thick aluminum plate) of 0.5×0.5 was selected
as the representation of a typical size EUT.
The proposed method consists in the measurement of reflection
coefficient, Γ, with and without the conductive reflective plate
emulating the EUT presence. It is possible to compute Γ through the
measurement of the antenna input impedance, ZA, using (1), where Z0
is the characteristic impedance of the transmission line [13]. It is also
feasible to compute the magnitude of the reflection coefficient using the
VSWR at the antenna input port (1). Measuring ZA using a Vector
Network Analyzer instead of the more conventional and simple VSWR
measurement obtained by power sensors, has several advantages among
which are: the ability to observe separately the effect of coupling
(changes of the antenna admittance) and the effect of reflections
(changes in the antenna resistance), allow to increase the measurement
speed, diminish the measurement noise, and reduce errors due to
intermediate elements such as directional couplers. However, any of
the above measurement techniques could be used taking into account

182 Pa´ez, Tremola, and Azpu´rua
the measurement capabilities of each laboratory.
|Γ| =
∣∣∣∣
ZA − Z0
ZA + Z0
∣∣∣∣ =
V SWR− 1
V SWR+ 1 (1)
In this experiment, when the reflection coefficient is measured
without the reflective plate, Γ0, the results provide information about
the normal input impedance of the transmit antenna inside the
semianechoic chamber. The second part consist on the placement of the
reflective plate over nine different positions of the UFA, as is explained
later, and in each position measuring the modified input impedance
of the transmit antenna in order to quantify the reflection coefficients
due to coupling and reflected energy, ΓEUT . In that sense, there is
a quantifiable relationship between the E field variation and ΓEUT
and Γ0 that it is derived from the Friss’ formula [14]. Therefore the
theoretical electric field in far field zone, E, is expressed in terms of the
distance R, the transmitted power, Pt, and the gain of the transmission
antenna, Gt, as shown in (2).
E =
√30GtPt
R (2)
In the same way, the transmitted and the incident power, Pi, are related
by,
Pt = Pi
(
1− |Γ|2
)
(3)
Substituting (3) into (2), results in the following equation,
E =
√30GtPi
R
√
1− |Γ|2 (4)
Assuming that the incident power at the antenna input port is
fixed, the difference between the electric field strength generated in
the center of the UFA with and without the EUT presence, ∆E, is
expressed by,
∆E = |EEUT − E0| =
√30GtPi
R
[√
1− |ΓEUT |2 −
√
1− |Γ0|2
]
(5)
Then, the relative change in the E-field within the UFA due to EUT
presence, ∆Er, is,
∆Er(%)=100·
∣∣∣∣
EEUT − E0
E0
∣∣∣∣=100·
∣∣∣∣∣∣
√
1− |ΓEUT |2 −
√
1− |Γ0|2√
1− |Γ0|2
∣∣∣∣∣∣
(6)
Consequently, expressing (6) in decibels,
∆Er(dB) = 20 log
(
1 + ∆Er(%)100
)
(7)

Progress In Electromagnetics Research B, Vol. 29, 2011 183
It must be noticed that since ∆Er depends on frequency, f , location
of the reflective plate within the UFA, l, chamber characteristics and
type of the transmit antenna, the uncertainty contribution associated
will also be different for each test site. In this work the uncertainty
contribution corresponding to the relative change in the E-field within
the UFA, uEUT , was calculated taking the worst case approach,
considering it as the maximum value of ∆Er within the whole
frequency range for each one of the reflective plate positions.
uEUT = max (∆Er(f, l))
{ f ∈ [80, 1000]MHz
l ∈ {1, 2, 3, 4, 5, 6, 7, 8, 9} (8)
3. EXPERIMENTAL SETUP AND PROCEDURE
3.1. Measurement the Relative Change in the E-field within
the UFA Due to EUT Presence
The experiment consists in measuring the reflection coefficient at the
antenna port with and without a reflective plate that serves as a
representation of a EUT. The dimensions of the reflective plate were
chosen to cover a grid of 0.5m×0.5m within the semianechoic chamber
UFA. The reflective plate was placed in nine (9) different positions,
Figure 4. Experimental arrangement inside semi-anechoic chamber.

184 Pa´ez, Tremola, and Azpu´rua
matching its vertices with the points where the electric field probe was
placed for field calibration according to IEC 61000-4-3. A graphical
representation of the experimental arrangement inside semianechoic
chamber is shown in Figure 4.
The reflective plate was placed in each position because, from
a theoretical standpoint, the EUT can be placed anywhere inside
the UFA. Also, the size of the reflective plate is comparable to a
typical size device that is tested in a 3m semianechoic chamber,
making the results realistic and representative. To hold the reflective
plate, we used a plastic mast, of the same kind used to locate the
isotropic electric field probe for field calibration. The measurements
were performed all over the frequency band required by IEC 61000-
4-3 (80MHz to 1GHz), in both antenna polarizations (vertical and
horizontal), using a calibrated Vector Network Analyzer (VNA) placed
outside the semianechoic chamber. In the presence of the reflective
plate, the measurements were repeated for the nine selected positions
with the reflective plate grounded and with reflective plate isolated. A
Diagram of the measurement setup is shown in Figure 5.
Figure 5. Diagram of the measurement setup.
Figure 6. Diagram of validation setup.

Progress In Electromagnetics Research B, Vol. 29, 2011 185
3.2. Validation of the Measurements
The results were validated by measuring the reflected power and power
delivered to the antenna input during the execution of a test according
to IEC 61000-4-3, with and without the presence of the reflective plate
in the nine (9) selected positions, using the power meters included in
the IEC 61000-4-3 test system. A diagram of the validation setup is
shown in Figure 6.
4. RESULTS
As explained before, the input impedance of the antenna (High
Gain Log-Periodic R&S R©HL046) was measured with and without the
reflective plate. Figure 7(a) shows the real part of the impedance. As
Antenna Input Resistance without EUT Antenna Input Reactance without EUT
Frequency [GHz]
Inp
ut
Re
sis
tan
ce
[Oh
m]
Inp
ut
Re
act
an
ce
[Oh
m]
0.08 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Frequency [GHz]
0.08 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
40
30
20
10
0
-10
-20
-30
-40
90
80
70
60
50
40
30
20
(a) (b)
Figure 7. Antenna input impedance. (a) Resistance. (b) Reactance.
-6
-4
-2
0
2
4
6
-6
-4
-2
0
2
4
6Changes of Transmit Input Resistance Position 5 Changes of Transmit Input Reactance Position 5
Re
sis
tan
ce
Di
ffe
ren
ce
[O
hm
]
Re
ac
tan
ce
Di
ffe
ren
ce
[O
hm
]
Frequency [GHz]
0.08 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80.9 1
Frequency [GHz]
0.08 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
(a) (b)
Figure 8. Change in antenna input impedance for: Reflective plate in
position 5, antenna horizontally polarized and with the reflective plate
isolated. (a) Resistance. (b) Reactance.

186 Pa´ez, Tremola, and Azpu´rua
-6
-4
-2
0
2
4
6
-6
-4
-2
0
2
4
6Changes of Transmit Input Resistance Position 5 Changes of Transmit Input Reactance Position 5
Re
sis
tan
ce
Di
ffe
ren
ce
[O
hm
]
Re
ac
tan
ce
Di
ffe
ren
ce
[O
hm
]
Frequency [GHz]
0.08 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Frequency [GHz]
0.08 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
(a) (b)
Figure 9. Change in antenna input impedance for: Reflective plate in
position 5, antenna horizontally polarized and with the reflective plate
grounded. (a) Resistance. (b) Reactance.
expected, the real part of the impedance of the antenna is designed
to work close to 50Ω. Figure 7(b) shows the imaginary part of
transmit antenna impedance. The following measurement results were
taken with the antenna set in horizontal polarization; nevertheless
the measurements were also performed for the vertical polarization
case. The results of antenna input impedance measurements provide
a benchmark for assessing changes in the input impedance, which in
turn may be associated with, reflections on the EUT, EUT-antenna
coupling and hence changes in the reflection coefficient.
The change in the antenna input impedance due to EUT presence
was measured for each of the nine positions, shown in Figure 4, for
both polarizations, with the reflective plate grounded and with the
reflective plate isolated. As an example the results for position 5 are
shown in Figures 8 and 9. The results show a maximum change in
antenna input resistance and antenna input reactance of approximately
6Ω near 200MHz.
The Figure 10 shows the spatial average and the spatial maximum
of relative electric field deviation. The average and the maximum were
taken over all nine positions in each frequency, with the reflective
plate isolated and with the reflective plate grounded. As shown
in Figure 10, although there are differences in the Relative Electric
Field Deviation measured with the antenna vertically polarized and
horizontal polarized for frequencies below 200MHz, these differences
do not affect the contribution of uncertainty since the maximum of both
curves are approximately equal to 0.32 dB. Figure 10 also shows that
measurements made with the reflective plate grounded and isolated are
not significantly different.
Figure 11 shows the expected correspondence of the VSWR at

Progress In Electromagnetics Research B, Vol. 29, 2011 187
Relative Electric Field Deviation Relative Electric Field Deviation
Relative Electric Field Deviation Relative Electric Field Deviation
Spatial average
Spatial maximun
Spatial average
Spatial maximun
Spatial average
Spatial maximun
Spatial average
Spatial maximun
E r
ela
tive
[dB
]
Frequency [GHz]0.08 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Frequency [GHz]
0.08 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
(a) (b)
Frequency [GHz]0.08 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Frequency [GHz]
0.08 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
E r
ela
tive
[dB
]
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
E r
ela
tive
[dB
]
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
E r
ela
tive
[dB
]
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
(c) (d)
Figure 10. Relative electric field deviation. (a) Antenna horizontally
polarized and reflective plate isolated. (b) Antenna vertically polarized
and reflective plate isolated. (c) Antenna horizontally polarized
and reflective plate grounded. (d) Antenna vertically polarized and
reflective plate grounded.
antenna input port calculated through VNA measurement results and
the data obtained using the validation setup (Figure 6). The difference
between the VSWR calculated using ZA measurement results and
the VSWR measured directly by power sensors is explained by the
fact that the signal generator and the power amplifier, used in the
validation setup, introduce more noise and harmonics than the VNA,
and also because of the error associated with the automatic gain control
that maintain the antenna input power fixed. Therefore, the results
obtained using the VNA show smoother frequency dependence than
the results found using power sensors.
The procedure was repeated with the antenna placed for vertical
polarization obtaining similar results to the previous case of horizontal
polarization, showing the expected correspondence.

188 Pa´ez, Tremola, and Azpu´rua
VSWR in Transmit Antenna Input Port. Position 5
VSWR calculated from Input impedance
VSWR measured using power sensors
Frequency [GHz]
0.08 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
VS
WR
1.9
1.8
1.7
1.6
1.5
1.4
1.3
1.2
1.1
1
Figure 11. VSWR verification with the reflective plate in position 5,
antenna horizontally polarized and reflective plate isolated.
Histogram of Relative Electric Field
Relative Electric Field Deviation
Re
lat
ive
Fr
eq
ue
nc
y
-0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
0.18
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
Figure 12. Histogram of relative electric field deviation, ∆Er.
Applying the criteria defined in (8) the measurements and
calculations show that the uncertainty contribution due to EUT
presence in RF Immunity Testing according IEC 61000-4-3, for
the particular case described in this paper, is 0.32 dB. That value
should be reported in the uncertainty budget. To include this
contribution to the uncertainty budget is necessary to know the
distribution of data; however it is not possible to foresee the exact
probability density function that best fits the phenomenon of field
variations within the UFA due to interaction EUT-Antenna. The
relative (statistical) frequency histogram of ∆Er, shown in Figure 12,
exhibits an asymmetric behavior, which does not correspond to a
rectangular distribution as assumed in [6] nor to a triangular or normal
distribution. Instead, a U-shaped distribution is more likely to be

Progress In Electromagnetics Research B, Vol. 29, 2011 189
applicable [5]. Nevertheless, further research should be conducted to
conclude on the use of this contribution within a budget of uncertainty.
The relative frequency, shown in Figure 12, was calculated, dividing the
number of measurement data points included in each bin normalized
by total number of elements of the ∆Er(f) vector.
5. CONCLUSIONS
The method proposed constitutes an experimental way to quantify the
uncertainty by the presence of EUT due to Antenna-EUT coupling
and reflected energy back to the source antenna on a semianechoic
chamber. This method was performed, measuring antenna input
impedance using a VNA and was validated through power sensor
measurement using the complete measurement system corresponding
to a test according IEC 61000-4-3 to ensure the results. The relative
change of the electric field magnitude caused by the presence of the
EUT has its maximum at 120MHz, and represents a deviation of
0.32 dB for the worst case position. Hence the contribution associated
to the uncertainty budget is 0.32 dB, which is not a depreciable
quantity. Data show that ∆Er has an asymmetrical distribution
around its mean value, not corresponding to a rectangular, triangular
or normal behavior. The experiments performed also show that the
EUT presence by itself does not compromise the field uniformity. This
could be explained as a consequence of the superposition principle of
electromagnetic field theory, in which the main components of field
are due to the antenna radiation, and the secondary components are
consequence of the fields induced in the metallic parts of the EUT.
Measurements made with the reflective plate grounded and isolated
showed no significant difference. In the same way, measurements done
with the antenna in vertical and horizontal polarization showed no
significant differences. The method could also be useful to evaluate
semianechoic chambers by comparing the electric field deviation within
the UFA between them. The next investigation is to evaluate this
method using different transmit antennas to know which one introduces
a minor uncertainty due to the phenomenon explained in this work.
REFERENCES
1. Williams, T., EMC for Product Designers, 4th edition, 164–184,
Newness, Oxford, 2007.
2. Williams, T. and S. Baker, “Uncertainties of immunity
measurements,” Main Report of the DTI-NMSPU Project R2.2b1,
Schaffner EMC Systems and Elmac Services, 2002.