TCP of 20 Mobile Phones
Measured in Reverberation Chamber
Procedure, Results, Uncertainty and Validation
PER-SIMON KILDAL AND CHARLIE CARLSSON
Preface
This report is a result of projects for TCO Development AB (www.tcodevelopment.com) during 2001.
The measurement method is a result of research in the antenna group at Chalmers University
of Technology (www.elmagn.chalmers.se/elmagn/antenna). The intended primary application
was to measure radiation efficiencies of antennas for all types of mobile and wireless terminals, such as mobile phones and Bluetooth terminals. In the present report we describe how
the method can be used to measure the total radiated power of such terminals. The total radiated power of phones are herein referred to as Telephone Communication Power ® (TCP® )1.
The TCP measurements of the twenty phones documented in this report have been performed
in Bluetest® Reverberation Chamber RC800. We have also received five phones from Gert
Anger at SSI (Swedish Radiation Protection Authority). These are the same models as five of
the 20 phones set. The five phones have been measured in a much larger reverberation
chamber at FOI (Swedish Defense Research Establishment) in Linköping. Olof Lunden is
responsible for the chamber at FOI, but Charlie Carlsson of Bluetest has done the
measurements with Bluetest equipment.
We also show some results from the Master thesis of Nikolay Serafimov at Chalmers, in
which he compares the total radiated power of phones measured in two anechoic chambers
and two reverberation chambers. His project was supported by Sony Ericsson Mobile Communications in Lund.
The procedure for measuring TCP is now adopted as part of the TCO’01 Certification of
Mobile Phones, see www.tcodevelopment.se. The brief version of the measurement procedure
included in the TCO’01 description can be found in Appendix A of this report. We have here
also corrected an error in the formula for P refA( f i ) in the original document.
This report also contains manuscripts of five journal articles about measurements of small
antennas in reverberations chambers (Appendices B-F). Three of these have already appeared
in Microwave and Optical Technology Letters. The last two are under review in the same journal.
The authors are grateful for the comments and corrections to this report from Yngve Hamnerius (Professor at Chalmers University of Technology) and Kjell Fransson (Associate Professor at Stockholm University).
Chalmers, 2002-02-04
Per-Simon Kildal (www.kildal.se)
Professor at Chalmers University of Technology and founder of Bluetest ® AB2
1.
®The
names Telephone Communication Power and TCP are registered by TCO.
2. Bluetest AB is a start-up company that commercializes reverberation chambers for measuring radiation efficiency, TCP
and effective diversity gain. Bluetest also offers measurements on a commercial basis. Information about Bluetest AB can
be found at www.bluetest.se. The address is Chalmers Teknikpark, 41288 GOTHENBURG, Sweden. Bluetest AB can be
contacted via info@bluetest.se or simon@kildal.se.
© Bluetest AB
February 4, 2002
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January 28, 2002
Summary and Conclusion
We have developed a procedure by which the radiated power of mobile phones can be measured in a reverberation chamber. This radiated power is by TCO referred to as the Telephone
Communication Power (TCP). During the measurements the phone can be located in talk position near a head phantom.
We have measured TCP of 20 different phone models in Bluetest RC 800 reverberation chamber when they are located in the different talk positions defined by CENELEC [3] relative to a
head phantom, and we have investigated the uncertainty of the results. The Bluetest RC 800 is
so small that it can pass through an 80 cm wide door opening.
The investigations have been done both a head phantom filled with brain-equivalent liquid and
with a solid polymer head-and-shoulder phantom. We have not seen any difference in measurement uncertainty which relates to the different loading of the two chambers which these
two phantoms represent.
The expanded measurement uncertainty ( 2σ ) is estimated to be 1. dB or better.
Validations against results measured in an anechoic chamber show that the maximum differences between a TCP result from the Bluetest chamber and a corresponding value from the
anechoic chamber is 1.00 dB and 1.56 dB in the GSM 900 and 1800 MHz bands, respectively.
The value at 900 MHz is very close to the theoretical predictions, even though the experimental value includes also the contribution from the uncertainty of the anechoic chamber. At 1800
MHz the uncertainty is slightly larger than at 900 MHz although it theoretically should have
been smaller. This needs more investigation. In both frequency bands the uncertainties are
acceptable.
TCP results measured in the Bluetest RC 800 chamber are compared with results measured
with the same instrumentation in a much larger reverberation chamber. The standard deviation
of the difference between the results is 0.32 dB and 0.62 dB in the GSM 900 and 1800 MHz
bands, respectively. The value at 900 MHz agrees well with the theoretical standard deviation
of 0.275 dB due to the statistics in the chamber. The value at 1800 MHz is larger than the theoretical value of 0.09 dB, but still reasonable.
The accuracy is sufficiently good to resolve clearly differences in absorption in the head phantom due to different antenna types, different talk positions of the phone and different phones,
as well as the differences in TCP of different phones in the different talk positions of the
phones. Our results show also that the uncertainty is sufficiently good to resolve variations
between different individuals of the same phone model.
The TCO’01 certification specifies a value of the mean TCP over the four talk positions. This
will have an expanded uncertainty that is better that of each single TCP value. The value is
about 0.7 dB in both bands.
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February 4, 2002
CONTENT
Preface ......................................................................................................................................... i
Summary and Conclusion............................................................................................................ i
CONTENT.................................................................................................................................iii
1.0
Introduction ................................................................................................................................ 1
1.1
Definition of TCP .......................................................................................................... 1
1.2
CENELEC defined "cheek" and “tilted” positions of the mobile phone in relation to
the phantom ................................................................................................................... 3
1.2.1
Definition of the "cheek" position:.................................................................. 3
1.2.2
Definition of the "tilted" position:................................................................... 3
1.3
Reverberation chamber.................................................................................................. 3
1.3.1 Measuring radiation efficiency in reverberation chamber ............................... 3
1.3.2 Measuring TCP in reverberation chamber ....................................................... 4
1.3.3 Techniques used to improve measurement accuracy of TCP........................... 5
1.3.4 Description of Bluetest 1st, 2nd and 3rd generation prototype chambers........ 7
1.4
GSM standard transmit levels and frequencies ............................................................. 7
1.4.1 Explanations of dBm versus W ........................................................................ 7
2.0
Procedure for Measuring TCP .................................................................................................... 9
2.1
Requirements of measurement setups ........................................................................... 9
2.1.1 Reverberation chamber..................................................................................... 9
2.1.2 Head phantoms ............................................................................................... 11
2.1.3 Environmental conditions............................................................................... 11
2.1.4 Instrumentation and data acquisition.............................................................. 11
2.1.5 Mobile phone holder ...................................................................................... 11
2.2
Measuring the reference level (Calibrating the chamber) ........................................... 11
2.3
Measuring the TCP of a phone.................................................................................... 13
2.3.1 Positioning the phone ..................................................................................... 13
2.3.2 Base station simulator .................................................................................... 13
2.3.3 Measuring pulse power with a spectrum analyzer ......................................... 13
2.3.4 Definition of measurement cases ................................................................... 14
2.3.5 Presentation of results .................................................................................... 15
2.4
Bluetest’s optimum mode stirring sequence................................................................ 15
3.0
Measured TCP Results ............................................................................................................. 17
3.1
TCP of 20 mobile phones measured in Bluetest RC 800 ............................................ 17
3.1.1 Description of the phones and phantoms ....................................................... 17
3.1.2 Results with definition of head loss ............................................................... 17
3.1.3 Comments to results ....................................................................................... 19
3.1.4 Measurement problems .................................................................................. 23
4.0
TCP Measurement Accuracy.................................................................................................... 25
4.1
Comparison of TCP of five phones measured in Bluetest RC 800 and in large
reverberation chamber at FOI...................................................................................... 25
4.1.1 Definition of the phones and phantoms.......................................................... 25
4.1.2 Description of measurements at FOI.............................................................. 25
4.1.3 Phone positions and results ............................................................................ 25
4.2
Statistical analysis of results in different reverberation chambers .............................. 30
4.2.1 GSM 900 transmit band ................................................................................. 30
4.2.2 GSM 1800 transmit band ............................................................................... 31
4.3
Experimental investigations of inaccuracies due to instrumentation .......................... 31
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4.4
4.5
4.6
4.7
4.8
5.0
Experimental verification of errors due to losses in phones chassis ........................... 31
Experimental verification of repeatability of positioning the phone........................... 32
Validation in anechoic chamber .................................................................................. 33
4.6.1 Radiation efficiencies ..................................................................................... 33
4.6.2 TCP values .................................................................................................... 34
Theoretical accuracy of Bluetest RC800 from mode density...................................... 34
Estimate of overall uncertainty.................................................................................... 36
References ................................................................................................................................ 39
Appendix A.TCP method: Brief description of TCP test method as included in TCO’01 ..................... 1
Appendix B.Plane wave study: Manuscript of the scientific article
"Study of Distributions of Modes and Plane Waves in Reverberation Chambers for
Characterization of Antennas in Multipath Environment",
by K. Rosengren and P-S. Kildal,
Microwave and Optical Technology Letters, Vol. 30, No 20, pp. 386-391, Sept. 2001 ............ 1
B.1
Introduction ................................................................................................................... 1
B.2
Mode and plane wave descriptions of a rectangular cavity........................................... 2
B.3
Results for the Chalmers and FOA chambers ............................................................... 4
B.4
Weighting the plan wave density. ................................................................................. 5
B.5
Conclusion..................................................................................................................... 7
B.6
Acknowledgement......................................................................................................... 7
B.7
References ..................................................................................................................... 7
B.8
Figures .......................................................................................................................... 9
Appendix C.Platform stirring: Manuscript of the journal article
”Characterization of terminal antennas in reverberation chambers: Improved accuracy by
platform stirring”,
by K. Rosengren, P-S. Kildal, C. Carlsson and J. Carlsson,
Microwave and Optical Technology Letters, Vol. 30, No 20, pp. 391-397, Sept. 2001............ 1
C.1
Introduction ................................................................................................................... 1
C.2
Description of reverberation chamber and measurement set-up. .................................. 2
C.3
Measured Results........................................................................................................... 4
C.4
Correlation functions. .................................................................................................... 6
C.5
Accuracy........................................................................................................................ 6
C.6
Conclusion..................................................................................................................... 7
C.7
Acknowledgement......................................................................................................... 8
C.8
References ..................................................................................................................... 8
C.9
Figures ........................................................................................................................... 9
Appendix D.Impedance: Manuscript of the journal article
“Measurement of free space impedances of small antennas in reverberation chambers”,
P-S. Kildal, J. Yang and C. Carlsson,
Microwave and Optical Technology Letters, Vol. 32, No. 2, pp 112-115, Jan., 2001............... 1
D.1
Introduction ................................................................................................................... 1
D.2
Theory............................................................................................................................ 1
D.3
Measurements................................................................................................................ 2
D.4
Conclusion..................................................................................................................... 3
D.5
Aknowledgements ......................................................................................................... 3
D.6
References ..................................................................................................................... 3
D.7
Figures ........................................................................................................................... 4
Appendix E.Polarization stirring: Manuscript of the journal article
"Detection of a polarization imbalance in reverberation chambers and how to remove it when
measuring antenna efficiencies",
P-S. Kildal, C. Carlsson,
submitted to Microwave and Optical Technology Letters, Nov. 2001. ..................................... 1
E.1
Introduction ................................................................................................................... 1
E.2
Initial measurements...................................................................................................... 2
E.3
Theory............................................................................................................................ 3
E.4
Experimental results ...................................................................................................... 7
E.5
Conclusion..................................................................................................................... 7
E.6
References ..................................................................................................................... 7
E.7
Figures ........................................................................................................................... 9
Appendix F.Diversity gain: Manuscript of the journal article
"Definition of Effective Diversity Gain and How to Measure it in a Reverberation Chamber",
Per-Simon Kildal, Kent Rosengren, Joonho Byun and Juhyung Lee
submitted to Microwave and Optical Technology Letters, Nov. 2001. ..................................... 1
F.1
Introduction ................................................................................................................... 1
F.2
Calculation of diversity gain and effective diversity gain............................................. 2
F.3
Measurement procedure in reverberation chamber ....................................................... 3
F.4
Results ........................................................................................................................... 4
F.5
Conclusion..................................................................................................................... 4
F.6
References ..................................................................................................................... 4
F.7
Figures ........................................................................................................................... 6
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1.0 Introduction
A mobile phone must radiate in order to work. Thereby it is also unavoidable that part of the
radiated power is absorbed in the human head. This absorption is characterized in terms of a
Specific Absorption Rate (SAR), and there exist requirements to the maximum allowed value
of the SAR. These values have been determined by considering the possibility of health hazards. It has therefore been an issue that the SAR value should be as low as possible, without
actually mentioning the fact that a phone must radiate in order to work satisfactory. TCO has
therefore in their new quality and environmental labelling of mobile phones - the TCO’01
Certification of Mobile Phones [1]- introduced a complement to the SAR value. This is the
maximum power the phone can utilize for communication, and it is called Telephone Communication Power (TCP). This is meant to ensure that phones radiate sufficient power to work
properly. The TCP can be measured in many ways. E.g., it can be measured in a standard
anechoic chamber. The purpose of the present report is to describe how we at Bluetest AB
measure it in a reverberation chamber. This has many advantages over an anechoic chamber.
The anechoic chamber needs to be several meters in cross section, whereas the reverberation
chamber we use is 0.8m x 1.05m x 1.6m in size. The measurements take also much shorter
time. Chalmers and Bluetest AB have developed a number of patent-applied improvements1 to
to the reverberation chamber technique. We will describe these improvements, and show that
they provide a measurement accuracy comparable with that of a good anechoic chamber.
1.1 Definition of TCP
The TCP is the power leaving a closed surface, which surrounds the phone and the head phantom when these are located far from other objects. It is the maximum available power, which
can be provided by the phone if the antenna on the phone were ideally matched to the output
impedance of the phone, minus the power which is reflected due to an actual mismatch at the
antenna port, minus the power which is dissipated in the antenna, minus the power which is
absorbed in the head phantom.
The TCP is the figure of merit of a mobile phone, when it is transmitting. The higher the TCP,
the better the phone will work in the transmit mode. On the other hand, the possible radiation
hazards are characterized in terms of a Specific Absorption Rate (SAR) distribution that
should be as low as possible or at least below some standardized limits. Both the TCP and the
SAR are proportional to the maximum power that can be radiated by the phone. Therefore, a
high quality phone must provide a good compromise between high TCP and low SAR. This is
possible by directing the radiation from the phone away from the head.
The TCP is proportional to the radiation efficiency of the antenna on the phone, measured with
the head phantom present. The radiation efficiency as defined in [2] has three contributions:
1. The reflections due to impedance mismatch between the phone antenna and the transmission line that connects the phone antenna to the receive and transmit amplifiers inside
the phone.
1. TCO Development AB and Bluetest AB have reached an agreement regulating the rights to use the TCPmethod and the improvements of the same. Companies that wish to test the radiation of their mobile phones
may, for internal purposes, use the TCP-method and its improvements freely. This free usage, however, does
not include the right to use any equipment that is covered by Bluetest AB's patent rights. Please contact TCO
Development AB or Bluetest AB if you have any questions regarding this matter.
© Bluetest AB
January 28, 2002
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2. The absorption in the phone antenna itself, including the chassis of the phone.
3. The absorption in the phantom.
The less absorption in the head, the lower is the SAR. Thus, the best compromise between
high TCP and low SAR is to make the antenna radiate away from the phantom (head).
Thereby, the absorption in the phantom will decrease so that the radiation efficiency increases.
:
Figure 1. Definition of the reference lines and points, on the phone and on the
phantom and initial position, from [3].
Figure 2. "Cheek" and “tilted” positions of the mobile phone on the left side, from [3].
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1.2 CENELEC defined "cheek" and “tilted” positions of the mobile phone
in relation to the phantom
The TCP needs to be measured when the phone is in use and effected by the human head. For
SAR measurements the human head is replaced by a head phantom, and there exists well
defined positions of the phone relative to the head phantom for which the tests are to be performed, see Section 6.1.4 of the European Standard EN 50361 of SAR testing introduced by
CENELEC [3]. We have therefore decided to use these positions also for the TCP tests. The
positions are referred to as "cheek" and "tilted" positions on left and right sides of the phantom, and we have chosen to include the descriptions of them here, in the same way as they
appear in [3]
1.2.1 Definition of the "cheek" position:
a) position the device with the vertical centre line of the body of the device and the horizontal
line crossing the centre of the ear piece in a plane parallel to the sagittal plane of the phantom
(“initial position” see Figure 1 on page 2). While maintaining the device in this plane, align
the vertical centre line with the reference plane containing the three ear and mouth reference
points (M, RE and LE) and align the centre of the ear piece with the line RE-LE;
b) translate the mobile phone box towards the phantom with the ear piece aligned with the line
LE-RE until the phone touches the ear. While maintaining the device in the reference plane
and maintaining the phone contact with the ear, move the bottom of the box until any point on
the front side is in contact with the cheek of the phantom or until contact with the ear is lost.
1.2.2 Definition of the "tilted" position:
a) position the device in the "cheek" position described above;
b) while maintaining the device in the reference plane described above and pivoting against
the ear, move it outward away from the mouth by an angle of 15 degrees or until contact with
the ear is lost.
1.3 Reverberation chamber
The present tests make use of a so-called reverberation chamber. The reverberation chamber is
well known within the EMC area. Its theory is described in detail in [4]-[8]. It has recently
also been used to characterize antennas. The reverberation chamber is also called a mode
stirred chamber, as it contains several cavity modes, which are stirred mechanically to provide
several statistically independent field distributions. These field distributions correspond to
what in mobile communications result from multipath propagation, as shown in [9]. The
mechanical stirrers can have many forms, see Figure 3 on page 4. The reverberation chamber
from Bluetest AB makes use of two plate stirrers. One of these can be moved across the back
wall of the chamber, and the other can be moved over a complete horizontal cross section in
the upper part of the chamber.
1.3.1Measuring radiation efficiency in reverberation chamber
The antenna group at Chalmers has shown that reverberation chambers can be used to measure
radiation efficiency of antennas [10]-[11]. In order to improve accuracy we have developed
© Bluetest AB
January 28, 2002
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Figure 3. Photos of Bluetest’s reverberation chamber for measuring TCP and
radiation efficiency. The left photo shows the 2nd generation prototype chamber with
1.6 m height. The right photo shows the interior of the 3rd generation chamber with
phantom head and phone, inside which the reported phone measurements have been
performed. The commercial Bluetest® Reverberation Chamber RC800 is the same as
the latter [22]. The irregular plates on the rear wall and above the phantom are the
mechanical stirrers. The head phantom is located on a rotatable plate.
platform stirring [12] and polarization stirring [13], which will be described in more detail
below. We have also shown that it can be used to measure the “free space” input reflection
coefficient of small antennas in the vicinity of some object such as a head phantom [14]-[15].
With “free space” reflection coefficient we mean the reflection coefficient, as it would be seen
if the antenna and the object were located in free space. We have also shown that reverberation
chambers can be used to measure effective diversity gain very accurately, if the phone has
more than one antenna and makes use of diversity [16]. Some results of measurements of radiation efficiency and input reflection coefficients are given in [17]-[19]. The experimental
results have been verified towards numerical results for a simple validation case [19]. This
validation case is a halfwave dipole at distance from a PVC cylinder filled with brain equivalent tissue. In reference [20] the Bluetest chamber is characterized, and the set-up for antenna
measurements is described. Measurements of both radiation efficiency and TCP in Bluetest’s
chamber are in [21] validated against measurements in another reverberation chamber and in
two anechoic chambers. A short summary of the latter is given in Section 4.6 on page 33 of
the present report.
1.3.2Measuring TCP in reverberation chamber
The above-mentioned measurement of antenna radiation efficiency in reverberation chambers
has been extended and modified to measuring TCP. The procedure is as follows (see also
Section 1.3.3 on page 5 where the improvements of the chamber are described, and
Section 2.0 on page 9 where the procedure is described in more detail):
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1. We locate a transmitting phone in the chamber, as far away as possible from a receive
antenna, which is part of the interior of the chamber. In the Bluetest chamber the receive
antenna is fixed to the wall of the chamber and often referred to as the fixed antenna. We
measure the received power level at the fixed antenna for a number of positions of the
mechanical stirrers, when the phone is transmitting with maximum power. This means
that we actually measure only at the transmit frequency of the phone. It is also possible
to measure by using a measurement receiver of another kind or a pulse analyzer.
2. We average the received powers over the positions of the mechanical stirrers.
3. Finally, we multiply a reference level with this average power, to get the TCP. The reference level can be determined very accurately as described below and in Section 2.2 on
page 11.
The reference level is obtained by locating a calibration antenna inside the chamber and by
using a network analyzer to measure the transfer function between the calibration antenna and
the receive antenna. The calibration antenna must have a known radiation efficiency. The reference level (or the average transfer level) is calculated by averaging the transfer function over
many positions of the mechanical stirrers. There must be exactly the same lossy objects inside
the chamber during the calibration measurements and during the phone measurements. This
means that the head phantom must be located on the platform inside the chamber in both
cases. Theoretically, the phone should also be located inside the chamber when the reference
level is measured. The reason is that the chassis of the phone may contain lossy materials that
will reduce the Q of the chamber and therefore also the average transfer level. This may erroneously appear as a reduction in the TCP, which it is not. Of the same reason the calibration
antenna should be located inside the chamber when the phone is measured. However, due to
the heavy loading of the chamber caused by the head phantom, the additional losses due to the
materials in the chassis of the phone are very small for those phones we have measured.
Therefore, the reference level can be the same for all the different phones, which is a great
advantage.
When the reference level is being measured, the calibration antenna must be located at least
0.7 wavelengths away from the head phantom. When the free space TCP of the phone is measured, the phone must also be located at least 0.7 wavelengths away from the head phantom.
The phone and calibration antennas must not have radiating parts closer than 0.5 wavelengths
from the chamber walls, floor or ceiling. These distances are empirical and known from work
in the EMC area.
The measurement accuracy depends on the number of independent power distributions, which
the chamber can produce at the measurement frequency, see [4]. This number increases linearly with the volume of the chamber and the frequency squared, but it is also strongly dependent on the loading of the chamber, how the mechanical mode stirrers are designed, and how
the measurements are performed.
1.3.3Techniques used to improve measurement accuracy of TCP
In order to ensure as good accuracy as possible, Chalmers and Bluetest AB have implemented
the following patent-applied improvements of the measurement procedure described above
[22]:
1. We have designed two plate-formed mechanical stirrers, both of which can be moved
across one complete chamber wall and a horizontal cross section of the chamber. They
© Bluetest AB
January 28, 2002
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can be moved in two ways relative to each other, either simultaneously or sequentially,
the latter for higher accuracy, [12] and [20].
2. We have designed a platform stirrer, upon which the head phantom, phone and calibration antenna are located during the measurements. The platform can be rotated to different angular positions. Averaging is performed over positions of the mechanical stirrers
at each angular position of the platform, as well as over angular platform positions, for
improved accuracy. This reduces the error due to direct coupling between the receive
antenna and the calibration antenna (or phone), in addition to increasing the number of
independent power samples [12] by a factor that is close to 25.
3. Measurements in reverberation chambers of different sizes have shown that the polarization inside the chamber is non-uniform. The received average power levels may differ
with as much as 2 dB between two orthogonal orientations of the calibration antenna.
This is certainly not acceptable. In the Bluetest chamber we have improved this by using
polarization stirring [13], i.e. by means of three receive antennas that are orthogonal
polarized, and to average the power levels obtained by them. The three antennas are
actually three monopoles, each one mounted orthogonally to different walls of the chamber (back wall, sidewall and roof). The reference level does now not depend significantly on whether the calibration antenna is oriented vertically or horizontally.
4. The reference measurements are done with a network analyzer. Therefore, we have
access to the reflection coefficient S 11 of the three fixed receive antennas, and we can
use this to remove variations in S 21 due to S 11 , so as to get a corrected S 21 which varies
more smoothly with frequency. This makes it possible to use frequency stirring (i.e.
averaging over a certain frequency band) even when the receive antenna is not well
matched, in order to get a more accurate reference level, without worsening the frequency resolution of the reference level. The effect of S 11 must be added to the reference level again after the frequency stirring has been done, in order to get the correct
reference level. See Section 2.2 on page 11 for the details.
We have also patent-applied additional improvements of the chamber, but they have only
shown to be advantageous in connection with radiation efficiency measurements and not TCP
measurements, so they will not be mentioned here.
In addition to the above, we average the received power levels from the phone over the transmit frequency band in order to obtain a better measurement accuracy. This frequency averaging is normally in mode stirred chambers referred to as frequency stirring. By doing this, we
cannot resolve frequency variations of the TCP over the transmit bands. However, the transmit
GSM bands are very narrow (25 MHz at 900 MHz and 75 MHz at 1800 MHz), so there is no
reason why an average level should be a less suitable measure of the communication ability of
the phones than another choice. It is possible to extend the procedure to resolve such frequency variations in the 1800 MHz band and still use the Bluetest RC800 chamber, if this later
is required. In order to resolve it in the 900 MHz band, a larger reverberation chamber must be
used.
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© Bluetest AB
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Table 1. Main characteristics of Bluetest’s prototype reverberation chambers
1st, G1
2nd, G2
3rd, G3
Width
0.79 m
0.79 m
0.79 m
Depth
1.045 m
1.045
1.045 m
Height
1.01 m
1.6 m
1.6 m
Location of plate stirrers
on back wall &
side wall
on back wall &
above phantom
on back wall &
above phantom
Rotatable platform stirrer
on floor between
2 plate stirrers
and 2 walls
on floor between
1 plate stirrer
and 3 walls
on floor between
1 plate stirrer
and 3 walls
Types of receive antennas
helical on wall
helical on wall
3 orthogonal
monopoles
Chamber generation
1.3.4Description of Bluetest 1st, 2nd and 3rd generation prototype chambers
The characteristics of the different reverberation chambers used during this project are given
in the Table 1 on page 7. The monopoles of the G3 chamber are located orthogonal to the back
wall, side wall and roof of the chamber. The heights of the G2 and G3 chambers are chosen
carefully in order to get as high mode density as possible in the transmit GSM 900 MHz band,
as described in [9]
1.4 GSM standard transmit levels and frequencies
The GSM standard specifies some RF power classes and their tolerances. The phones belong
to power class 4 for the GSM 900 MHz band and class 1 for GSM 1800. The standard power
levels of these two classes are shown in the table. The tolerances are in both cases 2 dB.
Table 2. GSM transmit levels
Standard power level
Acceptable range
GSM 900
GSM 1800
33 dBm
30 dBm
31 - 35 dBm
28 – 32 dBm
The transmit frequency bands of GSM are defined by the following table.
Table 3. GSM transmit bands
Transmit band
GSM 900
GSM 1800
890.2 – 914.8 MHz
1710.2 – 1784.8 MHz
1.4.1Explanations of dBm versus W
Telephone Communication Power (TCP) is measured in watts (W) or preferably in dBm. To
measure a level in dBm means to measure it in “dB relative to 1 mW”. The dBm value is
obtained by taking 10 times the logarithm to the value in milliwatts (mW). 1 mW = 1W/1000.
© Bluetest AB
January 28, 2002
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Thus, a power level in dBm becomes
( P ) dBm = 10 ⋅ log ( P ⋅ 1000 )
when P is the level in W. It is advantageous to use values in dBm compared to W because they
provide a better representation of relative levels. A difference of 3 dB between two dBm values represents always a factor 2 between the W levels.
Some example values are:
27 dBm = 0.5 W
30 dBm = 1 W
33 dBm = 2 W
36 dBm = 4 W
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© Bluetest AB
2.0 Procedure for Measuring TCP
This section describes the procedure for measuring TCP in a reverberation chamber as specified in TCO’01 Certification of Mobile Phones, see Appendix A of the present report. The
measurements reported in the present report follows this procedure. The mode stirrer sequence
is not specified in the TCO’01 document. Bluetest has for the results in this report used the
sequence described in Section 2.4 on page 15.
2.1 Requirements of measurement setups
2.1.1 Reverberation chamber
The measurement setups both for the chamber calibration and the TCP measurement are illustrated in Figure 4 on page 10. Both setups are composed of the reverberation chamber with
mechanical stirrers and three receiving antennas (also referred to as the fixed antennas) for
polarization stirring, and two head phantoms (one for use at 900 MHz and another for 1800
MHz). If the chamber is small it must additionally be provided with a rotatable platform stirrer
to provide sufficient accuracy, as shown in Figure 4 on page 10. The three receiving antennas
must be orthogonal linearly polarized over the frequency ranges of the measurements. The
three orthogonal polarized receiving antennas may be monopoles connected orthogonally to
three different and orthogonal walls (including roof/floor) of the chamber. The three receiving
antennas are connected to an electronic coaxial switch by means of three coaxial cables A, B
and C. The reverberation chamber can have an inner volume as small as a minimum of 1.25
m3 if platform stirring is implemented, but must be larger than 8 m3 if there is no such stirring
facility.
Linearly polarized dipole antennas are used for calibration of the chamber, one for each band.
These shall have a reflection coefficient better than -10 dB over the frequency band used,
when measured at their input connectors.
The reference level of the chamber is different at different frequencies. It shall be measured as
described in Section 2.2 on page 11 in each band used. The reference level shall be measured
both when the calibration antenna is oriented for vertical polarization and when it is oriented
for horizontal polarization. These two values shall differ by less than the specification in
Table 4 on page 9. In order to obtain values for comparison with the results in the table, the
reference levels shall be measured for both orientations of the calibration dipole at 8 different
positions of the dipole inside the chamber. The average, standard deviation and maximum
deviation shall be evaluated by comparing results for both polarizations over the whole set of
8 measurements. Alternatively, the levels for the two polarizations of the calibration antenna
at 1 MHz intervals between 800 MHz and 1 GHz for the GSM 900 band (and between 1600
MHz and 2000 MHz for the GSM 1800-1900 band) can be measured, and thereafter the average, standard deviation and maximum of the difference between the two sets of values over
these frequency ranges are calculated.
Table 4 Specifications of differences of measured reference levels in each frequency band
between using vertically and horizontally polarized calibration dipoles
.
Average
Standard deviation
0.2 dB
© Bluetest AB
0.5 dB
January 28, 2002
Maximum
1.0 dB
9
A
B
C
Switch
D
E
2
1
Network
Analyzer
F
A
B
C
Switch
D
rf in
Spectrum
Analyzer
Base station
simulator
Figure 4. Illustration of measurement setup in a small reverberation chamber for
calibration (upper) and TCP measurement (lower). The network analyzer, the
spectrum analyzer, the polarization switch, the two mechanical stirrers, and the
rotatable platform can be controlled from a PC.
.
10
January 28, 2002
© Bluetest AB
2.1.2 Head phantoms
The phantoms used in the tests should fulfill the requirements in Section 5.2 of EN 50361 on
SAR measurements. It is admissible to use two phantoms, one for the GSM 900 MHz band
and another for the GSM 1800-1900 MHz band. They shall be filled with the brain-equivalent
liquids specified in Section 5.2 of EN 50361 [3].
2.1.3 Environmental conditions
The tests shall be performed in an indoor laboratory where the ambient temperature shall be in
the range 15 °C – 30 °C and the variation shall not exceed ± 2 °C during the tests.
2.1.4 Instrumentation and data acquisition
The two different measurement setups make use of a network analyzer, a spectrum analyzer
(or a power meter or a measurement receiver) and a base station simulator. A PC controls the
network analyzer, the spectrum analyzer, the base station simulator and the coaxial switch, as
well as the step motors for the mechanical stirrers and the platform stirrer (if used).
2.1.5 Mobile phone holder
The mobile phone must be fixed to a mobile phone holder that satisfies the requirements given
in Section 5.5 of EN 50361 [3].
2.2 Measuring the reference level (Calibrating the chamber)
The calibration setup is shown in the upper part of Figure 4 on page 10.
First calibrate the network analyzer at its ports 1 and 2.
Connect cable D to port 1 of the network analyzer and cable A to port 2. Measure the relative
transmission factor TA of cable A plus the switch plus cable D. Make sure the switch is set to
permit transmission between cables A and D. Measure, in the same way, the relative power
transmission factors TB and TC of cables B and C including the switch and the cable D. Note
that TA, TB and TC are always smaller than 1.
Measure the attenuation LdipdB of the calibration dipole (in dB). This can be done by measuring the reflection coefficient RdB, at the input port of the dipole, when the feed gap between
the dipole arms is short-circuited. Then, LdipdB = RdB/2, and the dipole transmission factor
(smaller than 1) becomes
Tdip = 10
– Ldip ⁄ 10
(1)
Connect the single output of the switch, via cable D, to port 1 of the network analyzer. Connect cables A, B and C between the switch and the connectors to each of the three receiving
antennas.
Mount the calibration dipole on a holder inside the chamber. Connect cable F between the connector of the calibration dipole and a connector that makes a connection through the floor or
wall (shown in the center of the rotatable plate in the example in Figure 4 on page 10). On the
other side of the wall (or floor) there shall be a cable E connecting this to port 2 of the network
analyzer. If the chamber is provided with a rotatable plate stirrer, the calibration dipole shall be
located on the plate, and the cable E shall be connected to cable F via a rotary joint.
© Bluetest AB
January 28, 2002
11
Recalibrate the 0 dB level of the network analyzer three times, once for each cable A, B and C.
This shall be done for cable A by connecting together the dipole end of cable F and the monopole end of cable A. Similarly for cables B and C. Store the three calibration sets A, B and C.
Connect cable F to the dipole again.
Locate the head phantom inside the chamber in such a way that it is not closer to any wall,
ceiling or floor than 0.5 wavelengths λ. Make sure that this is the case at all positions of the
rotatable platform (if such a platform is used). Use a phantom that is filled with the correct liquid for the band to be measured. For large reverberation chambers, it may be necessary to load
the chamber with more absorbing material than the head phantom, otherwise some phones
may not work properly inside the chamber. If this is needed, exactly the same material must be
present inside the chamber when the phones are measured as when the reference level is measured.
Position the calibration dipole inside the chamber in such a way that all its parts are not closer
to any wall, ceiling or floor than 0.5 λ and at least 0.7 λ away from the phantom. The phone
shall be located outside the chamber, but the phone holder must be located inside the chamber.
(See the second last paragraph of Section 2.2.3 about the calibration procedure.)
Measure the S-parameters, when the switch is in the position corresponding to cable A, for all
the chosen positions of the mechanical stirrer and the platform stirrer (if used), and over the
whole GSM transmit band plus 12 MHz on each side of it (for 25 MHz frequency stirring).
The frequency interval shall be 1 MHz.
The measured reflection coefficient S11 has two additive contributions: One due to the reflection from the antenna port itself (deterministic) and the other due to the chamber (statistic).
The same applies to S 22 . Therefore, calculate the averages of the complex values of S 11 and
S 22 , and average them further over a 5 MHz bandwidth. The remaining parts are the free
space reflection coefficients S 11 and S 22 of the fixed receiving antenna A and the calibration
dipole, respectively.
Take the measured values S 21 and calculate
2
S 21
P = ----------------------------------------------------2
2
( 1 – S 11 ) ( 1 – S 22 )
(2)
For each of the selected frequencies f i for measuring the phone (see Section C.2.2.3), calculate the average P A ( fi ) of P , by averaging P over all stirrer positions and over a 25 MHz
band centered around each fi .
Calculate the reference transfer function of the chamber PrefA ( f i ) when using antenna A at
each frequency f i by using
2
PA ( f i ) ( 1 – S 11 )TA
PrefA ( f i ) = ------------------------------------------------T dip
(3)
Repeat the above for the other fixed antennas B and C by using the switch to obtain PrefB ( f i )
12
January 28, 2002
© Bluetest AB
and PrefC ( f i ) , respectively.
2.3 Measuring the TCP of a phone
The phone measurement setup is shown in the lower part of Figure 4 on page 10.
2.3.1 Positioning the phone
Mount the mobile phone in the holder and position it at the desired position relative to the
head phantom. The mobile phone shall be tested in 5 positions: “free space position”, which in
the chamber means more than 0.7 wavelengths away from the phantom, “right and left cheek
positions”, and “right and left tilted positions”. The cheek and tilted positions are the same as
those defined in Sections 6.1.4 of EN 50361 on SAR measurements [3]. They are also defined
in Section 1.2 on page 3 of the present report.
The mobile phone shall be turned on, and use its internal transmitter during the TCP measurements. The battery and accessories shall be those specified by the manufacturer. The battery
shall be fully charged before each measurement.
2.3.2 Base station simulator
The base station simulator shall be located outside the chamber and connected to a fixed
antenna inside the chamber, by means of a wall-mounted coaxial connector with a centre conductor going through the wall. This antenna can also be a monopole.
The base station simulator controls the output power and frequency (channel) of the mobile
phone. The mobile phone shall transmit at its highest output peak power level allowed by the
system.
The signal emitted by the base station simulator is several orders of magnitude lower than the
output level of the phone and will therefore not cause any errors in the power measurements. If
the transmitted power is measured by using a measurement receiver or a spectrum analyzer in
the zero span mode (which means that it is measured at the transmit frequency of the phone
and not at its receive frequency) the base station simulator could not cause errors, even if radiating at higher levels.
2.3.3 Measuring pulse power with a spectrum analyzer
The pulse power can, as mentioned above, be measured with different measurement instruments. This section describes how it can be done with a spectrum analyzer. Measurements
with other instruments can be done in a similar way.
The phone transmits pulses at a certain pulse repetition rate. The spectrum analyzer shall be
operating in a zero span pulse detection mode that triggers at the front of each pulse in the
pulse train. It is thus possible to read the pulse level at the same position relative to the front of
the pulse, at each measurement. Read the pulse power levels at three different time delays relative to the pulse front (choose 50, 150 and 250 µsec.), as shown in Figure 5 on page 14, and
use the median value as the pulse power level in the calculations below.
The base station simulator shall control the phone to transmit at 5 frequencies or more (one at
© Bluetest AB
January 28, 2002
13
123
0
1
2
3
5
4
ms
Figure 5. Illustration of GSM pulse, which is triggered at t 0 = 0ms , as it would be
seen on the screen of a spectrum analyzer in the zero span mode. The time positions
for measuring the pulse level are at the three markers 1, 2 and 3, the first at
t 1 = 50µs , the second at t 2 = 150µs , and the third at t 3 = 250µs .
a time) distributed with equal spacing over the whole transmit band.
Set the switch to measure power from receiving antenna A. Measure and save pulse power
levels for all the positions of the platform stirrer and mechanical stirrer and for all the frequency points used. Average the saved pulse power levels over all stirrer positions. The result
of the averaging is PavA ( f i ) . Repeat this for receiving antennas B and C to get P avB ( f i ) and
PavC ( f i ) .
The TCP in W of the phone is finally obtained by
1TCP = --N
P (f ) P (f ) P (f )
- + -------------------- + --------------------∑ 1--3- ------------------P
(f ) P
(f ) P
(f )
N
1
avA
i
avB
i
avC
i
refA
i
refB
i
refC
i
(4)
where N is the number of frequency points.
2.3.4 Definition of measurement cases
The TCP tests shall be performed in the “free space position” of the phone as well as in all
four positions of the phone relative to the phantom.
If the mobile phone has a retractable antenna, all of the tests described above shall be performed both with the antenna extended and with the antenna retracted. When considering
multi-mode and multi-band mobile phones, all of the above tests shall be performed in each
transmitting mode/band with the corresponding maximum peak power level.
14
January 28, 2002
© Bluetest AB
2.3.5 Presentation of results
The measurement protocol shall contain all the five TCP values in W, i.e. for free space, right
cheek, left cheek, right tilt and left tilt positions. They shall be given for each band/mode/
antenna of the phone. In addition, the average TCP value of the four talk positions shall be calculated and given in W for each band/mode/antenna. The values shall be given with a maximum uncertainty of 2.0 dB.
2.4 Bluetest’s optimum mode stirring sequence
Bluetest’s reverberation chambers makes use of two mechanical mode stirrers, platform
stirring and polarization stirring. (In addition we use frequency stirring as explained in
Section 2.2 on page 11 and Section 2.3 on page 13.) We have for our reverberation chamber
Bluetest RC800 found the stirring approach below to be very efficient in terms of
measurement time as well as giving accurate results.
We rotate the platform to 25 different positions, equally spaced over 360 degrees. The
mechanical stirrers are moved simultanously to 25 different positions. At each platform
position we measure at two positions of the two mechanical stirrers. This is done by the
following sequence:
1. We measure for all three polarizations and all frequencies when the platform and
mechanical stirrers are not moving.
2. We move both the two mechanical stirrers one step simultaneously.
3. We measure for all three polarizations and all frequencies when the platform and
mechanical stirrers are not moving.
4. We rotate the platform one step.
5. We measure for all three polarizations and all frequencies when the platform and
mechanical stirrers are not moving.
6. We move both the two mechanical stirrers one step simultaneously.
7. We measure for all three polarizations and all frequencies when the platform and
mechanical stirrers are not moving.
8. We rotate the platform one step.
9. And so on until we have moved the platform to all 25 positions.
In this way we get 50 measurements. Investigations have shown that all these measurements
are independent at 900 MHz. Together with the frequency stirring we get a sufficient number
of independent measurements for the good accuracy documented in Section 4.0 on page 25 in
this report.
© Bluetest AB
January 28, 2002
15
16
January 28, 2002
© Bluetest AB
Figure 6. Photos of the 20 phones used in the test.
3.0 Measured TCP Results
3.1 TCP of 20 mobile phones measured in Bluetest RC 800
3.1.1 Description of the phones and phantoms
The different phones tested are shown in Figure 6 on page 17 and defined in Table 5 on
page 18 and Table 6 on page 19. The antenna code is an abbreviation for external (E), built-in
(BI) and extractable (EL), which is used in the graphs to follow in order to easily separate
results for phones with different antenna types. The phones are letter-coded from A to X in the
graphs in such a way that it is not possible to correlate results with phone models.
All phones were measured in a fully charged position. We tested the effect of the battery not
being fully charged on one phone. For this phone the free space level went down by 1 dB after
the phone had been used in the measurement chamber with full TCP for 30 minutes.
The tests followed the test procedure given in Section 2.3 on page 13. Two Generic Head
Phantom V3.5 from Schmid & Partner Engineering AG were used, one filled with tissue
equivalent liquid for 900 MHz and the other for 1800 MHz, as specified in [3].
3.1.2 Results with definition of head loss
Figure 7 on page 20 shows the TCP in dBm for all measured talk positions of the phones; free
space, cheek right, cheek left, tilt right and tilt left. Figure 8 on page 21shows the head loss in
dB. The results are sorted in such a way that phones with extractable antennas are to the left,
with external antennas in the middle, and with built-in antennas to the right. Within each
antenna group, the phones are sorted according to decreasing average TCP and the average
© Bluetest AB
January 28, 2002
17
Table 5. Definitions of the 20 phones. Two of the phones are measured with an alternative
non-standard antenna, which can be extracted. The alternative antenna is measured both
extracted and non-extracted, so that the total number of measured cases are 24.
Mobile phones
Manufacturer
Alcatel
Ericsson
Ericsson
Ericsson
Ericsson
Ericsson
Ericsson
Ericsson
Ericsson
Ericsson
Motorola
Motorola
Motorola
Nokia
Nokia
Nokia
Nokia
Nokia
Panasonic
Samsung
Siemens
Siemens
Siemens
Sony
Model
OneTouchClub db
A2618s
R310s
R520m & IAT-10
R520m & IAT-10 (ne)
R520m
T20s
T28s & IAT-10
T28s & IAT-10 (ne)
T28s
P7389
V2288
V3688
3310
6210
6250
7110
8210
EB-GD92
SGHM100
C35i
S35i
S40
CMD-Z5
Antennatype
External
External
External
Extractable
External
External
External
Extractable
External
External
External
External
External
Built-in
Built-in
Built-in
External
Built-in
External
External
External
Built-in
Built-in
External
Ant.
Code
E
E
E
EL
E
E
E
EL
E
E
E
E
E
BI
BI
BI
E
BI
E
E
E
BI
BI
E
IMEI
332039536321890
520253512650080
520080614226200
520329510009230
520257196344390
520094717964210
449176082976570
449240072458290
448835083743630
350102809574590
449333700120500
350001100345480
448904108504840
449309109952780
449317876048830
520028980074800
449191529808150
449197526667490
350077800389310
457025066437010
Origin
TCO
GEAB
GEAB
GEAB
GEAB
GEAB
GEAB
GEAB
GEAB
GEAB
GEAB
GEAB
TCO
GEAB
TCO
GEAB
GEAB
GEAB
TCO
GEAB
TCO
GEAB
GEAB
GEAB
head loss in dB, respectively. The maximum head loss for a specific phone is the difference
between the TCP value in free space and the TCP value in the worst case, i.e. the lowest TCP
value measured for that phone. The average head loss is the difference between the TCP value
in free space and the average TCP of all the four talk positions of the phone. The latter is
obtained by averaging the dBm values. This head loss value is due to both antenna mismatch
and absorption in the head. The head loss represents a quality factor of the antenna on the
phone. The lower head loss the better is the antenna. We see that the extractable antennas of
phones H and L are clear winners in the 900 MHz band.
Figure 9 on page 22 shows the head loss in W for all cases, compared with published SAR
values. The results are sorted according to antenna type as the previous graphs, and within
each antenna group the results are sorted in such a way that the phones with the smallest head
loss in W is to the left. The maximum (or average) head loss in W is the difference between
the free space TCP in W and the TCP in W of the worst case (or the average TCP). The head
loss in W is a measure of how much power in W that disappears due to loss in the head and
mismatch. There seems to be a correlation between high head loss in W and SAR within each
antenna group.
18
January 28, 2002
© Bluetest AB
Table 6. Phone sizes and published SAR values
Mobile phones
Manufacturer
Alcatel
Ericsson
Ericsson
Ericsson
Ericsson
Ericsson
Ericsson
Ericsson
Ericsson
Ericsson
Motorola
Motorola
Motorola
Nokia
Nokia
Nokia
Nokia
Nokia
Panasonic
Samsung
Siemens
Siemens
Siemens
Sony
Model
OneTouchClub db
A2618s
R310s
R520m & IAT-10
R520m & IAT-10 (ne)
R520m
T20s
T28s & IAT-10
T28s & IAT-10 (ne)
T28s
P7389
V2288
V3688
3310
6210
6250
7110
8210
EB-GD92
SGHM100
C35i
S35i
S40
CMD-Z5
Ant.
Code
E
E
E
EL
E
E
E
EL
E
E
E
E
E
BI
BI
BI
E
BI
E
E
E
BI
BI
E
Size in (mm)
Length Width Thickness
122
52
22
131
52
16
138
53
25
98
54
18
96
96
130
136
83
113
129
141
125
102
118
106
118
118
112
88
50
50
44
50
42
49
47
59
53
45
40
44
46
46
44
49
13
13
15
21
10
22
19
25
16
18
16
13
14
21
22
17
SAR*
0,79
0,94
1,27
0,83
0,75
1,19
0,76
0,72
1,07
1,19
0,99
1,06
*SAR-values are taken from Sunday-Times web page december 2000
3.1.3 Comments to results
We see that all phones have free space TCP values at 900 MHz in the range 29-32.2 dBm,
whereas the GSM standard is 33 dBm +/- 2 dB. At 1800 MHz all phones except two have
values between 27 and 29.3 dBm when the GSM standard is 30 dBm +/- 2dB. Two phones
have very low free space TCP at 1800 MHz. The extractable antennas are very good at 900
MHz. There is not much difference between built-in and external antennas at 900 MHz,
whereas the built-in antennas show typically 1 dB smaller head loss at 1800 MHz. The TCPs
vary much more with the position of the phones for phones with external antennas than for
phones with built-in antennas. The built-in antenna seems to be less sensitive to how the phone
is used. The head loss is between 2.5 and 9 dB at 900 MHz, whereas it is between 1 and 4 dB
at 1800 MHz. We should here mention that the present results do not take into account the
effect of a users hand.
© Bluetest AB
January 28, 2002
19
Free space
35
34
33
32
31
Mean TCP
Cheek right
TCP in dBm
Tilt right
Cheek left
Tilt left
GSM900 band
TCP (dBm)
30
29
28
27
26
25
24
23
22
Free space
35
Tilt right
Cheek left
A (BI)
E (BI)
U (BI)
T (BI)
B (BI)
C (BI)
G (E)
J (E)
F (E)
V (E)
X (E)
Cheek right
TCP in dBm
32
31
D (E)
W (E)
O (E)
N (E)
I (E)
MeanTCP
34
33
Tilt left
GSM1800 band
U (BI)
B (BI)
T (BI)
E (BI)
C (BI)
A (BI)
V (E)
W (E)
K (E)
J (E)
X (E)
R (E)
D (E)
G (E)
P (E)
N (E)
Q (E)
I (E)
S (E)
O (E)
F (E)
M (E)
L (EL)
30
29
28
27
26
25
24
23
22
21
20
H (EL)
TCP (dBm)
K (E)
Q (E)
S (E)
P (E)
R (E)
M (E)
H (EL)
L (EL)
21
20
Figure 7. TCP at GSM 900 and GSM 1800 bands in 5 positions for 20 phones.
20
January 28, 2002
© Bluetest AB
0
© Bluetest AB
January 28, 2002
B (BI)
C (BI)
E (BI)
A (BI)
U (BI)
T (BI)
D (E)
K (E)
N (E)
G (E)
Mean head loss in dB
J (E)
A (BI)
E (BI)
T (BI)
U (BI)
B (BI)
C (BI)
V (E)
F (E)
X (E)
S (E)
G (E)
O (E)
W (E)
Mean head loss in dB
O (E)
W (E)
J (E)
Q (E)
D (E)
R (E)
K (E)
N (E)
M (E)
P (E)
I (E)
H (EL)
L (EL)
Head loss in dB
9
S (E)
7
P (E)
F (E)
V (E)
10
X (E)
I (E)
R (E)
M (E)
Q (E)
H (EL)
L (EL)
Head loss in dB
10
Max head loss in dB
GSM900 band
8
7
6
5
4
3
2
1
0
Max head loss in dB
9
8
6
GSM1800 band
5
4
3
2
1
Figure 8. Maximum and average head loss at GSM 900 and 1800
21
Mean head loss in W
2,5
Max head loss in W
SAR values
2,0
W and W/kg
Head loss in W and SAR value in W/kg
GSM900 band
1,5
1,0
0,5
U (BI)
C (BI)
B (BI)
T (BI)
A (BI)
E (BI)
T (BI)
E (BI)
C (BI)
A (BI)
B (BI)
S (E)
R (E)
V (E)
F (E)
U (BI)
Mean head loss in W
2,5
M (E)
Q (E)
O (E)
X (E)
W (E)
G (E)
P (E)
K (E)
J (E)
D (E)
N (E)
I (E)
H (EL)
L (EL)
0,0
Max head loss in W
2,0
Head loss in W
GSM1800 band
W
1,5
1,0
0,5
O (E)
D (E)
N (E)
F (E)
G (E)
S (E)
P (E)
J (E)
K (E)
M (E)
I (E)
W (E)
X (E)
R (E)
V (E)
Q (E)
H (EL)
L (EL)
0,0
Figure 9. Head loss in W compared with published SAR values at GSM 900 and GSM
1800.
22
January 28, 2002
© Bluetest AB
3.1.4 Measurement problems
It should be mentioned that we had problems to mount phone F in cheek position. When we
mounted it in cheek position according to the defined procedure, the open cover plate of the
keys touches the head so that the body of the phone is in a slightly tilted position rather than a
cheek position.
When we measured in the Bluetest G1 chamber, Phone U did not work in free space position.
In the other four positions it worked fine. The present measurements are done in the G3
chamber, in which case we had no such problem.
© Bluetest AB
January 28, 2002
23
24
January 28, 2002
© Bluetest AB
4.0 TCP Measurement Accuracy
4.1 Comparison of TCP of five phones measured in Bluetest RC 800 and in
large reverberation chamber at FOI
4.1.1 Definition of the phones and phantoms
The measurements presented in this chapter has been performed on the phones in Table 7 on
page 25. Note that there are two sets of five phones, referred to as TCO phones and SSI
phones. The TCO phones are five of the 20 phones described in Section 3.1.1 on page 17. The
results for these phones are actually a subset of the results described in Section 3.1.2 on
page 17.
The five SSI phones were provided to us by the Swedish Radiation Protection Institute (SSI).
They were measured both at FOI and in the Bluetest RC 800 chamber.
The tests followed the test procedure given in Section 2.3 on page 13. Two Generic Head
Phantom V3.5 from Schmid & Partner Engineering AG were used, one filled with tissue
equivalent liquid for 900 MHz and the other for 1800 MHz, as specified in [3].
Table 7. Definition of the 5 phones
Mobile phones
Manufacturer
Ericsson
Ericsson
Motorola
Nokia
Panasonic
Model
T20s
T28s
V3688
3310
EB-GD92
Antennatype
External
External
External
Built-in
External
Ant.
Code
E
E
E
BI
E
IMEI (TCO-phone)
520257196344390
520094717964210
448835083743630
350102809574590
449317876048830
IMEI (SSI-phone)
520257191753000
520034515651670
448835095761360
350005104381010
449317876783990
4.1.2 Description of measurements at FOI
The measurements at FOI were done by Charlie Carlsson of Bluetest with Bluetest’s spectrum
analyzer and data acquisition system in FOI’s large reverberation chamber of 37 m3 size. Olof
Lunden was responsible for the chamber at FOI. The chamber had to be loaded with both head
phantoms (the one for 900 MHz and the one for 1800 MHz) and an RF absorber of size about
0.7 m x 0.7 m x 0.05 m, otherwise the chamber level was too high for the phones to work
properly. Polarization stirring was implemented by using two log periodic antennas and one
ridge horn. No platform stirring was implemented.
4.1.3 Phone positions and results
The phones were measured relative to the head phantom in the same positions as defined
before. We have in the same way as in the previous section given the phones a letter code in
order to prohibit that results are correlated with the phone models. This letter code is different
from the code used in the previous section.
© Bluetest AB
January 28, 2002
25
The results are shown in the figures on the next pages. We see that the agreement between the
results in the two chambers is remarkably good, see Figure 10 on page 27 and Figure 11 on
page 28. When we in Figure 12 on page 29 compare the two sets of phones in the same chamber, we see systematic differences for some phones. In particular this is easy to see for phone
model A (in both bands), but also for phone models B and C at 900 MHz and phone models
see there are some systematic differences, such as for phone E at 1800 MHz. This can be
explained as individual variations between the phones, due to different production series or
production tolerances. The results are analyzed statistically in Section 4.2 on page 30.
26
January 28, 2002
© Bluetest AB
Free space, Bluetest
Free space, FOI
35
34
GSM 900 band, SSI phones
33
Cheek right, Bluetest
Cheek right, FOI
32
31
TCP (dBm)
30
Cheek left, Bluetest
Cheek left, FOI
29
28
27
Tilt right, Bluetest
Tilt right, FOI
26
25
Tilt left, Bluetest
Tilt left, FOI
24
23
22
Mean TCP, Bluetest
Mean TCP, FOI
21
20
A
B
C
D
E
Free space, Bluetest
Free space, FOI
32
31
GSM 1800 band, SSI phones
30
Cheek right, Bluetest
Cheek right, FOI
29
28
TCP (dBm)
27
Cheek left, Bluetest
Cheek left, FOI
26
25
24
Tilt right, Bluetest
Tilt right, FOI
23
22
Tilt left, Bluetest
Tilt left, FOI
21
20
19
Mean TCP, Bluetest
Mean TCP, FOI
18
17
A
B
C
D
E
Figure 10. Comparison of TCP of the five SSI phones measured in the Bluetest chamber
and in the FOI chamber. All positions (free space, cheek right and left, tilt right and left) in
addition to the average of the talk positions.
© Bluetest AB
January 28, 2002
27
10
9
Mean, Bluetest
Mean, FOI
GSM 900 band, SSI phones
8
Cheek right, Bluetest
Cheek right, FOI
Head loss (dB)
7
6
Cheek left, Bluetest
Cheek left, FOI
5
4
Tilt right, Bluetest
Tilt right, FOI
3
2
Tilt left, Bluetest
Tilt left, FOI
1
0
A
B
C
D
E
10
9
Mean, Bluetest
Mean, FOI
8
GSM 1800 band, SSI phones
Cheek right, Bluetest
Cheek right, FOI
Head loss (dB)
7
6
Cheek left, Bluetest
Cheek left, FOI
5
4
Tilt right, Bluetest
Tilt right, FOI
3
2
Tilt left, Bluetest
Tilt left, FOI
1
0
A
B
C
D
E
Figure 11. Comparison of head loss of the five SSI phones measured in the Bluetest
chamber and the FOI chamber. All positions
.
28
January 28, 2002
© Bluetest AB
35
34
GSM 900 band, TCO phones left, SSI phones right
33
Cheek right, TCO
Cheek right, SSI
32
31
30
TCP (dBm)
Free space, TCO
Free space, SSI
Cheek left, TCO
Cheek left, SSI
29
28
27
Tilt right, TCO
Tilt right, SSI
26
25
Tilt left, TCO
Tilt left, SSI
24
23
22
Mean TCP, TCO
Mean TCP, SSI
21
20
A
B
C
D
E
32
31
GSM 1800 band, TCO phones left, SSI phones right
30
Cheek right, TCO
Cheek right, SSI
29
28
27
TCP (dBm)
Free space, TCO
Free space, SSI
Cheek left, TCO
Cheek left, SSI
26
25
Tilt right, TCO
Tilt right, SSI
24
23
22
Tilt left, TCO
Tilt left, SSI
21
20
19
Mean TCP, TCO
Mean TCP, SSI
18
17
A
B
C
D
E
Figure 12. Comparison of TCP of the five TCO phones and the five SSI phones when they
are measured in the Bluetest chamber. All positions (free space, cheek right and left, tilt
right and left) in addition to the average of the 4 talk positions.
© Bluetest AB
January 28, 2002
29
4.2 Statistical analysis of results in different reverberation chambers
We have compared the TCP and head loss levels measured in the chambers at Bluetest and
FOI, both those presented in Section 4.1 on page 25 and previous measurements without
polarization stirring. We have calculated the average difference as well as the standard deviations when we compare each TCP level (in dBm) measured in one chamber with the corresponding TCP level in another chamber, and correspondingly for the head loss (in dB). The
use of dBm and dB values in the analysis is consistent with [23] for multiplicative contributions. The averages and standard deviations are gathered in Table 8 on page 30 and Table 9 on
page 31. The average values represent systematic deviations, whereas the standard deviations
represent statistic variations. The chambers marked Bluetest G2 and G3 in the tables are the
second and third generation prototype chambers, respectively, as defined in Table 1 on page 7.
G3 has polarization stirring whereas G2 has not, and G3 is the same as the commercialized
Bluetest RC 800 chamber. The marks FOI1 and FOI2 in the tables correspond to the FOI
chamber without and with polarization stirring, respectively. One column in each table shows
also for which measurement sets polarization stirring has been used.
4.2.1 GSM 900 transmit band
We see that we have removed a systematic error of 0.7-0.9 dB when we introduced polarization stirring. The comparison between TCPs measured at Bluetest G3 and FOI show good
agreement with a standard deviation of 0.32 dB on the TCP and 0.43 dB on the head loss. The
last row in the table shows comparison between two different individuals of the same phone
models, i.e. comparisons between the set of TCP values for the five TCO phones and the set
for the five SSI phones. We see a systematic difference (i.e. an average difference) in the head
loss. By studying the results in Figure 12 on page 29 we can explain this. We see that two
TCO phones have lower TCP in all the talk positions (i.e. larger head loss) than the corresponding SSI phones. Such behavior can be caused by a difference in the impedance match of
the antennas on the two phones when they are close to the head. The impedance match is normally the most tolerance sensitive electrical characteristic of a small antenna, so it may very
well be different for the SSI individual and the TCO individual. We see that our measurement
Table 8. Average deviations, standard deviations and maximum deviations in dB of
matched pairs of TCP levels and head losses (same model in same position) measured at
900 MHz in two different chambers. The analysis is based on 25 TCP values (included the
free space TCP values) for each chamber and 20 head loss values. In the last line marked
Bluetest G3 two different phone individuals of the same model are compared when they
are measured in the same Bluetest chamber (G3 = RC 800 chamber).
Summary GSM 900, all values in dB
Polarization
Chambers
stirring? Phones
Aver.
Bluetest G2-G3
no-yes
TCO-TCO 0,86
Bluetest G2-FOI1
no-no
TCO-TCO -0,06
Bluetest G3-FOI1
yes-no
TCO-TCO -0,72
Bluetest G3-FOI2
yes-yes SSI-SSI
0,13
Bluetest G3
30
yes-yes
SSI-TCO
0,29
TCP
St. dev.
0,99
0,66
0,57
0,32
Max.
2,91
1,53
1,78
1,21
Aver.
-0,50
-0,16
-0,31
0,00
Head loss
St. dev.
1,11
1,00
0,66
0,43
Max.
2,92
2,70
1,14
1,31
0,82
1,66
-0,78
0,93
1,85
January 28, 2002
© Bluetest AB
accuracy (G3-FOI2 comparison) seems to be better than the variations between different
phone individuals (TCO-SSI comparison in G3).
4.2.2 GSM 1800 transmit band
The results in the GSM 1800 MHz band should theoretically show better accuracy than at 900
MHz. They do not. The reason may be that our stirrer sequence is not optimum for this band.
It may be possible to improve this. In spite of this, the accuracy is good. The results show also
here a big improvement by using polarization stirring.
Table 9. Average deviations, standard deviations and maximum deviations of matched
pairs of TCP levels and head losses (same model in same position) measured at 1800
MHz in two different chambers. The analysis is based on 25 TCP values (included the free
space value) for each chamber and 20 head loss values. In the last line marked Bluetest
G3 two different phone individuals of the same model are compared when they are
measured in the same Bluetest chamber (G3 = RC 800 chamber).
Summary GSM 1800, all values in dB
Polarization
Chambers
stirring? Phones
Bluetest G2-G3
no-yes
TCO-TCO
Bluetest G2-FOI1
no-no
TCO-TCO
Bluetest G3-FOI1
yes-no
TCO-TCO
Bluetest G3-FOI2
yes-yes SSI-SSI
TCP
Aver. St. dev. Max.
-1,07
0,48
1,98
-0,78
0,66
1,82
-0,27
0,57
1,72
-0,27
0,62
1,37
Head loss
Aver. St. dev.
-0,19
0,56
-0,74
0,71
-0,59
0,70
-0,22
0,65
Max.
1,14
2,05
1,71
1,34
Bluetest G3
-0,49
-0,10
1,29
yes-yes
SSI-TCO
0,36
1,17
0,48
4.3 Experimental investigations of inaccuracies due to instrumentation
We use a spectrum analyzer to measure the received power. There may be systematic errors in
the results if this is not well calibrated. Therefore, we generated a 1 dBm GSM pulse by a
Fluke 6062 generator and a R&S SML01 generator and measured these pulse levels with both
the spectrum analyzer (HP E7402A EMC Analyzer) and a pulse power meter (Boonton
4500A). The maximum positive and negative differences between the two measurements in
the two frequency bands are showed in the table below.
Table 10. Maximum difference between power level measured with spectrum analyzer and
power level measured with pulse power meter (891-914 MHz and 1711-1783 MHz).
Frequency band
Fluke generator
R&S generator
GSM 900
+0.02/-0.05 dB
+0.19/-0.2 dB
GSM 1800
+0.13/-0.54 dB
0.00/-0.29 dB
4.4 Experimental verification of errors due to losses in phones chassis
In Section 1.3.2 on page 4 we wrote "There must be exactly the same lossy objects inside the
chamber during the calibration measurements and during the phone measurements. This
© Bluetest AB
January 28, 2002
31
means that the head phantom must be located on the platform inside the chamber in both
cases. Theoretically, the phone should also be located inside the chamber when the reference
level is measured. The reason is that the chassis of the phone may contain lossy materials that
will reduce the Q of the chamber and therefore also the average transfer level. This may erroneously appear as a reduction in the TCP, which it is not. Of the same reason the calibration
antenna should be located inside the chamber when the phone is measured. However, due to
the heavy loading of the chamber caused by the head phantom, the additional losses due to the
materials in the chassis of the phone are very small for those phones we have measured.
Therefore, the reference level can be the same for all the different phones, which is a great
advantage."
In order to see how large these errors may be, we calibrated the chamber according to the procedure in Section 2.2 on page 11, but with an extra calibration dipole inside the chamber. This
dipole must be terminated with 50 Ohms. Thereafter we did a new calibration, but with the
Ericsson R310s inside the chamber instead of the extra dipole. The difference between these to
calibration cases is the loading due to the chassis of the phone, if we assume that the antenna
on the phone loads the chamber eaqually much as the extra dipole. This will be the case in the
working bands of the phone, where it’s antenna is supposed to be impedance mathched. Afterwards, we removed the Ericsson phone and located instead a Nokia 7110 inside the chamber.
Both these two phones are rather large. From these two measurements between 830 and 1000
MHz we saw the following:
1. The net transfer function of the chamber did not depend on whether the phone was ON or
OFF when it was located inside the chamber. We tested this for the Ericsson phone only.
2. The net transfer function with the Nokia phone inside was between 0.15 and 0.3 dB
lower than the level with no phone inside.
3. The net transfer function with the Ericsson phone inside was between 0.15 dB higher and
0.3 dB lower than the level with no phone inside.
From this we can expect the error due to the simplified calibration procedure to be maximum
0.3 dB, and it will only be present for large phones.
4.5 Experimental verification of repeatability of positioning the phone
The positioning of the phone in its cheek and tilt positions is also a source of error. We have
investigated this by repeated measurements with small changes in the physical positioning of
the phones, using exactly the same setup in the chamber (i.e. exactly the same phantom position and stirrer position). First, we took a phone with a built-in antenna and measured it both
without and with a 1.6 mm cardboard piece between the phone and the phantom. The TCP
increased by 0.29 dB with the cardboard. When we did the same for a phone with an external
antenna the TCP increased with 0.21 dB. Thereafter, we located and measured the phones in
cheek position in the reference plane as defined in Section 1.2 on page 3, and we repeated
exactly the same measurement after we had turned the phone 3 deg upwards around an axis
through the ear, and 3 deg downwards. The TCP of the phone with the external antenna
decreased by 0.59 dB. Thus, the TCP of phones with external antennas are very sensitive to
the angular location of the reference plane, and this angular location is very difficult to accurately establish in a practical measurement situation. Therefore, it is reasonable to expect that
the TCP may easily vary by some tenths of dB if the measurements are done by different operators. Phones with external antennas are also very sensitive to the tilt angle in tilted position
32
January 28, 2002
© Bluetest AB
and is very different at different sides of the head. These results mentioned here are valid at
900 MHz. At 1800 MHz the head loss is half that at 900 MHz, so the sensitivity to the positioning should also be smaller by a factor 2.
4.6 Validation in anechoic chamber
Nikolay Serafimov has in [21] gathered the results of measuring 10 different mobile phone
models in two anechoic chambers and two reverberation chambers. The phones were measured in an intended user position, in which the phones are located in contact with the cheek of
the phantom in such a way that the length of the phone makes 45 deg with the vertical and the
speaker of the phone is located outside the ear of the phantom. The TCP was measured in this
position only. In addition, each of the same phone models were provided with a cable attached
to the antenna of the phone in such a way that it disturbed the antenna performance as little as
possible. The cable left the chassis of the phone on one side under a 90 deg angle in order to
disturb the performance as little as possible. The radiation efficiencies of the cable-fed phone
antennas were also measured.
In these validation measurements Serafimov used a different phantom than the one we have
used in our own measurements. This was a solid head-and-shoulder phantom manufactured by
ECE Co in Japan and made available for these tests by Sony Ericsson Mobile Communications AB. The dielectric properties of grey brain cells are in the ECE phantom obtained by
polymer filled with glass and graphite, ε r = 50 + j25 .
4.6.1 Radiation efficiencies
Table 11. Statistical deviations between radiation efficiencies in dB measured in Bluetest
RC 800 chamber and in an anechoic chamber at Saab Ericsson Space AB. The results are
based on comparing 24 radiation efficiency values for each chamber.
Frequency band
Mean deviation
Standard deviation
Max deviation
GSM 900
0.01 dB
0.72 dB
1.43 dB
GSM 1800
-0.18 dB
0.55 dB
-1.54 dB
The radiation efficiencies were measured at three frequencies in each band; band center and
edges. For the anechoic chamber these were three frequency points (880 MHz, 925 MHz and
960 MHz in GSM 900, and 1710 MHz, 1780 MHz and 1880 MHz in GSM 1800), whereas the
Bluetest results where frequency stirred (averaged) over 25 MHz bandwidth around these frequencies. The statistical analysis of the difference between the Bluetest results and the result
in the anechoic chamber that was expected to be most accurate are presented in the table
above. The comparison shows that the two sets of results are very similar, which means that
the Bluetest chamber is very accurate. The variations of the radiation efficiency between the
three frequencies are also very similar in the two chambers.
© Bluetest AB
February 5, 2002
33
4.6.2 TCP values
Table 12. Statistical deviations between TCPs measured in Bluetest RC 800 chamber and
in an anechoic chamber at Sony Ericsson Mobile Communications AB. The results are
based on comparing 9 values for each chamber.
Frequency band
Mean deviation
Standard deviation
Max deviation
GSM 900
-0.00 dB
0.57 dB
-1.00 dB
GSM 1800
-0.00 dB
0.86 dB
-1.56 dB
The total radiated power was in the anechoic chambers measured at two frequencies in each
band (880.2 MHz and 914.8 MHz in GSM 900, 1710.2 MHz and 1780.0 MHz in GSM 1800),
whereas it in the Bluetest RC 800 chamber was measured as described in Section2.3 on
page13 as an average over the GSM 900 and GSM 1800 MHz bands. The statistical analysis
of the difference between the results are shown in the table above. In this case we compare
with results obtained in the anechoic chamber at Sony Ericsson Mobile Communications in
Lund. The reason is that the chamber of Saab Ericsson Space AB was not available for TCP
measurements during Serafimov’s Master project, so his report does not contain any results
from there. It should be noted that only relative power measurements were performed in the
anechoic chamber, and that in [21] the level of one phone was set to be equal in both chambers
when calculating the statistical deviations. Therefore, the values presented there for the maximum deviations and the mean deviations suffer from systematic discrepancies that has nothing
to do with the measurement accuracy, but rather with the way the results are analyzed. Hence,
we have here recalculated the maximum deviation after all the results have been adjusted so
that the mean deviations are zero between the two chambers, see the table.
4.7 Theoretical accuracy of Bluetest RC800 from mode density
The accuracy of the TCP measurements in the reverberation chamber depends on many
factors including the size of the chamber [4]-[5], the bandwidth of the frequency stirring [12],
and whether or not platform stirring [12] and polarization stirring [13] are implemented. We
have gathered the different contributions to the accuracy in the table in the next section. Here,
we will describe how the accuracy depends on the chamber size. The number of excited modes
in the chamber when we frequency stir (i.e. average) over a bandwidth B is
-------- ⋅ ( B + ∆f )
Mex = ∂M
∂f
(5)
where ∆f is the average mode bandwidth in the chamber (see [5] for determining this), and
3
2
∂M
-------- = ( ( 8π ) ⁄ c ) LWHf
∂f
(6)
is the mode density with c the velocity of light, f the frequency, and L, W, H the length, width
and height of the chamber, respectively. The characteristics of the mode stirrers also
contribute to the accuracy, in particular if the mode bandwidth and stirring bandwidth is small.
Then, the number of independent field samples may be much larger than M ex . If we neglect
this possibility, we get as a worst case for large chambers that the standard deviation of an
estimate of the average power radiated by the phone will be [4], [12]
34
February 5, 2002
© Bluetest AB
σ = 1 ⁄ Mplatform ⋅ M ex
(7)
where Mplatform is the number of independent positions of the rotatable platform.
The Bluetest chamber has M platform = 25 independent platform positions at 900 MHz, if the
phantom and phone is located on the platform halfway between the chamber wall and the
center of the platform.
For small chambers the chamber modes may be unevenly distributed in frequency, so (5) is no
longer representative. We will as a worst case for small chambers (i.e. Bluetest at 900 MHz)
assume that we only have one mode present over the average mode bandwidth ∆f . This means
that we over a stirring bandwidth B has M freq = B ⁄ ( ∆f ) modes. Then, by using
M platform = 25 independent samples per frequency point, we get
σ = 1 ⁄ Mplatform ⋅ M freq
(8)
In order to get sufficient confidence in the measured results, we will assume that the accuracy
required is twice the standard deviation, i.e. we will use 2σ values. This is in [23] referred to
as expanded uncertainty. They represent a 95 % confidential interval. The results based on the
models in (7) and (8) (worst cases for large and small chambers, respectively) are shown in dB
for different chamber volumes V = LVH in Table13 on page35. We have also values both
with and without platform stirring.
Table 13. Theoretical accuracy (2σ values) of measuring a power level in reverberation
chambers of different sizes and kind (B = frequency stirring bandwidth). The frequency
stirring bandwidth is in all cases assumed to be B = 25 MHz.
Expanded uncertainty for different chambers (theory)
0.92 GHz
1.8 GHz
Bluetest RC 800 chamber, 25 platform positions
0.55 dB
0.18 dB
Bluetest RC 800 chamber without platform stirring,
1.73 dB
0.88 dB
Large 8 m 3 chamber without platform stirring,
0.7 dB
0.35 dB
Large 37 m 3 chamber at FOI, without platform stirring,
0.25 dB
0.12 dB
We see from the above that a small chamber like Bluetest RC 800 needs to be equipped with
platform stirring; otherwise the size must be 8 m 3 to get acceptable accuracy. We see also that
the theoretical accuracies are reasonable when we compare them with the measured standard
deviations presented in Section4.2 on page30, except that the measured accuracy at 1800
MHz is worse than at 900 MHz, whereas it theoretically should have been better at 1800 MHz.
To compare we must remember to multiply the theoretical values above by 1.4 (i.e. 2 ), and
in addition include the accuracy of the chamber values we compare with. The factor 1.4 is
present because we need to measure two independent power values (reference level and actual
power value) to get the TCP. When we compare results in two chambers with the same
accuracy, we can multiply the theoretical values in the table by a factor 2.
© Bluetest AB
February 5, 2002
35
4.8 Estimate of overall uncertainty
We can now estimate the overall uncertainty of the Bluetest RC 800 chamber from the studies
in Section4.2 on page30 to Section4.7 on page34. We have gathered the estimates in
Table14 on page37.
The contribution due to chamber statistics has a theoretical lower limit which we studied in
Section4.7 on page34. This must contain both the uncertainty of the reference level and the
test level, and it depends on the mechanical stirring, platform stirring and polarization stirring.
If we use the theoretical values in Table13 on page35 we get 0.55 dB at 900 MHz and 0.18
dB at 1800 MHz for both the reference level and the test level. The estimates could also be
based on measuring at least 5 phones in two very different chambers, using the same network
analyzer and power meter, such as in Section4.2 on page30. If we compare the Bluetest G3
and FOI chambers and assume that the FOI chamber is much more accurate than the G3 chamber, we get the following 2σ values for the uncertainty of the Bluetest chamber: 0.64 dB at
900 MHz and 1.24 dB at 1800 MHz. We have reasons to believe that the large uncertainty at
1800 MHz is due to a polarization problem in the FOI chamber, so we use instead the theoretical level. We have entered the theoretical values into the table.
The pulse power meter (e.g. spectrum analyzer in zero span mode) has a limited accuracy. We
use the maximum values in Section4.3 on page31.
Network analyzers give normally very accurate relative levels, so we will assume 0.1 dB in
both bands.
The effect of the simplified reference procedure was studied in Section4.4 on page31. The
chassis of the phone may cause up to 0.3 dB error.
The positioning of the phone was studied in Section4.5 on page32. Based on the values there,
we assume a maximum uncertainty due to differences in the positioning amounting to 0.4 dB
at 900 MHz and 0.2 dB at 1800 MHz.
We have not yet any experience to estimate the variations due to phantom type and variations
in the brain tissue equivalent liquid. Preliminary studies indicate very small variations due to
the liquid, whereas there are very big variations between phantom head models from different
manufacturers. We will at present neglect the contributions to the uncertainty from the phantom, which should be reasonable if the same phantom head type is used all places.
We can assume that all the uncertainty contributions described above are independent. Then,
we can add them in a root-mean-square (RMS) way, according to [23]. The resulting RMS
values represent the expanded 2σ uncertainty, as all contributions added are either 2σ values
or maximum values. The resulting expanded uncertainties are seen to be 0.95 dB at 900 MHz
and 0.67 dB at 1800 MHz.
We have in the table also added results from the validations described in Section4.6 on
page33. We should remember that these values also have uncertainties due to the limited
accuracy of the anechoic chambers used, so it is natural that the they are larger than our theoretical estimates. Still we believe that it should be possible to improve the accuracy of the
Bluetest chamber at in the 1800 MHz band, as this according to theory should be better than
the accuracy at 900 MHz. Still, both accuracies are acceptable.
The TCO’01 certification specifies a minimum level for the mean TCP taken over the four different talk positions. This mean TCP is naturally more accurate than the TCP at each position.
The contributions number 2 and 6 in the table will be reduced by a factor 2, which give total
36
February 5, 2002
© Bluetest AB
expanded theoretical uncertainties of 0.74 dB at 900 MHZ and 0.63 dB at 1800 MHz.
Table 14. Uncertainty breakdown analysis of the Bluetest chamber when measuring TCP.
GSM 900 MHz band
Error sources
GSM 1800 MHz band
Expanded ( 2σ ) or
maximum uncertainty
Expanded ( 2σ ) or
maximum uncertainty
1. Chamber statistics, ref level
0.55 dB
0.18 dB
2. Chamber statistics, test level
0.55 dB
0.18 dB
3. Power meter level
0.2 dB
0.5 dB
4. Network analyzer
0.1 dB
0.1 dB
5. Chassis of phone
0.3 dB
0.3 dB
6. Phone position
0.4 dB
0.2 dB
7. Phantom type
-
-
8. Permittivity & conductivity
-
-
Total expanded uncertainty
(RMS sum of above values)
0.95 dB
0.67 dB
Maximum error in measured
TCP values compared with
anechoic chamber
1.001 dB
1.561 dB
Maximum error in measured
radiation efficiency compared
with anechoic chamber
1.431 dB
1.541 dB
1 Note
that these maximum errors are due to uncertainties in the results of both chambers; the
reverberation chamber and the anechoic chamber.
© Bluetest AB
February 5, 2002
37
38
January 28, 2002
© Bluetest AB
5.0 References
[1] TCO’01 Certification of Mobile Phones; Requirements and test methods for quality and
environmental labelling, TCO Development, SE-114 94 Stockholm, Sweden, Nov. 12,
2001
[2] Per-Simon Kildal, Foundations of Antennas - A Unified Approach (Textbook containing
the interactive electronic handbook "Antenna Design Using Mathcad"), Studentlitteratur
(www.studentlitteratur.se/antennas), Sweden, Feb. 2000.
[3] EUROPEAN STANDARD EN 50361, Basic standard for the measurement of Specific
Absorption Rate related to human exposure to electromagnetic fields from mobile phones
(300 MHz - 3 GHz), CENELEC European Committee for Electrotechnical Standardization, rue de Stassart 35, B - 1050 Brussels, July 2001
[4] J. G. Kostas and B. Boverie, “Statistical model for a mode-stirred chamber”, IEEE Transactions on Electromagnetic Compatibility, Vol. 33, No. 4, pp. 366-370, Nov. 1991.
[5] D. A. Hill, M. T. Ma, A. R. Ondrejka, B. F. Riddle, M. L. Crawford and R. T. Johnk,
“Aperture excitation of electrically large, lossy cavities”, IEEE Transactions on Electromagnetic Compatibility, vol. 36, no. 3, pp. 169-178, August 1994.
[6] D. A. Hill, “Electronic mode stirring for reverberation chambers”, IEEE Transactions on
Electromagnetic Compatibility, vol. 36, no. 4, pp. 294-299, November 1994.
[7] D. A. Hill, “Plane wave integral representation for fields in reverberation chambers”, IEEE
Transactions on Electromagnetic Compatibility, vol. 40, no. 3, pp. 209-216, Aug. 1998.
[8] D. A. Hill, “Linear dipole response in a reverberation chamber”, IEEE Transactions on
Electromagnetic Compatibility, vol. 41, no. 4, pp. 365-368, November 1999.
[9] K. Rosengren and P-S. Kildal. ” Study of distributions of modes and plane waves in reverberation chambers for characterization of antennas in multipath environment”, Microwave
and Optical Technology Letters, Vol. 30, No 20, pp. 386-391, Sept. 2001.
[10] K. Rosengren, P-S. Kildal, J. Carlsson, O. Lundén. “Measurement of terminal antennas
performance in multimode reverberation chambers”, Antenn00, Nordic Antenna Symposium, Lund, Sweden. 12-14 Sep. 2000.
[11] K. Rosengren, P-S. Kildal, J. Carlsson, O. Lundén “A new method to measure radiation
efficiency of terminal antennas”, 2000 IEEE AP-S Conference on Antennas and Propagation for Wireless Communication, Nov. 6-8, 2000. Westin Hotel Waltham, Massachusetts
[12] K. Rosengren, P-S. Kildal, C. Carlsson and J. Carlsson, ”Characterization of terminal
antennas in reverberation chambers: Improved accuracy by platform stirring”, Microwave
and Optical Technology Letters, Vol. 30, No 20, pp. 391-397, Sept. 2001.
[13] P-S. Kildal, C. Carlsson, "Detection of a polarization imbalance in reverberation chambers and how to remove it when measuring antenna efficiencies", submitted to Microwave
and Optical Technology Letters, Nov. 2001.
[14] P-S. Kildal, J. Yang and C. Carlsson, “Measurement of free space impedances of small
antennas in reverberation chambers”, Microwave and Optical Technology Letters, Vol. 32,
No. 2, pp 112-115, Jan. 20, 2002.
[15] Jian Yang, Jan Carlsson, Per-Simon Kildal and Charlie Carlsson, "Calculation of selfimpedance and radiation efficiency of a dipole near a lossy cylinder with arbitrary cross
© Bluetest AB
January 28, 2002
39
section by using the moment method and a spectrum of two-dimensional solutions",
Microwave and Optical Technology Letters, Vol. 32, No. 2, pp 108-112, Jan. 20, 2002.
[16] Per-Simon Kildal, Kent Rosengren, Joonho Byun and Juhyung Lee, "Definition of effective diversity gain and how to measure it in a reverberation chamber", submitted to Microwave and Optical Technology Letters, Nov. 2001.
[17] K. Rosengren, Measuring radiation efficiency of terminal antennas in reverberation
Chambers, Thesis for Licentiate degree at Chalmers University of Technology, April
2001.
[18] R. Serrano, Study of losses due to head and hand of mobile phones with external and
built-in antennas in reverberation chamber, Master thesis at Department of Electromagnetics, Chalmers University of Technology, Aug. 2001.
[19] A. Wolfgang, FDTD simulations of a validation case for small antenna measurements in
reverberation chamber, report for project in Master program at Karlsruhe University, performed at Department of Electromagnetics, Chalmers University of Technology, Aug.
2001.
[20] C. Carlsson, Characterization of mode-stirred chamber and its set-ups for antenna measurements, Master thesis at Department of Electromagnetics, Chalmers University of
Technology (supported by Bluetest AB), Aug. 2001.
[21] Nikolay Serafimov, Radiation efficiencies of phone antennas and radiated power of
mobile phones measured in two anechoic chambers and two reverberation chambers,
Master thesis at Department of Electromagnetics, Chalmers University of Technology
(supported by Sony Ericsson Mobile Communications AB), Jan. 2002.
[22] A method and an apparatus for measuring the performance of antennas, mobile phones
and other wireless terminals, International patent application No PCT/SE01/00422, filed
February 26, 2001, priority March 31, 2000.
[23] Angivande av mätosäkerhet vid kalibrering (Examination of measurement uncertainty in
calibration), Publication EAL-R2-Sv, European cooperation for Accreditation of Laboratories, Swedish translation, Jan. 1999.
40
January 28, 2002
© Bluetest AB
Appendix A. TCP method: Brief description of TCP test method
as included in TCO’01
C
Test Methods
C.2.2 Procedure for Measuring TCP (Telephone
Communication Power) from GSM system
Mobile Phones
This section describes the procedure for measuring TCP in a reverberation chamber. TCP can
be measured in different possible ways. Described below is a method, using a reverberation
chamber, which has in practical tests been shown to give reliable results.
Definition of TCP
The TCP is the power leaving a closed surface, which surrounds the phone and the head
phantom when these are located far from other objects. It is the maximum available power,
which can be provided by the phone if the antenna on the phone were ideally matched to the
output impedance of the phone, minus the power which is reflected due to an actual mismatch
at the antenna port, minus the power which is dissipated in the antenna, minus the power
which is absorbed in the head phantom.
The TCP is the figure of merit of a mobile phone, when it is transmitting. The higher the TCP,
the better the phone will work in the transmit mode. On the other hand, the possible radiation
hazards are characterized in terms of a Specific Absorption Rate (SAR) distribution that
should be as low as possible or at least below some standardized limits. Both the TCP and the
SAR are proportional to the maximum power that can be radiated by the phone. Therefore, a
high quality phone must provide a good compromise between high TCP and low SAR. This is
possible by directing the radiation from the phone away from the head.
The TCP is proportional to the radiation efficiency of the antenna on the phone, measured with
the head phantom present.
C.2.2.1
Requirements of the measurement setups
Reverberation chamber
The measurement setups both for the chamber calibration and the TCP measurement are
illustrated in Figure 1. Both setups are composed of the reverberation chamber with
mechanical stirrers and three receiving antennae (also referred to as the fixed antennae) for
polarization stirring, and two head phantoms (one for use at 900 MHz and another for 1800
MHz). If the chamber is small it must additionally be provided with a rotatable platform stirrer
to provide sufficient accuracy, as shown in Figure 1. The three receiving antennae must be
orthogonal linearly polarized over the frequency ranges of the measurements. The three
TCO’01– Mobile phones
A1
A
B
C
Switch
D
E
2
1
Network
Analyzer
F
A
B
C
Switch
D
rf in
Spectrum
Analyzer
Base station
simulator
Figure 1. Illustration of measurement setup in a small reverberation chamber for
calibration (upper) and TCP measurement (lower). The network analyzer, the spectrum
analyzer, the polarization switch, the two mechanical stirrers, and the rotatable platform
can be controlled from a PC.
orthogonal polarized receiving antennae may be monopoles connected orthogonally to three
different and orthogonal walls (including roof/floor) of the chamber. The three receiving
antennae are connected to an electronic coaxial switch by means of three coaxial cables A, B
and C.
The reverberation chamber can have an inner volume as small as a minimum of 1.25 m3 if
platform stirring is implemented, but must be larger than 8 m3 if there is no such stirring
facility.
Linearly polarized dipole antennae are used for calibration of the chamber, one for each band.
These shall have a reflection coefficient better than -10 dB over the frequency band used,
when measured at their input connectors.
The reference level of the chamber is different at different frequencies. It shall be measured as
described in Section C.2.2.2 in each band used. The reference level shall be measured both
when the calibration antenna is oriented for vertical polarization and when it is oriented for
horizontal polarization. These two values shall differ by less than the specification in Table 1.
In order to obtain values for comparison with the results in the table, the reference levels shall
A2
TCO’01– Mobile phones
be measured for both orientations of the calibration dipole at 8 different positions of the dipole
inside the chamber. The average, standard deviation and maximum deviation shall be
evaluated by comparing results for both polarizations over the whole set of 8 measurements.
Alternatively, the levels for the two polarizations of the calibration antenna at 1 MHz intervals
between 800 MHz and 1 GHz for the GSM 900 band (and between 1600 MHz and 2000 MHz
for the GSM 1800-1900 band) can be measured, and thereafter the average, standard deviation
and maximum of the difference between the two sets of values over this frequency range are
calculated.
Table 1. Table 1. Specifications of differences of measured reference levels in each frequency
band between using vertically and horizontally polarized calibration dipoles.
Table 2.
Average
Standard deviation
0.2 dB
0.5 dB
Maximum
1.0 dB
Head phantoms
The phantoms used in the tests should fulfill the requirements in Section 5.2 of EN 50361 on
SAR measurements. It is admissible to use two phantoms, one for the GSM 900 MHz band
and another for the GSM 1800-1900 MHz band. They shall be filled with the brain-equivalent
liquids specified in Section 5.2 of EN 50361.
Environmental conditions
The tests shall be performed in an indoor laboratory where the ambient temperature shall be in
the range 15 °C – 30 °C and the variation shall not exceed ± 2 °C during the tests.
Instrumentation and data acquisition
The two different measurement setups make use of a network analyzer, a spectrum analyzer
(or a power meter or a measurement receiver) and a base station simulator. A PC controls the
network analyzer, the spectrum analyzer, the base station simulator and the coaxial switch, as
well as the step motors for the mechanical stirrers and the platform stirrer (if used).
Mobile phone holder
The mobile phone must be fixed to a mobile phone holder that satisfies the requirements given
in Section 5.5 of EN 50361.
C.2.2.2 Measuring the reference level (Calibrating the chamber)
The calibration setup is shown in the upper part of Figure 1.
First calibrate the network analyzer at its ports 1 and 2.
Connect cable D to port 1 of the network analyzer and cable A to port 2. Measure the relative
transmission factor TA of cable A plus the switch plus cable D. Make sure the switch is set to
permit transmission between cables A and D. Measure, in the same way, the relative power
transmission factors TB and TC of cables B and C including the switch and the cable D. Note
that TA, TB and TC are always smaller than 1.
Measure the attenuation LdipdB of the calibration dipole (in dB). This can be done by
TCO’01– Mobile phones
A3
measuring the reflection coefficient RdB, at the input port of the dipole, when the feed gap
between the dipole arms is short-circuited. Then, LdipdB = RdB/2, and the dipole transmission
factor (smaller than 1) becomes
. T dip
= 10
– Ldip ⁄ 10
(EQ 1)
Connect the single output of the switch, via cable D, to port 1 of the network analyzer.
Connect cables A, B and C between the switch and the connectors to each of the three
receiving antennae.
Mount the calibration dipole on a holder inside the chamber. Connect cable F between the
connector of the calibration dipole and a connector that makes a connection through the floor
or wall (shown in the center of the rotatable plate in the example in Figure 1). On the other
side of the wall (or floor) there shall be a cable E connecting this to port 2 of the network
analyzer. If the chamber is provided with a rotatable plate stirrer, the calibration dipole shall be
located on the plate, and the cable E shall be connected to cable F via a rotary joint.
Recalibrate the 0 dB level of the network analyzer three times, once for each cable A, B and C.
This shall be done for cable A by connecting together the dipole end of cable F and the
monopole end of cable A. Similarly for cables B and C. Store the three calibration sets A, B
and C.
Connect cable F to the dipole again.
Locate the head phantom inside the chamber in such a way that it is not closer to any wall,
ceiling or floor than 0.5 wavelengths λ. Make sure that this is the case at all positions of the
rotatable platform (if such a platform is used). Use a phantom that is filled with the correct
liquid for the band to be measured. For large reverberation chambers, it may be necessary to
load the chamber with more absorbing material than the head phantom, otherwise some
phones may not work properly inside the chamber. If this is needed, exactly the same material
must be present inside the chamber when the phones are measured as when the reference level
is measured.
Position the calibration dipole inside the chamber in such a way that all its parts are not closer
to any wall, ceiling or floor than 0.5 λ and at least 0.7 λ away from the phantom. The phone
shall be located outside the chamber, but the phone holder must be located inside the chamber.
(See the second last paragraph of Section 2.2.3 about the calibration procedure.)
Measure the S-parameters, when the switch is in the position corresponding to cable A, for all
the chosen positions of the mechanical stirrer and the platform stirrer (if used), and over the
whole GSM transmit band plus 12 MHz on each side of it (for 25 MHz frequency stirring).
The frequency interval shall be 1 MHz.
The measured reflection coefficient S 11 has two additive contributions: One due to the
reflection from the antenna port itself (deterministic) and the other due to the chamber
(statistic). The same applies to S 22 . Therefore, calculate the averages of the complex values of
S 11 and S 22 , and average them further over a 5 MHz bandwidth. The remaining parts are the
free space reflection coefficients S11 and S 22 of the fixed receiving antenna A and the
calibration dipole, respectively.
Take the measured values S21 and calculate
A4
TCO’01– Mobile phones
2
S 21
P = ----------------------------------------------------2
2
( 1 – S 11 ) ( 1 – S 22 )
(EQ 2)
For each of the selected frequencies f i for measuring the phone (see Section C.2.2.3),
calculate the average P A ( f i ) of P , by averaging P over all stirrer positions and over a 25
MHz band centered around each f i .
Calculate the reference transfer function of the chamber PrefA ( f i ) when using antenna A at
each frequency f i by using
2
P A ( fi ) ( 1 – S 11 )TA
PrefA ( fi ) = ------------------------------------------------Tdip
Repeat the above for the other fixed antennae B and C by using the switch to obtain PrefB ( f i )
and PrefC ( f i ) , respectively.
C.2.2.3 Measuring the TCP of a phone
The phone measurement setup is shown in the lower part of Figure 1.
Positioning the phone
Mount the mobile phone in the holder and position it at the desired position relative to the
head phantom. The mobile phone shall be tested in 5 positions: “free space position”, which in
the chamber means more than 0.7 wavelengths away from the phantom, “right and left cheek
positions”, and “right and left tilted positions”. The cheek and tilted positions are the same as
those defined in Sections 6.1.4 of EN 50361 on SAR measurements.
The mobile phone shall be turned on, and use its internal transmitter during the TCP
measurements. The battery and accessories shall be those specified by the manufacturer. The
battery shall be fully charged before each measurement.
Base station simulator
The base station simulator shall be located outside the chamber and connected to a fixed
antenna inside the chamber, by means of a wall-mounted coaxial connector with a centre
conductor going through the wall. This antenna can also be a monopole.
The base station simulator controls the output power and frequency (channel) of the mobile
phone. The mobile phone shall transmit at its highest output peak power level allowed by the
system.
The signal emitted by the base station simulator is several orders of magnitude lower than the
output level of the phone and will therefore not cause any errors in the power measurements. If
the transmitted power is measured by using a measurement receiver or a spectrum analyzer in
the zero span mode (which means that it is measured at the transmit frequency of the phone
and not at its receive frequency) the base station simulator could not cause errors, even if
TCO’01– Mobile phones
A5
123
0
1
2
3
5
4
ms
Figure 2. Illustration of GSM pulse, which is triggered at t 0 = 0ms , as it would be seen
on the screen of a spectrum analyzer in the zero span mode. The time positions for
measuring the pulse level are at the three markers 1, 2 and 3, the first at t 1 = 50µs , the
second at t 2 = 150µs , and the third at t 3 = 250µs .
radiating at higher levels.
Measuring pulse power with a spectrum analyzer
The pulse power can, as mentioned above, be measured with different measurement
instruments. This section describes how it can be done with a spectrum analyzer.
Measurements with other instruments can be done in a similar way.
The phone transmits pulses at a certain pulse repetition rate. The spectrum analyzer shall be
operating in a zero span pulse detection mode that triggers at the front of each pulse in the
pulse train. It is thus possible to read the pulse level at the same position relative to the front of
the pulse, at each measurement. Read the pulse power levels at three different time delays
relative to the pulse front (choose 50, 150 and 250 µsec), as shown in Figure 2, and use the
median value as the pulse power level in the calculations below.
The base station simulator shall control the phone to transmit at 5 frequencies or more (one at
a time) distributed with equal spacing over the whole transmit band.
Set the switch to measure power from receiving antenna A. Measure and save pulse power
levels for all the positions of the platform stirrer and mechanical stirrer and for all the
frequency points used. Average the saved pulse power levels over all stirrer positions. The
result of the averaging is PavA ( f i ) . Repeat this for receiving antennae B and C to get P avB ( f i )
and PavC ( f i ) .
The TCP in W of the phone is finally obtained by
A6
TCO’01– Mobile phones
N
1
TCP = ---N
∑
1
1--- P avA ( f i ) P avB ( f i ) PavC ( f i )-------------------- + -------------------- + -------------------3 PrefA ( fi ) P refB ( f i ) PrefC ( f i )
where N is the number of frequency points.
(EQ 3)
(EQ 4)
Definition of measurement cases
The TCP tests shall be performed in the “free space position” of the phone as well as in all
four positions of the phone relative to the phantom.
If the mobile phone has a retractable antenna, all of the tests described above shall be
performed both with the antenna extended and with the antenna retracted. When considering
multi-mode and multi-band mobile phones, all of the above tests shall be performed in each
transmitting mode/band with the corresponding maximum peak power level.
Presentation of results
The measurement protocol shall contain all the five TCP values in W, i.e. for free space, right
cheek, left cheek, right tilt and left tilt positions. They shall be given for each band/mode/
antenna of the phone. In addition, the average TCP value of the four talk positions shall be
calculated and given in W for each band/mode/antenna. The values shall be given with a
maximum uncertainty of 2.0 dB.
Uncertainty estimate
Test laboratories must provide an uncertainty analysis of their facility at each measured
frequency band. This analysis shall at least contain a breakdown of documented error
contributions, such as the one shown in Table 2. It must be possible to verify each contribution
in the table. The table below is from [1] where the different contributions are described in
detail. A brief description is also given below.
Table 3. Table 2. Uncertainty breakdown analysis of the chamber used when measuring TCP.
Table 4.
Error sources
Chamber statistics
Power meter level
Network analyzer
Chassis of phone
Phone position
Phantom type
Permittivity
&
conductivity
Expanded uncertainty
GSM 900 MHz band
Standard Uncertainty
GSM 1800 MHz
Standard Uncertainty
The contribution due to chamber statistics has a theoretical lower limit. This contains both the
uncertainty of the reference level and the pulse power level, and it depends on the mechanical
TCO’01– Mobile phones
A7
stirring, platform stirring and polarization stirring. The estimate in the table shall be based on
measuring at least 5 phones in two very different chambers. The same network analyzer,
spectrum analyzer and head phantom may be used, as well as using the same person to operate
the instruments. The different TCP values measured in each of the corresponding positions of
the phone (free space, cheek right and left, and tilt right and left) shall be compared for the two
chambers. This gives at least 25 independent TCP values. The standard deviation and
maximum deviation of these two sets of values can be used to calculate this contribution of the
standard uncertainty.
The pulse power meter (e.g. spectrum analyzer in zero span mode) has a limited accuracy. The
error must be checked against specification and calibration. By calibrating the power meter in
the actual frequency bands, the uncertainty can be reduced compared to the full band
uncertainty.
The network analyzer accuracy can be found in its manual. Note that all measurements
performed with the network analyzer are relative which reduces the uncertainty.
The calibration setup is somewhat simplified, in the sense that the effect of the chassis of the
phone on the reference level has been neglected. The correct way would have been to place the
phone inside the chamber and leave it on during the calibration while the reference level was
measured by means of the calibration level and the network analyzer. The phone would be
located at least 0.5 λ from the walls and the calibration dipole and the phantom. Similarly, the
calibration dipole (with its port terminated in a 50 Ohm load) should be in position inside the
chamber when measuring the pulse power from the phone by using the pulse power meter.
However, this calibration procedure is laborious when many phones are being tested, so the
error can instead be estimated by measuring for some large phones the difference in the
reference level due to the chassis as follows: First, a second lossless antenna (which must be
terminated ideally in 50 Ohms) is placed inside the chamber and the reference level measured.
Then the second lossless antenna is removed and replaced by the phone (which must be ON).
The difference between these two reference levels represents the error due to losses in the
chassis of the phone.
The positioning of the phone in its cheek and tilt positions is also a source of error. Part of this
error is included in the first ‘chamber statistics’ estimate. However, if the same operator is
measuring in both chambers, the error may be very small. Still, it is believed to cause some of
the larger uncertainties in [1] for some phones that are difficult to locate. The table should also
include an estimate of positioning errors. This is done by repeating a few times with small
changes in the physical positioning of the phones, using exactly the same setup in the chamber
(i.e. exactly the same phantom position and stirrer position).
References
[1] Per-Simon Kildal and Charlie Carlsson, “TCP of 20 mobile phones measured in a
reverberation chamber”, Bluetest report 2, Nov 2001 (available from Bluetest AB, Chalmers
Teknikpark, 41288 Gothenburg, Sweden, or from E-mail simon@kildal.se).
A8
TCO’01– Mobile phones
Appendix B. Plane wave study: Manuscript of the scientific article
"Study of Distributions of Modes and Plane Waves in Reverberation Chambers for
Characterization of Antennas in Multipath Environment",
by K. Rosengren and P-S. Kildal,
Microwave and Optical Technology Letters, Vol. 30, No 20, pp. 386-391, Sept. 2001
Study of Distributions of Modes and Plane Waves in
Reverberation Chambers for Characterization of Antennas in Multipath Environment
Kent Rosengren and Per-Simon Kildal
Kent Rosengren (kent.rosengren@intenna.se)
(www.intenna.se), Sweden
is
with
Intenna
Technology
AB
Abstract. A rectangular metallic cavity is known to support a number of resonant cavity
modes. Each of these modes can be described as a sum of eight plane waves incident from
different angles. This paper studies how these plane waves are angularly distributed in space,
which is of interest when the cavity is used to simulate multipath environment. The results
show that the angular distribution in space is uniform provided the three linear dimension of
the chamber are sufficiently large and do not deviate too much from each other. As an
example, two rectangular cavities with dimensions 1m x 0.8m x 1m and 5.5m x 2.5m x 3.5m
are in detail analyzed and shown to have uniform plane wave distributions. We also
demonstrate how the chamber geometry may be chosen in order to weight the angular plane
wave distribution in the elevation plane. A result of the study is that we detect a 25 MHz
frequency band with very few, modes in a small chamber designed for use with reduced
accuracy in the GSM 900 MHz band. We also propose how this chamber can be modified to
obtain uniform mode distribution over this frequency band.
B.1 Introduction
Today, the performance of small antennas for mobile or wireless terminals are often measured
and characterized as radiation patterns in the horizontal and vertical planes and for different
polarizations. However, such terminal antennas are subject to a diversity of incoming plane
waves. This is often referred to as multipath, and it is a result of scattering, refractions and
reflections of the propagating electromagnetic waves in the environment. The received fields
from all directions are added at the terminal antenna and result in random received power
amplitudes. By moving the terminal antenna or the surroundings, the received power
amplitude will vary in time as the probability function chi-square with two degrees of freedom
[1].
Reverberation chambers have been used for about a decade as a statistical electromagnetic
field generator for EMC measurements. The reverberation chamber is a metallic enclosure in
which the electromagnetic fields are stirred by mechanical means to obtain a field distribution
that is statistically isotropic and homogenous inside the chamber [2]. Such a chamber can be
described as a metal cavity that supports a number of resonant cavity modes. These modes are
This manuscript was published in
Microwave and Optical Technology Letters, Vol. 30, No 20, pp. 386-391, Sept. 2001
B1
characterized by their bandwidths and resonance frequencies. The bandwidths depend on how
much the chamber is loaded [3]. The resonance frequencies change when we move the
mechanical stirrer or stirrers inside the chamber. It has been shown theoretically that the
received power of an antenna inside a reverberation chamber is proportional to its radiation
efficiency [4]. It has also been experimentally proven that reverberation chambers can be used
to measure the radiation efficiency of antennas [5]-[7]. This is done by measuring the
transmission between a transmitting antenna and an antenna under test, both located inside the
chamber, for several different positions of the mechanical stirrers. The received power is a
stochastic variable that is chi-squared distributed with two degrees of freedom. By taking a
large number of samples obtained by moving the stirrers, averaging these over all stirrer
positions, and comparing this average with the averaged received power of a reference
antenna with know radiation efficiency, we get an estimate of the radiation efficiency of the
antenna under test.
It has already been shown that the field inside a reverberation chamber can be described in
terms of its plane wave spectrum [8]. The purpose of the present paper is to study the angular
distribution of these plane waves in order to see how it depends on chamber size and
geometry. This is of particular interest in order to relate its performance to the practical
multipath statistics obtained for different scenarios in wireless communication, in which case
the plane wave distribution normally is weighted in the elevation plane. The study is done for
some useful chamber sizes and for two existing chambers. One of these is a large chamber of
size 5.5m x2.5m x3.5m located at the Swedish Defense Research Establishment (FOA), herein
referred to as the FOA chamber. The other is a small chamber of size 1m x 0.8m x 1m, which
recently has been developed at Chalmers University of Technology and therefore is referred to
as the Chalmers chamber. The Chalmers chamber is intended for measuring terminal antennas
for mobile phones down to 900 MHz.
In connection with experimental related work, which went on in parallel with the writing of
the present paper, we experienced large inaccuracy of measured results in the Chalmers
chamber in a 25 MHz wide sub-band in the GSM 900 MHz band [7]. By using results of the
present study we are able to explain this inaccuracy as coming from a non-uniform mode
distribution in frequency. There is actually a hole in the mode distribution that coincides with
the inaccurate sub-band. In the present paper we also show how we can remove the mode hole
by changing one of the chamber dimensions.
B.2 Mode and plane wave descriptions of a rectangular cavity.
The field within a rectangular cavity with metallic walls can be described in terms of resonant
cavity modes also when there are disturbing obstacles inside the chamber, that may be lossy
and represent loads, providing the loading is not too heavy so that the actual resonances
vanish. We will study the nature of these modes. The chamber is thought of as being a plain
rectangular chamber without anything inside, and the loading represents perturbation to this.
Each of the resonant modes of the empty metallic cavity can be written as a superposition of
eight plane waves, except for a few which consist of only four plane waves. The plane wave
representation can be seen from the field solutions for the modes inside the cavity, as
described below.
We consider a cavity of dimensions a, b and c with perfectly conducting walls. Then, we have
2
2
TM
to solve the Helmholtz's homogenous equation (∇ + k )E z = 0 for both the TE - and TM z
B2
z
cases (relative to the z-direction). The boundary conditions are that the tangential field
components shall be zero at all walls. The TMz solutions, which satisfy the boundary
conditions, have an Ez-field of the following form [9]
 naπx 
 nbπy 
 ncπz 
 sin 
 cos

 a 
 b 
 c 
E zTM = AnTMn n sin 
a b c
(5)
where na=0, 1, 2, …, nb =0, 1, 2, … and nc= 1, 2, 3, … . Each combination of these na, nb and
nc represent one mode. The modes are only present whenever
na2 nb2 nc2
+
+
a2 b2 c2
k =π
(6)
where k = 2π λ is the wave number and λ is the wavelength. The corresponding resonance
frequency is
ν
n a2 nb2 nc2
=
+
+
2 a2 b2 c2
f res
(7)
where ν is the speed of light.
The TEz solutions, which satisfy the boundary conditions, have correspondingly an Hz-field of
the following form
 naπx 
 nbπy 
 ncπz 
 cos
 sin 

 b 
 c 
 a 
H zTE = AnTEn n cos
a b c
(8)
where na= 1, 2, 3, …, nb= 1, 2, 3, … and nc=0, 1, 2, … . The condition for the k-vector and the
resonance frequency is given by the same formula as for the TMz-case.
We now express the cosine and sine terms as exponentials and write the product in the
following form
e iu + e − iu e iv + e − iv e iw − e − iw
⋅
⋅
=
2
2
2i
+ e − iu + iv +iw + e −iu −iv +iw − e iu + iv −iw − e iu −iv −iw − e − iu +iv −iw − e − iu −iv − iw ) =
cos(u ) ⋅ cos(v ) ⋅ sin (w) = AnTEn n ⋅
a b c
= const ⋅ (e iu + iv +iw + e iu −iv + iw
= const ⋅
∑e
± iu ± iv ± iw
Finally, we can write the Ez and Hz-fields of the TE- and TM-modes, respectively as
H zTE = AnTEn n ⋅
a
b
c
∑
ˆ r
e − jkk ⋅ r and EzTM = AnTMn n ⋅
a b
c
∑
ˆ r
e − jkk ⋅ r
(9)
r
ˆ
where r = xxˆ + yyˆ + zzˆ and k = (k a xˆ + kb yˆ + kc zˆ ) k with k a = ± na π a , k b = ± nbπ b and
k c = ± n cπ c where the ±signs must be permuted in order to get the eight different plane
∧
wave terms. Each term is seen to represent a plane wave propagating in the k direction, which
This manuscript was published in
Microwave and Optical Technology Letters, Vol. 30, No 20, pp. 386-391, Sept. 2001
B3
means that (5) represents a sum of eight plane waves for both the TEz and TMz modes, except
for the cases when one of the indices are zero. Then the modes can only be represented by four
waves.
A certain mode will theoretically only exist if the chamber is excited with a frequency exactly
at the resonance frequency of the mode. However, in reality, all the resonances have a finite
Q-value, corresponding to a finite bandwidth ∆f = f / Q . This is in particular true if the
chamber is loaded in some way, e.g. with a head phantom. Then, all resonances, which are
f − ∆f / 2 ≤ f res ≤ f + ∆f / 2
within the range
, will be excited by an excitation of frequency f .
When we measure in a reverberation chamber, the modes are stirred by mechanical means.
This stirring will cause the resonance frequencies to move, so that we may have an equivalent
mechanical stirring bandwidth B , which is larger than ∆f . We can also increase the number
of excited modes by varying the frequency f and averaging the results over a certain
bandwidth. The latter is referred to as frequency stirring. We loose frequency resolution in
the measurements by frequency stirring, but not with mechanical stirring.
We can now choose some cavity dimensions a, b and c, and a frequency bandwidth B ,
permute all indices na, nb and nc over a sufficiently large interval and find how many modes
that are within the frequency range f − B / 2 ≤ f res ≤ f + B / 2 . When the modes have been
found, we can calculate the angle of arrival of the corresponding plane waves from the
components ka, kb and kc of the k-vector by using
ϕ = arctan (k b / k a )
(
θ = arctan k b + k b / kc
and
2
2
)
(10)
B.3 Results for the Chalmers and FOA chambers
We have made a Matlab program for studying the modes and corresponding plane waves that
can be excited in the Chalmers chamber (1m x0.8m x1m) and in the FOA chamber (5.5m
x2.5m x3.5m). Figure 1 illustrates the propagation directions of all the plane waves in the
Chalmers chamber within the bandwidth 870-970 MHz. We have also studied the propagation
directions of the plane waves of the same chamber within the frequency band 1710-1880 MHz
and the results are similar but naturally with higher density of waves. The propagation
directions look very uniformly distributed, over the whole space. The results look similar for
the FOA chamber, but with much higher density of directions.
Further, we have for the Chalmers chamber divided the frequency band 870-970 MHz into 10
sub-bands, each 10 MHz wide. We have counted the number of plane waves in each sub-band,
see Table 1. A more detailed study shows that the plane waves are distributed quite uniformly
over the sphere, if the total number is sufficiently large. However, the total number of plane
waves within each sub-band varies strongly. This is severe when using a small reverberation
1 Nm
chamber, as the relative measurement accuracy goes as
, where N m is the number of
modes. There will be very bad accuracy within some sub-bands. This argues for much larger
frequency stirring than would otherwise be needed if the mode distribution were uniform with
frequency.
B4
We have studied the distribution of incidence angles for the plane waves in more detail for the
Chalmers chamber by plotting the cumulative distribution of all phi angles when we allow
theta to have any value, and visa versa, see Figures 2. The cumulative plot of phi increases
linearly with phi, which means that the distribution is uniform in phi. The cumulative plot of
the theta angle is compared with a theoretical sine-distribution, which is shown displaced by
the value 0.1 in Figures 2, and we see how well the two curves follow each other. A
cumulative sine-distribution of theta corresponds also to a uniform distribution over the
sphere. Thus, the Chalmers chamber has a very uniform distribution of propagation directions
of the plane waves associated with the cavity modes in the chamber, if the bandwidth is
sufficient large.
We will now study the uniform distribution in more detail. In Table 1 we counted the number
of plane waves that are present in a given sub-band of 10 MHz. In Figure 3 we have plotted
the number of modes that are present in a 25 MHz band when we sweep this same band over
the GSM 900 band. This is done for the Chalmers chamber, with dimensions a=1m, b=0.8m,
when we let c is vary from 0.8m to 2m in steps of 0.05m. At each step of c we count the
number of modes that are within a 25 MHz frequency bandwidth around a center frequency
ranging from 882 MHz to 957 MHz in steps of 1 MHz. We note that for c=1m, which is the
present height of the Chalmers chamber, and in the frequency range 902 to 915MHz we have
very low number of modes. Therefore, the measurement accuracy will be very low in this
range. We see that there is a clear advantage in increasing the height of the chamber to c=1.6m
where we have more modes and a better mode uniformity over the band.
The number of incident plane waves is related to the number of modes that can exist in the
chamber. The number of modes, predicted by Weyl's formula [2], N = 8π ⋅ V (3λ ) , increases
as the frequency increase in a given chamber volume V, where λ is the wavelength of the
plane wave. The mode density is the number of modes per frequency unit, i.e.
3
MD = ∂N ∂f = 8π ⋅ V
f res2
ν3
where f is the frequency and ν is the speed of light. The mode density indicates the number of
modes that can be excited over a unit bandwidth. The number of modes within a certain band
∆f is the mode density times the bandwidth. If we count the number of plane waves within a
certain frequency bandwidth and divide with the same bandwidth, we will get the mode
density times eight, since each mode is comprised of eight plane waves. We have also counted
the number of actual modes within each band. Both these results and the theoretical curve
from the above formula are plotted for the FOA chamber as the upper three curves in Figure 4.
The agreement is very good. We have also plotted the mode density in the smaller Chalmers
chamber, see the two lower curves in Figure 4. However, in this case we choose to plot the
number of modes over a 25 MHz band as a function of frequency, as this will appear better in
the figure. We see a similar no uniformity as in Figure 3. The intermediate curves are for a
modified Chalmers chamber with increased height c=1.6m. We see how the mode density
increases and becomes more uniform in relative terms when the height is increased.
B.4 Weighting the plan wave density.
In this section we will study the plane wave density when we change one of the dimensions of
This manuscript was published in
Microwave and Optical Technology Letters, Vol. 30, No 20, pp. 386-391, Sept. 2001
B5
the cavity.
Let us design the chamber so that the lengths a and b in the x- and y-directions are shorter than
the height c in the z-direction. We then have that the spacing between each ka and kb are larger
than between each kc since k a = ± na π a , k b = ± nbπ b and k c = ± n cπ c . Figure 5 shows
the grid in the k-space, along ka and kc for kb=0. Each dashed line is separated by π a and
π c , respectively. The intersections between the vertical k -direction, and the horizontal k c
a
direction, are nodes, which determines our k-vectors according to (2) in the previous section.
There are no nodes along the line where ka=0, as no node has na=0 and nb=0 at the same time.
In Figure 5 we have chosen the dimensions a=0.7 m, b=0.7 m and c=3 m. We see that the grid
along the kc-direction is more dense than along the ka-direction due to the big difference in the
chamber dimensions in the x and z directions. We have also drawn two circles in Figure 5.
These are representing the lower and higher limits on k in the chosen frequency band. The
inner circle represents 870 MHz and the outer 970 MHz. All modes that have k -vectors that
are confined between these circles will be present in the chosen frequency band. These
intersections are marked with a star in the figure. Note that there is a concentration of stars
along the ka-direction when nc is close to zero. Also note that, if the inner circle has slightly
smaller radius (i.e. a lower frequency) more k -vectors would be incorporated and increase the
concentration there. We could also decrease a in the x-direction so that ka increases and moves
the index na=-4 in between the circles and increase the concentration this same way. When we
know ka and kc, we can find θ from (6).
The plane wave density in different directions can be found by counting the total number of
plane waves within a given solid angle (i.e. a cone) around each direction. We have done this
by sweeping a solid cone, 50° cross-section, over a grid in phi and theta and plotted the plane
wave density as a contour plot on a unit sphere. The result shows that the elongated chamber,
a=0.7m, b=0.7m and c=3m, weights the plane wave distribution so that the plane waves
concentrate more in the azimuth plane. This can be thought of as a weighted multipath of the
kind that exists in urban environments. The plane wave density is higher in the azimuth plane.
The same elongated chamber does not, however, weight the plane waves in the frequency
band 1710-1880 MHz as much as in the 870-970 MHz band.
Figure 6 shows the plane wave density in a rectangular cavity where a and b are 0.7 m, and
where we change c from 2 m to 3 m in steps of 0.2 m. The intension is to see how the plane
wave density changes in the elevation plane when it is averaged over phi. We see that the
longer c the higher ratio between the max and mean values. We can divide the 870-970 MHz
band into two equal sub-bands and plot the same as in Figure 6. The result is then that the
mean plane wave density will remain the same as in the Figure 6 but with half the density.
Figure 7 shows the existing Chalmers chamber when we increase the height c from 1.2 to 2.8
m in steps of 0.4 m. We see that the chamber is too wide to obtain the desired change in the
elevation distribution. Thus, the actual elevation distribution we obtain by matching the
chamber height is quite sensitive to the lateral dimensions. A result of Figure 7 is also that we
can increase the height of the Chalmers chamber by up to 1.6 m without significantly effecting
the elevation distribution. It will still be rather uniform.
B6
B.5 Conclusion
We have shown from classical formulas that it is possible to express a rectangular cavity mode
as a sum of plane waves. These plane waves are uniformly angularly distributed within the
GSM frequency bands 870-970 MHz and 1710-1880 MHz, provided the three linear
dimension of the chamber are sufficiently large and do not deviate too much from each other.
Further, we have showed that it is possible to weight the plane wave distribution in the
elevation plane if we make the chamber very high, i.e., the height c must be very much larger
than the dimensions a and b in the horizontal plane. This modified elevation distribution have
similarities with the multipath statistics in a real urban environment and in an indoor/office
environment. However, such chambers can only be designed to fit specific bands, e.g., a
design for the GSM 900MHz band will not have the same elevation weighting in the GSM
1800 MHz band.
It is also a result of this work that we need to have a certain stirring bandwidth of the chamber
in order to have a sufficient number of modes to get a uniform distribution of plane waves.
This stirring bandwidth is in order of 25 MHz in the GSM 900 MHz band for the small
Chalmers chamber. This stirring bandwidth can be obtained without losing frequency
resolution in the measurements, if the loading of the chamber is significant or the mechanical
stirring is strong enough.
We have also detected a frequency region with very few modes in the Chalmers chamber, that
happens to coincide exactly with the GSM 900 MHz transmit band. We have also seen how
this mode hole can be removed and the mode density increased by increasing the height of the
chamber. This is in the process of being done.
B.6 Acknowledgement
This work was founded by Intenna Technology AB and an industrial PhD scholarship from
The Swedish Research Council for Engineering Sciences (TFR). The work would not have
been possible without the additional support from the Swedish Foundation for Strategic
Research (SSF). The Chalmers chamber is being commercialized by the start-up company
Bluetest AB (www.bluetest.se). The authors are grateful to Bo Olsson at Telia Research for
his discussions.
B.7 References
[1] J. G. Kostas and B. Boverie, "Statistical model for a mode-stirred chamber", IEEE
Transactions on Electromagnetic Compatibility, Vol. 33, No. 4, pp 366-370, Nov. 1991.
[2] Gus Freyer, Michael Slocum, Handouts from “Reverberation Chambers, Theory/
Experiment, Short Course”, arranged by EMC Services and Bofors Missiles 30 August - 3
September 1999 in Karlskoga, Sweden.
[3] D. A. Hill, M. T. Ma, A. R. Ondrejka, B. F. Riddle, M. L. Crawford and R. T. Johnk,
"Aperture excitation of electrically large, lossy cavities", IEEE Transactions on
Electromagnetic Compatibility, vol. 36, no. 3, pp. 169-178, August 1994.
[4] D. A. Hill, "Linear dipole response in a reverberation chamber", IEEE
Transactions on Electromagnetic Compatibility, vol. 41, no. 4, pp. 365-368, November 1999.
[5] K. Rosengren, P-S. Kildal, J. Carlsson, O. Lundén, “Measurement of Terminal Antennas
This manuscript was published in
Microwave and Optical Technology Letters, Vol. 30, No 20, pp. 386-391, Sept. 2001
B7
Performance in Multimode Reverberation Chambers”, Antenn00, Nordic Antenna Symposium,
Lund, Sweden, 12-14 Sep. 2000.
[6] K. Rosengren, P-S. Kildal, J. Carlsson, O. Lundén, “A New Method to Measure Radiation
Efficiency of Terminal Antennas”, 2000 IEEE AP-S Conference on Antennas and
Propagation for Wireless Communication, Waltham, Massachusetts, Nov. 6-8, 2000
[7] K. Rosengren, P-S. Kildal, ”Characterization of antennas for mobile and wireless
terminals in reverberation chambers : Improved accuracy by platform stirring”, submitted to
Microwave and Optical Technology Letters, March 2001.
[8] D. A. Hill, "Plane wave integral representation for fields in reverberation chambers", IEEE
Transactions on Electromagnetic Compatibility, vol. 40, no. 3, pp. 209-216, August 1998.
[9] Harrington, Time harmonic electromagnetic fields, McGraw-Hill, 1961
B8
B.8 Figures
Figure 1. Illustration of incoming plane waves in the Chalmers chamber within 870-970
MHz. The directions of the plane waves are drawn as straight lines towards the origin,
with a small patch at the ends of the lines. The patches can be thought of as small parts of
the associated wave fronts.
1
0.5 870-970 MHz
0
1710-1880 MHz
0
45
90
135
180
Theta (degrees)
1
0.5
1710-1880 MHz
870 -970 MHz
0
-180
-90
0
90
180
Phi (degrees)
Figure 2. Cumulative distribution of all theta (upper) and phi (lower) angles in the 870970 and 1710-1880 MHz bands in the Chalmers chamber.
This manuscript was published in
Microwave and Optical Technology Letters, Vol. 30, No 20, pp. 386-391, Sept. 2001
B9
Figure 3. Mode distribution for the Chalmers chamber with a=1m, b=0.8m, if we let the
height c vary from 0.8m to 2m in steps of 0.05m. At each step of c we count the number of
modes that are within a 25 MHz frequency bandwidth centered at different frequencies
ranging from 882 MHz to 957 MHz in steps of 1 MHz. We note that for the present height
c=1m and in the frequency range 902 to 915 MHz we have few modes. The mode density
and the mode uniformity can be significantly improved by increasing the chamber height
to c=1.6m.
B10
150
FO A (m od es/MHz)
M o de Density
c=1 .6 m
a
100
b
50
c =1m
Chalm e rs (m od es/25 MHz)
0
800
1000
1200 1400 1600
Frequency (M Hz)
1800
2000
Figure 4. Mode density in the FOA and Chalmers chambers. Curve a shows the total number
of plane waves divided by 8 in the FOA chamber. Curve b shows the total number of modes in
the FOA chamber and is more close to the predicted mode density by Weyl’s formula, which is
shown as the smooth dashed curves. Curve a is obtained by counting the number of plane
waves over a bandwidth of 10 MHz and dividing by 10 to get modes/MHz. Curve b is done in
the same way as curve a, but counting the modes instead. The lower curve shows the number
of modes counted over 25 MHz bandwidth in the Chalmers chamber with height c=1m. This
varies around the smoother predicted mode density by Weyl’s formula multiplied by a 25 MHz
bandwidth. The intermediate curve is the Chalmers chamber with increased height c=1.6m.
This manuscript was published in
Microwave and Optical Technology Letters, Vol. 30, No 20, pp. 386-391, Sept. 2001
B11
n =10
c
k
n =0
c
c
k
a
n =-10
c
n =-4
a
n =0
a
n =4
a
Figure 5. Illustration of the grid in k-space in the kakc-plane for an elongated chamber of
dimensions 0.7 m x 0.7 m x 3 m within 870-970 MHz. The nodes of the grid represent one TE
and one TM mode, except along ka=0 where there are no nodes. The nodes, which are
between the two circles, are excited if the frequency is between 870 and 970 MHz. The excited
nodes are marked with a star. In the figure we see a concentration of excited modes having
indices na=4 and na=-4. This concentration causes the field distribution to be weighted in the
xz-plane.
B12
M ean plane wave density
70
z=3m
60
z=2.8m
50
z=2.6m
z=2.4m
40
30
z=2.2m
z=2m
20
10
0
45
90
T heta
135
180
Figure 6. Plane wave density averaged over all phi. a and b are 0.7 m, and c varies from 2 m
to 3 m in steps of 0.2 m. The frequency band is 870-970 MHz.
This manuscript was published in
Microwave and Optical Technology Letters, Vol. 30, No 20, pp. 386-391, Sept. 2001
B13
70
M ean plane wave density
z=2.8m
60
50
z=2.4m
z=2 m
40
z=1.6m
30
z=1.2m
20
0
45
90
T heta
135
180
Figure 7. Plane wave density averaged over all phi. a=1.0 m, b=0.8 m, and c varies from 1.2
m to 2.8 m in steps of 0.4 m. This is the Chalmers chamber with different heights but c is
varied. The frequency band is 870-970 MHz.
Frequency band (MHz)
870-880
880-890
890-900
900-910
910-920
920-930
930-940
940-950
950-960
960-970
Number of plane waves
48
32
64
None
16
48
72
48
32
64
Table 5. Number of plane waves within each sub-band when the frequency band 870-970 MHz
is divided into 4 sub-bands. The results are valid in the Chalmers chamber (1 m x 0.8 m x 1
m). The plane waves belonging to different sub-bands are plotted in Figure 3 with different
markers to distinguish them in the plot.
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B14
B15
B16
Appendix C. Platform stirring: Manuscript of the journal article
”Characterization of terminal antennas in reverberation chambers: Improved accuracy
by platform stirring”,
by K. Rosengren, P-S. Kildal, C. Carlsson and J. Carlsson,
Microwave and Optical Technology Letters, Vol. 30, No 20, pp. 391-397, Sept. 2001.
Characterization of Antennas for Mobile and Wireless
Terminals in Reverberation Chambers:
Improved Accuracy by Platform Stirring
Kent Rosengren, Per-Simon Kildal, Charlie Carlsson, Jan Carlsson
Kent Rosengren (kent.rosengren@intenna.se) is with Intenna Technology AB
(www.intenna.se), Sweden (also PhD student at Chalmers),
Per-Simon Kildal (simon@elmagn.chalmers.se, www.kildal.se) is with Chalmers University
of Technology, Sweden.
Charlie Carlsson (charlie@elmagn.chalmers.se) is with Bluetest AB, Sweden.
Jan Carlsson (jan.carlsson@sp.se) is with Swedish National Testing and Research Institute,
Sweden.
Abstract. It has been demonstrated that the radiation efficiency of antennas can be measured
in reverberation chambers. The measurement accuracy is known to be better the larger size.
The present paper shows that the measurement accuracy can be significantly improved by
rotating the antenna under test. This is demonstrated in the 900 MHz GSM band by
measurements in a reverberation chamber of dimensions 1.0m x 0.8m x 1.0m. We refer to this
new stirring method as platform stirring.
C.1 Introduction
The increasing use of terminal antennas, i.e. physically and electrically small antennas
mounted on mobile devices, forces the antenna manufactures to fast develop new antenna
concepts. The terminal antennas are used in applications such as mobile phones operating in
the GSM, DCS and PCS bands. Also the Bluetooth concept is expanding, demanding a lot of
new antennas for use in a narrow band centered at 2.4 GHz.
For the manufactures to design a desirable antenna the time spent in the laboratory can be,
sometimes, very long. The design parameters are often the reflection coefficient S11 and the
radiation patterns measured in a few planes around the antenna. The reflection coefficient
describes how much of the available power that is reflected at the antenna port, but it does not
give any information about whether the rest of the power is radiated or dissipated in the
antenna. Therefore, the reflection coefficient alone cannot determine if the antenna is a good
or poor radiator. The full quality factor of a terminal antenna is the radiation efficiency. This is
defined in [1] to be the total radiated power divided with the maximum available power when
the antenna is impedance matched. Thus, the radiation efficiency includes the effects of
mismatch, as well absorption in the antenna and its near-in environment. To determine the
radiation efficiency, the radiation patterns must be measured over the whole far field sphere
with a standard gain horn and integrated. This is often time consuming and laborious and
This manuscript was published in
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C1
requires expensive equipment. An alternative is to measure it in a reverberation chamber as
described in [2]-[3] and shown in Figures 1, 2 and 3. The reverberation chamber, also called
mode stirred chamber, supports a statistical electromagnetic field that will surround the
Antenna Under Test (AUT), and the radiation efficiency can be found in a statistical sense
with good accuracy and very fast by stirring this field. The purpose of the present paper is to
show how the accuracy of this measured radiation efficiency can be improved by moving or
rotating the AUT during the measurements, which we refer to as platform stirring. It is known
from the theoretical paper [4] that the average received power in a reverberation chamber is
proportional to the radiation efficiency of the AUT.
C.2 Description of reverberation chamber and measurement set-up.
General about reverberation chambers
A reverberation chamber has metal walls and can support a large number of resonant cavity
modes. The modes are excited by a fixed antenna inside the chamber. The excitation of the
modes relative to each other can be changed by mechanical stirring or by frequency stirring
[5]. Mechanical stirring is obtained by moving metal objects inside the chamber. The
mechanical stirrers are often fan shaped. Frequency stirring is obtained by averaging results
over a certain frequency band. The two stirring methods change the mode distribution so that
the power received by the AUT, which also is located inside the chamber, will vary in a
stochastic manner in a similar way as in a uniform multipath environment [3]. We calculate
the average power received by the AUT over all stirrer positions and frequencies. The
radiation efficiency is then obtained as the ratio between this average power and the average
power received when the AUT is replaced by a reference antenna with known radiation
efficiency.
The power samples will follow the chi-square distribution, χ2, if the number of independent
excited modes in the chamber is sufficiently large and the stirring is sufficiently effective. The
effectiveness of the mode stirring can be determined by evaluating the correlation between the
power samples, and from this the number of independent samples. The larger this number is,
the more accurate is the estimate of the average received power [6], and hence also the
radiation efficiency of the AUT. We have in this paper evaluated the correlation as an
autocorrelation function [7][8] of a set of power samples, as explained in Section 4.
Platform stirring
We will show that the statistics of the received power samples can be improved by moving the
AUT to different positions inside the chamber. This will increase the accuracy of the measured
radiation efficiency, which will be demonstrated in Section 3. The improvements have the
following reasons:
1) The direct coupling between the AUT and the fixed excitation antenna represents an
error term, which gives a bias to the chi-square distribution of the modal fields. This
will in particular be pronounced in our chamber, as the chamber is small and heavily
loaded. The loading reduces the level of the statistic fields, but not necessarily of the
direct coupling. By moving the antenna to different positions, the direct coupling will
C2
change both in amplitude and phase, and the error introduced by it will be reduced
when the received power samples are averaged.
1) When the antenna is in a new position we have a different and independent mode distribution, so we effectively increase the number of independent power samples with a
factor which could be as large as the number of positions, if the separation between the
different positions is sufficiently large (larger than 0.5 wavelengths).
1) Since we are rotating the AUT, the associated plane waves of the modes that are incident on the AUT [3], will arrive from different directions for each position of the AUT.
This reduces possible systematic errors due to few modes, such as a possible no uniform distribution of the corresponding incoming plane waves over the sphere.
Validation case.
2.85 ⋅ (1 + j 0.0055) We have chosen the following test case to validate the use of
reverberation chambers for measuring radiation efficiency [2]-[3] of
antennas close to human tissue: We locate a dipole antenna at different distances from a lossy
cylinder, see Figure 1. This cylinder is a PVC-pipe with 40cm height and 11cm diameter, with
a wall thickness of 5 mm and a relative permittivity . The cylinder is filled with a mixture of
sugar, salt, water and Hydroxyethyl-cellulose (HEC), that has the same relative permittivity
(εr=41.2) and conductivity (σ=1.2) as gray brain tissue, according to a recipe from Schmid and
Partner [9]. In this way it is possible to first measure how much power that is received by the
dipole when it is away from the lossy cylinder (reference case), and thereafter to measure it
when the dipole is moved close to the lossy cylinder (test case). The ratio between the average
power Ptest for the test case and the average power Pref for the reference case is the same as the
ratio between the radiation efficiencies of the two cases.
The dipole antenna is a commercial calibrated dipole with adjustable arms and balun length.
This dipole is measured to have a loss in the feed and balun of together 0.13 dB. The arms of
the dipole has a thickness of 4mm, so the distance between the cylinder and the dipole is measured from the surface of the cylinder to the center axis in the arm of the dipole. The FDTDsimulations treats an infinitely thin dipole antenna located at the axis of the thick actual
dipole.
This validation case was chosen because it is simple to manufacture, and in addition it is simple to compute numerical results both for the impedance mismatch and the radiation efficiency of it. The computed results behind are obtained by FDTD.
Description of Chalmers chamber and its stirring methods.
The chamber used in the measurements has the dimension 1.0m x 0.8m x 1.0m
(Figure 1).
In the present paper we have measured in the frequency range 870 to 970 MHz, in steps of 1
MHz (101 points). This is slightly broader than the GSM-band 890-960 MHz.
The excitation antenna, which excites the modes in the chamber, is a monopole mounted to
one of the walls, close to a corner. The chamber has two mechanical stirrers. They are realized
as two plate formed paddles running along two joining walls. Each stirrer end is fastened to a
threaded rod that by rotation can move the stirrer along a complete wall length. The two
threaded rods of each paddle can be rotated in the same sense to translate the plate paddle
This manuscript was published in
Microwave and Optical Technology Letters, Vol. 30, No 20, pp. 391-397, Sept. 2001
C3
parallelly in such a way that its movement covers the surface of the whole wall. If the rods are
rotated opposite to each other the plate paddle appears as if it is turned around an axis at the
center of the wall, like a fan. In the following measurements the “turning” of the plate paddles
has been used.
We can move the paddle stirrers relative to each other in two ways. The first is to move the
two stirrers simultaneously to new positions. This is referred to as simultaneous stirring.
The second is to move one stirrer to a new position and then move the second stirrer through
all its positions. Thereafter, we move the first to a new second position and move the second
stirrer backwards through all the same positions as before. We continue in the same way for
more positions of the first stirrer. This is referred to as sequential stirring.
In addition to the simultaneous and sequential stirring of the two mechanical stirrers, the AUT
with lossy cylinder is located on a platform, which can be rotated. This is referred to as
platform stirring. The location of the AUT on the platform must be done with care. It should
be located as far as possible towards the rim, but still more than λ 2 from the wall in all
angular position of the platform.
The cable between the AUT and the network analyzer outside the chamber is going via a
rotary joint in the center of the turn able platform.
FDTD computations
The set-up is modeled in a commercial FDTD-code. The cylinder in the model has 100 mm
diameter and 300 mm length. It is filled with a material with relative permittivity εr=41 and
conductivity σ=1.2 S/m, which is the same as the liquid used in the measurements. A thin
shell with a relative permittivity 2.75 simulates the PVC-pipe that surrounds the cylinder, so
that the total diameter is 110 mm. The dipole is modeled as a thin wire of length 150 mm that
is fed in the center with a voltage generator in series with a 50 Ω resistor. The radiation field is
computed and from this the total radiated power Prad. The efficiency, is obtained as
erad = 10 log( Prad Pmax ) , where P
is the maximum power that the source can deliver to the
antenna when it is matched to 50 Ω. The efficiency is calculated at 920 MHz when the
distance between the thin dipole and the outer wall of the cylinder is 10, 20, 30, 40, 50, 70 and
100 mm. The cell size in the computation is 2 mm. The calculated radiation efficiency is
plotted in Figure 3 as circles.
max
C.3 Measured Results.
We use a network analyzer to measure the S-parameters between the port of the dipole and the
port of the fixed excitation antenna, for frequencies between 870 and 970 MHz in steps of 1
MHz. The S parameter samples are collected for each paddle position, and when the platform
with the AUT and lossy cylinder is rotated to different positions. The reference and test cases
are measured, with the same stirrer sequences. The test case is first measured and then the
reference case is measured after having moved the lossy cylinder away from the dipole (about
one wavelength).
The two lowest solid curves in Figure 2 show the average power levels as a function of
frequency when we have simultaneous plate stirring combined with platform stirring (10 x 10
positions). This gives totally 100 samples of the received power by the AUT. The upper of the
C4
two curves is located around –14dB. The dipole is located far away from the cylinder, making
this the reference level, i.e. the average transmission level of the chamber with the lossy
cylinder inside. The level fluctuates significantly with frequency over the band. The
fluctuations can be characterized in terms of a standard deviation around the true average
value. The dashed curve is obtained by frequency stirring the results of the solid curve by 10
MHz (10 frequency points with 1 MHz spacing). This corresponds to frequency smoothing on
the power levels before they are transformed into dB. The curve becomes much smoother and
represents now the average power level much better.
The lowest solid and dashed curves represent the same cases when the dipole is located at a
distance of around 2 cm from the cylinder. The level is lower because the radiation efficiency
of this case is lower.
The upper curves located around –3dB shows the difference between the two lower cases,
when they are frequency stirred with different window sizes. The longest solid curve, ending
5 MHz from the vertical axis of the graph, is obtained with 10 MHz frequency stirring. The
shortest solid curve, ending 30 MHz from the vertical axis of the graph, are obtained with 60
MHz frequency stirring, and similarly for the other curves (dotted and dash-dotted) that are
frequency stirred over 20 and 40 MHz windows. The curves represents the radiation efficiencies of the test case, because the dipole is well matched to free space over the whole band so
that the reference case has a radiation efficiency very close to unity.
The solid curve in Figure 3 shows the radiation efficiency in the Chalmers chamber measured
as described above at 920 MHz and frequency stirred over a 20 MHz window. The curve is
marked with diamonds when the center axis of the reference dipole is located at the distances
1, 2, 3, 4, 5, 7 and 10 cm from the lossy cylinder. We also show the results measured in the
larger chamber (5.5 x 2.5 x 3.5 meters) mentioned in [2]. These results are marked with
hexagrams when the center axis of the dipole is located at the distances 1.2, 2.2 and 5.2 cm
from the lossy cylinder. We have also computed the situation in an FDTD-code and the results
are marked with circles. The agreement is good between the three cases.
The measured radiation efficiency for our test case may vary somewhat over the frequency
band, but we expect the variation not to be large since the return loss from the reference dipole
doesn’t vary much over the frequency band considered.
Figure 4 shows the measured radiation efficiencies when platform stirring is used over an 870970 MHz frequency band. There are different curves when the center axis of the dipole is
located at the distances 1, 2, 3 and 5 cm from the lossy cylinder. The curves are quite smooth
even if we frequency stir only 10 MHz. This is shown by the longest solid curves for each
distance. The curves becomes smoother if we frequency stir over a larger window. This is seen
in the figure as the dotted, dashed and shortest solid curves representing 20, 40 and 60 MHz
frequency stirring respectively. Figure 5 shows the same curves but only for the distances 1
and 2 cm from the lossy cylinder, when we do not use platform stirring. The curves for the
different stirring bandwidths are marked as before. We see that the curves fluctuate very
much, even when we frequency stir over a 60 MHz window. Thus, the platform stirring have
caused significantly improvement of the accuracy.
One extra measurement (both for the reference and test cases) was taken for the distance 5 cm
and a large number of stirrer positions. The stirrers where flipped sequentially (Sequential
Stirring) and the AUT was moved (rotated) sequentially as well. The number of stirrer
This manuscript was published in
Microwave and Optical Technology Letters, Vol. 30, No 20, pp. 391-397, Sept. 2001
C5
positions and AUT positions where chosen to be 7, which gives a total of 7x7x7=343
positions. This amount of samples consumes much more measuring time, but it also increases
the accuracy.
We can estimate the accuracy of the radiation efficiency by calculating the standard deviation
of the radiation efficiency around its estimated mean value for different frequency smoothing
window sizes. The calculated standard deviations obtained from the curves in Figure 4 and 5
are shown in Table 1. We see that the accuracy is much better when platform stirring is used
than without. In the table we have also calculated the standard deviation for the case when 343
stirrer positions were used. We see that the accuracy is only slightly better than with 100
positions. We have also calculated the standard deviation for the results in the large chamber,
when no platform stirring has been used, and the accuracy is comparable to those obtained in
the Chalmers chamber when we used platform stirring.
Note that the standard deviations for large frequency windows are not accurate when
calculated the way we have done, as it is calculated from too few independent sets of power
samples. Therefore it is not shown in the table. We have typically only 10 independent set of
samples with a 10 MHz window and 5 with a 20 MHz window, over the 100 MHz band,
which we have measured.
C.4 Correlation functions.
We choose the set of samples available for all stirrer positions at one frequency point, and we
evaluate the autocorrelation function by correlating this with the same set of samples when
this is shifted by a number of stirrer steps. The shifting is done in such a way that the last
positions of the shifted set are moved to the first positions, which became empty when the set
was shifted (i.e. by assuming periodic stirrer steps). This shifted vector of samples is assumed
to be uncorrelated to the original sample vector if the correlation is below 0.37. If the samples
are uncorrelated already after one step (shift), the stirrer step size is so large that all power
samples are independent. Then, we can decrease the step size if we want to increase the
number of independent samples. If two or more neighboring samples are correlated with the
autocorrelation function larger than 0.37, we can increase the step size to reduce measurement
time.
We have calculated the autocorrelation for 100 paddle positions and without any platform
stirring in Figure 6, which shows the number of steps that we have to move the paddles to
have an auto correlation under the 0.37-limit. We see that over most of the frequency band we
have to move about 7 positions to get uncorrelated samples. This means that we have in
average about 100/7=14 independent stirrer positions. However, at some frequencies we see
peaks indicating that we have to move up to 20 or even 30 paddle positions to get uncorrelated
samples, which correspond to between 5 and 3 independent positions. These peaks appear in
those frequency sub-bands where there are few modes, caused by a non-uniform mode
density, as detected and explained in [3].
C.5 Accuracy.
The radiation efficiency of the test case is obtained as the ratio between measured average
power levels. Each of these levels is associated with a measurement accuracy that is
represented by a relative standard deviation [5]
C6
σ = 1 M indep
(1)
M indep is the number of independent power samples over which the averaging is
where
performed [6]. The accuracy of the measured AUT will therefore be [10]
σ AUT =
(σ ) + (σ )
2
2
where σref and σtest are the standard deviation of the estimates of Pref
and Ptest, respectively. We have in this paper measured Pref and Ptest in the same way, so
ref
test
σ ref = σ test and σ AUT = 2σ ref .
The number of cavity modes M within a given volume can be found by multiplying the
mode density with the bandwidth ∆f, i.e. [6]
M =
∂N
f2
∆f = 8πV 3 Λf
∂f
c
(2)
where c is the speed of light, V is the cavity volume and f the frequency. If we assume that
the number of independent power samples is equal to the number of excited modes in the
cavity, we can estimate the normalized accuracy σ AUT from the above equations by using
M indep = M . When the standard deviation is known from (1), we can transfer this to an
approximate dB value by using
(σ )
dB
1
1 + σ
= ± 10 log 
2
1 − σ



The probability that the estimate of an average level is within ± σ from its true value is 0.67
according to the theories in [7].
Table 1 shows the theoretical and measured standard deviations of the radiation efficiencies
evaluated at 920 MHz. The theoretical values are obtained by using ∆f equal to the bandwidth
of the frequency stirring, and σ AUT = 2σ ref . The platform is rotated to 10 different positions
during the platform stirring. To obtain theoretical values for this case, we multiply the number
of modes by the 10 platform positions, since we can think of the platform positions as
representing 10 independent cases, provided they are sufficiently separated in angle or
position. The measured standard deviations are better than the theoretical ones, but this can be
explained by the fact that the measured ones are inaccurate because they are calculated from
very few independent sets of power samples, as explained at the end of Section 3. Still, the
disagreement is not exceptionally large.
C.6 Conclusion
We have shown that the radiation efficiency of antennas can be measured in a reverberation
chamber. We have showed that the accuracy in a small chamber can be improved significantly
when we use platform stirring. It seems that it is possible to increase the number of
independent power samples with a factor equal to the number of platform positions, provided
This manuscript was published in
Microwave and Optical Technology Letters, Vol. 30, No 20, pp. 391-397, Sept. 2001
C7
each position of the antenna located on it is separated by more than λ 2 . This makes it
possible to measure the radiation efficiency with good accuracy even in a small reverberation
chamber. The resulting values and accuracies are comparable to those of a large chamber. We
can get good accuracy even with only 100 stirrer positions if we combine this with frequency
stirring over 20 MHz. The frequency resolution of the measured radiation efficiency will be 20
MHz when we use 20 MHz frequency stirring. The work in the present paper and in [3] has
also detected frequency ranges with reduced accuracy. This has stimulated to a modification
of the Chalmers chamber by increasing its height. This will increase the mode density, make it
more uniform, and, the distance between the fixed antenna and the AUT will increase
significantly, causing the direct coupling between the fixed antenna and the AUT to strongly
decrease.
The validation case has a much simpler geometry than a real phone antenna close to a human
head, but it contains the same characteristics including a very lossy object, so we believe the
conclusions about the measurement accuracy are representative also for real antenna
measurements.
C.7 Acknowledgement
This work was founded by Intenna Technology AB and an industrial PhD scholarship from
The Swedish Research Council for Engineering Sciences (TFR). The work would not have
been possible without the additional support from the Swedish Foundation for Strategic
Research (SSF). The Chalmers chamber is being commercialized by Bluetest AB
(www.bluetest.se).
C.8 References
[1] P.S. Kildal, “Foundations of Antennas – A Unified Approach”, Studentlitteratur, April
2000, www.studentlitteratur.se/antennas
[2] K. Rosengren, P.S. Kildal, J. Carlsson, O. Lundén, “Measurement of terminal antennas
performance in multimode reverberation chambers”, Antenn00, Nordic Antenna Symposium,
Lund,
[3] K. Rosengren. P.S. Kildal, ”Study of distributions of modes and plane waves in
reverberation chambers for characterization of antennas in multipath environment”,
submitted to Microwave and Optical Technology Letters, March 2001
[4] D. A. Hill, "Linear dipole response in a reverberation chamber", IEEE Transactions on
Electromagnetic Compatibility, vol. 41, no. 4, pp. 365-368, November 1999.
[5] D. A. Hill, "Electronic mode stirring for reverberation chambers", IEEE Transactions on
Electromagnetic Compatibility, vol. 36, no. 4, pp. 294-299, November 1994.
[6] J. G. Kostas and B. Boverie, "Statistical model for a mode-stirred chamber", IEEE
Transactions on Electromagnetic Compatibility, Vol. 33, No. 4, pp 366-370, Nov. 1991.
[7] Gus Freyer, Michael Slocum, Handouts from “Reverberation Chambers, Theory/
Experiment, Short Course”, arranged by EMC Services and Bofors Missiles 30 August - 3
September 1999 in Karlskoga, Sweden.
[8] Mats Bäckström, Olof Lundén, "Measurements of Stirrer Efficiency in Mode-Stirred
C8
Reverberation Chambers", FOA Report FOA-R--99-01139-612—SE from Defence Research
Establishment, S-581 11Linköping, Sweden, May 1999.
[9] Schmid & Partner Engineering AG, “Application note: Recipes for brain tissue simulating
tissue”, Zeughausstrasse 43, 8004 Zürich, Switzerland.
[10] J. Mc Ghee, M. J. Korczynski, I. A. Henderson, W. Kulesza, “Scientific Metrology”,
Lodart, pp 129.
[11] Charlie Carlsson, “Mode-stirred Chamber for Terminal Antennas”, Master thesis
April.2001, Chalmers University of Technology, Gothenburg, Sweden
C.9 Figures
Figure 1. The interior and set-up in the 1m-x0.8m-x1m Chalmers chamber with dipole, paddle
and platform stirrers (left). Close up of reference dipole antenna at a distance 10 mm from the
lossy PVC-cylinder (right). It should be noted that at the time of the actual measurements, the
shown support of the cylinder and the dipole were not ready, so the dipole and cylinder were
supported by blocks of styrofoam. The styrofoam was the same both during reference and test
measurements, so it has not introduced errors in the radiation efficiency.
This manuscript was published in
Microwave and Optical Technology Letters, Vol. 30, No 20, pp. 391-397, Sept. 2001
C9
Radiation efficienc y (average , dB )
0
-5
-10
-15
-20
87 0
890
9 10
93 0
FR E Q UE NC Y (MHz)
950
9 70
Figure 2. A typical relative radiation efficiency measurement in the 1m x 0.8m x 1m Chalmers
chamber. The upper curves correspond to the difference between the two lower curves, which
are the reference (middle curve) and test (lower curve) cases. The radiation efficiency is
plotted for the cases when frequency stirring is used over a 10 (longer solid curve), 20 (dotted
curve), 40 (dashed curve) and 60 MHz (shorter solid curve) windows. The standard
deviations in Table 1 are calculated by using these radiation efficiencies.
C10
Radiatio n efficiency (dB )
0
-1
-2
-3
-4
-5
-6
-7
1
D iamond: Measured in Chalmers chamber
Hexagram: Measured in FO A chamber
Circle: Calculated
2
3
4
5
6
7
8
9
Distance from lo ssy dielectric (cm)
10
Figure 3. Radiation efficiency versus distance between dipole and lossy cylinder measured in
the small 1m x 0.8m x 1m Chalmers chamber, and in a large 5.5m x 2.5m x 3.5m chamber at
FOA.
This manuscript was published in
Microwave and Optical Technology Letters, Vol. 30, No 20, pp. 391-397, Sept. 2001
C11
Radiation efficiency (average, dB )
2
0
5 cm
-2
3 cm
-4
2 cm
-6
1 cm
-8
-10
-12
870
890
910
930
950
FRE QUENCY (M Hz)
970
Figure 4. The radiation efficiency measured with platform stirring, for 1, 2, 3 and 5 cm
distances between the dipole and the lossy cylinder. The different curves are obtained by using
different frequency windows for the frequency stirring (10, 20, 40 and 60 MHz stirring), as
explained in the text.
C12
R adiation e ffic iency (average , dB )
2
0
-2
2 cm
-4
-6
1 cm
-8
-10
-12
87 0
890
9 10
93 0
FR E Q UE NC Y (MHz)
950
9 70
Figure 5. The radiation efficiency measured without platform stirring, for 1 and 2 cm
distances between the dipole and the lossy cylinder. The different curves are obtained by using
different frequency windows for the frequency stirring (10, 20, 40 and 60 MHz stirring), as
explained in the text.
This manuscript was published in
Microwave and Optical Technology Letters, Vol. 30, No 20, pp. 391-397, Sept. 2001
C13
Num ber of c orre lated stirrer steps
30
20
10
0
87 0
890
9 10
93 0
frequency (MHz)
950
9 70
Figure 6. The number of steps that the stirrer has to do, in order to have correlation under the
0.37-limit. The auto-correlation is calculated over 100 simultaneous paddle positions when
the platform is fixed.
C14
Distance
between Window size 10 MHZ
dipole and cylinder
PS
No PS
1cm
0.30
1.9
2cm
0.32
1.6
3cm
0.35
4cm
0.33
5cm
0.32
5cm, 343 stirrer pos. 0.24
Theoretical
0.78
2.6
Large chamber
0.28
Window size 20 MHZ
PS
0.14
0.22
0.22
0.19
0.25
0.21
0.55
-
No PS
1.5
1.1
1.65
0.15
Table 6. Standard deviations in dB of measured relative radiation efficiency in the Chalmers
chamber. They are obtained by averaging over all stirrer steps and when using frequency
stirring with different frequency windows. The table shows results both when platform stirring
is used (PS) and not used (No PS). The results on the bottom line are obtained in a large
chamber with dimensions 5.5m x 2.5m x 3.5m [2]. The calculation of the standard deviation is
based on only 10 (10 MHz window) and 5 (for 20 MHz) independent sets of power samples (at
different frequencies).
This manuscript was published in
Microwave and Optical Technology Letters, Vol. 30, No 20, pp. 391-397, Sept. 2001
C15
C16
Appendix D. Impedance: Manuscript of the journal article
“Measurement of free space impedances of small antennas in reverberation chambers”,
P-S. Kildal, J. Yang and C. Carlsson,
Microwave and Optical Technology Letters, Vol. 32, No. 2, pp 112-115, Jan., 2001.
MEASUREMENT OF FREE SPACE IMPEDANCES
OF SMALL ANTENNAS
IN REVERBERATION CHAMBERS
Per-Simon Kildal, Charlie Carlsson, Jian Yang
Kildal (www.kildal.se, simon@elmagn.chalmers.se) and Yang (yang@elmagn.chalmers.se)
are with Chalmers University of Technology, Department of Electromagnetics, S-41296
GOTHENBURG, SWEDEN. Carlsson is with Bluetest AB (www.bluetest.se), Sweden.
Abstract
We have recently shown that reverberation chambers can be used to measure the radiation
efficiency of antennas for wireless and mobile terminals. In the present paper we show that it
is possible in the same measurement set-up to measure the input impedance of the antenna, as
it would be seen when the antenna radiates in free space. If the antenna is located close to e.g.
a head phantom inside the chamber, we will measure the impedance of the antenna as it would
be seen if the dipole and the phantom is located in free space with the same location and
orientation relative to each other.
D.1 Introduction
Reverberation chambers are known from the EMC area. They are used to generate a statistical
field environment [2]. Small antennas for mobile and wireless terminals operate in a statistical
multipath environment, which has many similarities to the field in reverberation chambers.
The quality of such terminal antennas is characterized in terms of the radiation efficiency, the
definition of which can be found in [3]. We have previously shown that reverberation chambers can be used to simulate a uniform multipath environment [4] and to measure the radiation
efficiency of small antennas [5], [6]. The purpose of the present paper is to show that we also
can measure free space impedances in such chambers. This is a big advantage when developing and characterizing small antennas, because it completely eliminates the use of anechoic
chambers in connection with determination of the major performance of such antennas. We
can get good accuracy of the measurements in the GSM 900 MHz band even in chambers
which are so small that they can pass through normal doors. This is obtained by making use of
platform stirring [6].
D.2 Theory
When we locate an antenna in a reverberation chamber, we postulate that its reflection coefficient can be written as the sum of a deterministic free space part r fs plus a part r ch coming
from the chamber, i.e.
r ant = r f s + r ch
This manuscript was published in
Microwave and Optical Technology Letters, Vol. 32, No. 2, pp 112-115, Jan. 2002
(1)
D1
The chamber reflection coefficient r ch will depend on the positions of the two mechanical stirrers, and the platform stirrer. It is reasonable to assume that r ch is normally distributed in the
same way as the field at any location inside the chamber [2]. This means that the expected
mean of r ch over all stirrer positions in the chamber is zero. Therefore, if we evaluate the mean
of the total complex reflection coefficient
cient r fs , i.e.
r ant
r ant ,
r ant = r f s
we will get the free space reflection coeffi-
(2)
It should be noted that previously there has only been reported transmission power measurement in reverberation chambers, and averaging of these to get average power levels. The
present theory involves complex averaging, referred to by the abbreviation CA, of the reflection coefficient, and this enables the extraction of the free space reflection coefficient, according to the above. When the free space reflection coefficient has been found, the corresponding
impedance is given by a classical formula.
D.3 Measurements
In order to verify the above theory we have performed a test on the same validation case as
that described in [7]. This is a vertical dipole close to a circular PVC cylinder of 110 mm outer
diameter and 5.5 mm wall thickness (Figure 1). The cylinder’s height is 30 cm, and it is filled
with a human tissue equivalent liquid that has similar dielectric characteristics as grey brain
cells ( ε = 42, 24 , σ = 1, 0 S ⁄ m ). The distance between the axis of the dipole and the outer surface
of the PVC cylinder is chosen to be 10 mm, 20 mm, 55 mm and “infinity”. The latter corresponds to a free space location. We have used two dipoles. One dipole has arms and balun
with adjustable lengths, so that it could be tuned to 50 Ohms at 920 Mhz, when it radiated in a
free space location. The other was manufactured with a shielded balun for match to 50 Ohms
at 1800 MHz. We located each of the dipoles at different positions relative to the lossy cylinder and measured them both in an anechoic chamber and in a reverberation chamber. The
reverberation chamber is 1 m long, 0.8 m wide and 1.6 m high, see [4], [6], [7] and Figure 1. It
has two mechanical mode stirrers and a platform stirrer. The lossy cylinder was present inside
the reverberation chamber also when the free space case was measured, but located more than
0.5 wavelengths away from the dipole.
Figures 2 and 3 show the results of the measurements both for the 900 MHz and 1800 Mhz
cases. For the 900 MHz case we show both the results of averaging the complex reflection
coefficient, referred to as CA in the figures, and the results of averaging the power reflection
coefficient, referred to as PA in the figures, whereas we for the 1800 MHz case only show CA
results. The results in the reverberation chamber have been obtained by averaging over 30
mechanical stirrer positions, 10 platform positions, and in addition complex averaging (smooting) over a bandwidth of 22.5 MHz for the 900 MHz band and 60 MHz for the 1800 MHz
band. The latter values correspond to the frequency stirring used when measuring the radiation
efficiency. The figures also show the reflection coefficients when they are measured in an
anechoic chamber. In Figure 2a we also show a typical reflection coefficient in the chamber,
measured for one specific stirrer position. We see how large this reflection coefficient is, and
how much it is reduced by complex averaging over all stirrer positions. We also see how the
PA results always are higher than the CA results r fs . Actually, it is quite easy to show that
D2
r ant
2
2
2
= r fs + r ch > r fs
2
(3)
where r 2 means power averaging PA of the reflection coefficient r. Furthermore, we see that
the CA curves measured in the reverberation chamber in all cases are very close to the curves
measured in the anechoic chamber. The agreement is certainly sufficiently good for measurements of practical antennas for mobile phones and Bluetooth units. The accuracy is better the
closer to the lossy cylinder the dipole is. This is reasonable, as then the statistic field (i.e.
reflection coefficient) from the chamber is attenuated compared to the free space reflection
coefficient of the dipole.
D.4 Conclusion
We have postulated by simple argumentation that the complex average of the reflection coefficient of a small antenna inside a reverberation chamber must be equal to its free space reflection coefficient. The small antenna may be located close to an object, in which case the free
space reflection coefficient means the reflection coefficient when the antenna is located in the
same position relative to the object when both are located in free space. We have also proven
experimentally that this postulate holds. The chamber needs to be loaded with a lossy object in
order to get sufficient accuracy.
D.5 Aknowledgements
We are grateful to Andreas Wolfgang for providing the 1800 MHz results.
D.6 References
[2] J.G Kostas and B. Boverie, “Statistical model for a mode-stirred chamber”, IEEE Transactions on Electromagnetic Compability, Vol. 33, No 4, pp 366-370 Nov 1991
[3] P-S. Kildal, Foundations of Antennas - A Unified Approach, textbook coming with the
interactive electronic handbook Antenna Design using Mathcad, Studentlitteratur, Lund,
March 2000 (www.studentlitteratur.se\antennas)
[4] K. Rosengren, P-S. Kildal, “Study of distributions of modes and plan waves in reverberation chamber for characterization of antennas in multipath environment”, to appear in
Microwave and Optical Technology Letters, Sept 20, 2001.
[5] K. Rosengren, P-S. Kildal, J. Carlsson, O. Lundén, “Measurements of terminal antennas
performance in multimode reverberation chambers”, Proceedings of Swedish Antenna
Conference Antenn 00, Lund, Sweden, Sept 2000.
[6] K. Rosengren, P-S. Kildal, C. Carlsson, J. Carlsson, “Characterization of antennas for
mobile and wireless terminals in reverberation chambers: Improved accuracy by platform
stirring”, to appear in Microwave and Optical Technology Letters, Sept 20, 2001.
[7] J. Yang, J. Carlsson, P-S. Kildal and C. Carlsson, “Calculation at self impedance and radiation efficiency of a dipole near a lossy cylinder with arbitrary cross section by using the
moment method and a spectrum of two-dimensional solutions”, submitted to Microwave
and Optical Technology Letter, July 2001
This manuscript was published in
Microwave and Optical Technology Letters, Vol. 32, No. 2, pp 112-115, Jan. 2002
D3
D.7 Figures
Figure 1. Exterior (left) and interior (right) of reverberation chamber with set-up for
measuring reflection coefficient of a vertical dipole at distance from a lossy cylinder. The
reverberation chamber has two mechanical stirrers and a rotating platform stirrer. The
mechanical stirrers are located one on the back wall and the other in the ceiling of the
chamber. The reverberation chamber is available from Bluetest AB (www.bluetest.se).
D4
a) 900 MHz dipole,
d = ∞
b) 900 MHz dipole,
d = 55 mm
d) 900MHz dipole, d = 20 mm
d = 10 mm
Figure 2. Measured reflection coefficients of 920 MHz dipole at different distances d from the outer
surface of the lossy cylinder. The curves marked anechoic are measured in an anechoic chamber.
The curves marked CA (complex averaging) and PA (power averaging) are measured in the
reverberation chamber in Figure 1.
c) 900MHz dipole,
This manuscript was published in
Microwave and Optical Technology Letters, Vol. 32, No. 2, pp 112-115, Jan. 2002
D5
d = 55 mm
b) 1.8 GHz dipole, d = 20 mm
Figure 3. Measured reflection coefficients of 1800 MHz dipole at different distances d from
the outer surface of the lossy cylinder. The curves marked reverberation chamber are
measured in the chamber in Figure 1.
a) 1.8 GHz dipole,
D6
Appendix E. Polarization stirring: Manuscript of the journal article
"Detection of a polarization imbalance in reverberation chambers and how to remove it
when measuring antenna efficiencies",
P-S. Kildal, C. Carlsson,
submitted to Microwave and Optical Technology Letters, Nov. 2001.
DETECTION OF A POLARIZATION IMBALANCE IN REVERBERATION CHAMBERS AND HOW TO REMOVE IT BY POLARIZATION
STIRRING WHEN MEASURING ANTENNA EFFICIENCIES
Per-Simon Kildal, Charlie Carlsson
Kildal (www.kildal.se, simon@elmagn.chalmers.se) is with Chalmers University of Technology, Department of Electromagnetics, S-41296 GOTHENBURG, SWEDEN. Carlsson is with
Bluetest AB (www.bluetest.se), Chalmers Teknikpark, S-41288 Gothenburg, Sweden.
Abstract
We have previously shown that the radiation efficiency of small antennas can be measured
with good accuracy in reverberation chambers. The results are obtained by averaging several
measurements of the transmitted power between the antenna under test and a fixed antenna,
both located inside the chamber. Further investigations have shown that the results depend
strongly on the orientation of the antenna under test and thereby its polarization. In the present
paper we explain why it is like this, and we show how this imbalance can be removed by
polarization stirring, i.e. by using three orthogonal fixed antennas instead of one.
E.1 Introduction
Reverberation chambers are used to generate a statistically uniform field distribution, needed
for certain EMC tests. The statistical properties are obtained by mechanically stirring the
modes in the chamber. We have previously shown that the multiple mode fields inside reverberation chambers have similar characteristics as the multipath propagation environment
appearing in mobile communications in indoor and urban environment [8], provided the directions of arrival of the waves are distributed uniformly in space. The performance of a small
antenna located in such an environment is determined by its radiation efficiency. We use the
definition of radiation efficiency in [9], which accounts for contributions due to absorption in
the antenna and its close environment as well as reflections at the input port. We have shown
that it is possible to measure the radiation efficiency of small antennas in reverberation chambers, also when the antenna is located close to lossy objects such as a head phantom. The measurement accuracy is quite good even in a small chamber if we locate the test object on a
rotatable platform, referred to as platform stirring [10]. Furthermore, we have shown that it is
possible to use a reverberation chamber to measure the free space impedance of the antenna in
its position close to a possible lossy object [11]. With “free space impedance” we mean the
impedance the antenna (in its position close to the object) would see if both were located in
free space. In recent measurements we have discovered a polarization imbalance of up to several dBs that is present in chambers of different sizes. This polarization imbalance cannot be
This manuscript has been submitted to
Microwave and Optical Technology Letters, Nov. 2001
E1
explained by previous theories for reverberation chambers [12]-[14]. The purpose of the
present paper is to derive formulas that describe the polarization imbalance, to verify the theory by measurements, and to show how the polarization imbalance can be removed by polarization stirring, i.e. by using three orthogonally polarized fixed antennas instead of one. This is
very important in order to ensure repeatable and accurate measurements of the radiation efficiency.
It should be mentioned that polarization imbalances also are known from actual multipath
environments, see e.g. [15], but that we in our chamber want to remove it in order to create a
controlled environment for measuring radiation efficiency.
E.2 Initial measurements
A sketch of the instrument setup with reverberation chamber that is used in the present measurements is shown in Figure 1. The size of this chamber is 0.8m x 1.0m x 1.6m. The chamber
has two plate-shaped mechanical stirrers. One can be moved vertically along the back wall and
the other can be moved horizontally across the whole chamber cross-section. The figure shows
three wall-fixed monopoles, but initially there was only one. The antenna under test (AUT) is
shown to be a vertical halfwave dipole. It is located on a rotatable platform to improve accuracy [10].
We measure the S-parameters at the two antenna ports, i.e. between the port of one of the fixed
monopole (port 1) and the port of the half wave dipole (port 2) over the frequency band 700 to
1100 MHz. From these S-parameters we calculate the net transfer function G chamber by using
the following formula
1
G chamber = ---N
∑
2
S 12
----------------------------------------------------2
2
( 1 – S 11 ) ( 1 – S 22 )
(4)
S 11 is the complex mean of S 11 , and S 22 is the complex mean of S22 , where these means are
taken over all stirrer and platform positions. In addition they are averaged over a 5 MHz frequency window at each considered frequency (smoothing by a moving window). The summation in (1) is also taken over all stirrer and platform positions, and in this case a moving
frequency window of 25 MHz (frequency stirring); the total number of summed samples being
N. The complex averaging of S 11 and S 22 gives the free space reflection coefficients as
2
explained in [11]. The radiation efficiency of the AUT is proportional to G chamber ( 1 – S 22 ) .
Initially, when we used only one fixed monopole antenna, the net transfer function was always
significantly higher when the dipole was located parallel with the monopole (e.g. horizontally), than when the dipole was located with an orientation that was orthogonal to it (i.e. vertically). The discrepancy was present for many locations of the dipole and monopole. A
similar polarization imbalance was noticed with the same dipole during tests in a large (37 m3)
reverberation chamber at the Swedish Defence Research Institute (FOI), in which case the
fixed antenna was a log periodic antenna. Another person have reported to us even larger
polarization imbalances in a third medium sized chamber.
E2
We first solved the problem with the polarization imbalance in our chamber (Figure 1) by
replacing the wall mounted monopole antenna by a circularly polarized helical antenna, that
was mounted to the wall in such a way that the wall acted as a ground plane. Thereafter, we
improved the results further by using three orthogonally polarized fixed antennas. All the tests
were done when the chambers were loaded with a lossy cylinder of the same type as that
described in [10], and the dipole was located far away from this cylinder, i.e. at least 0.7 λ
away. The results of the tests with a helical fixed antenna and with three monopole fixed
antennas will be given after the next section that contains a simple theory of the polarization
imbalance.
E.3 Theory
A reverberation chamber supports a number of cavity modes. Each of these modes can be separated into eight interfering plane waves [8]. If one of these plane waves propagates in the
direction ( θ 1, ϕ 1 ) in the spherical coordinate system ( θ ,ϕ ) , the other waves propagate in the
directions
( θ 1, π – ϕ 1 ), ( θ 1, π + ϕ 1 ), ( θ 1, 2π – ϕ 1 ), ( π – θ 1, ϕ 1 )
(5)
( π – θ 1, π – ϕ 1 ), ( π – θ 1, π + θ 1 ), ( π – θ 1, 2π – ϕ 1 )
which corresponds to cos θ , sin θ , cos ϕ , and sin ϕ being equal for all waves. An antenna
radiates a spectrum of plane waves. If this antenna is a short monopole or dipole of direction
ˆl , the radiation field as a function of direction r̂ varies as
e
1
E ∝ ˆl 1 – ( ˆl 1 ⋅ r̂1 ) r̂1
(6)
see e.g. Section 3.4.1 in [9]. When the short dipole or monopole antenna is located inside a
reverberation chamber, it will excite the resonant modes being present at frequencies within
the average mode bandwidth of the chamber. Thereby, the plane waves corresponding to these
modes will be present.
We have in [8] shown that the plane waves are distributed quite uniformly in space if the
chamber and the mode bandwidth are sufficiently large. Therefore, the amplitudes of the plane
waves should in average over all the modes vary in the same way as they are excited, i.e.
according to (3).
The plane waves in (2) of a single mode are reflected by the walls of the chamber. Let us first
simply assume that there is a pure reflection and no coupling to the plane waves of other
modes. Then, a r̂1 direction ( θ 1, ϕ 1 ) will always reflect into one of the other directions r̂2 in
(2), so we do not create any coupling to the plane waves of different modes. The induced voltage at the terminal of a short receive dipole (AUT) of orientation ˆl is proportional to
2
V2 = E ⋅ ( ˆl 2 – ( ˆl 2 ⋅ r̂ 2 ) r̂ 2 ) , see [16] and Figure 2.22 in [9]. The received power in a load at the
port of the receive dipole will therefore by using (3) be proportional to
P ( r̂1, r̂ 2 ) = V2
2
ˆ
ˆ
= [ ˆl1 – ( ˆl 1 ⋅ r̂ 1 ) r 1 ] ⋅ [ l 2 – ( ˆl 2 ⋅ r̂2 ) r̂ 2 ]
This manuscript has been submitted to
Microwave and Optical Technology Letters, Nov. 2001
(7)
E3
When we treat one single mode, the eight plane waves can be grouped into four pairs, where
the two plane waves of each pair have opposite propagation directions. Therefore, for each
pair of plane waves we may write rˆ = – r̂ in (3), and we get
1
2
2
P ( r̂ ) = ˆl1 ⋅ ˆl2 – ( ˆl 1 ⋅ r̂ ) ( ˆl 2 ⋅ r̂ )
(8)
The total received power averaged over sufficiently many modes becomes
P tot (ˆl 1, ˆl 2 ) =
∫ ∫ P ( r̂ ) dΩ
4π
(9)
We will now evaluate this for different orientations ˆl 1 and ˆl 2 of the two dipoles. Let us first
recall that in the spherical coordinate system
r̂ = cos θ ẑ + sin θ ( cos ϕ x̂ + sin ϕ ŷ )
(10)
Then, we first choose ˆl1 = ˆl 2 = ẑ , and get
Ptot ( ẑ, ẑ ) =
2 2
32π
(
–
cos
1
θ ) sin θ dθ dϕ = --------∫∫
15
(11)
4π
Similarly, if lˆ1 = ẑ and lˆ2 = x̂ we get
P tot ( ẑ, x̂ ) =
∫ ∫ cos
4π
2
2
2
4π
θ sin θ cos ϕ sin θ dϕ = -----15
(12)
and the same for ˆl 2 = ŷ .
Thus, when we use a monopole (or dipole) to excite the chamber, and we receive with a
dipole, there is a difference in the net transfer function of the chamber, dependent on whether
the two antennas are parallel or not, of
Ptot ( ẑ, ẑ )
- = 8 , i.e. 9 dB
∆ G chamber = --------------------P tot ( ẑ, x̂ )
(13)
This result is too large to explain the measured discrepancy in our chamber. However, we
have not yet taken into account the mode coupling due to the mechanical stirring in the chamber.
Let us now introduce P Σ as the sum of the average power levels for all three orientations of ˆl 2 ,
i.e.
PΣ = P tot ( ẑ, ẑ ) + Ptot ( ẑ, x̂ ) + Ptot ( ẑ, ŷ )
Then, we may define relative polarized power levels according to
E4
(14)
P tot ( ẑ, ẑ ) 8
P z0 = ---------------------- = -----PΣ
10
P tot ( ẑ, x̂ ) 1
- = -----Px0 = --------------------P 0Σ
10
(15)
P tot ( ẑ, ŷ ) 1
- = -----Py0 = --------------------PΣ
10
Let us now assume that the mode stirring in the reverberation chamber works in the following
way, in statistical average over all modes:
The waves propagate back and forth. The stirrers are located along the walls, and they are so
efficient that each time a wave hits a wall with a stirrer, the power in this wave is evenly distributed between all waves of all modes on reflection. We choose to describe this in such a
way that the power after one reflection is distributed statistically according to
1
1
1
P z1 = --- P z0 + --- P x0 + --- P y0
3
3
3
1
1
1
P x1 = --- P z0 + --- P x0 + --- P y0
3
3
3
1
1
1
P y1 = --- P z0 + --- P x0 + --- P y0
3
3
3
(16)
Similarly, the n’th reflection causes
1
1
1
Pzn = --- Pzn – 1 + --- P xn – 1 + --- P yn – 1
3
3
3
1
1
1
Pxn = --- Pzn – 1 + --- P xn – 1 + --- P yn – 1
3
3
3
1
1
1
Pyn = --- Pzn – 1 + --- P xn – 1 + --- P yn – 1
3
3
3
(17)
The coupling to the other modes can be described in many other ways than (13) and (14), but
we will later see that the present model gives results that describes the polarization imbalance
quite well. By using (14), the total average power of the z-components of the fields become
2m
after several reflections (Note that the ( 1 ⁄ 3 ) sum in the formula represents contribution to
the z-component via coupling to the x- or y components, i.e. a factor 1/3 from z- to x- or ycomponents, and a factor 1/3 to couple back to the z-component.)
This manuscript has been submitted to
Microwave and Optical Technology Letters, Nov. 2001
E5
PZZ = P z0 + P z1 + … P zn + …
∞
= Pz0
∑
n
1
--- + Px0
 3
n=0
1 2
+  --- Pz0
3
∞
∑
n
1
--- + P y0
 3
n=1
∞
∑
n
2
1
--- +  1--- P x0
 3
 3
n=0
∞
=
1
---
∑  3
m=0
2m
∞
1
Pz0 ∑  ---
3
n=0
+
1
---
∑  3
n=1
∞
1
---
∑  3
n=1
∞
n
∞
1
Px0 ∑  ---
3
n=1
n
n
+…
(18)
∞
n
+ P y0
1
---
∑  3
n=1
n
9 3
1 3
1 3
= ---  --- P z0 + ---  --- Px0 + ---  --- P y0 
8 2
3 2
3 2
and correspondingly for the x- and y-components
9 3
1 3
1 3
PZX = ---  --- Px0 + ---  --- Pz0 + ---  --- P y0 



8 2
3 2
3 2  
(19)
PZY
9 3
1 3
1 3
= ---  --- Py0 + ---  --- Px0 + ---  --- P z0 
8 2
3 2
3 2
If we introduce the values for P x0 , Py0 and P z0 we get
12 + 1
13
∆ G chamber = --------------------------- = ------ , i.e. 3.4 dB.
6
3
--- + 4 + 1---
2
2
(20)
The platform stirring will affect the polarization ratio in such a way that if the antenna under
test is horizontally polarized in the xy-plane, it will in average over the platform positions
receive half the power from the x-component of the field and half from the y-component.
Therefore, if the fixed antenna is vertically polarized, we get
PZZ
------ , i.e. 3.4 dB
- = 13
∆ G V = -------------------------------1--6
( PZX + P ZY )
2
(21)
On the contrary, if the fixed antenna is horizontally polarized, we get
∆ GH
E6
1
1
PZY + --- P XY
PZY + --- P ZY
19
2
2
= ---------------------------- = ---------------------------- = ------ , i.e. 2.0 dB
PXY
P ZY
12
(22)
E.4 Experimental results
We have measured the polarization imbalance in the chamber shown in Figure 1 by using
three different wall-fixed monopole antennas, and a dipole as AUT. The chamber was during
the measurements loaded with two lossy cylinders of the same type as that used in [11].
Together these two cylinders represent slightly more loading of the chamber than the phantom
head shown in Figure 1 and used in other measurements. The measured results are shown in
Figure 2. The received power levels are averaged over 4 platform positions and 30 plate positions, and we have frequency stirred over 25 MHz. We see the variation of the net transfer
function of the chamber versus frequency for vertical and horizontal AUT, when we use all the
three monopole locations. We have also calculated the average polarization imbalance for
each monopole, by averaging the ratio of the values for vertical and horizontal AUT over the
whole frequency band 700 to 1100 MHz. The values are written into Table 1 and compared
with the theoretical values from the previous section. We see that our simple theory gives a
larger polarization imbalance than we measure. Still, we will in this paper be satisfied with the
simple theory as a qualitative measure.
The results of averaging the net transfer functions of the three monopole locations, are shown
in Figure 3. We see that now the polarization imbalance is almost completely removed. In the
same figure we show the net transfer function when a wall-mounted circularly polarized helical antenna is used. The helical antenna is better than a single monopole, but it is far from
being as good as polarization stirring by means of three monopoles. It seems to be best within
the frequency band where it was designed for circular polarization, which is around 900 MHz.
E.5 Conclusion
We have shown experimentally that it is possible to remove a 2-3 dB polarization imbalance
in reverberation chambers by using three orthogonally polarized fixed antennas and averaging
their transfer functions. We refer to this as polarization stirring. We have derived a simple
approximate theoretical model that explains the imbalance qualitatively. It should be possible
to improve the model to account for the actual radiation pattern of the antennas and not only
their polarization characteristics, but this was not found necessary at the present stage of the
work. The simple theory also implies that the polarization imbalance may be up to 9 dB in
reverberation chambers where the mechanical stirrers do not stir the fields satisfactory.
Table 7. Measured and theoretical values for polarization imbalance
∆G H
∆G H
∆ GV
Theoretical value
-2.0 dB
-2.0 dB
3.4 dB
Figure reference
2a
2b
2c
Measured value
-1.76 dB
-1.23 dB
2.06 dB
Mathematical symbol
E.6 References
[8] K.Rosengren and P-S. Kildal, “Study of distributions of modes and plane waves in reverberation chamber for characterization of antennas in multipath environment”, Microwave
and Optical Technology Letters, Vol. 30, No 20, pp. 386-391, Sept. 2001.
This manuscript has been submitted to
Microwave and Optical Technology Letters, Nov. 2001
E7
[9] P-S. Kildal, Foundations of Antennas - A Unified Approach, textbook coming with the
interactive electronic handbook Antenna Design using Mathcad, Studentlitteratur, Lund,
March 2000 (www.studentlitteratur.se\antennas)
[10] K. Rosengren, P-S. Kildal, C. Carlsson, J. Carlsson “Characterization of antennas for
mobile and wireless terminals in reverberation chambers: Improved accuracy by platform
stirring”, Microwave and Optical Technology Letters, Vol. 30, No 20, pp. 391-397, Sept.
2001.
[11] P-S. Kildal, C. Carlsson, J. Yang “Measurement of free space impedances of small antennas in reverberation chambers”, to appear in Microwave and Optical Technology Letters,
Jan. 2002.
[12] G Kostas and B. Boverie, “Statistical model for a mode-stirred chamber”, IEEE Transactions on Electromagnetic Compability, Vol. 33, No 4, pp 366-370 Nov. 1991
[13] D. A. Hill, “Linear dipole response in a reverberation chamber”, IEEE Transactions on
Electromagnetic Compatibility, vol. 41, no. 4, pp. 365-368, November 1999
[14] D. A. Hill, M. T. Ma, A. R. Ondrejka, B. F. Riddle, M. L. Crawford and R. T. Johnk,
“Aperture excitation of electrically large, lossy cavities”, IEEE Transactions on Electromagnetic Compability, Vol. 36, No. 3, pp. 169-178, Aug. 1994
[15] C. B. Dietrich, K. Dietze, J. R Nealy and W. L Stutzman “Spatial, polarization and pattern diversity for wireless handheld terminals”, IEEE Transactions on Antennas Propagation, Vol. 49, p.o. 1271-1281, Sep. 2001
[16] P-S. Kildal, “Equivalent circuits of receive antennas in signal processing arrays”, Microwave
and Optical Technology Letters, Vol. 21, No 4, pp. 244-246, May 20 1999.
[17] P-S. Kildal, “A method and an apparatus for measuring the performance of antennas,
mobile phones and other wireless terminals”, International patent application No PCT/
SE01/00422, filed February 26, 2001, priority March 31, 2000.
E8
E.7 Figures
A
B
C
Switch
D
E
2
1
Network
Analyzer
F
Figure 1. Schematic drawing of the reverberation chamber being used in the measurements
[17]. The chamber is equipped with two mechanical plate-shaped stirrers. The dipole
(antenna under test) and the lossy head phantom are located on a rotatable platform and
rotated inside the chamber (platform stirring). There are three orthogonal wall-mounted
monopoles in the upper section of the chamber for polarization stirring.
This manuscript has been submitted to
Microwave and Optical Technology Letters, Nov. 2001
E9
Net transfer function (dB)
-8
-8
Hor
Ver
-10
-8
Hor
Ver
-10
-12
-12
-12
-14
-14
-14
-16
-16
-16
-18
800
1000
Frequency (MHz)
a) right wall
-18
800
1000
Frequency (MHz)
Ver
Hor
-10
-18
800
1000
Frequency (MHz)
b) back wall
c) roof
Net transfer function (dB)
Figure 2. Net transfer function of chamber for different locations of the fixed monopole (right
wall, back wall and roof) and for horizontal (HOR) and vertical (VER) orientations of the
dipole (AUT).
-8
-10
-8
Hor
Ver
-10
-12
-12
-14
-14
-16
-16
-18
Hor
Ver
-18
800
1000
Frequency (MHz)
800
1000
Frequency (MHz)
a) three monopoles
b) helical
Figure 3. Net transfer function of chamber averaged over all three monopole locations (left),
and net transfer function when a wall-mounted circularly polarized helical antenna is used
(right). The two curves in each graph are for horizontal (HOR) and vertical (VER)
orientations of the dipole.
E10
Appendix F. Diversity gain: Manuscript of the journal article
"Definition of Effective Diversity Gain and How to Measure it in a Reverberation
Chamber",
Per-Simon Kildal, Kent Rosengren, Joonho Byun and Juhyung Lee
submitted to Microwave and Optical Technology Letters, Nov. 2001.
Definition of Effective Diversity Gain and How to Measure it in a
Reverberation Chamber
Per-Simon Kildal1, Kent Rosengren2, Joonho Byun3 and Juhyung Lee3
Per-Simon Kildal (simon@elmagn.chalmers.se, www.kildal.se is with Chalmers University of
Technology, Sweden. Kent Rosengren (kent.rosengren@intenna.com, www.intenna.com) is
with Intenna Technology AB, Sweden. Joonho Byun (joon00@samsung.com) is with
Wireless Terminal Division, Samsung Electronics Co Ltd, South Korea.
Abstract
The performance of cellular phones and other mobile or wireless terminals operating in
multipath propagation environment can be greatly improved by introducing different diversity
schemes. The improvement is characterized in terms of a diversity gain. We define an
effective diversity gain. This is an absolute measure of diversity gain and can therefore be
used to compare different diversity antennas. We also show how the effective diversity gain
can be measured in a reverberation chamber. Measured effective diversity gains agree much
better with theoretical diversity gains than measured values published previously.
F.1 Introduction
Reverberation chambers are used to generate a statistically uniform field distribution, needed
for certain EMC tests. The statistical properties are obtained by mechanically stirring the
modes in the chamber. We have previously shown that the multiple mode fields inside
reverberation chambers have similar characteristics as the multipath propagation environment
appearing in mobile communications in indoor and urban environment [1]. The performance
of a small antenna located in such an environment is determined by its radiation efficiency.
We use here the radiation efficiency definition in [2] that includes impedance mismatch,
losses in the antenna itself and losses in the near-in environment such as a head phantom. We
have previously shown that it is possible to measure the radiation efficiency of small antennas
in reverberation chambers, also when the antenna is located close to lossy objects. The
measurement accuracy is quite good even in a small chamber if we locate the test object on a
rotatable platform, referred to as platform stirring [3], see also Figure 1. Furthermore, we have
shown that it is possible to use a reverberation chamber to measure the free space impedance
of the antenna in its position close to a possible lossy object [4]. With this “free space
impedance” we mean the impedance the antenna (in its position close to the object) would see
if both antenna and object were located in free space. We have discovered a polarization
imbalance of up to several dBs that is present in reverberation chambers, and we have shown
how it can be removed by polarization stirring [5]. This polarization imbalance cannot be
This manuscript has been submitted to
Microwave and Optical Technology Letters, Nov. 2001
F1
explained by previous theories for reverberation chambers [6]-[8].
It is known that spatial, polarization or pattern diversity can be used to improve the
performance of mobile or wireless terminals operating in a multipath propagation
environment. Therefore, work is in progress to experimentally determine the diversity gains
that can be achieved [9]-[11]. This is done by changing or in other ways moving the diversity
antennas around in a real urban or indoor environment. The purpose of the present paper is to
show that diversity gain can be measured much simpler and in a very accurate manner in a
reverberation chamber. Two parallel dipoles are often used as a validation case for diversity
gain, such as in [9]. However, there is large discrepancy between measured and theoretical
diversity gains when plotted as a function of the spacing between the dipoles. In the present
paper we explain this discrepancy to be caused by a reduction in the radiation efficiency of the
reference case when the two dipoles are close. We define therefore an effective diversity gain
relative to an ideal single antenna with unit radiation efficiency, and we show how this can be
measured in the reverberation chamber. This effective diversity gain has the same dependence
on dipole spacing as the theoretical diversity gain given in [9]. The effective diversity gain of
diversity antenna is by using an arbitrary reference case given as the diversity gain relative to
the reference case multiplied with the radiation efficiency of this reference case.
It should be noted that small antennas for mobile or wireless terminals often are characterized
in terms of a Mean Effective Gain (MEG), see e.g. [10], rather than the radiation efficiency
used in the present paper. The MEG depends on the elevation distribution of the multipath
environment. This makes it inconvenient to use for comparing antennas because different
environments give different MEG for the same antenna. The radiation efficiency is a classical
term and very convenient. It is equal to the MEG plus 3 dB in a multipath environment with
uniform elevation and azimuth distribution.
F.2 Calculation of diversity gain and effective diversity gain
The received power level in a multipath environment with no line-of-sight is statistically
distributed as a Rayleigh function. This can be seen by plotting the probability that an arbitrary
power level sample is smaller than a certain power level, i.e. the cumulative probability
density function. Figure 2 shows such curves. In a diversity scheme with two antennas (also
called branches) the received power from each of them will have a Rayleigh shaped
probability density function. If we combine the two received levels according to a certain
diversity combination rule, the cumulative power distribution for the combined case will be
located to the right of the curves for the two branches. The diversity gain relative to the
reference branch, which normally is taken to be the stronger of the two branches, can then be
expressed as
Gdiv =
Pdiv
Pbranch ,
(23)
where Pdiv is the power level after diversity combining, and Pbranch is the power level of the
reference branch. The two power levels must be read at the same cumulative probability level,
which normally is taken to be 0.01, i.e. 1%. If the noise in the system is uncorrelated with the
signal, the diversity gain will also represent the ratio between the signal-to-noise ratios of the
diversity combined case and the strongest branch. Thus, when the power levels are given in
F2
dB along the abscissa axis of the cumulative probability density plot, we can obtain the
diversity gain in dB as the difference in power levels between the cumulative probability
distributions. The two power levels must be read for the same cumulative probability level.
The effective diversity gain can be expressed mathematically as
G effdiv =
Pdiv
⋅ (e radeff
Pbranch
)
branch
Geffdiv =
or
Pdiv
Pideal ;
(24)
(e )
where radeff branch is the radiation efficiency of the reference branch, and Pideal is the received
power level of a single antenna with unit radiation efficiency and located in the same
environment. Pdiv and Pbranch must also here be measured at the same cumulative probability
levels. In a cumulative probability density plot versus power levels in dB, the effective
diversity gain can be seen as the difference along the abscissa axis between the ideal reference
and the diversity curve at some specific probability level. The difference between the diversity
gain and the effective diversity gain is illustrated clearly in Figure 2.
F.3 Measurement procedure in reverberation chamber
The measurements were performed in the 0.8m x 1m x 1.6m chamber shown in Figure 1,
between 868 and 892 MHz. The reverberation chamber is provided with two plate-shaped
mechanical stirrers, platform stirring [3] and polarization stirring [5]. The chamber was during
the measurements loaded with a head phantom filled with tissue equivalent liquid. The two
dipoles are identical. They were located side-by-side with certain spacing. Both dipoles were
located more than 0.7λ away from the head phantom. Thereby, the head phantom will have
negligible effect on the radiation efficiency. The mutual coupling between the two dipoles will
reduce the radiation efficiency, both due to the associated impedance mismatch of the selected
branch, and due to absorption in the termination of the opposite branch (as this must be
connected to a receiver as well). The active branch could probably also be shorted or opencircuited, in which case the absorption would be smaller, but the mismatch of the active
branch would be higher. In order to account for this change in radiation efficiency, we
normalize all measured cases to an ideal reference case. This is one single dipole (branch)
when the other dipole (branch) is located so far away (>0.7λ) that there is negligible effect of
mutual coupling on the radiation efficiency. When we use this reference, the losses in the feed
cable are calibrated away, so that they are not part of the radiation efficiency. Thereby our
results show radiation efficiency and effective diversity gain of two diversity combined
lossless dipoles. The effect of impedance mismatch is included in the measured values of the
calibration case, but is removed from the calibration level (i.e. the reference case) by using the
processing described in [4].
The measurements are performed in the following way. We connect branch 1 to the network
analyzer and terminate branch 2 with a 50Ω load at its input port. We measure the
transmission between each of the three fixed monopoles and the dipole for 25 frequency
points between 868 and 892 MHz, 25 platform positions, 2 mechanical stirrer positions and 3
polarizations (monopoles). We gather the 25 x 25 x 2 x 3 = 3750 power transmission samples
and normalize them to the average power transmission level of the reference case, i.e. to the
net transfer function of the reference case as this is defined in [5]. We repeat exactly the same
measurement procedure for branch 2, with exactly the same stirrer frequency and stirrer
This manuscript has been submitted to
Microwave and Optical Technology Letters, Nov. 2001
F3
positions, and we normalize the samples in the same way as for branch 1. We have then
measured branch 2 in exactly the same environment as dipole 1. In order to find the diversity
gain, we combine the power samples of the two branches by selection combining (SC) and
maximal ratio combining (MRC) [12]. With SC we select for each of the 3750 equal
measurement situations always the branch with the highest power. The new set of power
samples is the set called “selection combining” in Figure 2.
F.4 Results
The results for the case that the dipoles are separated by 15mm, i.e. 0.05λ, are shown in Figure
2. The theoretical Rayleigh distribution with an average power level of unity is also shown.
We see that our reference level follows this very closely. Both these curves cross the 63%
level when the power level is 0dB, which is a characteristic of the Rayleigh distribution. The
cumulative distribution functions of the two branches have the same shape as the reference,
but they are shifted to the left because their radiation efficiency is lower. The curve for SC
shows a diversity gain relative to the single branches, and an effective diversity gain relative to
the ideal reference. These two gains depend on the cumulative probability level, which
therefore must be specified.
The results for 5 different dipole spacings are summarized in Figure 3. We have plotted the
diversity gain and effective diversity gain for SC, and the effective diversity gain for MRC, all
in dB at 1% probability level. We have also plotted the theoretical curve obtained by MRC as
given in [9]. We see that for MRC the theoretical diversity gain and the measured effective
diversity gain follow each other very closely. We also see that the measured SC curve for the
effective diversity gain is located 1.5 to 2 dB below the theoretical MRC curve. This agrees
well with what is known. The diversity gain relative to the strongest branch for SC has a very
different dependence on dipole spacing than the effective diversity gain.
F.5 Conclusion
We have introduced an effective diversity gain, which is an absolute measure of diversity
gain, and we have shown how it easily can be measured in a reverberation chamber. For the
measured diversity antenna (two dipoles located parallel and side-by-side), the effective
diversity gain for maximum ratio combining (MRC) shows the same dependence on dipole
spacing as the theoretical curve. Previously published measured results have not shown such
agreement.
F.6 References
[18] K. Rosengren and P-S. Kildal, “Study of distributions of modes and plane waves in reverberation chamber for characterization of antennas in multipath environment”, Microwave
and Optical Technology Letters, Vol. 30, No 20, pp. 386-391, Sep. 2001.
[19] P-S. Kildal, Foundations of Antennas - A Unified Approach, textbook coming with the
interactive electronic handbook Antenna Design using Mathcad, Studentlitteratur, Sweden, March 2000 (www.studentlitteratur.se\antennas)
[20] K. Rosengren, P-S. Kildal, C. Carlsson, J. Carlsson, “Characterization of antennas for
mobile and wireless terminals in reverberation chambers: Improved accuracy by platform
stirring.”, Microwave and Optical Technology Letters, Vol. 30. No. 20, pp. 391-397, Sep.
2001.
F4
[21] P-S. Kildal, Charlie Carlsson, Jian Yang, “Measurement of free space impedances of
small antennas in reverberation chambers”, to appear in Microwave and Optical Technology Letters, Jan 2002.
[22] P-S. Kildal, C Carlsson, "Detection of a polarization imbalance in reverberation chambers and how to remove it when measuring antenna efficiencies", submitted to Microwave and Optical Technology Letters, Nov 2001.
[23] J.G Kostas and B. Boverie, “Statistical model for a mode-stirred chamber”, IEEE Transactions on Electromagnetic Compability, Vol. 33, No. 4, pp 366-370, Nov. 1991
[24] D. A. Hill, M. T. Ma, A. R. Ondrejka, B. F. Riddle, M. L. Crawford and R. T. Johnk,
“Aperture excitation of electrically large, lossy cavities”, IEEE Transactions on Electromagnetic Compatibility, Vol. 36, No. 3, pp. 169-178, Aug 1994.
[25] D. A. Hill, “Linear dipole response in a reverberation chamber”, IEEE Transactions on
Electromagnetic Compatibility, Vol. 41, No. 4, pp. 365-368, Nov. 1999.
[26] Carl B. Dietrich, Jr., Kai Dietze, J. Randell Nealy, Warren L. Stutzman, “Spatial, polarization, and pattern diversity for wireless handheld terminals”, IEEE Trans. Antennas
Propagat., Vol. 49, No. 9, pp. 1271-1281, Sep. 2001.
[27] Bruce M. Green and Michael A. Jensen, “Diversity performance of dual-antenna handsets
near operator tissue”, IEEE Trans. Antennas and Propagat., Vol. 48,No. 7, pp. 10171024, July 2000.
[28] P. Hallbjorner, K. Madsén, “Terminal antenna diversity characterisation using mode
stirred chamber”, Electronics letters, Vol. 37, No 5, 1st March 2001, pp. 273-274.
[29] A. Turkmani, A. Arowojolu, P. Jefford, and C. Kellett, "An Experimental Evaluation of
the Performance of Two-Branch Space and Polarization Diversity Schemes at 1800
MHz," IEEE Trans. Vehic. Technol., Vol. 44, No. 2, pp. 318-326, May 1995.
[30] International patent application No PCT/SE01/00422, “A method and an apparatus for
measuring the performance of antennas, mobile phones and other wireless terminals”,
filed February 26, 2001, priority March 31, 2000.
This manuscript has been submitted to
Microwave and Optical Technology Letters, Nov. 2001
F5
F.7 Figures
Figure 1. Schematic drawing of the reverberation chambers used in the measurements [13].
The chamber is equipped with two mechanical plate-shaped stirrers. The two dipoles and the
lossy head phantom are located on a rotatable platform and rotated inside the chamber
(platform stirring). The three monopoles are used for polarization stirring.
F6
10
Dipoles separated 15 mm
0
Cumulative pro bability
Ideal re ferenc e
B ranch 1 and 2
se parate
10
-1
T he oretical
R ayleigh
Radiation effic ie ncy
branch 1 and 2
Se le ction co m bining
10
-2
Effective diversity gain at 1 %
D ive rs ity gain at 0.5%
-3
10
-30
-25
-20
-15
-10
-5
0
Relative po wer level (dB )
Figure 2. Cumulative probability density function of two parallel dipoles with 0.05λ spacing,
located in the reverberation chamber in Figure 1, based on 3750 measured power samples for
each branch.
This manuscript has been submitted to
Microwave and Optical Technology Letters, Nov. 2001
F7
12
Diversity Gain (dB)
10
8
6
4
2
0
0
Effective diversity gain (M RC)
Effective diversity gain (S C)
Diversity gain (S C)
Theo ry (M RC)
0.1
0.2
0.3
0.4
0.5
Antenna S pacing in wavelength (λ )
0.6
Figure 3. Diversity gain and effective diversity gain of two parallel dipoles as a function of
dipole spacing. The theoretical curve is by Maximal Ratio Combining (MRC), and the
experimental curved by Selection Combining (SC).
F8
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