A Guide To Antenna Measurements in mmWave
Reverberation Chambers
Citation for published version (APA):
Hubrechsen, A. (2023). A Guide To Antenna Measurements in mmWave Reverberation Chambers. [Phd Thesis
1 (Research TU/e / Graduation TU/e), Electrical Engineering]. Eindhoven University of Technology.
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A Guide To
Antenna Measurements in mmWave
Reverberation Chambers
PROEFSCHRIFT
ter verkrijging van de graad van doctor aan de
Technische Universiteit Eindhoven, op gezag van de
rector magnificus, prof.dr. S.K. Lenaerts, voor een
commissie aangewezen door het College voor
Promoties in het openbaar te verdedigen op
26 oktober 2023
door
Anouk Hubrechsen
geboren te Eindhoven
Dit proefschrift is goedgekeurd door de promotoren en de samenstelling van de
promotiecommissie is als volgt:
voorzitter:
1e promotor:
copromotor:
leden:
adviseur:
prof.dr.ing. A.J.M. Pemen
prof.dr.ir. A. B. Smolders
dr.ing. A. C. F. Reniers
prof.dr.ir. S. M. Heemstra
prof.dr. D. W. van der Weide (University of Wisconsin-Madison)
prof.dr. M. V. Ivashina (Chalmers University of Technology)
dr. K. A. Remley (National Institute of Standards and Technology)
Het onderzoek of ontwerp dat in dit proefschrift wordt beschreven is uitgevoerd in
overeenstemming met de TU/e Gedragscode Wetenschapsbeoefening.
(A Guide To) Antenna Measurements in mmWave Reverberation Chambers
Anouk Hubrechsen
Technische Universiteit Eindhoven, 2023
A catalog record is available from the Eindhoven University of Technology Library
ISBN: 978-90-386-5868-1
NUR: 959
Copyright ©2023 by A. Hubrechsen, all rights reserved
This work was performed in the Electromagnetics group of the Eindhoven University of
Technology.
This thesis was prepared with the LATEX 2ε documentation system
Reproduction: Gildeprint, Enschede, The Netherlands
Cover: Design by Nicole Tencha from The Right Studio
Meaningless is the time
Contents
Summary
xi
List of Abbreviations
xiii
List of Symbols
xiv
1
Introduction
1.1 Ready for Reverberation? . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 The Start of Resonant Research . . . . . . . . . . . . . . . . . . . . . . . . .
1.3 Societal Push toward Complex Devices . . . . . . . . . . . . . . . . . . . .
1.4 An Engineering Pull toward Simplicity . . . . . . . . . . . . . . . . . . . . .
1.5 Outline of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.6 Original Contributions of the Thesis . . . . . . . . . . . . . . . . . . . . . .
1
1
2
4
5
6
7
2
Verification of a mmWave Reverberation Chamber
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Usable Frequency Range . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 Lowest Usable Frequency . . . . . . . . . . . . . . . . . . . . . . .
2.2.2 Working Volume . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.3 Highest Usable Frequency . . . . . . . . . . . . . . . . . . . . . . .
2.3 Setting up the Chamber for Validation . . . . . . . . . . . . . . . . . . . . .
2.3.1 Stirred and Unstirred Energy: Antenna Placement . . . . . . . . . . .
2.3.2 Frequency-Dependent Setups and Settings . . . . . . . . . . . . . . .
2.3.3 Frequency Averaging . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4 Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5 Design of the Mode-Stirring Sequence . . . . . . . . . . . . . . . . . . . . .
2.5.1 Mode-Stirring Mechanisms . . . . . . . . . . . . . . . . . . . . . .
2.5.2 Coherence Angle: Autocorrelation . . . . . . . . . . . . . . . . . . .
2.5.3 Coherence Angle: Pearson Correlation . . . . . . . . . . . . . . . .
9
9
10
11
12
12
13
14
16
20
20
22
23
23
26
vii
VIII
2.5.4 Mode-Stirring Sequence . . . . . . . . . . . . . . . . . . . . . . . .
Chamber-Decay Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.6.1 Chamber-Decay Time Procedure . . . . . . . . . . . . . . . . . . . .
2.6.2 Absorption Cross Section . . . . . . . . . . . . . . . . . . . . . . .
2.6.3 Measurement Results . . . . . . . . . . . . . . . . . . . . . . . . . .
2.6.4 Atmospheric Attenuation . . . . . . . . . . . . . . . . . . . . . . . .
2.6.5 Antenna Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . .
Chamber Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Antenna Efficiency Examples . . . . . . . . . . . . . . . . . . . . . . . . . .
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
27
29
30
31
32
33
36
36
38
39
Systematic-Error Quantification for Estimating Antenna Efficiency
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Antenna-Efficiency Methods . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 Antenna-Replacement Method . . . . . . . . . . . . . . . . . . . . .
3.2.2 Three-Antenna Method . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.3 One- and Two-Antenna Methods . . . . . . . . . . . . . . . . . . . .
3.3 Effect of Noise on the Overestimation of Antenna Efficiency . . . . . . . . .
3.3.1 Noise Variance . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.2 Example: Efficiency for a Reconfigurable Antenna . . . . . . . . . .
3.3.3 Recognizing and Reducing the Effect of Noise in the One- and TwoAntenna Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4 Monostatic Scattering from Mode-Stirring Mechanisms . . . . . . . . . . . .
3.4.1 Mean and Variance of a Mode-Stirring Mechanism . . . . . . . . . .
3.4.2 Dependency on Starting Angle . . . . . . . . . . . . . . . . . . . . .
3.4.3 Optimized Stirrer Design . . . . . . . . . . . . . . . . . . . . . . . .
3.4.4 Correlation in S11,s . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.5 Enhanced Backscattering and Antenna Efficiency . . . . . . . . . . .
3.4.6 Further Optimization Steps and Discussion . . . . . . . . . . . . . .
3.5 Contributions of Unwanted Radiation . . . . . . . . . . . . . . . . . . . . .
3.5.1 Phased Array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5.2 Waveguide Leakage . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5.3 RF Probe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
43
43
44
45
45
46
48
48
49
50
52
52
56
58
60
61
65
68
68
70
74
75
Methods for Over-the-Air Testing of Integrated Devices
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Total Radiated Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.1 TRP Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
79
79
80
80
2.6
2.7
2.8
2.9
3
4
C ONTENTS
C ONTENTS
4.3
4.4
4.5
5
IX
4.2.2 Measurement Setup 100 GHz Example . . . . . . . . . . . . . . . . 81
4.2.3 Measurement results and Uncertainty . . . . . . . . . . . . . . . . . 83
Noise Figure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
4.3.1 Y-Factor Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
4.3.2 Reverberation-Chamber Noise-Figure Method . . . . . . . . . . . . 87
4.3.3 Measurement Setups . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.3.4 Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
4.3.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
Contactless Efficiency Method . . . . . . . . . . . . . . . . . . . . . . . . . 95
4.4.1 Contactless Characterization Method . . . . . . . . . . . . . . . . . 95
4.4.2 Measurement Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
4.4.3 Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
4.4.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
Conclusions and Recommendations
107
List of Publications
119
Bibliography
123
Acknowledgments
143
Curriculum Vitae
145
X
Summary
Reverberation chambers are amongst the most powerful characterization tools for wireless
systems. For power-based metrics of wireless systems that do not have a dependency on the
direction of radiation, a reverberation chamber is faster, more accurate, and cheaper compared
to the more traditionally used anechoic chamber. This advantage becomes even larger for testing millimeter wave devices. So what’s the catch? It’s very simple, a reverberation chamber
is a much less intuitive system than an anechoic chamber. This, among other reasons, is why
it has taken decades for the reverberation chamber to be more widely accepted in the radiofrequency engineering field. To aid in the accessibility of these systems for radio-frequency
engineers, this thesis is written as a practical guide for performing accurate reverberationchamber-based measurements. Important metrology (the art of measuring) concepts, such as
measurement uncertainty, are taken into account in all steps and methods.
The first part of the thesis is dedicated to verifying the functionality of a reverberation
chamber, without having any prior knowledge of its performance. To evaluate the most important performance metrics, the right choices in designing the setup should be made. What
type of antennas do you use? What instrumentation settings and mode-stirring sequence?
What post-processing algorithms? These aspects are extensively discussed with theory, practical examples and uncertainty analyses. The aspect of correlation between mode-stirring
samples is highlighted because of the important role in evaluating the choice of mode-stirring
sequence, which is crucial for the operation of the chamber. Another metric that is highlighted
is chamber-decay time, which is a metric that is very sensitive to changes in loss. It is unconventional to use within the reverberation-chamber community, but it is highly valuable in
isolating and differentiating different loss contributions from, for example, different materials
or atmospheric attenuation.
The second part of the thesis describes methods to evaluate antenna efficiency for passive
and connectorized devices with a vector network analyzer, and the errors that can occur in
doing so. Certain methods are significantly more sensitive than others to errors, and some
of them can be difficult to recognize. Effects that contribute to the measurement that have
a random behavior are almost indistinguishable from the random variable that is created by
mode stirring. This can happen due to noise, but also due to monostatic scattering from the
mode-stirring mechanisms. Lastly, unwanted radiation with its source either before or after
xi
XII
S UMMARY
the calibration plane can create large measurement errors. For example, a leaking waveguide
or a poorly shielded splitting network. For each effect that can create errors, we provide
solutions or workarounds, and methods for recognizing them.
The last part of the thesis focuses on measurement methods for active integrated antenna
systems. These measurements mainly rely on a spectrum analyzer and do not require a connection to the device under test. For transmitting systems, we explain the general approach
for measuring total radiated power with high-frequency examples. For a receiving system,
we introduce a new method to measure noise figure over-the-air, which was always difficult
to measure at millimeter wave frequencies within reasonable uncertainty. We also introduce a
new method to evaluate antenna efficiency when an antenna is integrated into a larger system.
This only scratches the surface of what is possible with reverberation chambers. For many,
it truly is the most powerful measurement tool they’ve never heard of.
List of Abbreviations
5G
ACS
AUT
BSE
BW
CCM
CEM
CTIA
5th Generation of Mobile Telephony
Absorption Cross Section
Antenna Under Test
Base-Station Emulator
Bandwidth
Contactless Characterization Method
Contactless Efficiency Method
Cellular Telecommunications and Internet Association
DUT
Device Under Test
EMC
Electromagnetic Compatibility
ENR
Excess Noise Ratio
EVM
Error-Vector Magnitude
FR2
Frequency Range 2
G/T
Gain to Noise Temperature
GUM
Guide to the Expression of Uncertainty in Measurement
HUF
Highest Usable Frequency
IEC
International Electrotechnical Commission
IEEE
Institute of Electrical and Electronics Engineers
IF
Intermediate Frequency
IFT
Inverse Fourier Transform
ITU
International Telecommunication Union
LNA
Low-Noise Amplifier
LUF
Lowest Usable Frequency
mmWave Millimeterwave
NB-IoT
Narrowband Internet of Things
NF
Noise Figure
NR
New Radio
OEW
Open-Ended Waveguide
OTA
Over The Air
PA
Power Amplifier
xiii
L IST OF A BBREVIATIONS
XIV
PCB
PDP
RBW
RC
RCN
RCS
RF
RFIC
RMS
RSS
SA
SAR
SGH
SNR
SOLR
SOLT
TAM
TRP
TU/e
VBW
VIRC
VNA
WR
WS
Printed-Circuit Board
Power-Delay Profile
Resolution Bandwidth
Reverberation Chamber
Reverberation Chamber Noise Figure
Radar Cross Section
Radio Frequency
Radio Frequency Integrated Circuit
Root-Mean Square
Root Sum of Squares
Spectrum Analyzer
Specific Absorption Rate
Standard-Gain Horn
Signal-to-Noise Ratio
Short Open Load Reciprocal
Short Open Load Thru
Two-Antenna Method
Total Radiated Power
Eindhoven University of Technology
Video Bandwidth
Vibrating Intrinsic Reverberation Chamber
Vector Network Analyzer
Waveguide Rectangular
Wilkinson Splitter
List of Symbols
α
δ
εr
ηaRad
ηaTot
Γ
Γin
1,2,3
Γl1,2,3
ĜRef
λ
µr
ω
σ
σRCS
σGRef
τAtmosphere
τChamber
τEmpty
τLoaded
τRC
B
c
CRC
D
e
eb
f
FDUT
Number of samples with a positive real part
Material skin depth
Relative Permittivity
Radiation efficiency of an antenna a
Total efficiency of an antenna a
Reflection coefficient
Measured reflection coefficients of the connectorized antenna for three load conditions in the CCM
Reflection coefficients of the three loads connected to the non-connectorized
antenna in the CCM
Chamber transfer function average over all antenna positions
Wavelength
Relative permeability
Angular frequency
Standard deviation
Radar-cross section
Standard deviation in chamber transfer function
Rate of decay due to atmospheric attenuation
Chamber-decay time without atmospheric loss
Chamber-decay time measured n an unloaded chamber
Chamber-decay time measured in a loaded chamber
Chamber-decay time
Noise bandwidth
Speed of light in a vacuum
Chamber constant
Slope of the PDP
Euler’s number
Enhanced backscattering constant
Frequency
Noise factor of a DUT
xv
XVI
FSA
FTot
G
GAnt
GCable
GDUT
GMeas
GRef,p
GRef
i
j
kB
L
LAtmosphere
LCables
LMism,Cable
LMism,WS
LPCB,WS
N
n
Nhot/cold
O
P
p
PAccepted
PAvailable
Phot/cold
Pm,hot/cold
PRadiated
PR
Pr
Q
QFD
QTD
QThrp
Qw
R
Sw
Si j,noise
Si j,paddles
L IST OF A BBREVIATIONS
Noise factor of a spectrum analyzer
Noise factor of a total system
Gain
Antenna gain
Gain of cables
Gain of DUT
Gain of the measurement system in a noise-figure measurement
Chamber transfer function for an antenna position p
Chamber transfer function
VNA port
VNA port
Boltzman Constant
Loss
Atmospheric attenuation
Losses in cables
Loss contribution from cable mismatch
Loss contribution from Wilkinson-Splitter mismatch
Losses in PCB from a Wilkinson Splitter
Number of mode-stirring samples
Mode-stirring sample
Hot and cold noise-power levels at the output of the DUT
Location of source
Number of antenna positions
Antenna position
Power accepted by the antenna port
Power available at the antenna port
Hot and cold noise-power levels inside the chamber
Measured output power at spectrum analyzer for hot and cold noise-power levels
inside the chamber
Power radiated by an antenna
Received power
Probability
Quality factor
Quality factor (frequency domain)
Quality factor (time domain)
Quality factor threshold extracted using a probability distribution
Quality factor contribution of the chamber walls
Correlation
Total wall surface area
Zero-mean contribution by noise to the stirred-energy component of Si j .
Zero-mean contribution by a mode-stirring mechanism to the stirred-energy
L IST OF A BBREVIATIONS
Si j,s
Si j
TDUT
TMeas
TPh
hot/cold
TSource
u
uA
uB
uc
ue
V
v
w
Y
Z
r
XVII
component of Si j
Stirred-energy component of Si j
S-parameter measured between VNA ports i and j
Noise temperature of the DUT
Noise temperature of the measurement system in an noise-figure measurement
Physical temperature
Hot and cold noise temperatures of the noise source
Uncertainty
Type A uncertainty
Type B uncertainty
Combined uncertainty
Expanded uncertainty
Chamber Volume
Number of scatterers
Lag shift in autocorrelation
Ratio between hot and cold noise-power levels at the output of the DUT
Number of loss mechanisms in the chamber
Distance between mode-stirring mechanism and antenna phase center
XVIII
Chapter one
Introduction
1.1 Ready for Reverberation?
This thesis is about a metal box called a reverberation chamber. A very special metal box
with capabilities that are of incredible value to the wireless testing community. Its complex
behavior and hidden features have been the subject of research for decades, with dedicated
scientists spending a lifetime investigating all the intricacies and unexpected effects. The
enigmatic ways of the reverberation chamber attract many, like a never-ending puzzle whose
missing pieces are always just out of reach, but the pursuit to solve it is fascinating.
Reverberation chambers were not always metal boxes. In fact, it all started by confining
sound instead of electromagnetic waves by using highly-reflective walls made from wood,
concrete, or hard plaster. The goal of these chambers was to diffuse any sound field as fast as
possible and by having a sound persist long after its first excitation. It’s this effect that gave
the reverberation chamber its name. The word reverberation is taken from the Latin word
reverberare meaning ‘to strike back’, which is a fitting description for a space that can keep
sound bouncing for several kilometers.
An acoustic reverberation chamber is an indispensable tool for testing noise and sound
levels [191]. One of the main applications is to measure the sound absorption of materials
commonly found in homes, public buildings, or cars. By following standardized test requirements, these materials can be tested and optimized to create a pleasant acoustic environment.
Concert halls and recording studios also rely on these techniques, where a certain level of
reverberation can enhance the listener experience by adding an extra musical dimension.
As the name suggests, electromagnetic reverberation chambers share many similarities
with acoustic ones. But how do they actually work? Both types of chambers are typically
much larger than the wavelength being studied, and they contain stationary or moving diffusers to create a field environment that is independent of direction and position. When
placing a microphone, antenna, or material in the chamber, it is as if waves arrive from all
directions at the same time with equal strength and intensity. Analogous to receiving, the
1
2
I NTRODUCTION
DUT
DUT
(a)
(b)
Figure 1.1: Illustration of the equivalent effect of an ideal reverberation chamber for (a) a
receiving and (b) transmitting device-under-test (DUT).
reverberation chamber acts as an integrating sphere for transmitters to test radiated output
power of devices. This is illustrated in Fig. 1.1. The isotropic and field-uniform environment
provided by an electromagnetic reverberation chamber makes it practical for testing wireless
metrics related to overall received, absorbed, scattered, or transmitted power.
1.2 The Start of Resonant Research
While the concept of acoustic reverberation chambers had been around since the 1920s [46,
191], it wasn’t until the late 1960s that researchers proposed its electromagnetic counterpart [222]. There is a significant distinction between the two in the way fields are diffused.
Acoustic reverberation chambers can achieve sufficient diffusion using only static diffusers,
whereas electromagnetic reverberation chambers often require the use of moving diffusers
[222]. Although static diffusers can be employed in electromagnetic reverberation chambers,
they tend to introduce higher uncertainty in the measurement [148]. This is because static diffusers alone are unable to effectively reduce the high maxima and minima caused by standing
waves, or modes, within the chamber.1 As a result, a different approach is necessary. This is
where mode stirring or tuning comes into play. 2 .
1 There have been works that used a combination of static and moving diffusers by, for example, placing
circular domes on the chamber walls [9, 133, 194, 195]. These can also be beneficial for antenna placement for
reducing unstirred energy (see Chapter 3) [128][P28].
2 In the past, the practice of mode-stirring involved the continuous movement of a mode-stirring mechanism
while taking measurements, whereas mode-tuning entailed stepping the mechanism over discrete positions and
collecting measurements for each of them [50] Today, the term mode-stirring is often used to describe both
1.2: T HE S TART OF R ESONANT R ESEARCH
3
The approach to mode stirring is wonderfully simple. By introducing an electrically-large
metallic structure into the chamber, referred to as a mode-stirring mechanism, the distribution
of modes within the chamber is effectively altered per position. This mechanism holds the
secret to its operation. When the mode-stirring mechanism is moved far enough, the mode
distribution of the chamber undergoes significant changes. For instance, a physical location
that initially experienced a field minimum due to destructive interference can be transformed
into experiencing a field maximum through constructive interference after the mode-stirring
mechanism is repositioned. In a typical measurement procedure, numerous (typically over
100 [57]) measurements are taken, with each measurement corresponding to a distinct position of the mode-stirring mechanism, a so-called mode-stirring state. While the mode-stirring
process is inherently deterministic, the collective behavior of all mode-stirring states mimics
a stochastic process. This allows for the use of statistical approaches, forming the foundation
of most reverberation-chamber measurement techniques.3
The main reason that reverberation chambers were designed was to solve measurement
issues in the field of electromagnetic compatibility (Electromagnetic Compatibility (EMC)).
It was common practice to use shielded enclosures at the time, however, an important issue
of using such enclosures was mentioned by the designer of the first electromagnetic reverberation chamber: “Repeatability errors of 25 dB are not uncommon, and relating the data
to open-field values is practically impossible” [151]. The mode-stirring approach solved this
issue and would soon after that become a field of research of its own, with many others developing their own reverberation chambers in the next decade [20, 49, 51, 53, 64, 152, 159,
187]. Reverberation chambers have proven their value in EMC applications to this day, because they can generate a high field strength inside the chamber with limited input power,
making them an ideal choice for testing radiated immunity and other similar applications.
One notable distinction between EMC and antenna testing is that EMC testing allows for a
higher level of uncertainty, primarily due to its focus on lower frequencies [102].
With the wireless revolution happening in the 1980s, reverberation chambers gained popularity in wireless testing for measuring antennas and integrated devices for both continuouswave and modulated-signal measurements. Research groups worldwide have made significant advancements in testing metrics such as total isotropic sensitivity, diversity gain, and
total radiated power, while continuously improving measurement methods to meet the evolving needs of the market [8, 12, 34, 53, 54, 67, 86, 92, 97, 119, 130, 132, 167, 176, 202,
225]. To comprehend why the reverberation chamber can play a large role in next-generation
applications, it is necessary to understand what the challenges of these applications and their
role in society will be.
approaches while referring to the difference between them as stepped and continuous mode stirring. We use this
terminology throughout the thesis.
3 It is a common assumption that the reverberation-chamber results can be modeled as a stochastic process.
Whether this assumption is correct should be taken into account in all measurements. There are many cases
where these models do not yield a correct measurement result, as we will show in Chapter 3.
4
I NTRODUCTION
1.3 Societal Push toward Complex Devices
In an attempt to enhance the well-being of our society, technology continues to evolve to offer
assistance in our lives, whether it’s about extending our capabilities or taking over certain
tasks. The ability to communicate wirelessly has shaped our world, impacting individuals,
societies, geopolitics, and even extending to outer space. Wireless communications have
brought us closer and farther apart simultaneously, but one thing is for sure: (r)evolution is
unstoppable. At the time of writing, the first millimeter-wave networks of 5th Generation
of Mobile Telephony (5G) are being rolled out, while publications are already speaking of
6G-and-beyond with applications far beyond human comprehension such as digital twinning,
quantum computing, and artificial intelligence [4].
The rapid and exponential growth of these technologies creates an insatiable demand for
data, which has been driving the transition to higher frequencies for several decades. This
shift is necessary due to a constant scarcity of available bandwidth at lower frequencies. The
definition of ‘lower frequencies’ is relative to the time we live in. This also relates to Edholm’s
law, which states that the required bandwidth and data rate doubles every 18 months [43].
To keep up with this trend, existing semiconductor technologies are continuously pushed to
their limits while promising new technologies keep emerging [63, 120, 121, 172]. The main
limiting factor in this progress is manufacturing capabilities.
High-frequency applications have the imminent aspect of having a small form factor due
to their small wavelength. This allows but also necessitates us to design highly-integrated
systems, where, for example, the antenna and amplifiers are integrated on a chip [1, 41, 112,
116]. A benefit is that high-frequency modules take up less real estate in devices such as
virtual-reality glasses or cell phones [36]. However, it also presents challenges because the
manufacturing process and materials exhibit unpredictable behavior. Factors such as aging of
packaging and substrate materials can cause changes in their loss tangent and relative permittivity, significantly impacting antenna performance over time [124]. Furthermore, materials
tend to have higher losses at high frequencies, up to a point where it becomes a challenge to
have the wave radiate out of the substrate at all [113]. This makes efficiency and total radiated
power both crucial performance metrics [121].
The use of phased-array topologies in these devices, which is necessary to overcome the
high free-space path loss, adds another layer of complexity as they typically consist of multiple antennas with connected amplifiers and other high-frequency circuitry. Each element
and corresponding circuitry in the array behaves differently and can impact the overall system performance, with a large factor being mutual coupling. Engineers spend their time
predicting and overcoming these effects, among others, by using modeling software before
manufacturing their devices. Modeling techniques are becoming ever more accurate, but the
inconvenient truth of high-frequency wireless-system design is that the actual performance
shown by measurements (in other words, the validation of the model) often does not match
the simulation [121, 182].
1.4: A N E NGINEERING P ULL TOWARD S IMPLICITY
5
1.4 An Engineering Pull toward Simplicity
Possibly one of the greatest paradoxes in the field of high-frequency hardware is that we
possess a considerable amount of knowledge about designing highly complex systems, but
have, in comparison, a limited understanding of measuring them. Validating one’s model
with measurements is a step that is regularly underestimated in terms of time and complexity
by both academics and engineers [182]. For low-frequency conducted measurements, there is
ample instrumentation available to perform accurate measurements without needing to have
extensive knowledge about the measurement system. A reason that it is so easy is because
of the standardized 50-Ohm environment. With the antenna integrated with the circuitry, the
connector becomes the air. This makes measurements much more complex, while engineers
long for the simplicity of conducted measurements.
Traditionally, antenna measurements were often associated with anechoic chambers [182].
While anechoic chambers are effective in measuring the direction of radiation, they come with
certain limitations. These chambers can be challenging to operate due to their sensitivity to
antenna positioning, which becomes increasingly difficult for high frequencies [29, 156, 234].
Additionally, direct far-field anechoic chambers are typically large in size, and sampling a full
sphere can be time-consuming. To measure a metric such as total radiated power, sampling
a full sphere and subsequent post-processing are required, making the process unnecessarily
complicated. In contrast, a reverberation chamber can achieve similar results in a fraction of
the time and is often as straightforward to operate as a conducted measurement when designed
appropriately [54, 59, 176, 201]. Especially for high-frequency measurements or for antennas
with a low directivity, the accuracy of an anechoic chamber degrades, while a reverberation
chamber can maintain its accuracy [P1],[19, 42, 66].
This begs the question of why their usage is not common in the antenna-measurement
community. As quoted by one of its researchers [54]: “Reverberation chambers can provide
a testing scenario where a large number of plane waves propagate along ideally all possible
directions. The well-known price to pay for this simplification is the loss of intuitive understanding of the undergoing physical phenomena leading to the test results, and the important
issue of having hardly repeatable testing conditions. We acknowledge the fact that the average testing conditions are repeatable, but the exact configuration is actually not.4 ” In other
words, a line-of-sight situation using a single plane wave is much easier to understand than a
superposition of many.
Currently, a revolution is underway in the world of measurement instrumentation, driven
by an imperative need for ease of use. Breaking the fourth wall of thesis: I am convinced that
the measurement process for over-the-air testing can be greatly simplified by leveraging the
potential of reverberation chambers, but that progress is held back by a lack of comprehen4 Theoretically, the exact configuration is repeatable because a reverberation chamber is deterministic, but
since a small change in the chamber can significantly alter the mode distribution, it is difficult to obtain a
repeatable testing scenario for a single mode-stirring state.
6
I NTRODUCTION
sive understanding regarding their operation. In order to support the wireless community in
utilizing reverberation chambers effectively, this thesis serves as a comprehensive guide for
performing millimeter-wave measurements in a reverberation chamber.
1.5 Outline of the Thesis
This thesis focuses on measuring metrics that are related to measuring power-based metrics
related to overall received, transmitted, scattered, or absorbed power, for devices and antennas
that transmit or receive unmodulated signals.
Before starting a measurement in a reverberation chamber, it needs to be validated. Chapter 2 describes how to perform such a validation for a millimeter-wave reverberation chamber
designed at Eindhoven University of Technology. It addresses the design and validation of a
mode-stirring sequence using correlation. The chapter focuses on evaluating loss effects in
the chamber using chamber-decay time, which is a metric that is very sensitive to changes. It
can also be used to evaluate individual loss contributions. We use it to show that atmospheric
loss has a significant contribution to chamber loss for certain frequencies. We introduce the
concept of measurement uncertainty and use it to evaluate the measurement uncertainty of
several measurements shown in this thesis. We show that the chamber can be used to measure
antenna efficiency between 24 and 140 GHz.
In Chapter 3, we describe that certain antenna efficiency measurements are sensitive to
measurement errors. Specifically, the one- and two-antenna methods. We show that physical
effects that exhibit a behavior that is random in magnitude and phase, such as noise or monostatic scattering from a mode-stirring mechanism, can lead to large errors in antenna-efficiency
measurement. Other errors can be created by sources of unwanted radiation from behind or in
front of the calibration plane. We provide several approaches to identifying and overcoming
these issues. The measurements in this chapter are focused on measuring passive antenna
systems using a vector network analyzer.
Reverberation chambers can be used to measure metrics for integrated devices, which
is the focus of Chapter 4. We start by showing an example of a total-radiated power measurement using a spectrum analyzer. After, we use those same concepts to measure the noise
figure and gain of receiving metrics in an over-the-air method, by introducing a new simplified
method that only requires a spectrum analyzer. Lastly, we introduce the contactless-efficiency
method, which can measure the antenna efficiency in a contactless way of an antenna where
the load can be varied, such as in systems with a switch to switch between a receiving and
transmitting mode.
It should be noted that a very large field of research in reverberation-chamber research
is related to the measurement of modulated signals, because of its characteristics to mimic a
Rayleigh-fading environment. This generally requires the chamber to be loaded with Radio
Frequency (RF) absorber, which requires different measurement approaches. For the sake of
brevity, this is not included in this thesis, but we refer the reader to the following publications
1.6: O RIGINAL C ONTRIBUTIONS OF THE T HESIS
7
for a more extensive description [119, 176]. (to be added)
1.6 Original Contributions of the Thesis
This thesis has the following original contributions:
• A reverberation-chamber validation is carried out in the 20-140 GHz frequency range,
see Chapter 2.
• Antenna-efficiency and total-radiated-power measurements are carried out up to
140 GHz, with uncertainty analysis, see Chapter 2 and 4.
• It is shown that atmospheric loss has a measurable effect on reverberation-chamber
measurements by using absorption-cross-section concepts and by writing atmospheric
attenuation in terms of chamber-decay time, see Chapter 2.
• It is shown that the Pearson correlation approach is more reliable to evaluate the physical effects of a mode-stirring sequence as compared to the more commonly-used autocorrelation approach. see Chapter 2 and 3.
• It is shown that noise can lead to an overestimation of stirred-energy components because its behavior as a complex random variable becomes indistinguishable from the
complex random variable describing the reverberation chamber, see Chapter 3.
• The aforementioned effect is most prominent in the stirred component of the measured
reflection coefficient, and therefore, affects the one-antenna method more than the twoantenna method, while the three-antenna method is less easily affected, see Chapter
3.
• It is shown that the measured variance of monostatic scattering from a mode-stirring
mechanism leads to an overestimation of the stirred-energy components of the reflection
coefficients, while hardly affecting transmission coefficients, see Chapter 3.
• It is shown that radar-cross-section models can be used to identify and optimize modestirring mechanisms, see Chapter 3.
• The starting position of the mode-stirring mechanism impacts the measured variance.
The impact is largest when the mode-stirring sequence contains angles where the antenna directly illuminates the chamber corner, see Chapter 3.
• Two optimized mode-stirring mechanisms are introduced to reduce the impact of monostatic scattering, see Chapter 3.
8
I NTRODUCTION
• We show that the quality of an antenna-efficiency measurement should be evaluated
by not only evaluating correlation for transmission coefficients but also for the stirredenergy components of the reflection coefficients, see Chapter 3.
• The enhanced-backscattering constant can be used to identify errors in the measurement
that stem from errors due to random effects such as noise or monostatic scattering from
the mode-stirring mechanism, see Chapter 3.
• Errors due to monostatic scattering from the mode-stirring mechanism manifest themselves in the early-time behavior. It is shown that the correlation drops significantly
when the early-time behavior is cut out, see Chapter 3.
• We show that the lowest correlation occurs for an antenna position where it is not
pointed at the stirrer, see Chapter 3.
• For sufficient samples, Pearson correlation coefficients above 0.01 can already be linked
to physical effects and measurement errors, see Chapter 3.
• It is shown that unwanted radiation from a power splitter can lead to an overestimation
of efficiency when it is treated as thermal loss, see Chapter 3.
• Unwanted radiation behind the calibration plane can lead to a measurement error that
is approximately twice as large as the magnitude of the leaked energy. This is shown
for a case with leaking waveguides, see Chapter 3.
• An RF probe station can be placed inside a reverberation chamber to measure the efficiency of probed antennas. It is shown that a calibration substrate can start radiating
when an RF probe is landed on it, see Chapter 3.
• We show that the methods for measuring total radiated power in a reverberation chamber are scalable up to at least 100 GHz, see Chapter 4.
• A reverberation chamber can be used to generate uniform high or low noise-power
levels inside, which can be used to perform an over-the-air Y-factor method to extract
noise figure and gain, see Chapter 4.
• A simplified measurement to measure noise figure in a reverberation chamber is introduced, which reduces uncertainty, see Chapter 4.
• The contactless characterization method can be used to extract S-parameters, even when
the environment is highly chaotic, see Chapter 4.
• Stirred-energy components and antenna efficiency can be measured in a contactless
manner, by applying the contactless characterization method to each mode-stirring position, see Chapter 4.
Chapter two
Verification of a mmWave
Reverberation Chamber
2.1 Introduction
Reverberation chambers might seem simple in principle, but their complexity lies in the finetuning of settings. Choosing the right settings is crucial for ensuring accurate results, while
small misconfigurations can lead to nonsensical results. Standardized test methods can help
optimize the settings and performance of a chamber. However, for chambers operating in the
Millimeterwave (mmWave) range, currently no set of user guidelines is available that dictates
the settings. In this chapter, we introduce the most important concepts for such guidelines
by validating a novel mmWave reverberation chamber, and by describing all necessary steps.
The chamber to be validated is designed at Eindhoven University of Technology (TU/e), with
the goal of performing antenna measurements in the 20-140 GHz range (see Fig. 2.1) [P20,
P21]. This is the first reported chamber to do so for such a wide range of frequencies, but it
is not the first mmWave Reverberation Chamber (RC) [67, 198, 218].
There are three steps to characterizing a reverberation chamber:
1. Estimate the expected frequency of operation from the chamber geometry.
2. Design the setups for validation, including the mode-stirring sequence.
3. Measure the most important chamber metrics and test the performance with reference
antennas.
The outline of this chapter is also organized as such. Step 1 is described in Section 2.2.
Step 2 is described in Section 2.3, where we also describe the process of estimating measurement uncertainty in Section 2.4, for a frequency range of 24-140 GHz. In Section 2.5,
This chapter is based on P2,P3,P7,P8,P13,P15-18,P20,P28 and P29
9
10
V ERIFICATION OF A MM WAVE R EVERBERATION C HAMBER
Figure 2.1: The mmWave RC including an antenna setup used for 24-40 GHz.
we demonstrate how a mode-stirring sequence should be correctly designed. Step 3 contains
measuring the most important chamber-performance metrics such as chamber-decay time, described in Section 2.6. We use this metric to show the effects of atmospheric attenuation and
to estimate antenna efficiency in Section 2.8. We evaluate overall chamber loss in Section 2.7
and the work is concluded in Section 2.9.
2.2 Usable Frequency Range
When presented with a reverberation chamber, its geometry can provide users with some
of the most important information on its operational frequency before having taken a single
measurement. A well-operating chamber supports many (to be quantified) modes. Intuitively,
fewer modes occur at frequencies where the wavelength is large in comparison to the chamber
dimensions [25]. Below the cut-off frequency of the cavity, not a single mode fits in the
chamber. A threshold can be defined where enough modes fit inside the chamber to perform
an accurate measurement (‘accurate’ is subjective to the application). This threshold is often
referred to as the Lowest Usable Frequency (LUF), and can be estimated from the chamber
size. A similar threshold exists for the Highest Usable Frequency (HUF), which, just like
the LUF, highly depends on the materials used, chamber size, and RF shielding. For most
lower-frequency chambers, the HUF is defined at the frequency where the chamber shielding
is no longer effective. This can be, for example, due to honeycomb filters used to provide
2.2: U SABLE F REQUENCY R ANGE
11
the chamber with ventilation. These are often specified up to 18 or 40 GHz, which is why
manufacturers often specify their chamber HUF at these values [184].
2.2.1 Lowest Usable Frequency
The dimensions of the reverberation chamber to be validated are 0.5 x 0.6 x 0.8 m3 , from
which we can predict the LUF. According to the International Electrotechnical Commission
(IEC) standard, a rule-of-thumb for the LUF of the chamber is that it occurs at ‘a frequency
slightly above three times the first chamber resonance’ [102]. This approach is suitable for
Electromagnetic Compatibility (EMC) purposes but this rule is less suitable for antennameasurement purposes because it is defined for an allowed uncertainty due to a lack of spatial
uniformity of 3 dB (1 σ ). It should be noted that this is specified for the variation of the
maximum field strength, while the average of the measured power is used for antenna measurements. Nonetheless, uncertainties above 2 dB (≈ 2σ ) are unacceptably high for wireless
device measurements [57],[P7,P9], but even that level of uncertainty would be high for an
antenna-efficiency measurement. Therefore, a larger size margin is recommended when using basic mode stirring. We do not provide a specific threshold here because there are many
approaches to overcome having fewer modes.1 We merely provide this explanation to obtain
a rough approximation of the operational frequency of the chamber. The precise range can
only be estimated with measurements, and even then, the term ‘accurate measurement’ is
highly subjective to the application.
The LUF of the chamber to be validated should be lower than 24.25 GHz, because it
should support the lowest 5G New Radio (NR) Frequency Range 2 (FR2) band (24.25 GHz).
In this case, the frequency is over 40 times higher than the first resonance, which is significantly higher than the IEC rule-of-thumb. Another rule-of-thumb is based on the mode
distribution [56], which requires at least 60-100 modes with a modal density of at least
1.5 modes/MHz at the LUF [102, 233]. In the chamber to be validated, approximately
1.03 × 106 modes are present at 24 GHz, with a modal density of 128 modes/MHz. This
is also significantly higher, so it is expected that the chamber can be used within the specified
frequency range, given a good mode-stirring sequence.
Some works mention that the width, length, and height of the chamber should be chosen
to avoid an equal ratio to optimize spatial uniformity [67]. The chamber to be validated abides
by that rule for most frequencies, but it should be noted that this requirement becomes less
relevant when a large number of modes fits inside the chamber.
1 We will detail this in the next sections, but when mechanical mode-stirring only does not alter the mode
distribution sufficiently, the fields can be sampled at a different location by moving the antenna, or frequency
stirring can be used.
12
V ERIFICATION OF A MM WAVE R EVERBERATION C HAMBER
2.2.2 Working Volume
The working volume of the chamber is the volume in which a Device Under Test (DUT)
can be placed while still meeting operational requirements, which can be derived from the
chamber size. A rule-of-thumb is that the working volume starts at λ /2 from the walls [57,
91, 146], and that the DUT size should not be larger than 8 % of the chamber volume [57]. In
the chamber to be validated, that allows for DUTs with dimensions less than approximately
25 cm (approximately 20 wavelengths for 24.25 GHz). Note that the material of the DUT
(such as large cooling blocks) can load the chamber and reduce the chamber uniformity, see
[176].
2.2.3 Highest Usable Frequency
Because of a traditional focus of the EMC community on lower frequencies, little prior work
has focused on the HUF of a chamber. In general, it is expected that chambers can remain
operational until chamber loss, including leakage, becomes too significant. In this case, the
variation between paddle positions becomes smaller and mode-stirring less effective, leading
to a higher uncertainty [161].
A theoretical approach to evaluate a threshold for the HUF is presented in [98], where the
chamber quality (Q) factor needs to significantly surpass a threshold given by
Qthrp =
4
π
3
2/3
3V 1/3
,
2λ
(2.1)
where V is the chamber volume and λ the wavelength. The subscript in Qthrp denotes that the
threshold is based on a probability distribution.2
The theoretical chamber Q-factor is given by
Qw =
3V
,
2Sw δ µr
(2.2)
where Sw is the total wall surface area, δ is the wall material skin depth, and µr is the relative permeability of the wall. In the chamber to be validated, the walls are made out of
aluminum with a chromated surface finish to avoid oxidation. For the lowest intended operating frequency of 24 GHz, Qw = 3 × 105 , which is significantly higher than the threshold
Qthrp = 160.1. For the highest intended operating frequency of 140 GHz, Qw = 6.9 × 105 and
Qthrp = 993.7. While this threshold is satisfied, the measured Q can still be significantly lower
due to leakage and the additional material losses from, for example, the stirring mechanisms
and the DUT , which is not taken into account in this threshold estimation. It should again
2 This equation occurs in literature without the factor 3 in the numator, but this threshold is based on a more
stringent condition of a probability distribution [98]. This threshold denotes the Q-factor where stirred energy
surpasses the unstirred energy when using isotropic antennas.
13
2.3: S ETTING UP THE C HAMBER FOR VALIDATION
Mode-stirring
mechanisms
Motor with
shielding
To motor
controller
Fixed
connection
Reference position stirrer
Sensor
Door
Shielding
layer
Shielded
feedthrough
Separate bottom
plate with
shielding layer
Flexible
connection
with stirrer
Figure 2.2: Illustration of the reverberation chamber shown in Fig. 2.1, including inset
figures on the configuration of the motors.
be stressed that these equations have many assumptions and leave out many effects that happen in practice. Therefore, they merely provide a rough estimation of the highest operational
frequency.
To avoid leakage, several measures are taken in the chamber to be validated. For example, two shielding layers are present near the door (see Fig. 2.1), and connections between
different plates are welded, tightly screwed together, or conductive foam is placed in between
connections3 . All parts of the chamber are named in Fig. 2.2. The motor connection to
move the mode-stirring mechanism is shielded by metallic bearings within the motor, which
is a similar approach to shielding stirrers commonly used in lower-frequency reverberation
chambers [176]. A part of this chamber that could potentially be sensitive to leakage is the
connection near the bottom plate. It is not welded to the other parts of the chamber but was
screwed on with a band made from conductive foam, with screws placed 1 cm apart from
each other.
2.3 Setting up the Chamber for Validation
We have shown an approximation of the usable frequency range of the chamber, from which
we can expect theoretical operation in at least the 24-140 GHz band. However, there are
many more aspects that need to be taken into account when setting up the chamber before
performing a measurement. For example, antenna placement is crucial to obtain a usable
measurement, but also the instrumentation settings used, calibration, etc.
3 In this work, we did not measure the shielding effectiveness of the chamber.
14
V ERIFICATION OF A MM WAVE R EVERBERATION C HAMBER
S21
S11
S11,s
Ant. 1
Calibration
plane
S21,s
Ant. 2
2
1 VNA
Figure 2.3: Illustration of the origins of unstirred- (⟨Si j ⟩) and stirred-energy contributions
(Si j,s ).
2.3.1 Stirred and Unstirred Energy: Antenna Placement
To produce an optimal reverberation-chamber measurement, the ratio between stirred and
unstirred energy should be sufficiently high [135]. When this is the case, it is likely that the
measurement behaves as a stochastic process - a crucial condition in almost every equation
used for post-processing RC measurements.4 It is expected that the field distribution changes
significantly when moving a mode-stirring mechanism, such that no two mode-stirring samples are alike, but in practice, this is not always the case. Therefore, each RC measurement
consists of a stirred- and unstirred-energy component.
The unstirred-energy component is composed of contributions to the field that do not
change for different stirrer positions. The stirred-energy component is composed of contributions from paths that have interacted with one or more mode-stirring mechanisms in such a
way that they are different for each stirrer position (zero-mean contributions). An illustration
of stirred and unstirred energy is shown in Fig. 2.3. Contributions to the unstirred-energy
components can come from the direct coupling between the antennas in an S21 measurement
or the reflection coefficient of the antenna in an S11 measurement, or a bounce of a wall that
does not interact with the paddle (as shown by the orange path in Fig. 2.3). The unstirredenergy component is generally described by the mean of the measured S-parameter and is
illustrated as such in Fig. 2.3. It shows that ⟨S11 ⟩ is comprised of the antenna reflection coefficient and direct reflections from the walls. The stirred-energy component is generally
described by the variance of an S-parameter, where the unstirred energy is subtracted as
⟨|Si j,s |2 ⟩ = ⟨|Si j − ⟨Si j ⟩|2 ⟩,
(2.3)
4 In Chapter 3, we show how fast these commonly-used models break down when an incorrect setup is used.
15
2.3: S ETTING UP THE C HAMBER FOR VALIDATION
Unstirred-energy
component
Measurement with
unstirred energy
(nonzero mean)
Stirred-energy
component
Measurement
without unstirred
energy (zero mean)
Figure 2.4: Illustration of an RC measurement for a single frequency, where each point corresponds to an S21 measurement for a single mode-stirring state. The blue and orange scatter
plots illustrate the same measurement, where one is affected by unstirred energy adding a
non-zero-mean contribution.
where i and j correspond to the Vector Network Analyzer (VNA) ports, and where i can be
equal to j.
The stirred-energy component, or variance, of the measured S-parameter, consists of contributions from the different stepped-paddle positions, which can be modeled as a random
variable. The paddle contributions are not truly random because the variation in the RC channel is deterministic and repeatable from one measurement to the next. However, for a wellstirred chamber, the variation of samples taken over paddle positions is modeled as random
since it has a complex Gaussian distribution (Rayleigh in magnitude) [92]. Unstirred energy
can introduce errors and increase the uncertainty in the measurement and should therefore be
minimized. An example of an RC measurement with and without unstirred energy is illustrated in Fig. 2.4. Each point corresponds to the measured S21 for a single mode-stirring state,
for a single frequency. Here, we show a combination of 100 mode-stirring states. The blue
scatter plot corresponds to a measurement with no unstirred energy (zero mean). Unstirred
energy creates an offset, which is illustrated in the orange scatter plot (nonzero mean). In an
S11 measurement, unstirred energy is unavoidable because it contains the antenna mismatch.
Most measurement methods do not use S11 , but the ones that do subtract the unstirred energy,
as we will show in Chapter 3.
The ratio between stirred and unstirred energy is often described by the chamber K-factor
and is highly dependent on the antenna placement [128]. This is also illustrated in Fig. 2.3.
In most RC, large errors can occur when the antennas are placed by an untrained user, as we
will show in Chapter 3 [P3]. Several aspects need to be taken into account when placing the
antenna inside the chamber, which are all related to reducing unstirred energy.
16
V ERIFICATION OF A MM WAVE R EVERBERATION C HAMBER
• The antenna needs to be placed in such a way that its performance is not changed
due to the presence of the chamber; This can happen when the antenna is placed too
close to objects, such that its impedance mismatch is changed. A similar result can
occur when a direct or multipath component returns to the antenna. In an antenna with
integrated electronics, this can lead to loading of, for example, the power amplifiers,
which alters its performance and leads to an unrealistic measurement. In general, the
unstirred-energy component of an S11 measurement should only consist of the antenna
mismatch.
• The direct or indirect mutual coupling between the two (or more) antennas in the chamber needs to be as low as possible; This is generally achieved by pointing the antennas
away from each other, with a different polarization.5
• The antennas need to be placed in such a way that the majority of the fields interact with
one or more mode-stirring mechanisms. The Institute of Electrical and Electronics Engineers (IEEE) Recommended Practice for Antenna Measurements [103] recommends
pointing them at the mode-stirring mechanism, but care should be taken when doing
so.6
At mmWave frequencies, devices generally have high directivity, which makes the measurement susceptible to a high K-factor when not placed carefully. A high K-factor also
translates to a high level of correlation, which will be used in later sections to evaluate the
chamber performance. There have been works where deliberately a high K-factor was created to test different (Rician distributed) channel behaviors [99], but for the measurements
performed in this work, we tried to reduce the K-factor as much as possible.
2.3.2 Frequency-Dependent Setups and Settings
In this section, we describe the setups used to validate the chamber. The setups are designed
to have as much flexibility in antenna positioning to optimize antenna placement, and the
instrumentation settings are chosen to achieve optimal results. The setup settings for each
frequency band are shown in Table 2.1. The setups are shown in Fig. 2.1 and Fig. 2.5. For
all setups, the same VNA is used with an Intermediate Frequency (IF) bandwidth of 1 kHz.
We chose this setting to optimize the ratio between sweep time and dynamic range. All other
setup-design choices are frequency-specific.
5 While subjective, we have found that often the best approach to placing antennas in a reverberation chamber
is by visually evaluating rays being directly or indirectly coupled between antennas.
6 In Chapter 3, we show that this can create large errors when using the one- and two-antenna methods for
estimating antenna efficiency. For the chamber validation, this approach is acceptable because the metrics used
here depend on S21 , which is less sensitive to these types of errors.
17
2.3: S ETTING UP THE C HAMBER FOR VALIDATION
(a)
(b)
(c)
Figure 2.5: A single antenna position of the setups for the verification of the frequency bands
(a) 50-67 GHz, (b) 70-90 GHz, (c) 90-140 GHz, including a zoom-in of the antennas used.
18
V ERIFICATION OF A MM WAVE R EVERBERATION C HAMBER
• 20-40 GHz; We used two Standard-Gain Horn (SGH) antennas with coaxial-towaveguide adapters to connect them to the cables, which all have 2.92 mm connectors.
We performed a coaxial Short Open Load Thru (SOLT) calibration. We used a third
antenna to estimate antenna efficiency with the three-antenna method. This was also an
SGH antenna. We used dedicated 2.92 mm coaxial bulkhead adapters.
• 50-67 GHz; Similar to the previous setup, higher-frequency SGH antennas were used
(Waveguide Rectangular (WR)15), with WR15-1.85 mm adapters. All cables and bulkhead adapters used have 1.85 mm connectors. We performed an SOLT coaxial calibration.
• 70-90 GHz; For this setup, frequency extenders needed to be used. We used WR12
ones with 13 dBm output power. We used dedicated WR12 bulkhead adapters to prevent waveguide leakage. 7 To have flexibility in antenna placement, we connected the
used SGH and Open-Ended Waveguide (OEW) antennas and waveguides with 1 mmconnector flexible cables and WR12-1mm adapters, as can be seen in Fig. 2.5. We
performed a coaxial SOLT calibration.
• 90-140 GHz; In this setup, no cables were used. Therefore, flexibility in positioning
was achieved by adding and removing pieces of waveguide. We used a waveguide Short
Open Load Reciprocal (SOLR) calibration since the rigidity of the waveguides does not
allow for connecting both ports to a thru standard. We placed the waveguides in such a
way that they could be connected to each other using multiple waveguides to be able to
perform a reciprocal measurement for calibration. We used WR8 waveguides and SGH
and OEW antennas, and WR8 frequency extenders with an output power of 8 dBm.
Most setups had a VNA frequency resolution of 200 kHz. A larger frequency spacing of
500 kHz was used for the 90-140 GHz due to the limit of the number of frequency samples
on the VNA. A narrow resolution is necessary to estimate chamber-decay time because it
requires a time-domain response to be calculated, as we will show. In that case, having a high
frequency resolution yields a longer time interval to use for calculation. The 40-50 GHz band
was not included due to restrictions in the available hardware. However, it can be assumed
that the chamber operates as expected within that range if the performance in the surrounding
bands does too. The calibration was performed near the location of the antenna fixtures, which
changed for each antenna position. Care was taken that only small cable movements occurred
between the calibration and the measurement. Here we define the Antenna Under Test (AUT)
as the combination of antenna including adapter, so the calibration reference plane is between
the adapter and the cable or waveguide.
7 As we will show in Chapter 3, this can cause large measurement errors.
Freq. Band (GHz)
24-40
50-67
70-90
90-140
Connectors
2.92 mm
1.85 mm
WR12 + 1mm
WR8
Antennas
3 SGH (+adapt.)
3 SGH (+adapt.)
2 SGH (+adapt.) + 1 OEW (+adapt.)
2 SGH and 1 OEW
Extenders
No
No
Yes
Yes
Cal.
SOLT
SOLT
SOLT
SOLR
Table 2.1: Measurement settings per frequency band.
Resolution
200 kHz
200 kHz
200 kHz
500 kHz
VNA Output Power
0 dBm
0 dBm
13 dBm
8 dBm
2.3: S ETTING UP THE C HAMBER FOR VALIDATION
19
20
V ERIFICATION OF A MM WAVE R EVERBERATION C HAMBER
2.3.3 Frequency Averaging
In RC measurements, it is common practice to perform frequency averaging in postprocessing [33, 176]. Frequency averaging is a trade-off between capturing frequencydependent behavior and reducing uncertainty. This was shown in [P9,P23] for Narrowband
Internet of Things (NB-IoT) applications. The frequency-averaging bandwidth should be tailored to each individual measurement, taking antenna bandwidth and antenna Q-factor into
account. In the validation of this chamber, we chose broadband SGH antennas with high efficiency so that a wider averaging bandwidth can be chosen. In mmWave applications, broad
bandwidths are also required. For the measurements shown for chamber validation, we chose
a post-processing averaging bandwidth of 100 MHz, using a running-average algorithm. This
relates also to frequency stirring, which will be described in Section 2.5.
2.4 Uncertainty
To assess the reliability of the measurements performed in the mmWave RC, it is crucial to estimate measurement uncertainty. Measurement uncertainty is “the doubt about the true value
of the measurand that remains after making a measurement” [169]. A measurand is “a quantity, object, or property intended to be measured”. While comparing a single measurement to
a reference has a certain value, it is much more valuable to estimate the spread that a certain
measurement can have when reproduced several times, considering realistic changes (such as
a new calibration, a different time of day, etc.). It can be used to conclude that a difference
between a reference value and the measured value is not significant when they are within each
other’s uncertainty bounds, or whether they are in ‘good agreement’ [83]. In general, there is
some subjectivity to the choice of method used to estimate uncertainty as multiple approaches
can be in accordance with the Guide to the Expression of Uncertainty in Measurement (GUM)
[115]. Therefore, the approach used should be extensively described to allow for it to be reproduced and evaluated. The goal should always be to perform an uncertainty analysis under
conditions that are realistic to the testing conditions.
Uncertainty contributions come in various types, but they are generally related to random
and systematic effects [115, 169, 182, 208]. An uncertainty due to a systematic effect is
repeatable and creates a measurement offset or bias. In many cases, these effects can be
calibrated out or removed in post-processing. This is generally not the case with uncertainties
due to random effects. These can come from contributions such as the stability of the VNA
or deviations in temperature. An illustration of random and systematic errors is shown in
Fig. 2.6. In loaded RC measurements, the largest uncertainty due to random effects is usually
the uncertainty due to a lack of spatial uniformity [176],[P9]. This is related to the variation in
antenna positioning within the chamber. In unloaded chambers, the number of mode-stirring
samples can also have a significant effect on the uncertainty. This should be checked with a
significance test [179].
21
2.4: U NCERTAINTY
Set of
observations
Random error
(precision)
Total error
(accuracy)
True
value
Systematic error
(trueness)
Figure 2.6: Illustration of measurement errors.
In an uncertainty analysis, individual uncertainty components are assessed and combined,
to estimate the uncertainty of the final results. This can be done using brute-force methods
such as a Monte-Carlo approach, but the most general approach is to combine the uncertainties using a Root Sum of Squares (RSS) approach [58, 115]. The advantage of the MonteCarlo approach is that it can retain correlations between errors and the approach eliminates
the restriction of Gaussian distributed errors inherent in the RSS approach.
In such an analysis, uncertainties are often categorized as Type A and Type B uncertainties
[115]. Type A uncertainties are those extracted using statistical methods. For example, by
measuring the stability of the VNA by performing many measurements and assessing the
standard deviation. Type B uncertainties are those extracted from other means. For example,
by taking a value out of a datasheet. This would also mean that an uncertainty can be Type A,
but when that value is used by another user for another analysis, it turns into a Type B. They
are not to be confused with uncertainties due to random or systematic effects, as both Type A
and B uncertainties can be related to either one.
The only Type A uncertainty that we take into account in the uncertainty analysis of the
mmWave RC is the reproducibility of the setup. Reproducibility is defined in [115] as the
“closeness of the agreement between the results of measurements of the same measurand
carried out under changed conditions of measurement”. To characterize reproducibility, we
perform nine different measurements, taken on different days and antenna positions, where
a new calibration was performed each time.8 In this case, the measured standard deviation
between measurements contains many uncertainties due to random effects, such as the VNA
8 Oftentimes, this uncertainty is described as the chamber lack of spatial uniformity.
We do not use this
terminology here since there are many more uncertainty contributions in this measurement. We do acknowledge
that the largest uncertainty contribution is likely due the chamber lack of spatial uniformity.
22
V ERIFICATION OF A MM WAVE R EVERBERATION C HAMBER
and extender stability, the movement of the cables after calibration, the random effects from
the calibration itself, and the chamber lack of spatial uniformity. Adding these effects separately to the uncertainty budget would yield an unrealistic penalty to the full measurement
uncertainty, because several uncertainties would be considered multiple times.This could lead
to a conclusion that a measurement is not significantly different from its reference, and that
they are in agreement while they are not.
All Type B uncertainties that we take into account in this work are taken from the
datasheets of the instrumentation and previous works on systematic errors in connectors and
waveguide transitions [108, 109]. For the calibration, we included the systematic uncertainty
due to physical errors in the connector.9
The uncertainty contribution can be combined by an RSS approach as
q
(2.4)
uc = u2A + u2B ,
where uc is the combined uncertainty and uA and uB are the standard uncertainties from the
Type A and B estimates, respectively. This approach neglects correlations between errors,
assuming that the variances are all independent.Usually, the uncertainty estimate is described
as a 95 % confidence interval, which corresponds to approximately two standard deviations.
However, with a limited number of samples used to estimate the Type A contributions, there
is a chance that the uncertainty estimate is not a good representation. This effect is taken into
account using a coverage factor k, where the expanded uncertainty is estimated by
ue = kuc .
(2.5)
k depends on the degrees of freedom, computed according to [115]10 .
2.5 Design of the Mode-Stirring Sequence
To perform a reverberation-chamber measurement within reasonable uncertainty (which is
subjective to the application), enough ‘independent’ mode-stirring samples should be acquired, which can then be averaged to obtain metrics such as total radiated power or antenna
efficiency. The way these samples are acquired can have a large effect on the measured result. Therefore, a good mode-stirring sequence needs to be designed. This is defined as ‘a
collection of mode-stirring samples that form a single, averaged measurement from which a
quantity of interest is estimated’ [57]. We first describe the different types of mode-stirring
mechanisms, and then introduce the concept of correlation which is crucial to evaluating the
sequence. We use correlation to assess how far the mode-stirring mechanism in the chamber
to be validated needs to be moved in order to effectively alter the mode distribution. We then
use these values to design and validate the entire sequence.
9 These were not available for all calibration kits due to manufacturer confidentiality, so we used values found
in previous works that have estimated such uncertainties for similar calibration kits [108, 109, 110].
10 In this case, k is 2.14, corresponding to 14 degrees of freedom, computed according to (G.2b) of the [115]
2.5: D ESIGN OF THE M ODE -S TIRRING S EQUENCE
23
2.5.1 Mode-Stirring Mechanisms
Before evaluating the mode-stirring mechanisms, it should be acknowledged that there are
many different methods to obtain a sufficient number of mode-stirring samples. To do so, a
combination of different mechanisms may be used. This becomes especially useful when one
mode-stirring mechanism becomes less effective for certain conditions11 , or when a single
mode-stirring mechanism cannot provide enough uncorrelated samples [P4]. In this thesis,
the only mode-stirring mechanism used is ‘mechanical mode-stirring’. That is, moving a
mechanical - usually metallic - structure within the chamber such that the mode distribution
within the chamber is effectively altered. The main shape used in reverberation chambers is
the Z-folded paddle stirrer, as shown in Fig. 2.1, but also used in [102, 119, 176]. However,
in the literature other shapes have been investigated [13, 14, 47, 202, 220, 237]. There also
exists a Vibrating Intrinsic Reverberation Chamber (VIRC), where the chamber walls are
mode-stirring mechanisms. The walls are made of metal-laced fabric and mode stirring is
carried out by vibrating the walls [132].
There are many other approaches to obtaining more independent samples. The most popular one is sampling the field at a different place by moving a receiving antenna to a different
place by use of a turntable or robotic arm (position stirring) [21, 57, 176, 231], or by using
multiple receiving antennas and switching between them [30]. For the sake of brevity, we
summarize common methods and refer the reader to the mentioned references for more information: stirring by repositioning the source [147], by changing the boundary conditions
with metasurfaces [87, 101, 207], by changing the reactive loads of antennas present in the
chamber [190, 215], or by discrete frequency stirring. In the latter, averaging over uncorrelated frequency samples yields more samples, at the cost of losing frequency-dependent
information [137, 138, 143].12
Next, we evaluate how far a mode-stirring mechanism needs to be moved for it to sufficiently alter the mode distribution within the chamber.
2.5.2 Coherence Angle: Autocorrelation
Intuitively, a mode-stirring mechanism creates a larger or smaller change to the mode distribution in the chamber when it is moved with a larger or smaller distance or angle, respectively.
This change is dependent on the shape, type of movement, and the physical and electrical size
11 For loaded chambers, which are often used in device testing, mechanical mode stirrers alter the mode
distribution in the chamber much less as compared to an unloaded case. This reduces the chamber uniformity
and increases measurement uncertainty. To overcome this, it is a standardized practice to use platform or source
stirring, which does not stir by altering the chamber mode distribution, but by sampling the field at a different
physical position [57].
12 This is used to evaluate the shielding effectiveness of airplanes, where the Rayleigh environment of the
aircraft is modulated as a reverberation chamber without mode-stirring mechanisms [137, 138]. With discrete
frequency stirring, only a single sweep is necessary, which leads to saving a week of testing time per airplane a valuable technique when testing costs several hundred thousand dollars per day.
24
V ERIFICATION OF A MM WAVE R EVERBERATION C HAMBER
of the mode-stirring mechanism and the chamber that surrounds it. This includes the materials present in the chamber and the placement of the antennas. The minimum movement of
the mode-stirring mechanism required to create a significant change in the mode distribution
is defined by the coherence angle or coherence distance, depending on the type of movement
of the mode-stirring mechanism [102].
The reverberation chamber to be validated has two traditional Z-folded aluminum rotational stirrers. This shape has been shown to perform well for both lower-frequency and
mmWave RC [67, 177, 198, 218]. In previous works on mmWave chambers, the coherence
angle of the Z-folded stirrer appeared to be in the order of only a few degrees due to the many
modes the chamber supports as compared to lower frequencies. This yields, especially for
a combination of two stirrers, a large number of uncorrelated samples [198]. The latter is
necessary to reduce uncertainty [21, 102, 126, 134, 167].
A mode-stirring mechanism has created a significant change to the mode distribution
when two samples are below a certain threshold of correlation. Correlation is ‘a statistical measure that expresses the extent to which two variables are related,’ and is commonly
used to evaluate the performance of an RC , and the quality of the measurements performed in
it [12, 84, 85, 86, 94, 145, 163, 168, 237]. When two samples are below a certain level of correlation, they are deemed independent, even though there is still some correlation. The choice
of threshold and correlation approach is subjective and based on many assumptions, but for
several RC metrics such as coherence angle it is common practice to use an autocorrelation
approach with a threshold of 0.3 or 0.37 [21, 102, 126, 134, 167].
The coherence angle or distance can be calculated for each frequency f by using the
autocorrelation function over a sequence of N mode-stirring samples of a single stirrer
R( f , w) =
N−w
∗ ( f,n
S21 ( f , nw )S21
∑w=1
w+1 )
,
N−w
∗ ( f,n )
∑w=1 S21 ( f , nw )S21
w
(2.6)
where S21 ( f , nw ) corresponds to the measured transmission coefficient for a mode-stirring
sample nw , for a lag shift w ∈ Z [167], and where ∗ denotes the complex conjugate [102]. The
number of lag shifts necessary for the autocorrelation to drop below the threshold is defined
as the coherence angle or distance. This lag shift should be chosen small enough to be able
to estimate the coherence angle or distance accurately. The minimum achievable lag shift for
the estimation of the coherence angle of the mode-stirring mechanisms used in the mmWave
RC is 0.5◦ due to the limited resolution of the motors used. This corresponds to 720 samples.
Note that, to be able to distinguish correlation using a low threshold properly, enough samples
should be used. A few examples of this are given in Appendix A.
An example of the autocorrelation of the vertical stirrer for various frequencies computed
over 720 lag shifts is shown in Fig. 2.7. The general interpretation of such a graph is that the
last occurrence below the threshold is used to extract the coherence angle. This occurs at lag
shifts 73, 4, and 3 for 51.5, 59, and 67 GHz, respectively. Since one lag shift corresponds to
0.5◦ , the corresponding coherence angles would be 36.5◦ , 2◦ , and 1.5◦ . This can be repeated
25
2.5: D ESIGN OF THE M ODE -S TIRRING S EQUENCE
1
51.5 GHz
59 GHz
67 GHz
Correlation
0.8
0.6
0.4
0.2
0
-360
-240
-120
0
120
240
360
Lags
Figure 2.7: Autocorrelation of the stirrer for various frequencies in the 50-67 GHz frequency
band.
Coherence Angle (°)
1.4
Coherence Angle
1.2
1
0.8
0.6
26.5
30
52
55
60
65
70
Frequency (GHz)
Figure 2.8: Coherence angle over frequency, computed using autocorrelation.
for every frequency, resulting in Fig. 2.8. This large difference is caused by the effect that
occurs at 51.5 GHz, where the correlation first drops below the threshold, but surpasses it
again after. According to Section A.3. of IEC 61000-4-21, samples are uncorrelated when
the magnitude of the correlation coefficient for increasing shifts drops below and remains less
than the threshold value [102]. This is highly frequency dependent, and is the cause for the
discontinuities in Fig. 2.8. It should be noted that the coherence angle is usually averaged
over the same frequency-averaging bandwidth as used in the post-processing of the results,
which is 100 MHz in this case. For a lower frequency-averaging bandwidth, a higher variation
across frequency would be observed in 2.8.
26
V ERIFICATION OF A MM WAVE R EVERBERATION C HAMBER
2.5.3 Coherence Angle: Pearson Correlation
Even though the previously described approach is common practice, there are fundamental
issues with it, which lead to misinterpretations of the physical effects of the stirrer. They
have been reported various times [167, 178], but are only initially being adopted by standards
groups. There are several important issues regarding autocorrelation:
1. The autocorrelation does not define the correlation between two mode-stirring samples,
but merely provides an estimate of the trend that occurs within the sequence of samples.
Therefore, evaluating the number of lag shifts as the minimum movement necessary is
not correct.
2. The autocorrelation approach assumes that the coherence angle does not vary over the
movement of the mode-stirring mechanism. This may lead one to believe that the stirrer
is performing well, even though it only does so on average. Critical placements creating
high correlation are missed.
3. The answer is highly dependent on the order in which the operator picked the samples.
In general, autocorrelation only gives an indication of the physical similarity between samples
when the measurements are deliberately taken over a predictable sequence. Therefore, using
it to describe a combination of effects likely underestimates correlation, as it fails to capture
individual high-correlated samples. For example, when using it to detect correlation within
an independent realization13 when the data were not taken in a predictable order, or when
correlated samples do not correspond to sequential samples. An example of this is shown in
Appendix A, but it is also well described in [178].
A correlation method that is less sensitive to these constraints and allows for distinguishing physical effects due to the mode-stirring mechanism, is the Pearson-correlation approach,
which has been applied to evaluate RC performance [85, 126, 163, 164, 168, 237],[P19]. The
Pearson correlation approach is given by
R(i, n) =
cov(x, y)
,
σx σy
(2.7)
where cov(x, y) is the covariance between two variables x and y, and σx and σy are the standard
deviations of x and y. x and y are both arrays of frequencies for a single mode-stirring sample.
The Pearson correlation method allows for a direct comparison between two mode-stirring
samples, overcoming the issues with autocorrelation. This makes the Pearson method more
suitable for uncovering physical effects related to the stirring mechanism or sequence. The
downside is that the correlation needs to be computed over a larger frequency range, making
certain effects that are frequency-specific more difficult to distinguish.
13 A combination of sufficient uncorrelated mode-stirring samples, that is independent of another combination
of mode-stirring samples
27
2.5: D ESIGN OF THE M ODE -S TIRRING S EQUENCE
(a)
(b)
Figure 2.9: Correlation between all angles of the Z-folded mode-stirring mechanism for (a)
20-40 GHz and (b) 50-70 GHz.
Fig. 2.9 shows the Pearson correlation between all angular positions of the vertical modestirring mechanism (720 positions), over a 20-40 GHz and a 50-70 GHz frequency band. The
results show that there is a low correlation between angles that are more than a few degrees
apart from each other. This result can be used to obtain a coherence angle for each angular
position of the mode-stirring mechanism, using the same 0.3 threshold. The coherence angle
for each mode-stirring sample is between 1.5 and 2 degrees, approximately. This is relatively
close to the autocorrelation estimate, but larger discrepancies can occur with mode-stirring
mechanisms that have, for example, a non-linear movement, as shown in [P19]. When the
sequence contains more mode-stirring mechanisms that move at the same time, it is likely
to achieve a correlation below the threshold with a movement lower than their individual
coherence angles.
2.5.4 Mode-Stirring Sequence
All RC measurements described in this thesis are based on the concept that the combination
of many mode-stirring states can be assumed to create an environment that behaves as a
stochastic process [123]. This is only true when the following conditions are met that relate
to correlation:
1. All mode-stirring samples are below a certain level of correlation (threshold),
2. Enough mode-stirring samples are obtained.14
14 The Cellular Telecommunications and Internet Association (CTIA) Test Plan requires at least 100 uncor-
related samples, but preferably 200 or 400 [158]. This is based on a trade-off between uncertainty and time
28
V ERIFICATION OF A MM WAVE R EVERBERATION C HAMBER
The first item is directly related to the quality of the mode-stirring mechanism and its effective
movement. It should be stressed that correlation is a result of physical effects. Those same
physical effects tend to yield a higher measurement uncertainty [21], however, correlation in
itself is not a cause of uncertainty.15
An optimized mode-stirring sequence consists of enough uncorrelated samples (at least
100 [102]). This number of mode-stirring samples has been shown to be enough to obtain
an accurate measurement [35, 102], where the uncertainty from the number of mode-stirring
√
samples is approximately 1 N [123, 176]. There are many works that have focused on
evaluating the number of effective samples in RC measurements through various statistical
approaches such as correlation [84, 85, 88, 134, 145, 163, 164, 168, 237]. These works are
relevant in the field of EMC where RC are used close to their LUF, so it is challenging to
generate sufficient low-correlated samples. For the chamber used in this work, that is less
relevant, because, as mentioned in Section 2.2, we use the chamber well above its LUF. We
found that by stepping the mode-stirring mechanisms with a minimum angle spacing greater
than the coherence angle, it can, in general, be expected that they are uncorrelated. For the validation of the chamber, we chose to use N = 100 mode-stirring samples, acquired using a 36◦
angle spacing for both the horizontal and vertical stirrer.16 Since this is significantly higher
than the coherence angle computed with both the autocorrelation and Pearson-correlation
methods, it is expected that this can lead to a mode-stirring sequence with low correlation
between its samples.
To validate that the measurement can be used to estimate metrics such as antenna efficiency, a mode-stirring sequence should be checked for correlation within that sequence. The
mode-stirring sequence in the validation experiments consists of nine independent realizations
to evaluate uncertainties related to the reproducibility of the chamber, with 100 mode-stirring
samples within that realization. The correlation within an independent realization is often referred to as within correlation. The correlation between independent realizations is referred to
as between correlation. For the latter, it is common practice to also use the Pearson correlation,
which we applied to the measured results. In the 24-40 GHz band, the highest correlation was
0.217, and for the 50-67 GHz, 70-90 GHz and 90-140 GHz bands 0.201, 0.192, and 0.290,
respectively. This is all below the threshold of 0.3, verifying sufficient independence between
the independent realizations. This is necessary to estimate uncertainty.
For the within correlation, previous works used an autocorrelation approach. However,
[123].
15 It should be noted that it is common practice to also perform goodness-of-fit tests, to check whether the
data have a Gaussian distribution (Rayleigh in magnitude) [67, 102, 155, 203]. The goodness-of-fit test can
be a valuable tool, although subjective to the choice of bin size. While related, we found that methods based
on correlation analysis provide more information on the quality of the mode-stirring sequence when using a
continuous-wave excitation for a single frequency.
16 In this sequence, each position of a single mechanism occurs ten times. Note that this sequence could be
further optimized by avoiding this by combining it with smaller angle increments.
29
2.6: C HAMBER -D ECAY T IME
(a)
(b)
Figure 2.10: Correlation between all mode-stirring samples (n) for a single independent
realization in the (a) 20-40 GHz range and the (b) 50-70 GHz range.
since the mode-stirring sequence is built up with samples acquired by moving multiple mechanisms, this approach is not suitable as it will likely not provide information on the physical
effects causing correlation. A few examples showing this issue are shown in Appendix A.
The correlation between all mode-stirring samples in one independent realization is shown in
Fig. 2.10, where it is shown that all mode-stirring samples have a correlation below 0.3.
Lastly, we used stepped mode stirring in this work. While outside of the scope of this thesis, it is, for Total Radiated Power (TRP) measurements, common practice to use continuous
stirring [52, 202, 205], where multiple mode-stirring mechanisms are moving continuously
and samples are obtained every few milliseconds. This significantly speeds up measurement
time, at the cost of increased uncertainty, and possible frequency shifts due to the Doppler
shift created by the moving mode-stirring mechanisms [30, 44, 90, 158].
2.6 Chamber-Decay Time
The chamber-decay time, or time constant, is the time it takes for the fields in the chamber to
have decayed by 1/e, where e is Euler’s number, after the maximum field strength has been
reached in the chamber [221, 235].17 Chamber-decay time is one of the most valuable metrics
since it is the most sensitive to changes in losses. For example, just the placement of an antenna in the room adds a measurable change in the rate of loss from which antenna efficiency
can be extracted [129], and the placement of a material in the room creates a measurable
perturbance from which the so-called Absorption Cross Section (ACS) can be measured [60].
17 In the optical domain, this is often referred to as cavity ring down.
30
V ERIFICATION OF A MM WAVE R EVERBERATION C HAMBER
-55
90 GHz
115 GHz
140 GHz
|S21|2 (dB)
-60
-65
-70
-75
-80
-85
0
0.5
1
1.5
2
Time ( s)
Figure 2.11: Power-delay profile of the RC for various frequencies in the 90-140 GHz band.
The chamber-decay time should be as long as possible to be able to perform sensitive measurements, so it is important to characterize it in an unloaded chamber.
2.6.1 Chamber-Decay Time Procedure
The chamber-decay time is extracted from the slope of a fitted curve of the exponentiallydecaying part of the chamber its Power-Delay Profile (PDP). The PDP is captured by the
Inverse Fourier Transform (IFT) of the measured transmission through the chamber, ⟨|S21 |2 ⟩.
Since the rate of decay is frequency dependent, the PDP is estimated for a smaller frequency
band, for multiple center frequencies. For the validation of this chamber, we used center frequencies spaced by 5 MHz, and a calculation bandwidth of 100 MHz.18 The width of the
band dictates the resolution in the time domain, and the resolution in the frequency domain
dictates the time frame that can be evaluated. Therefore, RC measurements that depend on
computing the chamber-decay time need a high frequency resolution. As discussed in Section 2.3, using a larger calculation bandwidth acts as frequency smoothing, so care should be
taken when there is behavior that is very selective over frequency. An example of the PDP
of the mmWave RC for three frequencies is shown in Fig. 2.11. A frequency resolution of
500 kHz was used here, which allows for evaluating a time-domain response between 0 and
2 µs. Since the rate of decay in the chamber is only captured by the exponentially-decaying
part, the chamber build-up time (or early-time behavior), and very-late-time behavior are cut
off from the PDP [100, 221]. The early-time behavior captures the time it takes for the modes
in the chamber to reach steady state, and the very-late-time behavior captures the part in time
where the signal has reached the noise floor [34, 100]. The latter is not visible in Fig. 2.11
because of the limited time frame. In Fig. 2.11, the curve is fitted on the data between 0.15
18 A more accurate estimate can be obtained by using a narrower spacing between center frequencies, but
5 MHz was chosen for post-processing speed.
31
2.6: C HAMBER -D ECAY T IME
and 1.8 µs. The slope of this fitted band in dB/s, D, is used to estimate the chamber-decay
time as
10 log10 (e)
τRC =
.
(2.8)
D
This curve-fitting procedure makes the metric significantly more sensitive to changes in the
chamber than a frequency-domain approach, which allows for distinguishing low loss contributions. Besides that, evaluating RC data in the time domain is valuable in uncovering
physical effects in the performance of the chamber [34, 86], as we will show in Chapter 3.
2.6.2 Absorption Cross Section
In a reverberation chamber, the contribution of various loss mechanisms to the rate of decay
can be written as
1
1
1
1
=
+
+ .... +
,
(2.9)
τRC τLoss1 τLoss2
τLossZ
where the total rate of decay can be separated into contributions from various (Z) loss mechanisms such as: material loading, the metallic wall losses, chamber leakage, antenna loading,
and more [92, 95].
This same concept can be used to evaluate the contribution of certain loss mechanisms by
performing a measurement with and without loading the chamber with that loss mechanism
as follows
V
ACS =
c
1
τLoaded
−
1
τEmpty
,
(2.10)
where the ACS is the absorption cross section of the loss mechanism, and where c is the
free-space wave propagation speed [60]. The concept started in acoustic RCs in the early
1900s and is in some ways analogous to the approach we use today [46, 191]. For the sake of
brevity, we do not provide all details here, but it should be acknowledged that there are many
efforts happening in ACS characterization. It is widely used for general material characterization to extract, for example, permittivity, loss tangent, and Specific Absorption Rate (SAR)
[23, 72, 80, 81, 89, 92, 95, 209, 212, 228, 229]. We provide a short summary of applications:
ACS measurements are used to characterize RF absorber material at lower frequencies for
the purpose of predicting the amount of chamber loading necessary to perform measurement
using modulated signals [5, 7, 48, 176], to predict RF loading in electromagnetic environments [71, 157, 196, 199] and to characterize general materials such as Printed-Circuit Board
(PCB) and building materials [73, 160, 192]. It is also used by the biomedical community
for SAR and dosimetry purposes [16, 68, 71, 150, 198, 199, 212, 236], and in combination
with temperature [117]. It can be used to estimate the loading effect of structures necessary
to place antennas in the working volume of the RC , which relates to uncertainty [39, 40],
and a similar time-domain-based concept can be used to estimate scattering properties of materials, such as total scattering cross section and even Radar Cross Section (RCS) [24, 27,
32
V ERIFICATION OF A MM WAVE R EVERBERATION C HAMBER
54, 136, 174, 227]. ACS measurements have also been shown to yield accurate results at
mmWave frequencies for various applications [6, 68, 192]. Metrologists that originate from
an optics background would appreciate that the method to obtaining absorption cross section
is related to cavity ring-down spectroscopy [22]. In the validation of the chamber, we use
ACS-measurement concepts to isolate loss contributions from cable jackets [P24] and from
atmospheric attenuation [P2].
2.6.3 Measurement Results
In the 24-40 GHz, 50-67 GHz, and 60-90 GHz bands, a frequency spacing of 200 kHz is used.
This allows for evaluating a time interval of 0-5 µs. To isolate the exponentially-decaying part
of the PDP , the time intervals 0.5-3 µs, 0.1-0.7 µs, and 0.1-2 µs are used for the 24-40 GHz,
50-67 GHz, and 70-90 GHz bands, respectively. For each frequency, a window of 100 MHz
around that frequency is used to compute the chamber-decay time. The chamber-decay time
versus frequency is shown in Fig. 2.12.
The chamber-decay time is, for the majority of the frequency range, around 0.3 µs. While
there have been no works on mmWave chambers above 70 GHz, those that have been presented show a similar or shorter chamber-decay time (< 0.2 µs [6, 200], < 0.3 µs [192])
compared to the chamber presented in this work [P20]. The chamber-decay time of chambers
operating at lower frequencies is generally longer [P24]. This may be related to shielding
and increased losses from materials. These losses, among others, are not taken into account
in (2.2), which can also be noted when the measured chamber-decay time is compared to the
theoretical one given by Qw /ω [97], where ω = 2π f . The theoretical τRC is significantly
higher as it declines from 1.8 to 0.8 µs in the 24-140 range. Note that the measured Q is still
significantly larger than Qthrp across the entire band and that the measured τRC values are long
enough for accurate antenna measurements, as we will show.
Fig. 2.12 also shows that the rate of decay hardly increases with increasing frequency in
the 24-140 GHz range, showing that the stored energy remains high over the entire frequency
because the overall chamber loss increases. This, among other metrics, shows the high shielding performance of this chamber. A longer τRC can be observed in the 90-140 GHz band since
there was less lossy material in the chamber due to the usage of waveguides. The uncertainty
is slightly higher because, to generate different positions, pieces of waveguide and supporting
material had to be added or removed, which creates differences in the losses in the chamber.
It should be noted that the measured longer and shorter values of τRC correspond directly
with the positions that had less and more material in the chamber, respectively, showing the
sensitivity of this metric.
A large discontinuity in the chamber-decay time occurs in the 50-67 GHz band, since the
losses are significantly higher in that band. This additional loss is imposed by the 1.85 mm
cables, since the plastic jacket or sheath of this specific cable absorbs some of the energy in
the chamber [P24]. The cables used for other frequency bands have different types of jackets.
To verify that this discontinuity is caused by the cable sheath, we measured the ACS of the
33
2.6: C HAMBER -D ECAY T IME
0.5
( s)
0.3
RC
0.4
0.2
0.1
0
RC
RC
30
60
80
Corrected for cable ACS
100
120
140
Frequency (GHz)
Figure 2.12: Chamber-decay time over frequency including uncertainty, and a correction for
the cable-jacket loss in the 50-67 GHz band.
cable in a separate measurement campaign according to (2.10). The ACS of the cable was
between 0.0013 and 0.0019 m2 across the frequency band. Using (2.10), we corrected the
measured chamber-decay time such that it does not include the losses imposed by the cable
jacket. The results are shown with the blue curve in Fig. 2.12. The discontinuity reduces
significantly when corrected for the cable-jacket absorption loss, where it roughly follows a
similar trend as compared to the other bands. Note that the corrected curve is merely used
for a rough estimation of the behavior of the chamber without the cable jacket. It does not
show error bars because it would not accurately represent the chamber for such a lower-loss
situation, and the ACS uncertainty was not estimated.
2.6.4 Atmospheric Attenuation
Atmospheric attenuation is generally presented as a rate of decay, which is usually in dB/km.
Therefore, it can also be written as the time it takes for the signal to decay by 1/e, similar to
chamber-decay time [221], as
τAtmosphere =
10 log10 (e)
,
0.3LAtmosphere
(2.11)
where LAtmosphere is the atmospheric attenuation in dB/km. Fig. 2.13 shows the International
Telecommunication Union (ITU) model ([107]) of the standard sea level atmospheric attenuation in both ways, where it is shown that a high rate of decay corresponds to a short decay
time.
Similar to (2.9), the atmospheric losses can be subtracted from the measured τRC , with the
goal of showing that the effect of atmospheric loss is significant. This can be done as follows
1
τChamber
=
1
τRC
−
1
τAtmosphere
,
(2.12)
34
Atm. loss (dB/km)
( s)
Atmosphere
10
50
40
30
20
5
10
0
40
60
80
100
120
( s)
15
Atmosphere
Atmospheric Loss (dB/km)
V ERIFICATION OF A MM WAVE R EVERBERATION C HAMBER
0
140
Frequency (GHz)
Figure 2.13: Atmospheric attenuation in dB/km on the left y-axis and in terms of chamberdecay time on the right axis.
where τChamber is the combination of all losses in the chamber except for the atmospheric loss.
The measured results for each frequency band are shown in Fig. 2.13. Note that the
uncorrected result is the same as those shown in Fig. 2.12. For each band, the chamber-decay
time over frequency is shown on the left axis in blue, and the atmospheric losses in (dB/km)
are shown on the right axis (note the difference in vertical-axis values between the different
bands). We state that the effect of the atmospheric loss is significant when τChamber (computed
using (2.12)) is outside of the error bars of the measured τRC , where the error bars correspond
to the 95 % confidence interval. Fig. 2.13(a-c) show that this is the case for the 50-67 GHz and
90-140 GHz bands, where it is clear that there is a correlation with the peaks in atmospheric
attenuation. While the significance of the effect depends on the chamber loss, it can be seen
that the atmospheric losses become significant at approximately 2 dB/km. Note that we do
not show the results between 24 and 40 GHz, because, as can be seen in Fig. 2.13, the effect
of atmospheric loss in that band is negligible.
The additional loss imposed by the atmosphere impacts the sensitivity of the measurements. However, this rate of decay still allows for accurate measurements with a low uncertainty, as indicated by the error bars. With prospects of antenna measurements needing
to move up towards the terahertz regime, the role of atmospheric loss will increase. For example, above 500 GHz the peaks can be in the order of 10000 dB/km (considering the same
model). This corresponds to a τAtmosphere of 0.0014 µs. Assuming that τChamber would be
in approximately the same order as the lower-frequency measurement results, the measured
chamber-decay time would be completely dominated by the atmospheric loss. This makes
measurements depending on chamber-decay time, such as the ACS of materials or antenna
efficiency, infeasible in a similar setting. A solution to this issue could be to adapt the chamber to be in a climate-controlled setting without humidity, or to be, for example, filled with
nitrogen [P27].
35
0.14
RC
RC
( s)
RC
Measured
Atm. loss (dB/km)
20
Corrected for Atm. Loss
0.13
15
0.12
10
0.11
5
0.1
50
55
60
65
0
Atmospheric Loss (dB/km)
2.6: C HAMBER -D ECAY T IME
Frequency (GHz)
RC
( s)
0.3
RC
RC
Measured
Atm. loss (dB/km)
Corrected for Atm. Loss
0.5
0.29
0.45
0.28
0.4
0.27
0.26
70
0.55
0.35
75
80
Frequency (GHz)
(b)
85
0.3
90
Atmospheric Loss (dB/km)
(a)
36
0.35
RC
0.34
RC
Atm. loss (dB/km) 2.5
Measured
Corrected for Atm. Loss
2
( s)
0.32
RC
0.33
0.31
1.5
1
0.3
0.5
0.29
90
100
110
120
130
0
140
Atmospheric Loss (dB/km)
V ERIFICATION OF A MM WAVE R EVERBERATION C HAMBER
Frequency (GHz)
Figure 2.13: Measured chamber-decay time including uncertainty with the chamber decaytime corrected for atmospheric loss on the left y-axis in blue, and the atmospheric loss in
dB/km is shown on the right axis in orange, for the (a) 50-67 GHz, (b) 70-90 GHz, and (c)
90-140 GHz bands. The results in (a) and (c) show that the atmospheric attenuation has a
significant effect on chamber-decay time.
2.6.5 Antenna Efficiency
A major advantage of chamber-decay time is that it solely portrays the losses inside the chamber, and does not include the efficiencies of the antennas that are used to measure it. The
frequency-domain counterpart, QFD does contain the antenna efficiency. Therefore, the efficiencies of the antennas can be estimated using
η1 η2 =
QFD
,
QTD
(2.13)
2
where QFD = 16πλ V ⟨|S21 |2 ⟩ and where QTD = ωτRC . Therefore, with a third antenna, and
three transmission-coefficient measurements, the efficiency of all three antennas can be estimated, without the need for a reference antenna with a known efficiency. This is the concept
behind the RC -based three-antenna method [97]. More details on these methods are provided
in Chapter 3.
2.7 Chamber Loss
The most generic approach for evaluating chamber loss is to use the chamber transfer function
which is given by
⟨|S21 |2 ⟩N
GRef = tot tot ,
(2.14)
η1 η2
where ⟨·⟩ is an ensemble average, N the number of mode-stirring samples, S21 is the measured
transmission coefficient, and η1tot and η2tot are the total efficiencies of both antennas used. The
37
2.7: C HAMBER L OSS
-25
GRef
GRef Corrected for cable ACS
GRef (dB)
-30
-35
-40
-45
GRef
GRef Corrected for cable ACS
30
60
80
100
120
140
Frequency (GHz)
Figure 2.14: Chamber transfer function over frequency, including a correction for the losses
of the cable jacket used in the 50-67 GHz band.
total efficiency is defined here by the ratio between the radiated power, and the power available
at the input of the antenna [97]. By evaluating this loss, we can estimate if the measurement
is within the dynamic range of the instrumentation.
The measured GRef is shown in Fig. 2.14. For all bands, the losses do not surpass 42 dB,
which is, considering cable, waveguide, and antenna loss (in the order of a few dB), well
within the dynamic range of the measurement instrumentation. The results show that the
chamber is likely to stay operable at frequencies well above 140 GHz.
When measured over several independent positions, as confirmed by computing a Pearson
correlation analysis between all positions, the standard deviation between different measurements of GRef can yield an estimate for the uncertainty from the setup reproducibility as
v
u
P
u 1
σGRef = t
(2.15)
∑ (GRef,p − ĜRef),
P − 1 p=1
where GRef,p is the chamber transfer function for an antenna position p, P is the total number
of antenna positions and ĜRef is the average over all positions.19 It should be noted that we
expect the same chamber loss for each position. For heavily loaded chambers, the uncertainty
due to lack of spatial uniformity generally dominates the uncertainty budget [176].
The standard deviation in GRef is shown in Fig. 2.15. As mentioned in Section 2.2, σGRef
corresponds in this measurement to the measurement reproducibility, which includes uncertainty due to lack of spatial uniformity, but also uncertainty due to random effects of the
19 We performed a significance test to validate the usage of this equation to estimate the standard deviation as
shown in [179] and [P9]. Note that the significance test is sensitive to the choice of which samples are chosen to
be within a single independent realization, which impacts the relation between them, and hence, also the result
of the significance test, even though it would not impact an end-result metric such as TRP or antenna efficiency.
38
V ERIFICATION OF A MM WAVE R EVERBERATION C HAMBER
1
(dB)
0.8
G
Ref
0.6
0.4
0.2
G
0
30
60
80
100
120
Ref
140
Frequency (GHz)
Figure 2.15: Standard deviation of the chamber transfer function over frequency.
measurement instrumentation, cables, and calibration. For the 24-40 GHz and 70-90 GHz
bands, σGRef never surpasses 0.2 dB (approximately 1 % in antenna efficiency, similar to
[200]). The 50-67 GHz band shows a higher uncertainty than the other frequency bands because the chamber loss is higher in this measurement, which reduces spatial uniformity [176].
The uncertainty also increases above 110 GHz, which is likely related due to the fact that the
losses increase, but also due to changes in losses between positions because of added waveguides and supporting structures (similar to the increased uncertainty in chamber-decay time),
as can be seen in Fig. 2.5.
It should be noted that σGRef may be reduced when more mode-stirring samples are used.
This, among other metrics, makes the uncertainty due to the chamber’s lack of spatial uniformity mostly a metric about the measurement setup and settings instead of only the chamber
geometry. For example, in [197], a σGRef of 0.02 was reported for a mmWave RC with similar losses ( -35 dB at 45 GHz). The main difference is that in those measurements 2500
mode-stirring samples were used. With more low-correlated samples, the variation within
an independent realization reduces [123], and, therefore, it is expected that also the variation
between them reduces when the independent realizations are uncorrelated.
2.8 Antenna Efficiency Examples
To demonstrate the performance of the chamber in terms of antenna-efficiency measurements,
we show examples of the measured antenna efficiency for some of the antennas used in this
work, including the expanded uncertainty as given in Table 2.2. We use the three-antenna
method for the estimation of antenna efficiency, as this approach has few assumptions, does
not require a reference antenna with a known efficiency, and does not require all three antennas to be in the chamber at the same time (in contrast to the antenna-replacement method)
[97],[P7].
39
2.9: C ONCLUSION
Table 2.2: Uncertainty Budget for Radiation Efficiency
Uncertainty
Reproducibility (Rand.)
Calibration (Syst.)
Combined
Expanded (k=2.14)
24-40
(GHz)
1.2 %
0.1 %
1.2 %
2.6 %
50-67
(GHz)
1.3 %
0.1 %
1.3 %
2.8 %
70-90
(GHz)
1.3 %
1%
1.6 %
3.4 %
90-140
(GHz)
1.4%
< 0.1 %
1.4 %
3.0 %
The uncertainty budget for radiation efficiency is shown in Table 2.2. For the reproducibility uncertainty, we report the average uncertainty across the band, since this component varies
slightly over frequency. This component of uncertainty is 1.3 % for both the 50-67 GHz band
and the 70-90 GHz band, because it is dominated by the lack of spatial uniformity, which is,
as discussed in Section 2.7, similar for both bands. The uncertainty component that is higher
in the 70-90 GHz band is the calibration systematic uncertainty, as described in Section 2.3.
This is caused by the higher sensitivity of the 1 mm connector cables, as compared to the
1.85 mm ones [110]. The systematic error due to the calibration in the 90-140 GHz band
is expected to be negligible, due to the use of a waveguide calibration [108]. The expanded
uncertainty, which corresponds to the 95 % confidence interval, is below 4 % for all bands.
Figs. 2.15a-d show the antenna efficiencies of the horn antennas depicted in Figs. 2.1 and
2.5(a-c), respectively. The error bars correspond to the expanded uncertainties reported in Table 2.2 (95 % confidence interval). In Fig. 2.15a-c, the reported efficiency is the efficiency of a
horn antenna including adapter. In Fig. 2.15d, the reported efficiency is that of a horn antenna
including a piece of waveguide. The losses imposed by the adapters are approximately 5 % at
24-40 GHz, 20 % at 50-67 GHz, and 15 % at 70-90 GHz (the adapters in the 50-67 GHz band
are of lower quality). The radiation efficiencies of these type of horn antennas without adapter
are expected to be approximately 95 % according the manufacturer reports, which results in
expected radiation efficiencies of the antennas we used including adapter of approximately
90 %, 75 %, and 80 % in the 24-40 GHz, 50-70 GHz, and 70-90-GHz bands, respectively.
The manufacturer of the 90-140 GHz horn antenna reported an expected radiation efficiency
of 98 %. As shown in the results, the measured efficiencies are close to the expected results,
and, for the majority of the bands, within uncertainty. This, including the low measurement
uncertainty of this chamber, validates that antenna efficiency can be measured accurately in a
reverberation chamber up to 140 GHz.
2.9 Conclusion
This chapter described the validation process of a reverberation chamber operating in the 24140 GHz frequency band, including uncertainty analysis and antenna-efficiency examples up
to 140 GHz. The mode-stirring sequence is verified using Pearson’s correlation, which has
been shown to be more suitable for uncovering physical effects in the chamber as compared to
40
V ERIFICATION OF A MM WAVE R EVERBERATION C HAMBER
Efficiency (%)
100
80
60
40
tot
20
0
Horn
Rad
Rad
26
28
30
32
34
36
Horn
Expected
38
40
Frequency (GHz)
(a)
Efficiency (%)
100
80
60
40
tot
20
0
50
Horn
Horn
Rad
Expected
Rad
52
54
56
58
60
62
64
66
68
Frequency (GHz)
(b)
Efficiency (%)
100
80
60
40
tot
20
0
70
Horn
Rad
Rad
75
80
Frequency (GHz)
(c)
85
Horn
Expected
90
41
2.9: C ONCLUSION
Efficiency (%)
100
80
60
40
tot
20
0
90
rad
rad
100
110
120
130
Expected
140
Frequency (GHz)
(d)
Figure 2.15: Measured and expected antenna efficiencies of various SGH antennas operating
in the (a) 24-40 GHz, (b) 50-67 GHz, (c) 70-90 GHz, and (d) 90-140 GHz bands, all including
error bars corresponding to the expanded uncertainty.
the more generally used autocorrelation approach. The chamber has low losses (below 42 dB)
and predicts that the chamber can be operated at frequencies higher than 140 GHz. The loss
in the chamber can be evaluated more sensitively by using the chamber-decay time. Using
that property, we showed that atmospheric loss has a significant effect on the chamber-decay
time, by isolating it from the chamber effects using the absorption-cross-section approach.
The chamber can be used to estimate antenna efficiency with an expanded uncertainty below
3.5 % for all bands. The use of waveguides and frequency extenders for higher frequencies
yields a reproducibility uncertainty of below 1.4 %. We conclude that the chamber can be
used up to 140 GHz to obtain accurate measurements of wireless mmWave devices.
42
Chapter three
Systematic-Error Quantification for
Estimating Antenna Efficiency
3.1 Introduction
For antennas and wireless systems operating at high frequencies, loss management is crucial.
Effects such as manufacturing errors, surface roughness, and material aging can affect the
performance of the antenna, which drastically reduces its efficiency [45, 82, 121, 124, 140,
149, 170]. These effects become more significant for frequencies above 100 GHz, where it
even becomes challenging to have the antenna radiate at all [1, 121]. This is true for, for
example, an antenna on chip or an antenna in package [113, 140]. Many loss contributions
are not fully taken into account in simulations, making it important to measure the antenna
efficiency [1, 41, 116, 121].
In Chapter 2, we have shown that a reverberation chamber can be used to accurately
characterize efficiency of high-frequency antennas. Similar verification procedures have been
carried out for lower-frequency chambers, using many different methods to estimate antenna
efficiency [59, 79, 97, 102, 118, 126, 129, 131, 210, 224],[P4]. Of all antenna-efficiency
measurement methods, certain methods are significantly more susceptible to measurement
errors than others, which can be difficult to identify. In this chapter, we identify various effects
that can cause significant systematic errors using certain efficiency methods, and provide users
with ways to deal with those errors.
The outline of this chapter is organized as follows. First, we describe the most-commonly
used antenna-efficiency approaches in Section 3.2. Section 3.3 describes the systematic errors
created by noise, which, due to its random nature, cannot be distinguished from stirred energy
for low-efficiency antennas. We show this by evaluating the efficiency of the same low-totalefficiency antenna with different methods. In Section 3.4, we show that methods depending
This chapter is based on P2, P4, P6, P9, P10, P19 and P29
43
44
S YSTEMATIC -E RROR Q UANTIFICATION FOR E STIMATING A NTENNA E FFICIENCY
Pradiated
ηtot
Pradiated
Mismatch
correction
Pavailable
ηrad
Paccepted
Figure 3.1: Illustration of the definitions of total and radiation efficiency.
on the stirred-energy component of the measured reflection coefficient are susceptible to large
systematic errors, when an antenna is pointed at a mode-stirring mechanism. This is caused
by monostatic scattering acting as a random variable and therefore, contributing to the measured stirred energy. We show that this effect occurs with the traditional Z-folded stirrer, and
introduce alternative solutions to overcome this problem. Finally, we describe the systematic
effects of unwanted radiation from Radio Frequency (RF) circuitry, waveguide leakage, and
RF probe radiation in Section 3.5. The chapter is concluded in Section 3.6
3.2 Antenna-Efficiency Methods
There are many different approaches for measuring antenna efficiency in a reverberation
chamber [59, 79, 97, 102, 118, 126, 129, 131, 210, 223, 224],[P4]. However, the most
commonly-used methods are the antenna-replacement method and the one-, two- and threeantenna methods [97, 102]. In this section, we describe them extensively, along with their
advantages and constraints. We refer to the total antenna efficiency as “the ratio between the
radiated power and the power arriving at the antenna port”, and we refer to the radiation efficiency as “the ratio of the radiated power and the power accepted by the port” [97, 104]. This
is illustrated in Fig. 3.1. Reverberation-chamber measurement methods generally estimate
the total antenna efficiency, from which the radiation efficiency may be derived by correcting
for the mismatch at the antenna port.
45
3.2: A NTENNA -E FFICIENCY M ETHODS
3.2.1 Antenna-Replacement Method
According to the IEC standard [102], when an antenna-replacement method (using three antennas) is used to assess antenna efficiency, one antenna with a known efficiency is required
to be used as a reference antenna. A second antenna may be any other antenna whose operational band is within the band of interest. The transmission coefficient between the two
antennas is measured as a reference, S21,Ref . Then, the reference antenna is replaced with the
AUT , and the transmission coefficient between those two antennas is measured, S21,AUT . The
total efficiency of the AUT can then be calculated as
tot
ηAUT
=
⟨|S21,AUT |2 ⟩N tot
η ,
⟨|S21,Ref |2 ⟩N Ref
(3.1)
tot is the total efficiency of the reference antenna.
where ηRef
The antenna-replacement method assumes that the chamber loss does not change significantly when the reference antenna is replaced with the AUT . In reality, this may not the case,
where any discrepancy will lead to an over- or under-estimation of the AUT ’s efficiency.
This can be overcome by placing all three antennas in the chamber at the same time. A bigger
challenge of this method is that an antenna with a known efficiency is required. To overcome
this, non-reference antenna methods have been developed and are described next.
3.2.2 Three-Antenna Method
A few of the most common non-reference antenna methods are the RC-based one-, two-,
and three-antenna methods presented in [97], which are also mentioned in the IEEE Recommended Practice for Antenna Measurements [103]. They are based on the assumption that
the chamber’s quality factor (Q) as determined in the time domain (QTD ) does not contain
the losses due to the antennas’ efficiencies (because the early- and late-time behavior are removed, and the antenna efficiencies do not significantly contribute to the rate of decay), while
the Q determined in the frequency domain (QFD ) does (both of these metrics can be extracted
from an S21 measurement) [P8,P7]. Therefore, the efficiencies can be extracted by dividing
the two according to (2.13). From there, the three-antenna method equations can be extracted,
given by
s
s
⟨|S21,s |2 ⟩N ⟨|S31,s |2 ⟩N
CRC
η1tot =
,
(3.2a)
ωτRC
⟨|S32,s |2 ⟩N
s
s
⟨|S21,s |2 ⟩N ⟨|S32,s |2 ⟩N
C
RC
η2tot =
,
(3.2b)
ωτRC
⟨|S31,s |2 ⟩N
s
s
⟨|S31,s |2 ⟩N ⟨|S32,s |2 ⟩N
C
RC
η3tot =
,
(3.2c)
ωτRC
⟨|S21,s |2 ⟩N
46
S YSTEMATIC -E RROR Q UANTIFICATION FOR E STIMATING A NTENNA E FFICIENCY
2
2
1
v-1
v
O
1
v-1
v
O
O'
(a)
(b)
Figure 3.2: An illustration of (a) coherent and (b) incoherent addition of fields for v scatterers. Coherent addition occurs when the source and receiver are placed at the same location
(O = O′ ) and incoherent when they are at different locations (O ̸= O′ ). The illustration is
based on [18].
2
V
where CRC = 16π
. This approach assumes that all antennas are present in the chamber
λ3
at the time of measurement. This constraint can be overcome by estimating τRC for each
configuration. These equations are derived from equations that assume an unloaded chamber,
the assumption is that the losses in the RC are dominated by the chamber walls [92]. A more
extensive derivation of these equations, along with their assumptions, is given in Appendix B.
3.2.3 One- and Two-Antenna Methods
The three-antenna method can be simplified to a method where only two antennas are necessary, the so-called two-antenna method. This is based on an additional assumption related
to backscattering enhancement. As mentioned in [17], ‘Backscattering enhancement may be
revealed when the wave field is scattered by a system of chaotically distributed scatterers’,
among many other effects. This concept can be applied to overmoded cavities [3] and shows
that it can be translated to a reverberation chamber. The first time this was reported in a
reverberation-chamber context was for acoustic applications in [38], and for electromagnetic
ones in [130]. Backscattering enhancement is the concept that, in an environment with many
scatterers, fields add coherently when transmitter and receiver are placed at the same location
and incoherently when they are not [37, 38, 106, 130, 219].
Coherent scattering was first reported in [219], and is illustrated in Fig. 3.2. In (a), a
path between v scatterers is illustrated, showing that the forward and backward paths take the
same route. Therefore, they arrive with the same phase and the fields add coherently. In (b),
it is illustrated that they take a different route and an incoherent addition occurs. A distance
47
3.2: A NTENNA -E FFICIENCY M ETHODS
between transmitter and reciever of more than λ /2 is often used as a rule-of-thumb where a
coherent addition does not occur anymore [38]. The ratio between coherent and incoherent
addition is called the enhanced-backscattering constant, eb . When scattering occurs, eb tends
to be higher than one [17]. For cavities with a large number of modes such as a waveguide [3],
or systems with a large number of scatterers and individual rays, eb tend to converge to two
[130]. Many works have put efforts into researching the concept of enhanced backscattering
in RF reverberation chambers [35, 127, 211, 230, 232], where some have used it as a tool to
characterize chamber performance [61, 139].1
Coherent addition occurs in a reverberation chamber when the transmitter and receiver
are at the same place, which corresponds to an S11,s measurement. Subsequently, incoherent
additions occur when having them at different places, which corresponds to an S21,s measurement. However, dividing the two does not yield the enhanced backscattering constant of the
RC, since they are also affected by the antenna radiation efficiency. To overcome this, [97]
introduced an alternative description where it is assumed that the enhanced backscattering
constant does not change for position, polarization, and orientation as
eb =
⟨|S11,s |2 ⟩ ⟨|S22,s |2 ⟩
=
,
⟨|S21,s |2 ⟩ ⟨|S21,s |2 ⟩
(3.3)
which can be rewritten as
p
⟨|S11,s |2 ⟩⟨|S22,s |2 ⟩
eb =
.
(3.4)
⟨|S21,s |2 ⟩
To understand that the radiation efficiency is not included in this formulation, one may
write ⟨|S21,s |2 ⟩ as combination of loss introduced by the RC and by the antenna as
⟨|S21,s,RC |2 ⟩ηrad,2 ηrad,1 , where ⟨|S21,s,RC |2 ⟩ is the loss contribution of the RC to the measured
S21 (same as GRef ). The two-antenna-method estimate is obtained by substituting (3.4) into
(3.2), giving
s
s
CRC
ωτRC
η1tot =
s
η2tot =
CRC
ωτRC
s
⟨|S11,s |2 ⟩
,
eb
(3.5a)
⟨|S22,s |2 ⟩
.
eb
(3.5b)
The one-antenna-method estimate can be estimated by assuming eb = 2 as
s
r
⟨|S11,s |2 ⟩
CRC
tot
η1 =
.
ωτRC
2
(3.6)
Generally, the three-antenna method is the most accurate method. However, when it comes
to the two- and one-antenna methods, it highly depends on the setup which one is more accurate. Due to their dependency on stirred-energy components of reflection-coefficient measurements, they are sensitive to errors. This is because other effects with a random behavior
1 The latter is not to be advised, because, as we will show, there are many effects that can impact e that are
b
not related to the quality of the chamber itself.
48
S YSTEMATIC -E RROR Q UANTIFICATION FOR E STIMATING A NTENNA E FFICIENCY
can influence the measured variance, leading to a systematic error in the measurement. The
first one is noise.
3.3 Effect of Noise on the Overestimation of Antenna
Efficiency
In this section, we show that large systematic errors can occur in the one- and two-antenna
methods, because the noise contribution can surpass the contribution of the RC to the measured variance, or stirred-energy component, of an S-parameter [P8][224]. We show an example of an efficiency measurement affected by noise, and ways to recognize and reduce this
effect.
3.3.1 Noise Variance
As described in Section 2.3, the stirred-energy component in an RC measurement can be
modeled as a random variable. Electronic noise from the measurement setup, including instrumentation, will act as a random variable as well (see [P10]) and hence, contributes to the
variance of an RC measurement. This occurs especially with low received signal levels as occurs in antennas with low total efficiency or at mmWave frequencies where transmitted power
levels may be low. Thus, the variance of an S-parameter to the first order of approximation
can be written as a combination of contributions from the paddles and the noise as
⟨|Si j,s |2 ⟩ = ⟨|Si j,paddles + Si j,noise |2 ⟩N ,
(3.7)
where Si j,noise and Si j,paddles are the zero-mean contributions to the stirred energy by the noise
and the mode-stirring mechanisms, respectively, and where i and j are the corresponding
VNA ports the antennas are connected to [P8]. In this case, i can be equal to j. Including a
dependency on noise in these equations is key to understanding the susceptibility to noise of
these antenna-efficiency methods, as the relation between the paddle and noise contributions
directly relates to the Signal-to-Noise Ratio (SNR).2
For antennas with a high total efficiency and for chambers with low losses, the contribution of the noise to ⟨|Sii,s |2 ⟩ and ⟨|Si j,s |2 ⟩ is negligible compared to the contribution of the
paddles. However, for antennas with a low total efficiency (due to either a high mismatch
or loss) this may not be the case, as the contribution of the mode-stirred energy can be less
than that of the noise. As can be derived from (3.7), this increased relative contribution of
the noise can lead to an overestimated variance of the S-parameter, which consequentially
leads to an over- or underestimated efficiency (see (3.5) and (3.2)). Inherently, this effect
2 We refer the reader to [P10] for an extensive analysis of the probability distributions of the noise in S-
parameter VNA measurements.
49
3.3: E FFECT OF N OISE ON THE OVERESTIMATION OF A NTENNA E FFICIENCY
One-Antenna Method
Two-Antenna Method
Three-Antenna Method
Antenna-Replacement Method
Efficiency (%)
30
20
10
0
1.2
1.4
1.6
1.8
2
2.2
2.4
2.6
2.8
Frequency (GHz)
Figure 3.3: Estimated total efficiency for a reconfigurable antenna, computed using three
different methods.
becomes more significant in the measured Sii of a low-total-efficiency antenna (given a second high-total-efficiency antenna), assuming ⟨|Sii,noise |2 ⟩ ≈ ⟨|Si j,noise |2 ⟩. In such a case, the
waves contributing to the mode-stirred energy (Sii,paddles ) experience twice the attenuation of
the low-total efficiency antenna (round trip) compared to only once for transmission parameters (single trip), as illustrated in Fig. 2.3. Since the one- and two-antenna methods use
S-parameters where i = j, they are more susceptible to noise effects than the three-antenna
method, which only uses S-parameters where i ̸= j. Note that this effect is hard to distinguish from regular reverberation-chamber behavior. The measured Sii is usually well above
the noise floor, while its stirred energy component may be below the noise floor. Especially
when one does not know the efficiency of an antenna, this effect can remain unnoticed.
3.3.2 Example: Efficiency for a Reconfigurable Antenna
The magnitude of the systematic error created by noise is highly dependent on many parts
of the setup, such as the VNA settings and output power level, antennas, chamber loss, etc.
However, to show that noise can yield a significant error for certain antenna-efficiency methods, while not in others, we show an example of a low-efficiency reconfigurable antenna [36].
This is because the efficiency of mmWave antennas is typically lower, which is expected to be
even more significant at higher frequencies [121]. The antenna was tuned to 1.4 GHz and has
a high rejection band adjacent to the band of operation. Overall, the antenna has a low total
efficiency, leading to a value of S11,s that is close to, or below the noise floor for a large part
of the frequency band. The measurements were performed in a lower-frequency chamber and
we refer the reader to [P8] for a more extensive explanation of the setup and chamber used.
Fig. 3.3 shows the radiation-efficiency result of a measurement of the reconfigurable antenna. The error bars correspond to the 95 % confidence interval. The full uncertainty analysis
50
S YSTEMATIC -E RROR Q UANTIFICATION FOR E STIMATING A NTENNA E FFICIENCY
eb
120
PVNA = -8 dBm
100
PVNA = -8 dBm, Repeat
80
PVNA = 0 dBm
60
PVNA = 12 dBm
Ideal (eb = 2)
40
20
0
1.2
1.4
1.6
1.8
2
2.2
2.4
2.6
2.8
Frequency (GHz)
Figure 3.4: Enhanced backscatter constant for two repeats with VNA signal power -8 dBm,
and one repeat with a 12 dBm signal power, compared to the ideal value of eb = 2, as it
would be in the one-antenna method. eb relies directly on S11,s and is therefore overestimated
as well. For increased signal powers, hence higher SNRs, the eb estimate gets closer to a
realistic value (approximately 2), but even then, S11,s is not significantly higher than the noise
floor, creating an overestimation in eb .
is extensively described in [P8]. It can be seen that the antenna-replacement and three-antenna
methods yield a similar best-estimate result and a similar uncertainty. However, the two- and
one-antenna methods significantly overestimate the efficiency. The
p overestimation is more
significant in the one-antenna methodqdue to the dependency on ⟨|S11,s |2 ⟩, where the twop
⟨|S11,s |2 ⟩. The measurements that have a significant
antenna method has a dependency on
noise contribution also have a larger measurement uncertainty as shown in Fig. 3.3 [P8].
3.3.3 Recognizing and Reducing the Effect of Noise in the One- and
Two-Antenna Methods
If one does not know the expected efficiency of the AUT , it can be hard to tell whether
or not the two-antenna method efficiency estimate is affected by noise, since S11 can have
a high SNR , while S11,s may not. An intuitive approach to uncover the noise effect is by
investigating the estimated eb . It is valuable to know that eb should be approximately two [35,
211], but since the calculation of the estimate directly depends on Sii,s as well (see (3.4)), the
calculated estimate can deviate significantly further from those values. Therefore, observing a
significant difference between the expected eb and the calculated estimate can be an indicator
of the noise effect. An example of this is shown in Fig. 3.4, where the eb was measured
between two antennas, where one antenna had a 50 dB attenuator connected to it. In this
case the S11,s was attenuated by approximately 100 dB, bringing it below the VNA noise
floor, while the S21,s remains well above it. The measurement was repeated for various VNA
power levels. For all frequencies, the eb estimate is much higher than usual and, therefore,
3.4: M ONOSTATIC S CATTERING FROM M ODE -S TIRRING M ECHANISMS
(a)
51
(b)
Figure 3.5: Illustration of the different setups in the RC to test monostatic scattering from
both the mode-stirring mechanism and the corner, with the antenna pointed at the stirrer at
(a) 0 degrees and (b) 20 degrees. We also tested 35 degrees.
this measurement is likely significantly affected by noise. Increasing the VNA output power
and, hence, increasing the SNR if the signal source noise is not dominant, reduces the eb (see
Fig. 3.4).
As shown in Fig. 3.4 for a -8 dBm VNA output power, the effect is repeatable when
the setup is not changed. Therefore, the high uncertainty levels in Fig. 3.3 for the one- and
two-antenna methods remain unexplained. It was noted that moving the antenna to a different
position in the chamber created this large uncertainty. We expect that this is caused by changes
in unstirred energy (hence, in the measured reflection coefficient). When the stirred-energy
component is low, variations in the unstirred one can create even larger variations in the
stirred-energy component (see (2.3)).
Another approach to recognize the effect in the two-antenna method, is by evaluating the
efficiency of the measurement antenna used, as this is calculated using the same variables (see
(3.5)). If this is far from an expected reference, the measurement is likely affected. In general,
for low-efficiency antennas (e.g. antennas on-chip or in-package [121]), it is recommended
to use methods that do not depend on S11,s . Amongst those presented in this chapter, methods
such as the modified two-antenna technique proposed in [224] also managed to remove this
dependency and show a reduction in the noise effect, but at a cost of additional assumptions
from the one-antenna method.
52
S YSTEMATIC -E RROR Q UANTIFICATION FOR E STIMATING A NTENNA E FFICIENCY
Figure 3.6: Illustration of the 0-degree setup in the RC to test monostatic scattering.
3.4 Monostatic Scattering from Mode-Stirring Mechanisms
In addition to noise, there can also be other effects in the measurement that have a random
behavior, which in turn affects the variance in a similar way. One of the most significant
being monostatic scattering from mode-stirring mechanisms. Monostatic scattering happens
when a wave transmitted by an antenna is directly reflected back to that antenna by the modestirring mechanism. In the IEEE Recommended Practice for Antenna Measurements [103], it
is recommended to point the antennas at the mode-stirring mechanisms, but this risks getting
significant measurement errors using traditional RC architectures. In this section, we show
examples of this effect, where we quantify the magnitude of the systematic error in the oneand two-antenna methods for the mmWave RC design presented in Chapter 2. We also present
possible solutions with a change in stirrer design.
3.4.1 Mean and Variance of a Mode-Stirring Mechanism
Any mode-stirring mechanism is designed to create reflections in the chamber that behave
as randomly as possible. Therefore, a wave encountering the mode-stirring mechanism ideally reflects in a different direction, depending on the position of the mechanism (a type of
bistatic scattering). However, for many commonly-used mode-stirring mechanisms, waves
3.4: M ONOSTATIC S CATTERING FROM M ODE -S TIRRING M ECHANISMS
53
are directly reflected back to the source. Such effects were uncovered earlier in [173, 175],
where a measured RCS pattern of an object was overestimated due to direct reflections of
a mode-stirring mechanism. The effect on the variance was also shown in [35, 62], but the
reason behind it was not uncovered.
In practice, monostatic scattering from mode-stirring mechanisms has a component affecting the measured mean, and one affecting the variance, as we will show, which is highly
dependent on the position of the antenna. The Z-folded stirrer and the corner of the RC it
is placed in front of, consist of many different corner-reflector types of shapes, which are
notorious for high monostatic scattering [198, 204]. Intuitively, this effect would be the most
significant when an antenna is pointed directly at the stirrer. Due to the rotation of the stirrer,
the reflected wave differs in terms of phase and magnitude per position of the mode-stirring
mechanism and then arrives at the antenna. Therefore this effect has a measurable mean and
variance affecting the unstirred and stirred components of S11 , respectively.
We show this effect by performing a measurement, with the antenna positioned at three
different angles toward the mode-stirring mechanism. An illustration of the setups are shown
in Fig. 3.5, and a photo of the 0-degree setup in Fig. 3.6. The results of these measurements
are shown in Fig. 3.7. It is shown that the stirred-energy component of S21 (c) does not
show systematic differences between the three angles. However, the unstirred component of
S11 (b), which should correspond to only the reflection coefficient, differs per angle. This is
most significant when the antenna is pointed directly at the stirrer (0 degrees). In that case,
an additional ripple occurs. The stirred-energy component (a) shows the most significant
difference between the three angles, with a large systematic error at 0 degrees, but also for 20
degrees, including a ripple effect. Variations in the stirred-energy component can be caused
by differences in unstirred energy (see (2.3)), however, as can be seen in Fig. 3.7, in this case
the variation in stirred energy is not only related to the variation in unstirred energy.
The measured S11,s should only contain the chamber loss and twice the antenna efficiency
[97]. Since the losses did not change per setup, no difference between the setups is expected,
like the measured S21,s . The same holds for the measured ⟨S11 ⟩. The impact of monostatic
scattering in antenna-efficiency measurements remained uncovered since most measurements
depend on S21 , such as the antenna-replacement method.
To quantify the mean and variance of the monostatic scattering, we use the radar equation
as
S11,ReflStirrer =
G2Ant σRCS λ 2
,
(4π)3 r4
(3.8)
where S11,ReflStirrer is the impact of the monostatic scattering from the stirrer on S11 , GAnt
is the antenna gain, σRCS is the radar cross-section of the mode-stirring mechanism, and r is
the distance between the stirrer and the antenna phase center. In this case, σRCS has a non-zero
variance and mean, where each individual point corresponds to one position of the stirrer. It
is visible that the most significant factor is the distance to the stirring mechanism, and that the
54
S YSTEMATIC -E RROR Q UANTIFICATION FOR E STIMATING A NTENNA E FFICIENCY
| S11,s |2 (dB)
-25
Z-Fold 0 Degrees
Z-Fold 20 Degrees
Z-Fold 35 Degrees
-26
-27
-28
-29
31
32
33
34
35
36
37
38
39
Frequency (GHz)
(a)
| S11 | (dB)
-20
Z-Fold 0 Degrees
Z-Fold 20 Degrees
Z-Fold 35 Degrees
-25
-30
-35
-40
31
32
33
34
35
36
37
38
39
Frequency (GHz)
(b)
| S21,s |2 (dB)
-29
Z-Fold 0 Degrees
Z-Fold 20 Degrees
Z-Fold 35 Degrees
-30
-31
-32
-33
31
32
33
34
35
36
37
38
39
Frequency (GHz)
(c)
Figure 3.7: Measured S-parameters when an antenna is pointed directly at the Z-folded stirring mechanism at different angles.
55
3.4: M ONOSTATIC S CATTERING FROM M ODE -S TIRRING M ECHANISMS
-24
|S11,s|2
-26
-28
-30
-32
-34
31
32
S11,s Ant. 40° + S11,ReflStirrer
S11,ReflStirrer
S11,s Measured, Ant. 40°
S11,s Measured Ant. 0°
33
37
34
35
36
38
39
Frequency (GHz)
Figure 3.8: Contributions to the stirred component of S11 . The measured S11,s for an antenna
pointed at the mode-stirring mechanism at 0 degrees (blue dashed), and 40 degrees (red),
including an estimate of S11,ReflStirrer (yellow), which we added to the 0-degree measurements
(blue solid).
effect is significantly higher for a high-gain antenna. The latter was also found in [62]. The
gain of the antenna, the distance to the mode-stirring mechanism, and the frequency are all
known.
To predict σRCS , we show a measurement setup where the antenna is placed at two different angles with respect to the stirrer. In the first setup, an antenna was pointed at the stirrer
at 0 degrees, and in the second setup at 40 degrees. The results are shown in Fig. 3.8. Note
that the difference in S11,s between the two setups is even larger in this case as compared to
the ones shown in Fig. 3.7. Since the setup is the same as in Fig. 3.6, this is likely due to
the starting position of the mode-stirring mechanism, as we will show in the next section. In
the 40-degree case, S11,s is a combination of a random variable that describes well-stirred RC
behavior, and of a random variable that relates to the direct reflection of the mode-stirring
mechanism. In the 40-degree case, it is assumed that the former random variable is dominant. Therefore, a rough estimate of σ can be obtained in an iterative fashion by using
S11,s,40 Degrees = S11,s,0 Degrees + S11,ReflStirrer , where each term is a complex random variable.
We found that this holds for a variance of σ of 0.5, when modeling σ as a complex random
variable. This can be seen in Fig. 3.8, where S11,ReflStirrer increases over frequency. As can
be deduced from (3.8), this is caused by the increasing antenna gain over frequency of the
SGH antenna used. We acknowledge that this estimate is rough and, in these setups, less
repeatable. However, it does provide insight into the physical effects of the RC, which tend
to be less intuitive to understand. These approaches may be useful to optimize mode-stirring
mechanisms, by simulating its RCS. This is a topic for future research.
To show the significance of this effect on antenna efficiency, we computed the efficiency
using one of the measurements presented in Section 2.3. The results are shown in Fig 3.9. In
56
S YSTEMATIC -E RROR Q UANTIFICATION FOR E STIMATING A NTENNA E FFICIENCY
Efficiency (%)
150
100
tot
50
25
tot
2-Ant. Method
tot
3-Ant. Method
1-Ant. Method
30
35
40
Frequency (GHz)
Figure 3.9: Efficiency computed using the one- two- and three-antenna methods.
this position, the antennas are pointed at an angle at the mode-stirring mechanisms. It can be
seen that the one- and two-antenna methods produce an estimate far outside of the uncertainty
of the three-antenna method, because of the overestimated S11,s (see (3.5) and (3.6)). With the
two-antenna method, this causes an underestimation of the efficiency of the second antenna
(see (3.5)). The overestimation varies significantly per position, increasing uncertainty.
3.4.2 Dependency on Starting Angle
Intuitively, the magnitude and phase of the reflected wave are highly dependent on not only the
antenna position but also the stirrer position. Since only a small set of stirrer positions is used
(only ten), there is also a dependency on the starting angle of the mode-stirring mechanism.
For example, for certain angles, the antenna points directly at the corner of the RC behind the
mode-stirring mechanism, which can give a large reflection. This is illustrated in Fig. 3.10.
The variation of S11,s over different starting angles of the stirrer can be seen in Fig. 3.11,
where we performed a measurement with the stirrer starting at different angular positions. As
discussed in the previous subsection, it can be seen that S11,s is overestimated for each case
where the antenna is pointed directly at the stirrer, as compared to one where the antenna
is pointed at an angle. In addition to that, without moving the antenna, different results are
obtained for different angular starting positions of the stirrer.
The stirrer position corresponding to 90◦ is shown in Fig. 3.11, and the angles are defined
clockwise. For the 90◦ starting angle, it can be seen that very little of the surface area of the
stirrer is illuminated and that the corner behind the mode-stirring mechanism, that acts as a
corner reflector, can create a high reflection. With the 36◦ angle steps, this occurs twice. Due
to this angular spacing, the results of 20◦ and 90◦ setups give similar results, as the angles
are only two degrees apart. This shows that the corner behind the mode-stirring mechanism
can have a very dominant effect on the measurement, similar to the findings in [173, 198].
57
3.4: M ONOSTATIC S CATTERING FROM M ODE -S TIRRING M ECHANISMS
Figure 3.10: Illustration of a stirrer position where the corner behind it can create a large
direct reflection.
-25
| S11,s |2
-26
-27
-28
-29
Ant. 0°, Stirrer 0°
Ant. 0°, Stirrer 20°
Ant. 0°, Stirrer 90°
Ant. 45°, Stirrer 90°
31
32
33
34
35
36
37
38
39
Frequency (GHz)
Figure 3.11: Difference in S11,s per starting angle of the mode-stirring mechanism.
58
S YSTEMATIC -E RROR Q UANTIFICATION FOR E STIMATING A NTENNA E FFICIENCY
Figure 3.12: Optimized design of the mode-stirring mechanism, the Tilted-plate stirrer.
Possibly, these effects can be reduced by changing the corner behind the mode-stirring mechanism, or by adapting the mode-stirring mechanism so that it has no position where the corner
is significantly illuminated. Next, we will do the latter.
3.4.3 Optimized Stirrer Design
Mode-stirring mechanisms can be optimized to have low monostatic scattering, in addition
to considering its performance in terms of coherence angle and spatial uniformity. Without
changing the shape of the external chamber, we introduce a simple adjustment to the Z-folded
stirrer, including measured results, which is a first step to reducing the overestimation of S11,s .
We only make adaptations to the vertical stirrer.
For the optimized design we focused on reducing the corner-reflector effect by rotating
each individual plate by approximately 45 degrees as compared to the Z-folded stirrer. This
is shown in Fig. 3.12. This also makes sure that the situation in Fig 3.10 where the corner
behind the stirring mechanism is always covered by some of the surface area of the stirring
mechanism. The surface area and tilting angle of the individual plates are approximately the
same as with the Z-folded stirrer, as this is expected to give a similar coherence angle and
uniformity. We refer to this stirrer as the ‘Tilted-plate’ stirrer.
We performed the same measurement as the one shown in Fig. 3.7, with the same starting
angle, but now with the Tilted-plate stirrer. The results are shown in Fig. 3.13. We only show
59
3.4: M ONOSTATIC S CATTERING FROM M ODE -S TIRRING M ECHANISMS
| S11,s |2 (dB)
-26
-27
-28
-29
-30
Tilted 0 Degrees
Tilted 20 Degrees
Tilted 35 Degrees
31
32
33
34
35
36
37
38
39
Frequency (GHz)
(a)
| S11 | (dB)
-20
Tilted 0 Degrees
Tilted 20 Degrees
Tilted 35 Degrees
-25
-30
-35
-40
31
32
33
34
35
36
37
38
39
Frequency (GHz)
(b)
Figure 3.13: Measured (a) S11,s and (b) ⟨S11 ⟩ of the Tilted-plate stirrer for different antenna
positions.
60
S YSTEMATIC -E RROR Q UANTIFICATION FOR E STIMATING A NTENNA E FFICIENCY
metrics related to S11 for the sake of brevity, but it should be noted that there is no significant
variation in S21,s . The results show a reduction of the systematic overestimation of S11,s for
both the 20- and 0-degree cases, as compared to the Z-folded stirrer case. When the antenna
is pointed at 20 degrees, the effect is not significant anymore in S11,s . In the 0-degree case,
there is still an overestimation for the higher frequencies. The unstirred-energy component
also shows an overestimation and added ripple effect for 0 degrees and at certain places a
small overestimation at 20 degrees.
Note that we merely provide this new design to show that the impact of monostatic scattering can be mitigated by implementing small changes to the design. It is expected that the
mode-stirring mechanism can be optimized much further. In the next section, we provide
another small change that reduces monostatic scattering.
3.4.4 Correlation in S11,s
A very clear indication of monostatic scattering is an increased correlation in S11,s . It is not
common practice to evaluate this component, but, as we will show, this should be a crucial
step in evaluating data used to compute antenna efficiency. We evaluate the correlation of the
stirred-energy components between all mode-stirring samples using the Pearson correlation.
We use the entire frequency band here, to obtain an average estimate of correlation within
the band.3 For the sake of brevity, we only show the most relevant stirred-energy components. The results are shown in Fig. 3.14. Note that, to clearly visualize correlation above a
threshold, we changed the color map limits to a maximum of 0.5.
We first evaluate the Z-folded stirrer with the antenna pointed directly at the stirrer (0
degrees, Fig. 3.14(a-c)). The S11,s correlation has many samples above the threshold4 , while
no two different samples are correlated in S21,s . Distinct patterns can be observed in the
correlation of both S11,s and S22,s . The ‘blocks’ of 10x10 mode-stirring samples in the S11,s
correlation occur because of the mode-stirring sequence chosen, where the vertical stirrer
moves with 36 degrees every ten samples, and the horizontal one moves with 36 degrees
every sample. The latter also explains why the pattern occurs every ten samples for S22,s .
These patterns can be used to uncover, for example, angles of mode-stirring mechanisms
that are sensitive to monostatic scattering. For S11,s , high correlation occurs between the
samples 20 < n < 30 and 70 < n < 80. These sets of samples are approximately spaced 180
degrees apart and correspond to a stirrer position similar to the one shown in Fig. 3.10 where
the corner of the chamber behind the stirrer is directly illuminated. In S22,s , one position
has a higher correlation that occurs every ten mode-stirring samples. Using these results,
certain positions can be avoided or removed from the measurement. They can also be used to
compare the quality of different mode-stirring mechanisms.
3 To assess frequency-dependent behavior, the correlation should be computed over many small bands.
4 As mentioned in Appendix A, correlation can already be distinguished above 0.1 using the Pearson corre-
lation with this number of samples.
3.4: M ONOSTATIC S CATTERING FROM M ODE -S TIRRING M ECHANISMS
61
Pointing the antenna at an angle towards the mode-stirrer is expected to reduce direct
reflections, and hence, the correlation. This is shown in Fig. 3.14(g) and (h). For the sake of
brevity, we only show the correlation of S11,s for these cases, as they had the most significant
difference. It can be seen that the overall correlation is lower, but that for 20 degrees, there
are still many samples above the threshold. For all cases, a higher correlation corresponds to
a higher overestimation of S11,s .
The results for the Tilted-plate stirrer are shown in Fig. 3.14(d-f) for the antenna at 35
degrees, (i) for the antenna at 0 degrees, and (j) for the antenna at 20 degrees. For the 35degree case, all correlation values between different mode-stirring samples are below 0.37,
showing a significant improvement. Certain values are above a threshold of 0.3 for the 0degree case (i). A pattern related to the mode-stirring sequence still exists, showing that there
is still monostatic scattering present. It can also be seen in Fig. 3.12 that for certain positions,
the corner of the chamber is still directly illuminated by the horn antenna. To improve this,
we added bent corners to the stirrer and took another measurement at 20 degrees. The stirrer
is shown in Fig. 3.15, and the correlation in S11,s is shown in Fig. 3.14(k). For this case,
all values between different mode-stirring samples never cross a correlation of 0.2, which is
significantly lower than the correlation of the Z-folded and Tilted-plate stirrers. We refer to
this stirrer as the ‘Bent-plate’ stirrer.
3.4.5 Enhanced Backscattering and Antenna Efficiency
An overestimation of S11,s inherently creates an overestimation of eb , considering that S21,s is
hardly affected. This can be seen in Fig. 3.16 for the previously described cases. For all cases,
eb is higher than two. Previous works have noted that this occurs in high-frequency chambers
because high-frequencies are less easily diffused [225]. However, this is not supported by
the results shown in this work. We argue that indeed the waves diffuse less quickly, but that
it is mainly a result of monostatic scattering that is higher when using a high-gain antenna.
For example, the results in the 70-90 GHz and 90-140 GHz bands do not show an eb that is
significantly higher as compared to the 20-40 GHz band (see Fig. 3.17). For a combination
of antennas that have a lower antenna pair gain, eb is even lower. Position stirring may also
reduce eb .
To investigate the cause of the overestimated S11,s , we highlight the time-domain behavior. The results for three cases are shown in Fig. 3.18. It can be seen that S11,s converges
to the same value for each case, however, all cases show certain peaks in the early-time behavior. For the Z-folded case with the antenna at 0 degrees, these are significantly higher. It
is expected that these are due to standing waves between the antenna and the mode-stirring
mechanism with the chamber corner behind it, because the distance between them corresponds to the distance between the peaks.5 Similar effects can be seen in the other case, but
5 Note that these peaks were also observed in a lower-frequency chamber in [34], which also reported in an
increased eb [35]
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S YSTEMATIC -E RROR Q UANTIFICATION FOR E STIMATING A NTENNA E FFICIENCY
(a) ⟨|S11,s |2 ⟩
(b) ⟨|S22,s |2 ⟩
(c) ⟨|S21,s |2 ⟩
(d) ⟨|S11,s |2 ⟩
(e) ⟨|S22,s |2 ⟩
(f) ⟨|S21,s |2 ⟩
(g) ⟨|S11,s |2 ⟩
(h) ⟨|S11,s |2 ⟩
(i) ⟨|S11,s |2 ⟩
(j) ⟨|S11,s |2 ⟩
(k) ⟨|S11,s |2 ⟩
Figure 3.14: Correlation of stirred-energy components of the Z-folded stirrer with the antenna pointed at 0 degrees (a-c) and the Tilted-plate stirrer with the antenna at 35 degrees
(d-f), and the correlation in S11,s for the Z-folded stirrer with the antenna at (g) 20 degrees
and (h) 35 degrees, the Tilted-plate stirrer for (i) 0 degrees and (j) 20 degrees, and (k) the
Bent-plate stirrer at 20 degrees.
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3.4: M ONOSTATIC S CATTERING FROM M ODE -S TIRRING M ECHANISMS
Figure 3.15: A setup using the Bended-plate stirrer.
3
2.8
Z-Fold 0 Degrees
Z-Fold 20 Degrees
Z-Fold 35 Degrees
Tilted 0 Degrees
Tilted 20 Degrees
Tilted 35 Degrees
eb
2.6
2.4
2.2
2
31
32
33
34
35
36
37
38
39
Frequency (GHz)
Figure 3.16: Enhanced-backscattering constant for various antenna placements, for the Zfolded and Tilted-plate stirrer.
64
S YSTEMATIC -E RROR Q UANTIFICATION FOR E STIMATING A NTENNA E FFICIENCY
2.8
Horn-Horn
Horn-OEW
eb
2.6
2.4
2.2
2
95
100
105
110
115
120
125
130
135
Frequency (GHz)
Figure 3.17: Enhanced-backscattering constant for two different antenna setups, for the Zfolded stirrer.
Magnitude (dB)
-40
-50
-60
-70
-80
S11,s Z-Folded 0 Degrees
S21,s Z-Folded 0 Degrees
S11,s Tilted 35 Degrees
S11,s Ant. pointed at wall
S11,s Bent-Plate 20 Degrees
0
0.5
1
1.5
Time (s)
2
2.5
3
10-8
Figure 3.18: Time-domain response of S11,s showing the early-time behavior. When the
antenna is pointed to the stirrer, high peaks occur in the early-time behavior.
3.4: M ONOSTATIC S CATTERING FROM M ODE -S TIRRING M ECHANISMS
65
the peaks are significantly lower. Especially in the 3-5 ns interval, many peaks occur for all
cases, which correspond to the first reflections of the mode-stirring mechanism and chamber
corner. It is clear that these effects do not occur in the measured S21,s , as it is hardly affected
by different antenna positions. To show that effects in the early-time behavior cause the overestimation in eb , we performed time-gating to remove the first 30 ns and estimated eb . Both
cases with and without time-gating are shown in Fig. 3.19. It can be seen that eb drops down
to two after removing the early-time effect.6 A similar effect is shown in [61], and can be
evaluated using the correlation of the time-gated S11,s in Fig. 3.20(a). Compared to the nontime-gated version in Fig. 3.14(a), it can be seen that all correlation values between different
mode-stirring samples are below 0.05, showing the significant contribution of the early-time
behavior. Chamber-decay time is not dependent on early-time behavior. Therefore, τRC extracted from S11 gives a similar result as the one extracted from S21 .
Fig. 3.18 shows that almost regardless of the type of stirrer, significant reflections occur
in the early-time behavior when the antenna is pointed towards the stirrer. Therefore, the
recommendation given in [103] to point the antenna at the stirrer in the two-antenna method
may not be the best option. To show this, we performed another measurement in a later
measurement campaign. The setup is similar, but now the antenna is pointed at an angle
towards the wall (see Fig. 3.21). The result is also shown in Fig. 3.18. It can be seen that
still, a peak occurs because the antenna was placed towards a corner of the chamber, but
the reflections were significantly lower than in the other cases. This is also visible in the
correlation in Fig. 3.20(b), where the correlation between different mode-stirring samples is
below 0.15 for all cases. This is much lower than the earlier reported values. Therefore,
the most significant improvement can be achieved by not pointing the antenna at the modestirring mechanism or the corner of the chamber, and also by not pointing toward a corner,
or by eliminating corner reflections as was done in [198]. We expect that this effect can be
improved even further when structures are added to the RC that create more chaos in the
chamber, such as placing a pyramid on the wall or ceiling [P28].
3.4.6 Further Optimization Steps and Discussion
The adjustment to the Z-folded stirrer is small but creates a significant improvement in the
measured S11,s . However, there is still a measurable effect from monostatic scattering. Currently, all RC methods rely on wisely placing an antenna or wireless device, which makes it
less user-friendly. Especially in the case of an active antenna, the backscattered wave can load
the amplifiers present in the system, degrading the performance of the DUT. In these cases,
the measurement environment is not representative of the intended operational environment,
and care should be taken in positioning the antenna inside the chamber. In these cases, it
is not recommended to point the antenna at the mode-stirring mechanism but rather angled
6 This approach cannot be used to adapt the measurement in post-processing because it will miss certain loss
contributions in the S-parameters.
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S YSTEMATIC -E RROR Q UANTIFICATION FOR E STIMATING A NTENNA E FFICIENCY
3
eb timegated
eb
eb
2.8
2.6
2.4
2.2
2
31
32
33
34
35
36
37
38
39
Frequency (GHz)
Figure 3.19: Enhanced-backscattering constant of the Z-folded stirrer at 0 degrees, with and
without time gating.
(a) ⟨|S11,s |2 ⟩
(b) ⟨|S11,s |2 ⟩
Figure 3.20: Correlation of stirred-energy components of the Z-folded stirrer with the antenna pointed at 0 degrees, with the early-time behavior time gated out (a) and a setup with
the Z-folded stirrer, but with the antenna pointed at an angle towards the wall of the chamber.
3.4: M ONOSTATIC S CATTERING FROM M ODE -S TIRRING M ECHANISMS
67
Figure 3.21: Setup when the antenna is not pointed towards a mode-stirring mechanism but
at an angle towards a wall of the chamber.
toward one of the walls to avoid a direct reflection.
For future mode-stirring mechanisms and chamber designs, the RCS concept can be used
to optimize any mode-stirring mechanism to have reduced monostatic scattering. Additionally, the concept could also be used to design a bistatic scattering that is as high as possible but
changes significantly between different positions. The effect due to the corner could possibly
be reduced by replacing it with a mirror with a focal point on the mode-stirring mechanism.
Or, optimized shapes could be designed using artificial intelligence by only simulating the
mechanism with the corner, without performing a computationally-heavy simulation of the
full chamber. This could lead to unconventional shapes of the chamber walls, but give users a
foolproof way of antenna placement [P28]. We expect that other types of mode-stirring may
be less susceptible to these issues.
We also showed that correlation can create an overestimated eb , and that correlation values just below the commonly-used thresholds of 0.3 or 0.37 are still unacceptable for these
types of measurements. In fact, we would recommend that any correlation that is above the
correlation noise floor (see Appendix A) is significant and should be addressed. We have
found that a mean correlation of 0.05 can already be linked to an eb of approximately 2.2.7
A correlation above 0.1 links, in these setups, eb to values of 2.5. Future research should
7 This is given that enough samples are used such that the correlation noise floor is below this value.
68
S YSTEMATIC -E RROR Q UANTIFICATION FOR E STIMATING A NTENNA E FFICIENCY
focus on defining a threshold that is low enough to ensure acceptable measurement quality.
Another approach is that the correlation algorithm could be used to select a low-correlated
subset. This way, all mode-stirring samples that have a high correlation can be removed from
the mode-stirring sequence in post-processing, to create the lowest systematic error.
3.5 Contributions of Unwanted Radiation
The last source of errors we describe in this chapter are errors created by unwanted radiation,
which can occur before or after the calibration plane. With unwanted radiation, we mean all
radiation that occurs that is not part of what the user defined as the DUT [182]. We describe
three cases where unwanted radiation can create large systematic errors. The goal of this
section is merely to illustrate these effects.
3.5.1 Phased Array
An important metric to quantify loss management in phased-array systems is the antenna
efficiency [69]. Some previous works have measured the efficiencies of phased-array systems
in a reverberation chamber [10, 32, 210]. Most were performed in the sub-6 GHz band,
and only one performed measurements in the FR2 band by use of a total-radiated power
measurement [10]. To be able to measure a passive array, an RF beamforming system, such
as a Wilkinson splitter, needs to be added. As an example of such a system, we measured
an end-fire antenna array with eight ports, optimized for operation at 28 GHz. The setup is
shown in Fig. 3.22. RF beamforming was performed using a 1:8 Wilkinson Splitter (WS)
to realize a broadside beam, as shown in Fig. 3.23. The antenna is extensively described in
[P6]. For validation, we compare the results with simulations of the antenna, extracted from
time-domain simulations using CST Microwave Studio.
An issue can arise when this RF beamformer starts radiating. It is only present for measurement purposes and therefore not part of the DUT [182]. For this specific beamformer,
the unwanted radiation is very significant. We measured the radiated emissions of the splitter by measuring its radiation efficiency using the three-antenna method, where all ports are
terminated with 50-Ohm loads. As shown in Fig. 3.24, over 20 % of the power at the input is radiated. The error bars correspond to two standard deviations, extracted from nine
measurements at different locations.
We estimate the antenna efficiency of the total phased-array-antenna system using the
three-antenna method. Usually, the efficiency of only the antenna array is estimated by deembedding the RF beamformer including cables using a similar approach as presented in
[210]. However, this approach and other generic de-embedding methods do not take into account that losses that occur due to radiation remain inside the chamber. A correction for these
losses is then performed in the de-embedding process, and on top of that, the power inside
the chamber is also overestimated. This results in an overestimation of the efficiency of the
69
3.5: C ONTRIBUTIONS OF U NWANTED R ADIATION
Horizontal
Stirrer
Vertical
Stirrer
Antenna
Array
RF Beamformer
Measurement
Antenna
Figure 3.22: Setup of the phased-array system in the mmWave RC.
Splitter
Radiation
Splitter
Mismatch
Cable Loss
Antenna
Mismatch
Cable
Mismatch
Splitter
PCB Loss
Figure 3.23: The phased-array system that is placed inside the reverberation chamber, consisting of a phased-array antenna, cables, and a Wilkinson splitter with various losses quantified.
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S YSTEMATIC -E RROR Q UANTIFICATION FOR E STIMATING A NTENNA E FFICIENCY
Unwanted Radiation (%)
30
Rad
RF Beamformer
28
26
24
22
20
18
26.5
27
27.5
28
28.5
29
29.5
30
Frequency (GHz)
Figure 3.24: Radiation efficiency of the RF beamformer to characterize its unwanted radiation. The error bars correspond to the 95 % confidence interval.
antenna when de-embedding the RF beamformer. Especially in a reverberation chamber, conventional methods do not allow for distinguishing different sources of radiation. Therefore,
we extend the conventional de-embedding approach to include the radiation losses of the rest
of the system as follows
tot − η tot
ηTS
WS
,
(3.9)
rad )
LPCB,WS LMism,Cable LCables LMism,WS (1 − ηWS
where L corresponds to the losses due to various contributions, as shown in Fig. 3.23, and
tot is the total antenna efficiency (including mismatch) of the RF beamformer, corwhere ηWS
tot is the total efficiency of the total system. We
responding to its unwanted radiation. ηTS
assume that the efficiencies of the antenna and RF beamformer are uncorrelated here, and
acknowledge that this approach is not directly applicable to integrated systems.
The measured and simulated antenna-efficiency results are shown in Fig. 3.25. We show
the efficiency of the full setup, and that of the antenna alone, where the splitter and cables were
de-embedded using the conventional approach, and the approach using (3.9). As expected,
the efficiency estimate is higher for the antenna alone (when the splitter is de-embedded) as
compared to the full system. It can be seen that the efficiency is significantly overestimated
using the conventional approach (the efficiencies are above 200 %). However, when considering unwanted radiation, it is within 0.5 dB of the simulated values, showing the accuracy of
this method, and the necessity of taking unwanted radiation into account.
tot
ηAntenna
=
3.5.2 Waveguide Leakage
A significant problem in high-frequency measurements in an RC can be created by unwanted
radiation behind the calibration plane, for example from waveguide leakage. Low levels of
leakage can create large systematic errors, as we will show. The losses in the waveguides used
71
3.5: C ONTRIBUTIONS OF U NWANTED R ADIATION
10
Rad
Efficiency (dB)
Rad
Total System
Rad
Antenna, Embed. using (1)
Rad
Antenna, Embed. Conv.
Antenna Simulated
5
0
-5
26.5
27
27.5
28
28.5
29
29.5
30
Frequency (GHz)
Figure 3.25: Estimated radiation efficiencies in dB of the total system (black curve) casing,
and of the antenna with de-embedded splitter and cables using the conventional way (reddashed curve) and using (1) (blue-dotted curve), compared to simulations (blue-diamond
marked). Note that the conventional way of de-embedding yields a wrong estimate above
100 %.
-32
GRef (dB)
-33
GRef Mean
GRef with leaking waveguide
-34
-35
-36
-37
-38
70
75
80
85
Frequency (GHz)
Figure 3.26: Measured GRef with uncertainty from Fig. 2.14, with a case that is affected by
waveguide leakage.
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S YSTEMATIC -E RROR Q UANTIFICATION FOR E STIMATING A NTENNA E FFICIENCY
to guide the signal to the antenna are generally calibrated out. However, when these losses are
created by leakage, the leaked power remains inside the chamber. This gives an error in the
measured chamber loss, making it seem as though the additional power was radiated by the
antenna. The offset due to leakage, in combination with the introduced offset in calibration,
creates a total error that is roughly twice as high.
The frequency and magnitude of the leakage are highly dependent on the way the screws
that connect the waveguide pieces are tightened. While there are solutions for waveguides
that are less sensitive to leakage, it is still common practice to use waveguides with a flat
flange, tightened with four screws. Even with a dedicated torque wrench, it can happen that
the flanges are not tightly connected. For example, this happens when they are tightened one
by one. An example of a measurement where this was the case is shown in Fig. 3.26. The
measured chamber loss is significantly overestimated as the measurement lies outside of the
measurement uncertainty bounds from the results shown in Chapter 2. It can also be seen
that the leakage is frequency dependent. We only show an S21 -based metric here, but the
effect also occurs in S11,s in this measurement, and can even be larger there (e.g. the error
was almost 10 dB for the same measurement). How this error will manifest itself in antenna
efficiency highly depends on the method used.
To give another approximation of the magnitude of the error, we simulated the effect of
waveguide leakage by simulating a connection with a 10 µm gap, and by simulating connections where there is only a partial gap. The simulation model of the latter is shown in
Fig. 3.27. In Fig. 3.28, cross sections of the E-fields around the waveguide connections are
shown for a 10 µm gap. Significant leakage occurs at 80 GHz. Approximately 1.7 dB leaks,
as shown in the simulated S21 in Fig. 3.29. In the simulation model, ports 1 and 2 are defined
at the ins- and outputs of the waveguides. Considering that the leakage occurs behind the calibration plane, the calibration performs a correction for the 1.7 dB loss, but the leakage also
causes a 1.7 dB overestimation in the chamber loss because it stays inside the chamber. This
doubles the offset, leading to an error of approximately 3.6 dB, which corresponds roughly to
the error reported in Fig. 3.26. This can lead to a large error in efficiency (see (3.2)).
Lastly, we show a simulation of an example where two of the screws are more tightly
connected, creating a slight tilt or bend in the waveguide connection. To illustrate this effect,
we simulated several partial connections, where one with 50 % contact area is shown in
Fig. 3.27. As shown in the simulation results in Fig. 3.29, this creates a frequency shift
depending on the contact area. We also show a 65 % contact area result. It should be noted
that the effect can be overcome by carefully tightening the screws, so no tilting occurs in the
flanges. There are also waveguide flanges that are less sensitive to this [185].
Note that the goal of this section is merely to show that tightening the waveguide flanges
correctly is critical in reverberation-chamber measurements and that unwanted radiation behind the calibration plane can create errors that are twice as the leaked power magnitude. The
magnitude of the error is heavily dependent on the setup, but it is expected that the effect is
more significant as compared to an anechoic-chamber setup, because all the leakage remains
73
3.5: C ONTRIBUTIONS OF U NWANTED R ADIATION
Figure 3.27: Simulation model of a WR12 waveguide connection where two screws are more
tightly connected than others, creating a partial connection of the flanges.
60 GHz
80 GHz
(a)
(b)
90 GHz
(c)
Figure 3.28: Simulated leakage for a WR12 (E-band) waveguide connection.
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S YSTEMATIC -E RROR Q UANTIFICATION FOR E STIMATING A NTENNA E FFICIENCY
0
|S21| (dB)
-0.5
-1
-1.5
-2
-2.5
60
65
70
75
80
85
90
Frequency (GHz)
Figure 3.29: Simulation result of a WR12 waveguide connection, as shown in Fig. 3.27.
inside the chamber. Therefore, it gives a systematic error in the measured chamber loss, and
all metrics related to it, while in an anechoic chamber, an interference pattern or ripple would
be expected.
3.5.3 RF Probe
In this section, we show another example of unwanted radiation behind the calibration plane,
but from an RF probe. An RF probe is often used to connect a planar antenna operating
at a high frequency such as an antenna-on-chip, on-board or in-package. These probes are
far from ideal and radiation from the probe can disturb antenna measurements. It has been
shown various times that the probe can disturb radiation-pattern measurements in anechoic
environments [141, 142, 181, 182, 183]. In RC measurements, the radiation adds to the total
radiated power, and can, when calibrated out, cause similar errors as waveguide leakage. In
this section, we show an example of probe radiation in the chamber.
We placed a translation mechanism in the chamber that can move an RF probe with µm
precision, further referred to as a probe station. An example of a setup to measure an RFprobe-based antenna using this mechanism is shown in Fig. 3.30. We validated that the presence of the probe station does not impede the functionality of the RC significantly in terms
of uniformity. For such probed-based measurements, the RF probe needs to be calibrated.
This is often done using a calibration substrate. An example of such a setup is shown in
Fig. 3.31, where we landed the RF probe on a short and 50-Ohm termination on a calibration substrate and performed an antenna-efficiency measurement, treating the radiating body
that is the probe with calibration substrate as an antenna. We also performed a measurement
where the RF probe was not landed on the substrate. We acknowledge that the term efficiency
is odd for this purpose because a calibration substrate is not supposed to radiate (similar to
the radiating splitter earlier in this section). However, we keep the same terminology because
3.6: C ONCLUSION
75
we use the three-antenna method to characterize the radiation characteristics.
The results of the total antenna efficiency without calibrating the RF probe are shown in
Fig. 3.32. It can be seen that the total efficiency of an unterminated probe is very low, showing that hardly any energy is radiated. However, when the probe is landed on the calibration
substrate, over 20 % is radiated for certain frequencies for both the short and 50-Ohm terminations. We expect that this is caused by surface waves in the substrate which start to radiate.
This effect has been reported several times before in conducted on-wafer measurements [75,
153, 165, 166, 193, 206, 216, 217]. We acknowledge that the radiation can be mitigated by
choosing a different material to place the calibration substrate on, and by choosing different
calibration substrates. However, the reason we show this is to report that an RF probe when
landed to perform a measurement, radiation of the RF probe will contribute to the radiation
efficiency of the DUT , just like it does to the radiation pattern [141, 142, 153, 181, 183]. Depending on the setup-design choices that are made, this could potentially create large errors
in the measurement.
3.6 Conclusion
In this chapter, we have shown that large systematic errors can occur in the estimation of
antenna efficiency due to various reasons. We introduced several methods for estimating efficiency in RCs and compared them. While some methods can be used for active devices
(e.g. the three-antenna method and the antenna replacement method), we focused on passive
antennas in this chapter. A summary of the systematic errors that occurred in the measurements shown in this work is shown in Table 3.1.8 Several effects impact all methods, while
others only impact some. We merely show this table to provide a rough indication, because
it is highly dependent on the setup. A general user advice would be to use the three-antenna
method, or the IEC antenna-replacement method, as they are less sensitive to the errors discussed here.
We showed that influences that behave in a random way, such as noise or monostatic
scattering from the mode-stirring mechanism can have a large impact on the measurement
quality because they become indistinguishable from the random behavior of the RC. This
translates to an over- or underestimation of the antenna efficiencies when using the twoantenna method and leads to higher measurement uncertainty. With the one-antenna
qmethod,
p
p
S11,s .
this effect is even more significant because of its dependence on S11,s instead of
S21,s is less easily impacted, but it is possible when both antennas have a low total efficiency.
When the measurement is affected by noise, it can be difficult to recognize when the antenna
efficiency is not known because the full S-parameter can be well above the noise floor, while
the stirred-energy component is affected by noise. We showed that this can be recognized by
8 The errors in this table are absolute. That is, a 30 % reported systematic error could mean measuring 120 %
efficiency while it is 90 %. We report these errors merely as an indication.
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S YSTEMATIC -E RROR Q UANTIFICATION FOR E STIMATING A NTENNA E FFICIENCY
(a)
(b)
Figure 3.30: Probe station inside the RC, where an antenna setup is shown in (a), and a
zoomed-in figure of a probed patch antenna in (b).
77
3.6: C ONCLUSION
Figure 3.31: Setup of an RF probe on a calibration substrate.
Efficiency (%)
25
20
Probe Open
Probe Short Cal. Substrate
Probe Load Cal. Substrate
15
10
5
0
25
30
35
Frequency (GHz)
Figure 3.32: Total antenna efficiency of an RF probe left open and landed on various terminations on a calibration substrate.
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S YSTEMATIC -E RROR Q UANTIFICATION FOR E STIMATING A NTENNA E FFICIENCY
Table 3.1: Systematic errors in antenna efficiency reported in this Chapter.
Error
Contribution
Error
Magnitude
1-ant.
2-ant.
3-ant.
IEC
Noise
∼ 30 %
∼ 10 %
<1 %
<1 %
Monostatic
Scattering
∼ 40 %
∼ 15 %
<1 %
<1 %
Unwanted
Radiation
RF beamformer Waveguide
∼ 300 %
∼ 200 %
∼ 300 %
∼ 160 %
∼ 300 %
∼ 50 %
∼ 300 %
∼ 1-150 %
RF probe
∼ 20 %
∼ 20 %
∼ 20 %
∼ 20 %
evaluating the enhanced-backscattering constant.
We showed that a common practice in antenna placement, which is to point the antennas at the mode-stirring mechanisms, can create large measurement errors. This is because
monostatic scattering from the mode-stirring mechanisms causes direct reflections with varying phases and magnitudes in the early-time behavior of the chamber. This impacts the mean
and variance of the measured Sii , hence, the unstirred and stirred components. We showed
that this is mostly dependent on the position of the mode-stirring mechanism and the gain
and position of the antenna. We mitigated monostatic scattering with a different design, but
for each mechanism, large reflections occur in the early time. The best way to mitigate the
overestimation in Sii,s is to point the antenna angled toward one of the walls. These effects
are most easily recognized by evaluating eb , and by evaluating the correlation if Sii,s . We
conclude that a correlation threshold of 0.3 of 0.37 is likely too high. In our case, a measurement with a mean correlation above 0.05 can already be significantly affected. Future
research should focus on defining a general threshold, and on evaluating these thresholds in
other (lower-frequency) reverberation chambers.
Lastly, we showed three examples of how unwanted radiation can create large errors in
the estimate of antenna efficiency. We showed that radiation from other parts of the measurement system that are not considered part of the DUT can create errors when conventional
de-embedding approaches are used. We showed a case where a passive phased-array antenna
with an RF beamformer is measured, which leads to an approximately 6 dB overestimation
of the measured efficiency. We also showed an example of radiation that is created behind
the calibration plane, which was in this case created by a leaking waveguide. Leakage can
create an overestimation of the measured S-parameter, which can be twice as high due to a
calibration not taking into account that radiated energy remains inside the chamber. The magnitudes of the systematic errors are shown in Table 3.1. In the third example, we showed that
an RF probe placed on a calibration substrate can lead to a significant part of the signal being
radiated. While this highly depends on the setup, these effects should be taken into account
when measuring the antenna efficiency of antennas that need to be fed by an RF probe.
Chapter four
Methods for Over-the-Air Testing of
Integrated Devices
4.1 Introduction
The integration level of devices operating at mmWave frequencies is high to reduce losses
and costs. Additionally, high-frequency integrated devices often have (physically) small form
factors. There are many challenges in measuring small and highly-integrated devices. The
most significant one is that the antenna and the active components often cannot be separated.
However, even when they can be separated, testing them separately can give an unrealistic
idea of the system performance since the antenna and electronics can influence each other
when they are connected [70]. Especially in a phased-array topology, changing the beamforming settings can change many of these characteristics because, for example, the power
amplifiers experience different loading at the output. To add to the complexity, integrated systems sometimes have no RF input or there are integrated mixers present such that the input
and output frequencies are different.
In packaged systems, metrics related to the electronics and antennas both need to be measured over-the-air for integrated mmWave systems, and for many different settings. This
relates to testing typical ‘Radio Frequency Integrated Circuit (RFIC) metrics’ (e.g. spectral
regrowth, amplifier compression, intermodulation products, harmonic distortion in- and outof-band radiated emissions, spurious emissions, power gain, adjacent channel leakage ratio,
noise figure, etc.), but also typical antenna metrics (e.g. directivity, antenna gain, side-lobelevels, etc.). All these metrics can change when choosing a different beamforming setting.
To test all of these settings, it is necessary to perform fast and accurate Over The Air (OTA)
measurements.
Most RFIC metrics related to transmitting can be measured by evaluating the total raThis chapter is based on P1,P5,P7,P8,P24-26, P27, and P28.
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M ETHODS FOR OVER - THE -A IR T ESTING OF I NTEGRATED D EVICES
diated power (TRP) of the system for different settings of the electronics [65]. There are
standardized test methods for TRP measurements in RCs [58], making it ideal to use an RC
for fast characterization of many metrics of integrated systems. Measurements of TRP below
50 GHz have been performed in an RC [10, 180]. The same concept can also be applied to
received power, when there is access to a detector within the device, or when it has an RF
output. EMC standards exist at lower frequencies to measure time-varying system emissions
[102].
One of the most important receiving metrics of a wireless system is noise figure (Noise
Figure (NF)), which describes the amount of noise added by the system [122, 213]. It is
difficult to characterize NF over the air at mmWave frequencies. Existing methods, such as
the radiometric [15, 171] and Gain to Noise Temperature (G/T) methods [105, 111] are less
suitable for mmWave frequencies due to their dependency on device positioning, radiation
pattern, and form factor [74, 96]. This can easily lead to an uncertainty of several decibels.
In this chapter, we show that the mmWave RC can be used for accurate measurements
of TRP using a 100 GHz example, including uncertainty budget [P13] (Section 4.2). In Section 4.3, We introduce a new method to measure NF and system gain, which overcomes all
drawbacks of the previously mentioned methods by using the RC as a repeatable environment to create different noise-power levels [P5, P12, P14]. We describe a simplified method
of [P5], which eliminates the need for a VNA, so all measurements can be performed using
a spectrum analyzer. We show that this significantly reduces uncertainty. For these methods,
the device is characterized as a complete system due to its level of integration. To isolate the
performance of the antenna, we also introduce a new method in Section 4.4 that can estimate
the efficiency of an antenna when it is integrated into a device. This method is based on
contactless S-parameter measurements in an anechoic chamber and applied to an RC environment. A low-frequency proof-of-concept is shown for a connectorized antenna. The chapter
is concluded in Section 4.5.
4.2 Total Radiated Power
In this section, we describe the CTIA standardized test method for TRP measurements in an
RC and show an example in the mmWave RC [58]. We use a 100 GHz SGH antenna with a
signal generator as a proof-of-concept DUT, where we show with an uncertainty analysis that
the mmWave RC can be used for an accurate estimation of TRP to within +/- 0.5 dB with a
limited number of mode-stirring samples.
4.2.1 TRP Method
To measure TRP in an RC according to the standardized test method, a simple link budget
is solved [58]. A radiating device is placed inside the chamber together with a measurement
antenna that is connected to a detector. The power is measured at the detector (usually a
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4.2: T OTAL R ADIATED P OWER
Spectrum Analyzer (SA) or Base-Station Emulator (BSE) for cellular devices), and the losses
induced by the cables, the measurement antenna, and the chamber are subtracted in decibels,
which results in the TRP of the device. These loss contributions are unknown and need to be
characterized. The processes for measuring the TRP and the unknown losses are illustrated
in Fig. 4.1.
The losses of the cables and measurement antenna can be measured separately. The presence of the device adds losses to the chamber, so the chamber losses (GRef ) need to be characterized with the device inside1 . We refer to this measurement as the ‘chamber-loss measurement’2 . The chamber-loss measurement, illustrated in Fig. 4.1a, is performed using a VNA
(see (2.14)). An additional reference antenna is necessary here.
The TRP is estimated in a measurement when the DUT is radiating.3 This is referred to
in the standard as the ‘DUT measurement’, where the TRP is estimated using
TRP =
⟨PR ⟩N
,
tot G
Gref ηmeas
cable
(4.1)
where ⟨PR ⟩N is the received power at the detector, averaged over N mode-stirring states. The
losses in the chamber (GRef ), cable (Gcable ), and measurement antenna are then divided out
to obtain the total radiated power. Gref , is estimated according to (2.14). Note that the reference and measurement antennas and the DUT need to be present in the chamber in both the
chamber-loss and the DUT measurements so the losses in the chamber do not change between
both measurements. The DUT measurement is illustrated in Fig. 4.1b.
4.2.2 Measurement Setup 100 GHz Example
We apply the aforementioned method to a 100 GHz example. The measurements were performed in the mmWave reverberation chamber that was validated in Chapter 2. To be able to
have a good reference device, we used a signal generator connected to an SGH antenna as a
DUT. We determined this reference device’s output-power level at the antenna output by measuring the output power of the signal generator, and by adding the losses of the antenna and the
waveguide sections used to be able to bring the signal into the chamber. This leads to a TRP
estimate of 12.54 dBm (over a 1 MHz BW), with a center frequency of 100.002 GHz. Note
that the uncertainty of the reference device’s output-power level was not taken into account
in this work. We will further refer to this estimate as the ‘reference TRP’. The measurement
setup for the DUT measurement is shown in Fig. 4.2.
1 Small devices do not alter the chamber loss significantly and are not required to be present in the chamber
during precharacterization
2 In literature the chamber-loss measurement is often referred to as the ‘reference measurement’. We chose a
different name to avoid confusion with another reference measurement used to validate the TRP setup.
3 For low-frequency devices, the TRP is usually measured in combination with a BSE which configures the
device to transmit its maximum power. An SA, which is often integrated into the BSE, is then used to measure
the average received power across the channel BW.
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M ETHODS FOR OVER - THE -A IR T ESTING OF I NTEGRATED D EVICES
GRef
Ref.
antenna
GCable
DUT
Meas.
antenna
VNA
(a)
GRef
TRP
DUT
Meas.
antenna
50 Ω load (RF) Power
Detector
(b)
Figure 4.1: Illustrations of the general approach for (a) the chamber-loss measurement and
(b) the DUT measurement.
4.2: T OTAL R ADIATED P OWER
83
In Fig. 4.2, only two antennas are present in the chamber. Due to limited space in the
feedthrough section, it is not possible to feed three antennas into the chamber because dedicated waveguide feedthroughs had to be used. To prevent a significant change in Gref between
the DUT and chamber-loss measurements, we took the following approach: To perform the
chamber-loss measurement, we removed the DUT and replaced it with a reference antenna
with the same amount of waveguide pieces. This allows us to connect both the reference and
measurement antenna to a VNA. The setup is similar to the one in Fig. 4.2. For the chamber
loss measurement, a 200 kHz frequency spacing is used, with N = 100 mode-stirring samples
by stepping both mode-stirring mechanisms in 36-degree increments. The estimated efficiencies of the antennas used are given in Section 2.8. For the DUT measurement, we replaced the
reference antenna including waveguide pieces with the DUT (same model reference antenna
and waveguide pieces but different serial numbers, connected to an SA).
The received signal power is measured using an SA with a W-band harmonic mixer, which
automatically corrects for the change in amplitude due to the presence of the mixer. A photo
of the setup is shown in Fig. 4.2. For the SA, a frequency span of 25 MHz was measured, using
a 10 MHz Video Bandwidth (VBW) and a 1 MHz Resolution Bandwidth (RBW). The results
are averaged over N = 400 mode-stirring samples, by stepping both mode-stirring mechanisms in 18-degree increments. Note that the chamber loss measurement was performed with
less mode-stirring samples. This is because the uncertainty due to a lack of spatial uniformity
is also estimated with that number of samples in Section 2.7. Since the DUT measurement is
performed with more samples, it could be that this uncertainty component is slightly overestimated.
4.2.3 Measurement results and Uncertainty
The result of the chamber loss measurement is shown in Fig. 4.3. As can be seen, the measured chamber loss at 100.002 GHz is 38.06 dB. This does not include the efficiencies of the
tot and η tot ), using (2.14). The efficiencies of both
measurement and reference antennas (ηmeas
ref
antennas are estimated to be -0.46 dB. In this case, Gcable in (4.1) represents the losses in the
waveguide between the measurement antenna and signal analyzer. The measured losses were
2.40 dB, measured using a VNA. The measured received power ⟨PR ⟩N at the port of the signal
analyzer is shown in Fig. 4.4, which was -27.94 dBm at 100.002 GHz. Using (4.1), the measured TRP = 12.98 dBm, which is within 0.45 dB of the reference value. The time necessary
for this measurement is approximately 10 minutes, which is mainly due to the use of stepped
mode-stirring. By using continuous mode-stirring, the measurement time is dominated by
the sweep time of the signal analyzer, which is in the order of milliseconds, and shows a
significant potential to speed up measurement time (within one minute). Besides that, fewer
mode-stirring samples could be used, at the cost of an increased uncertainty.
An estimate of the uncertainty in this measurement is shown in Table 4.1. It is based
on the CTIA Certification Test Plan for lower-frequency measurements of large-form factor
devices [57, 58], where we did not include uncertainties that are deemed to be negligible
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M ETHODS FOR OVER - THE -A IR T ESTING OF I NTEGRATED D EVICES
Mode-stirring mechanisms
To Signal Generator
Feedthrough
To Signal Analyzer
Measurement Antenna
Figure 4.2: Photo of the TRP measurement setup. The signal generator and analyzer are
placed outside of the chamber but are not visible in this photo.
-37.9
GRef (dB)
-37.95
-38
-38.05
-38.1
-38.15
99
99.5
100
100.5
Frequency (GHz)
Figure 4.3: Chamber loss within the 99-101 GHz frequency band.
101
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4.2: T OTAL R ADIATED P OWER
-20
PR N (dBm)
-30
-40
-50
-60
-70
-80
99.99
99.995
100
100.005
100.01
100.015
Frequency (GHz)
Figure 4.4: Measured received power level at the signal analyzer, averaged over all N modestirring samples.
Table 4.1: Uncertainty Budget
Uncertainty Component
Chamber-loss Measurement
Chamber lack of spatial uniformity
Efficiency reference antennas
Mismatch VNA
Temperature variation
DUT Measurement
SA amplitude
Chamber lack of spatial uniformity
Miscellaneous uncertainty
Temperature variation
Mismatch SA
Expanded uncertainty
Standard Uncertainty
0.10 dB
0.10 dB
< 0.01 dB
< 0.01 dB
0.08 dB
0.20 dB
0.10 dB
< 0.01 dB
< 0.01 dB
0.54 dB
(< 0.01 dB). We expect some unquantified systematic errors in this work, since some of the
waveguide sections were disconnected and reconnected in between measurements. Besides
that, the uncertainty of the measurements performed to obtain the reference TRP was also
not taken into account. The uncertainty due to the chamber lack of spatial uniformity and in
the estimate of the antenna efficiencies were taken from previous measurement campaigns.
The SA amplitude stability was taken from the datasheet, and a miscellaneous uncertainty
is considered as recommended by the CTIA [57]. This leads to an expanded uncertainty of
0.54 dB, which is well below the 2.0 dB requirement mentioned in the CTIA [57]. Note
that the uncertainty is larger than the difference between the reference TRP and the measured
value of 0.44 dB, showing that the result is within the expected uncertainty bounds.
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M ETHODS FOR OVER - THE -A IR T ESTING OF I NTEGRATED D EVICES
4.3 Noise Figure
In this section, we describe a simplified version of the Reverberation Chamber Noise Figure
(RCN) method presented in [P5]. We immediately introduce the simplified version because it
requires fewer measurement steps and therefore, leads to a lower uncertainty. Moreover, all
measurements can be performed using a spectrum analyzer, unlike [P5], where also a VNA
measurement needs to be performed. The method is based on a Y-factor approach, where NF
and gain are extracted from the difference between a high and low noise-power level.
4.3.1 Y-Factor Method
NF is defined as the ratio between the SNR at the input and output of the DUT, and describes
the noise added by the DUT [2]. It is often referred to as noise temperature, because of the
dependence on temperature. This is because thermal noise is created by thermal agitation of
electrons, which increases for higher temperatures. For room temperature, the ambient noise
power is -174 dBm/Hz. If this is the input of an amplifier as DUT, that noise is amplified
by the DUT gain, and additional noise is added by the DUT, corresponding to its NF. For
receiving systems, it is crucial to characterize the NF, because the NF of a DUT directly
relates to the SNR.
The Y-factor method is a widely used method for noise-figure characterization. It can
be used to extract the NF and electronic gain of a system by subjecting the input of the
device to an environment with high and low noise-power levels, corresponding to a hot and
cold environment in terms of noise temperature. These environments are generally created
by turning a noise source off and on. Then, the noise power at the output of the device is
measured for both cases, Ncold and Nhot , respectively. The ratio between them is the Y-factor
given by
Nhot
.
(4.2)
Y=
Ncold
The noise temperatures of the noise source can be extracted from its Excess Noise Ratio
hot
(ENR), which is the noise power ratio between the on and off state temperatures, TSource
and
cold
TSource , respectively. These points can be plotted as the noise temperature at the input of the
DUT versus linear noise power at the output of the DUT, as illustrated in Fig. 4.5. A line
can be fitted through the two measured points, where the slope corresponds to the gain of the
DUT, and the intersection with the y-axis corresponds to the noise power added by the DUT.
The noise temperature of the DUT is calculated using (4.2), and is given by
hot −Y T cold
TSource
Source
TDUT =
,
Y −1
This work in this section was performed in collaboration with Tim Stek [P5,P12]
(4.3)
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4.3: N OISE F IGURE
Linear Noise
Power (W)
𝑁ℎ𝑜𝑡
𝑘𝐵𝐺𝐷𝑈𝑇 (slope)
𝑁𝑐𝑜𝑙𝑑
𝑁𝐷𝑈𝑇
𝑐𝑜𝑙𝑑
𝑇𝑆𝑜𝑢𝑟𝑐𝑒
Noise
Temperature (K)
ℎ𝑜𝑡
𝑇𝑆𝑜𝑢𝑟𝑐𝑒
Figure 4.5: Illustration of the Y-factor method.
and the DUT gain is given by
GDUT =
Nhot − Ncold
,
hot − T cold )
kB B(TSource
Source
(4.4)
where B is the bandwidth of the noise, and k is the Boltzmann constant [2].
When noise is measured, it should be taken into account that the receiving instrumentation, such as a spectrum analyzer, also has a NF contribution. In those cases, the total NF of
the DUT including instrumentation is measured. This can be described using Friis formula
for the cascading of noise factor stages
FTot = FDUT +
FSA − 1
,
GDUT
(4.5)
where FTot , FDUT , and FSA are the total, DUT, and SA NFs in linear scale, and where GDUT is
the gain of the DUT. The DUT NF can be estimated by performing a Y-factor measurement
of the total system, and a Y-factor measurement of the receiving system. Using (4.5), the NF
of the DUT can be isolated.
4.3.2 Reverberation-Chamber Noise-Figure Method
With the RCN method, we extend the Y-factor method to an OTA approach. This is because,
for integrated wireless devices, the different stages cannot be taken apart and it needs to be
measured over the air. The RCN method uses a reverberation chamber as a reference environment for the radiometric method to create a hot and cold noise environment in a repeatable
manner [P5]. We use the RC as a ‘wireless noise source’. This way, the Y-factor method can
be applied to estimate the NF, but methods such as the cold-source method can also be used.
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M ETHODS FOR OVER - THE -A IR T ESTING OF I NTEGRATED D EVICES
The RCN method was first introduced in [P5], but here we simplify the method such that
fewer calibration steps are necessary. This reduces uncertainty and allows all measurements
to be performed with an SA, instead of also needing to use a VNA [P5, P12, P26].
The simplified RCN does not require chamber pre-characterization, in which the transfer
function and the NF of the chamber are determined with a VNA. This is because we place both
the DUT and a calibration antenna with a known efficiency in the chamber at the same time, as
we will show. The procedure is illustrated in Fig. 4.6 and Fig. 4.7. Hot and cold environments
are created by placing an antenna inside the chamber with a noise source connected to it, and
by turning it on and off, respectively. Due to the inherent nature of an RC, the hot and cold
noise-power levels remain constant within the working volume of the chamber when averaged
over sufficient mode-stirring samples. In this way, the DUT can be placed anywhere in the
chamber, removing the positional constraints of the radiometric and G/T methods. Also, the
RC provides a shielded environment, making it not susceptible to outside noise influences,
which is not the case with the radiometric method.
To estimate the NF and gain of the DUT, a two-step calibration measurement needs to be
performed. The first step is to determine the hot and cold noise-power levels in the chamber,
Phot and Pcold , respectively. In the second calibration step, the NF and gain of the measurement
system are determined. The measurement system consists of a spectrum analyzer including
a pre-amplifier, and is illustrated in Fig. 4.6. In the first calibration step, the noise source is
connected to an amplifier and an antenna, Antenna 1, as shown in Fig. 4.6. The noise from the
noise source is amplified to overcome the losses in the RC, and Antenna 1 is used to transmit
the noise power into the RC. In the first calibration measurement, the DUT is placed inside
the RC, which is terminated with a 50Ω load. Additionally, a calibration antenna, Antenna 2,
with a known efficiency, ηant,2 , is placed in the chamber. The received power, Pm , is measured
using a spectrum analyzer, and averaged over N mode-stirring samples, obtained by changing
the position of the mode-stirring mechanisms. This is repeated for both noise-power levels
according to [58].
The noise temperature, Tmeas , and gain, Gmeas , of the measurement system, and the total
efficiency of Antenna 2, ηant,2 , should be subtracted (in dB) from the measured power, to
obtain the noise-power level at the aperture of Antenna 2, inside the chamber. The total efficiency can be obtained in a separate measurement campaign or by using a datasheet value, and
Tmeas and Gmeas are estimated using a second calibration measurement. In that measurement,
the noise source is connected to the measurement system and a Y-factor measurement is performed [P5]. The hot and cold noise-power levels inside the chamber can now be calculated
using
Tmeas
⟨Pm,hot/cold ⟩N
− kB
+ Tant,2 ,
(4.6)
Phot/cold =
Gmeas ηant,2
ηant,2
where ⟨Pm,hot/cold ⟩N is the measured output power at the spectrum analyzer, averaged over N
mode-stirring samples, when the noise source is turned on and off, respectively, and Tant,2 is
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4.3: N OISE F IGURE
the noise temperature of the calibration antenna (Antenna 2) that is estimated using
Tant,2 =
1 − ηant,2
Tph ,
ηant,2
(4.7)
where Tph is the physical temperature of the antenna.
After the two calibration steps, the DUT measurement can be performed. The DUT is
connected to the measurement system and the calibration antenna is terminated with a 50Ω
load. The DUT and antennas remain in the chamber for all measurements to keep a constant
chamber transfer function. Therefore, the noise-power levels Phot and Pcold , at the input of
Antenna 2 will be the same as the noise-power levels at the input of the DUT. Next, the noise
temperature, TDUT , and gain, GDUT , of the DUT can be estimated using the same approach
as in [P5]. The ratio Y = ⟨Pm,hot ⟩N /⟨Pm,cold ⟩N is used, where Pm,hot and Pm,cold are the measured power levels during the DUT measurement, when the noise source is turned on and off,
respectively. With this power ratio, the noise temperature of the DUT can be estimated using
TDUT =
Phot −Y Pcold Tmeas
−
.
kB (Y − 1)
GDUT
(4.8)
The gain of the DUT is calculated using
⟨Pm,hot ⟩N − ⟨Pm,cold ⟩N 1
.
(4.9)
Phot − Pcold
Gmeas
Note that this method is independent of knowing the chamber gain and NF, the efficiency of
Antenna 1, the ENR of the noise source used, etc. It only depends on accurately characterizing
the hot and cold noise-power levels in the chamber. That said, some knowledge about the
setup is necessary to choose the right setup settings for having the ideal hot and cold noisepower levels. These levels can be chosen by, for example, using a variable attenuator on the
transmitting side, and evaluating on the receiving end when the cold noise power level gets
below the noise floor, or when the amplifiers enter saturation for the hot noise-power level.
GDUT =
4.3.3 Measurement Setups
As an active DUT we used an SGH antenna, connected to a 6 dB attenuator and an amplifier,
as shown in Fig. 4.8, similar to [P5]. We used this device as a DUT, such that we could
make a reference measurement. This is the same approach as the one presented in [P5]. An
integrated device could not be used as a reference, because there was no accurate alternative
OTA method available to measure the NF of the complete device. The reference value was
obtained by performing a conducted Y-factor method on the amplifier (see Fig. 4.9), and by
measuring the efficiency of the antenna using the three-antenna method (converted to noise
temperature using (4.7)). Then, the NFs of both stages can be cascaded to obtain the NF
of the total system. Note that by using this approach, effects such as noise matching are
not taken into account due to the 50-Ohm environment for conducted measurements [78].
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M ETHODS FOR OVER - THE -A IR T ESTING OF I NTEGRATED D EVICES
PCold
PHot
DUT
Ant. 1
50 Ω
Noise
Source
Ant. 2
Spectrum
Analyzer
Measurement
System
Figure 4.6: Schematic overview of the first calibration Measurement.
PCold
DUT
PHot
Ant. 2
Ant. 1
50 Ω
Noise
Source
Spectrum
Analyzer
Measurement
System
Figure 4.7: Schematic overview of the DUT Measurement.
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4.3: N OISE F IGURE
Amplifier
Horn antenna
6 dB attenuator
Figure 4.8: The DUT used to validate the simplified RCN method.
Therefore, a 6 dB attenuator was placed between the antenna and the amplifier, such that the
RCN measurement is comparable to a 50-Ohm reference measurement. The system gain of
the DUT (approximately 16.5 dB) could be measured OTA in an accurate manner, by using
the three-antenna method. The RCN measurement is performed in the frequency band from
24 to 28.5 GHz. We used an RBW of 1 MHz and a VBW of 5 MHz so video filtering could
be neglected [2], and we used the Root-Mean Square (RMS) detector setting so no correction
factor for the noise-power density was required [189]. The mmWave RC was used with
N = 100 mode-stirring samples [P5, P21]. For each mode-stirring position, 10 random noise
samples were obtained. A frequency spacing of 1 MHz was used, and in post-processing, an
averaging BW of 500 MHz was used because of the broadband response of the DUT. The
noise source we used has an ENR of 12.08-13.24 dB, the amplifier at the transmitting side
has a gain of 40 dB, and the pre-amplifiers for the spectrum analyzer also have a total gain of
approximately 40 dB. The amplification should be sufficient to overcome the losses in the RC,
to obtain a sufficiently large difference between Phot and Pcold . At the same time, care should
be taken that the amplifiers are not driven into compression in the Phot case, which leads to an
underestimation of Phot , and therefore an underestimation of the gain, and an overestimation
of the NF (see Fig. 4.5). Some of these effects are well desribed and illustrated in [188].
The noise source, amplifiers, power supplies, and spectrum analyzer are placed outside of
the chamber, and connected to the antennas and DUT through a feedthrough panel to reduce
chamber loss. The complete setup is shown in Fig. 4.10.
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M ETHODS FOR OVER - THE -A IR T ESTING OF I NTEGRATED D EVICES
DC power
supply
Amplifier
6 dB attenuator
Noise source
RF connection to SA
Figure 4.9: Setup to characterize the Low-Noise Amplifier (LNA) with attenuator, using the
Y-Factor method.
Mode-stirring
mechanisms
DUT
Antenna 1
Feedthrough
Antenna 2
Figure 4.10: Setup inside the RC.
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4.3: N OISE F IGURE
Table 4.2: Uncertainty contributions per measurement
Uncertainty
Amplifier
Cables
SA Bandwidth (BW)
SA Trace stability
Noise Source
RC Uniformity
3-Antenna
x
x
x
Cal Meas 1
x
x
x
x
x
x
Cal Meas 2
x
x
x
x
x
DUT Meas
x
x
x
x
x
x
4.3.4 Uncertainty
The RCN method consists of two calibration measurements and a DUT measurement. The
uncertainty due to the random effects in each measurement is estimated by the standard deviation of multiple repeats for each measurement, where the repeats cover the spatial extent
of the working volume. The estimated uncertainty is a combination of effects, where each
measurement has different components contributing to the uncertainty. They are summarized
in Table 4.24 . The first calibration measurement and the DUT measurement are repeated
seven times, and the second calibration measurement is repeated ten times. The different
coverage factors corresponding to the limited number of samples are taken into account. The
uncertainty in the efficiency estimate of the calibration antenna is taken from the results in
Section 2.8.
The uncertainties of each measurement are shown in Table 4.3. The simplified RCN has
no increased uncertainty due to the additional assumption of having a calibration antenna with
a known efficiency, as the original RCN needed such an antenna as well. Therefore, they both
have the same uncertainty contribution related to radiation efficiency. The simplified RCN
does not depend on a chamber-loss measurement, so it has one less uncertainty contribution.
This is a significant improvement since the chamber-loss measurement uncertainty can be in
the order of 0.5 dB [P7], but this depends heavily on the setup. We estimate the uncertainty of
the final result with a Monte-Carlo simulation, considering the uncertainty of each separate
measurement and using a coverage factor of 2.45, as detailed in [P5].
4.3.5 Results
The results of the measured NF and gain, including error bars, are shown in Fig. 4.11 and
4.12, respectively. It can be seen that the uncertainty of the simplified RCN noise-figure
estimate overlaps with the reference and the original RCN results, showing that there is no
significant difference between them. However, the simplified RCN gain result does not overlap in two narrow parts of the band with the reference, and the original RCN gain result is,
4 The uncertainty due to the mismatch of the noise source was negligible, as shown in [P5].
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M ETHODS FOR OVER - THE -A IR T ESTING OF I NTEGRATED D EVICES
Table 4.3: Uncertainty of each measurement
Measurement
1st Calibration Meas: Phot/cold
2nd Calibration Meas: NF
2nd Calibration Meas: Gain
Radiation Efficiency Calibration Antenna
DUT Measurement: NF
DUT Measurement: Gain
Uncertainty
0.13 dB
0.02 dB
0.23 dB
1.39 %
0.16 dB
0.20 dB
Figure 4.11: Measured NF using the simplified RCN, compared with a reference measurement and original RCN result from [P5]
Figure 4.12: Measured gain using the simplified RCN, compared with a reference measurement and original RCN result from [P5]
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4.4: C ONTACTLESS E FFICIENCY M ETHOD
Table 4.4: Expanded Uncertainty of the Original and Simplified RCN Methods
System Gain
Noise Figure
Original RCN
1.00 dB
0.67 dB
Simplified RCN
0.75 dB
0.37 dB
overall, closer to the reference. We expect that this is because a different horn antenna and
waveguide-to-coaxial adapter are used, as compared to the reference and original RCN measurements in [P5]. The expanded uncertainty in the original RCN was 0.67 dB for NF an
1.00 dB for gain. For the simplified RCN this is approximately 0.37 dB for NF and 0.75 dB
for gain, showing the reduction in uncertainty due to the need for one less calibration step
(see Table 4.4). Since there are no alternative methods available for OTA NF measurements
at this frequency, the uncertainty estimate cannot be compared directly to previous experiments. However, lower-frequency experiments (below 5 GHz) using the radiometric and the
conducted Y-factor methods reported a standard uncertainty between 0.1 dB and 0.17 dB.
This is comparable to the 0.15 dB standard uncertainty of the simplified RCN method, showing the high accuracy achievable with this method. The RCN method is user-friendly, and can
also be applied in lower-frequency chambers, and for DUTs with a lower NF. Additionally,
since the (simplified) RC estimates the NF and gain of the complete device, effects such as
noise matching are taken into account in the measurement.
4.4 Contactless Efficiency Method
In this section, a method to estimate the efficiency of an antenna in a contactless manner
is introduced, the Contactless Efficiency Method (CEM) [P4]. It has been shown before
using a different method that efficiency can be characterized in a contactless manner using
an RC[129]. For this measurement, a switch connected to the antenna that can switch between three loads is necessary. In an integrated antenna system, such a switch is in many
cases already present to switch between the LNA and Power Amplifier (PA), as illustrated in
Fig. 4.13. Therefore, this method could potentially be used for such systems, if a third load
option is added, where the switch is not connected to either the LNA or PA (open termination). We describe the procedure of the CEM for a connectorized low-frequency antenna as
a proof-of-concept for such integrated mmWave applications, since a connectorized antenna
could provide a reference.
4.4.1 Contactless Characterization Method
The CEM is based on the concept of the contactless characterization method (CCM), which
has been applied numerous times to anechoic-chamber measurements to contactlessly characterize S-parameters [28, 31, 114, 154, 214]. The procedure is illustrated in Fig.4.14 and works
as follows. Two antennas are pointed towards each other, where one antenna is connected to
96
M ETHODS FOR OVER - THE -A IR T ESTING OF I NTEGRATED D EVICES
LNA
Rest of the
system
Open
Switch
PA
Antenna
element
Figure 4.13: An illustration of a system with an integrated antenna, where the CEM could
be used to estimate the antenna efficiency.
S21
Measurement
antenna
AUT
S11
S22
Γin
Γl
S12
Figure 4.14: Illustration of the Contactless Characterization Method (CCM).
97
4.4: C ONTACTLESS E FFICIENCY M ETHOD
Ant. A
(Meas.
antenna)
Short
Ant. B
(AUT)
Switch
Open
50 Ω
VNA
Figure 4.15: The setup of the CEM in the RC to estimate antenna efficiency.
a VNA, and the other antenna connected to a switch with three loads attached. The input
impedance Γin of the connectorized antenna is measured for three different load conditions of
the second antenna. From there, all S-parameters can be estimates as follows [28]:
 
  
l
l −1 Γin
1 Γin
S11
1 Γ1 Γ1
1

 = 1 Γin Γl Γl  Γin  ,
S22
2 2
2
2
l
l
S21 S12 − S11 S22
1 Γin
Γin
3 Γ3 Γ3
3

(4.10)
where Γl1,2,3 are the reflection coefficients of the three loads connected to the nonconnectorized antenna, and where Γin
1,2,3 are the measured reflection coefficients of the connectorized antenna for those three load conditions. Using loads that have the highest difference in impedance yields a larger measurable range, but any three known loads with a high
enough difference in impedance can be used. The method puts no restriction on the channel
conditions between the antennas, as was described in [28], as long as the channel is static.
Therefore, an RC can also be used, since each stirrer position is completely deterministic.
By placing the two antennas in the RC, and by switching between three different loads for
each stirrer position, the full S-parameter matrix can be extracted as if both antennas were
connected to a VNA. This procedure is illustrated in Fig. 4.15.
The S21 is estimated using (4.10), by taking the root of S21 S12 . This has two unique
solutions, where the real part is either positive or negative. If only the positive or negative
solutions are used in the RC measurement, the estimated real and imaginary parts of S21 do
not have a Gaussian distribution anymore. Since this is the assumption behind many RC
equations, this will result in a significant error in efficiency. Assuming that the measurement
is according to a well-stirred condition (so ⟨S12 ⟩ = 0), approximately 50 % of the samples
will have a positive real part, and approximately 50 % of the samples will have a negative
real part. Because an RC measurement consists of a finite number of samples, the probability
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M ETHODS FOR OVER - THE -A IR T ESTING OF I NTEGRATED D EVICES
of a sample having a positive or negative solution should be considered using a binomial
distribution, given by
N
Pr(Samples = α) =
N 0.5 ,
(4.11)
α
where α is the number of samples with a positive real part. To approximate the S21 distribution, 50 % of the samples is chosen at random to have a positive real part solution, and the
other 50 % is given a negative real part solution. It is unknown if the correct root is chosen
for each sample, but because of the low correlation and random spacing of the samples, this
is not expected to produce large errors in the ⟨|S21 |2 ⟩ estimate. The uncertainty due to the
probability that the samples are not separated equally is taken into account.
4.4.2 Measurement Setup
The measurement setup used is shown in Fig. 4.16. Two log-periodic antennas are placed
inside a 4.05 x 5.7 x 3.15 m3 RC. In Fig. 4.16, they are both connected to a VNA to have
a reference of the measured S-parameters. To show a proof-of-concept of the CEM, two
measurements were performed. In Setup 1, the blue log-periodic antenna is connected to the
switch and the silver log-periodic antenna is connected to a VNA. In Setup 2, this is the other
way around. The switch can switch between a short, open, and load termination. The measurement is performed in the 0.55-1.05 GHz frequency band, with 10001 frequency points.
These settings where chosen to be able to obtain an accurate estimate of chamber-decay time.
The VNA used an IF BW of 1 kHz, with 12 dBm output power. The output power is this
high to maximize the dynamic range. The chamber performance was verified in [P22,P19],
from which it was estimated that the oscillating-wall stirring mechanism could provide 33 uncorrelated samples. This is not sufficient to accurately estimate antenna efficiency [P22,P7],
so position stirring is applied with a turntable, and by placing the antenna at two different heights. We used 12 turntable angles and two antenna heights, which were verified to
yield uncorrelated samples. Therefore, the measurement consisted of 892 mode-stirring samples. The samples are divided over eight independent realizations, which is used to estimate
uncertainty. The division of the mode-stirring samples over the independent realizations is
described in Table 4.5.
4.4.3 Uncertainty
Similar to the uncertainty procedure described in Section 2.3, the variation between independent realization contains contributions from random effects such as cable movement, calibration, VNA trace stability, chamber lack of spatial uniformity, among others. Systematic
effects from the VNA or cables were assumed negligible. In the contactless measurement,
two additional uncertainties are taken into account. One of them is the uncertainty of the
switch. For each stirrer position, the switch switches between the three loads. We therefore
estimate its uncertainty from the standard deviation of a series of measurements of the switch,
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4.4: C ONTACTLESS E FFICIENCY M ETHOD
Figure 4.16: The setup of the Two-Antenna Method (TAM) in the RC at the TU/e.
Table 4.5: The stirring sequence of the independent realizations to estimate the uncertainty
due to lack of spatial uniformity
IR
Height
1
2
3
4
5
6
7
8
0m
0m
0m
0m
0.6 m
0.6 m
0.6 m
0.6 m
Turntable
Number of
Angles
positions
0, 120, 240
3
30, 150, 270
3
60, 180, 300
3
90, 210, 330
3
0, 120, 240
3
30, 150, 270
3
60, 180, 300
3
90, 210, 330
3
Paddle
Number of
positions
33
33
33
33
33
33
33
33
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M ETHODS FOR OVER - THE -A IR T ESTING OF I NTEGRATED D EVICES
(a)
(b)
Figure 4.17: The setup of the CEM in the RC at the TU/e.
101
4.4: C ONTACTLESS E FFICIENCY M ETHOD
connected to different loads. The other uncertainty is the uncertainty due to the assumption
that 50 % of the samples has a positive real part, and 50 % a negative real part. All uncertainties taken into account here are Type A uncertainties. The expanded uncertainty is estimated
using an RSS approach, with a coverage factor of 2.31 [115].
4.4.4 Results
The main challenge in using this method is the limited dynamic range. The RC poses a significant amount of losses on the measurement, and the measured difference in S11 between
the different loads is small (below -30 dB). In this measurement, the dynamic range is large
enough to estimate S21 and S22 accurately from an S11 measurement. However, the stirred
component of S22 (S22,s ) is not within the measurable range. This is because this measurement experiences at least four times the chamber loss. Therefore, we introduce an additional
assumption using the enhanced-backscattering constant, where we assume it to be equal to
two. Using (3.4), the stirred-energy component of S22 can be estimated by
⟨|S22,s |2 ⟩ =
4⟨|S12,s |2 ⟩
.
⟨|S11,s |2 ⟩
(4.12)
Note that this assumption can be easily overcome by using three antennas, and by applying
either the antenna-replacement or three-antenna method, since they are not dependent on
⟨|S22,s |2 ⟩. The estimated ⟨S22 ⟩ and ⟨|S22,s |2 ⟩ are shown in Fig. 4.18, where the contactless
result of Setup 1 is shown in (a), and Setup 2 in (b), where both results are compared to a
reference obtained by connecting both antennas to a VNA. The S-parameters extracted from
the contactless measurement are applied to the two-antenna method, where the chamberdecay time is calculated from the S11 measurement to optimize the dynamic range.
The measured S-parameters can be used to estimate the efficiency of the nonconnectorized antenna with all methods described in Section 3.2. To show a proof-of-concept,
we used the two-antenna method, and compared the results to a connectorized measurement
of that same method.The total and radiation efficiencies for both setups are shown in Figs 4.19
and 4.20, respectively. The uncertainty bounds of the contactlessly measured results overlap
across the entire band with the reference, showing a proof of concept of the CEM for low
frequencies. The uncertainties are shown in Table 4.6. The reference measurement had an
expanded uncertainty of 3.93 % for the total efficiency and 4.00 % for radiation efficiency.
This was higher for the CEM due to the uncertainty of the switch and the uncertainty due to
the assumption on the root solution of S21 , which was 3.98 % and 4.04 % for the total and
radiation efficiency, respectively. The radiation efficiency has a higher uncertainty due to the
correction for mismatch [33].
We conclude that more research is required to estimate the uncertainty of the CEM for
low-efficiency antennas or when using less-ideal loads because in those situations the dynamic
range is lower compared to the measurement setup described in this paper. The dynamic range
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M ETHODS FOR OVER - THE -A IR T ESTING OF I NTEGRATED D EVICES
Magnitude [dB]
-10
-15
| S22 | TAM
-20
| S22 | CEM
|S22,s|2 TAM
-25
-30
|S22,s|2 CEM
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
Frequency [GHz]
(a)
Magnitude [dB]
-10
-15
| S22 | TAM
-20
| S22 | CEM
|S22,s|2 TAM
-25
-30
|S22,s|2 CEM
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
Frequency [GHz]
(b)
Figure 4.18: Stirred (dotted line) and unstirred (solid line) components of S22 , measured
connectorized (red) and contactlessly (blue). Two-antenna method is abbreviated here as
TAM.
Table 4.6: Uncertainty contributions CEM and reference measurements.
Uncertainty
Repeatability
Switch &
Root Assumption
Expanded
Efficiency
Tot.
Rad.
Tot.
Rad.
Tot.
Rad.
Reference
1.70 %
1.73 %
3.93 %
4.00 %
CEM
1.70 %
1.73 %
0.14 %
0.14 %
3.98 %
4.04 %
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4.4: C ONTACTLESS E FFICIENCY M ETHOD
(a)
(b)
Figure 4.19: Total efficiencies of the AUT in (a) Setup 1 and (b) Setup 2, estimated using the
CEM and compared to the reference measurement. Two-antenna method is abbreviated here
as TAM.
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M ETHODS FOR OVER - THE -A IR T ESTING OF I NTEGRATED D EVICES
(a)
(b)
Figure 4.20: Radiation efficiencies of the AUT in (a) Setup 1 and (b) Setup 2, estimated using
the CEM and compared to the reference measurement. Two-antenna method is abbreviated
here as TAM.
4.5: C ONCLUSION
105
can be a limitation using the CEM5 . We acknowledge that the CEM is a long way from being
applied to fully integrated systems, however, if the dynamic range issue can be overcome
this method may be applicable for the characterization of integrated antennas operating at
mmWave frequencies.
4.5 Conclusion
In this chapter, we have introduced and validated various methods to characterize the transmitting and receiving performance metrics of integrated antenna systems. We showed a proofof-concept for 100 GHz TRP measurements in a mmWave RC, where the difference between
the reference and measured TRP is 0.44 dB, which is below the expanded measurement uncertainty of 0.54 dB. This uncertainty is below the 2.0 dB that is accepted by the CTIA for
sub-6 GHz measurements. Note that the performance of anechoic-chamber solutions reduces
for higher-frequency applications due to high uncertainties related to antenna placement and
absorber reflectivity [186], whereas the RC lends itself to be more scalable to higher frequencies due to the metal walls. We also introduced a new method to measure NF in an
OTA manner and simplified it in such a way that fewer calibration steps are needed. This
removed the need for a chamber-loss measurement, reducing the measurement uncertainty
from 0.67 dB to 0.37 dB for NF, and from 1.00 dB to 0.75 dB for gain. This uncertainty is
comparable to lower-frequency measurements of the radiometric method, showing the high
accuracy achievable with the RCN method. The method is user-friendly, as it is almost independent of device positioning, and all measurements can be performed using a spectrum
analyzer. Lastly, we introduced a contactless efficiency measurement to measure the isolated
antenna performance in an integrated antenna system. A low-frequency proof-of-concept with
a connectorized antenna showed that the S-parameters could be measured accurately since the
uncertainty bounds of the contactlessly estimated efficiency overlapped with a connectorized
result.
5 Potentially, this limitation can be overcome by using modulation with correlation detectors, which can
increase the measurable range significantly
106
Chapter five
Conclusions and Recommendations
Conclusions
Next-generation wireless systems operating at millimeter-wave frequencies require new innovative solutions for accurate measurements. This is mainly because of the higher level
of integration between electronics (or RFICs) and antennas. Metrics related to RFICs that
used to be measured in a conducted way (e.g. noise figure, harmonic distortion, intermodulation products, system gain, etc.) now need to be measured over the air, including the
antenna, because the connection between the antenna and electronics influences the system
performance. These issues are relevant for 5G mmWave phased-array systems that consist
of multiple RFICs and antennas, but also for systems operating above 100 GHz, where the
level of integration is even higher (e.g. antennas-on-chip or in-package). Settings of the
RFICs control the direction and magnitude of the beam. To properly characterize the system,
many settings need to be tested over a wide frequency band. This can take a long time in
a traditional anechoic chamber due to spatial sampling. A reverberation chamber is known
to measure overall power-based metrics within a fraction of the time, for lower frequencies.
In this thesis, we investigated the suitability of reverberation chambers for high-frequency
measurements, where we provided guidelines and potential issues on the way.
A rough idea of the operational frequency of a reverberation chamber can be given by
its size. We validated a reverberation chamber with an intended operation between 24 GHz
and 140 GHz. The chamber should be sufficiently large to fit a large number of modes. The
lowest-usable frequency according to the IEC EMC standard describes a situation that yields
an uncertainty that is too high for many antenna applications. At 24 GHz, the frequency
is over ten times higher than the IEC rule-of-thumb for the LUF. For high-frequency applications, the highest-usable frequency is of equal importance, which is the point where the
chamber loss starts to become too high to do a measurement within reasonable uncertainty.
In the chamber we validated, we showed that the chamber loss was -26 dB at 24 GHz, and
-41 dB at 140 GHz. This chamber loss is lower than previously reported in the literature. The
107
108
C ONCLUSIONS AND R ECOMMENDATIONS
uncertainty in chamber loss, measured with a limited number of mode-stirring samples (100)
was below 0.1 dB at 24 GHz, and 0.2 dB at 140 GHz. A lower uncertainty can be achieved
when using more mode-stirring samples.
Chamber-decay time is a metric that is more sensitive to evaluating loss contributions in
the chamber. For example, the effect of atmospheric loss can clearly be identified for certain
bands. When the atmospheric loss is higher than 1 dB/km, the effect was significant in the
chamber that was validated. This will become an issue when the RC is extended to even
higher frequencies, where the chamber loss can be completely dominated by atmospheric
loss. Measurements that depend on chamber-decay time, such as absorption cross-section or
antenna efficiency will be infeasible in a similar setting. A climate-controlled environment
could solve these issues.
The methods that are used at low frequencies to estimate antenna efficiency and total
radiated power can be used at mmWave frequencies. In the chamber that we validated, the
expanded uncertainty was below 3.5 % for all bands when measuring antenna efficiency with
the three-antenna method. For total radiated power, we performed a test at 100 GHz with an
expanded uncertainty of 0.53 dB. These uncertainties are well below the 2.0 dB requirement
mentioned in the CTIA standard. The testing time was approximately 10 min but at the time
of writing, the same measurement can be done within 1 min. This is valuable to test many
settings in a short time.
The one- and two-antenna methods are sensitive to large measurement errors because of
their dependence on Sii,s . First, the behavior of the reverberation chamber can be indistinguishable from the random behavior of electronic noise. This could lead to an overestimation
of the variance, which creates a systematic error. Because the antenna loss occurs twice in
Sii,s , this metric is more sensitive to errors due to noise when an antenna with low efficiency
is used. In a similar way, Sii,s can be overestimated when the antenna is pointed toward the
mode-stirring mechanism. This is part of the current IEEE Recommended Practice for Antenna Measurements, but we found it is better to not point the antenna at the mode-stirring
mechanism for the one- and two-antenna methods. Monostatic scattering from the modestirring mechanism has a higher magnitude than rays that have traveled through the entire
chamber, and they have a different magnitude and phase for each mode-stirring position. This
leads to an overestimation of the measured variance, which leads to an over- or underestimation of antenna efficiency. In the one-antenna method, this effect is larger than in the twop
antenna method, because the one-antenna method depends on S11,s and the two-antenna
qp
method on
S11,s . In this thesis, we reported errors up to 30 % for noise, and 40 % for
monostatic scattering. An open question in the RC research community on ‘why eb is not 2’
is therefore answered in this thesis, where it can be concluded that eb is mostly a metric of the
antenna-positioning choice, instead of the overall chamber quality. Larger errors can occur
when unwanted radiation impacts the measurement. Especially when the unwanted radiation
occurs behind the calibration plane (e.g. leakage from waveguides), the radiation remains inside the chamber, while the calibration creates a systematic offset for this loss. This roughly
109
doubles the systematic error in chamber loss. We reported errors of up to 400 % in this work.
The antenna efficiency of an antenna integrated into a wireless system is difficult to measure because it cannot be connected to measurement instrumentation. To show a proof-ofconcept of a method that may solve this issue, we applied the contactless characterization
method to extract all S-parameters by only measuring S11 , where the second antenna (the antenna under test) was connected to a switch that switches between short, open, and load terminations. In an integrated system, the switch between LNA and PA could be used potentially.
The contactless characterization method can be used in a highly-reflective environment, but
the measurable range is limited. To overcome this, we assumed eb = 2 to estimate S22,s . We
used the contactless measured S-parameters in the two-antenna method and compared it to a
connected case. The expanded uncertainty of the contactless efficiency method was approximately 4 %, which was only 0.1 % higher than the uncertainty in the connected measurement.
The method was performed below 1 GHz as a proof of concept.
Correlation is a key element in understanding the quality of a reverberation-chamber measurement. Generally used autocorrelation approaches merely evaluate the trend within a combination of mode-stirring samples, which makes it dependent on the order in which the samples are taken, while the chamber metrics that are evaluated are not dependent on this order
(e.g. mean or variance). Therefore, we propose to use a Pearson correlation approach that can
evaluate the similarity between mode-stirring samples, independent of the sampling order. A
potential downside is that frequency-dependent behavior is lost, but it can be overcome by
using small bands with sufficient frequency points. We show that the Pearson correlation can
be used to evaluate individual mode-stirring positions. For example, by evaluating the correlation of S11,s , errors due to monostatic scattering from the stirrer can be predicted. We found
that correlation well below the generally used threshold of 0.3 can already indicate systematic
errors. In this research, we found that a correlation above 0.05 in Sii,s can indicate a significant
measurement error.
We developed a new method to measure noise figure, which is an important characteristic
for receiving systems. The method uses a reverberation chamber as a wireless noise source
because it can be used to create a uniform noise-power level in the chamber. We introduce
a simplified method that only relies on the use of a spectrum analyzer, without performing
a chamber-loss measurement. The method uses a reference antenna with a known efficiency
and therefore skips a calibration step. This leads to reduced uncertainty. We used the Y-factor
method, which led to a 0.37 dB expanded uncertainty for noise figure in the 24-28.5 GHz
band. The wireless noise source can be used similarly to a conducted one and applied to the
same methods.
Recommendations
In this thesis, we aimed to extend and improve methods related to reverberation-chamber
methods, such that they are suitable for testing of mmWave wireless systems. These have led
110
C ONCLUSIONS AND R ECOMMENDATIONS
to new insights for future work, as there are numerous improvements that need to be made.
We make the following recommendations:
• Chamber geometries: The current geometries are likely sub-optimal. Part of this
relates to the research shown in Chapter 3, where we noted that conventional geometries of the mode-stirring mechanism can lead to significant errors when following the
recommended measurement practice. However, these issues go further. When measuring a phased-array antenna with integrated electronics in a reverberation chamber, care
should be taken to prevent reflections from returning to the device under test, as they
could load the PAs and change the device performance. Especially when beam steering, the directivity is high and because the array can scan over a large physical space,
it becomes difficult to find an antenna position that prevents this from happening. Reverberation chambers should be adapted to cater to these types of measurements, by,
for example, changing the structure of the walls and mode-stirring mechanisms, or by
adding metasurfaces. The usage of the latter is already reported in literature and could
lead to a significant performance increase in the chamber, and also an increase in the
working volume.
• Directional metrics: The easiest way to explain the potential of RCs in spatiallydependent metrics is by starting with an anechoic approach. In such approaches, the
fields are sampled at a single point in space, and all the rest of the radiated information
is not used because it is absorbed by the chamber walls. After that, a significant time
is spent recovering all that information by use of scanning. In an RC, all the information remains inside the chamber, but it is difficult to get it out. If that were possible,
radiation-pattern measurements may be performed as fast as a TRP measurement, or
even faster [55]. Already many efforts are occurring in the community in doing so,
where it has been shown that spatially-resolved information can be recovered in an RC
[26, 76, 77, 125, 144, 162, 226]. Most of them are based on correlation approaches,
which we expect to be the key to disrupting conventional antenna measurements.
• Modulated-signal measurements: Measuring modulated signals is a standardized
practice at low frequencies, where a connection with a device is made using a basestation emulator. The chamber is loaded with RF absorber to create a frequency-flat
response over a bandwidth of no more than 5 MHz, depending on the protocol that
is used. With the channel bandwidth increasing for next-generation systems, loading
the chamber becomes less preferable, because it deteriorates the chamber performance
significantly. A different approach would be to decode the signal at a later stage, but
it would require an accurate characterization of the channel imposed by the chamber
that goes further than just characterizing loss. Correlative algorithms might be used to
perform other complex measurements such as Error-Vector Magnitude (EVM).
• Chamber modeling: This thesis has been primarily focused on evaluating the validity of existing analytical models using measurements. These models assume that the
111
measurement can be modeled as a stochastic process. Since the chamber is fully deterministic, it would be valuable to include full-wave simulations to quantify fundamental
effects in the chamber, such as monostatic scattering from the mode-stirring mechanism
and the corner behind it. These simulations could be used to optimize the chamber geometry, which is something that was not part of this thesis.
In general, it is necessary to have a testing method that can measure both RFIC and antenna metrics within a short amount of time if we properly want to characterize devices, and
a trend toward these types of systems can already be observed in the market. We believe that
this can be achieved by, on the one hand, evaluating the chamber as a completely deterministic process, while on the other hand using correlative algorithms combined with stochastic
methods to extract otherwise unmeasurable quantities. Reverberation chambers have the potential to become the main method of over-the-air characterization because of their capability
to capture information within a short time frame at high accuracy.
Now all there is to do is to develop the methods and systems to do so [11].
112
Appendix A
In this Appendix, we highlight a few additional aspects related to the Pearson correlation
compared to the autocorrelation.
First, it is important to note that the sensitivity with which correlation can be recognized
within a dataset depends on the number of points. This is shown in Fig. A.1, where we
computed the Pearson correlation of a Gaussian-distributed random variable. It can be seen
that for a lower number of points, the computed correlation is higher. Therefore, a threshold
for a ‘correlation floor’ can be computed, above which correlation can be deemed significant.1
The threshold is given by
t
r= √
,
(5.1)
n − 2 + t2
where n is the number of points and where t corresponds to the 95 % percentile in the t table
[115]. The threshold corresponding to 100, 1000, and 10000 points is approximately 0.19,
0.06, and 0.02, respectively. This corresponds to the data in Fig. A.1, showing that when a data
point lies above the threshold, one can say with 95 % confidence that this is due to a significant
measurement effect, and not due to a lack of calculation points. Note that more research is
necessary to relate these effects to choosing a proper threshold for computing correlation
in an RC measurement. However, we show this example to highlight a potential issue in
defining a threshold, as correlation due to a lack of sampling points should not be confused
with correlation due to mode-stirring positions having a similar chamber mode distribution.
Another consideration is that a mode-stirring sequence can consist of contributions from
multiple mode-stirring mechanisms, or the data might not be taken in a predictable order. To
mimic this effect, we first show an example of a low-frequency oscillating-wall stirrer with
the dataset presented in [P19]. The mode-stirring mechanism was stepped in 1500 increments
and the Pearson correlation between sample 500 and all other samples is shown in Fig. A.2,
orange curve. When we scramble the data in a pseudo-random order and compute the Pearson
correlation again (note that now sample 500 is placed at 1005), it can be seen that the same
1 Note that having a value above this threshold in an RC measurement dataset can be insignificant to the final
result. However, a value above this threshold means that there is likely a significant physical effect in terms of
correlation.
113
114
A PPENDIX A
1
100 points
1000 points
10000 points
Correlation
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
0.8
1
Normalized interval
Figure A.1: Illustration of how the ‘correlation noise floor’ reduces when the correlation
is computed using more data points. In this case, the data points are taken from a random
variable.
correlation values are obtained. This shows the advantage of using the Pearson correlation
approach of being insensitive to the order in which mode-stirring samples are obtained.
To compare this to the more traditional autocorrelation approach, we used the same dataset
as used to compute the coherence angle of the mm-wave RC described in this work. The
mode-stirring sequence consisted of 360 steps of 1◦ , and we used data from the 25-40 GHz
range where the coherence angle was higher than 1◦ . Therefore, some correlation is expected.
We pseudo-randomized the data and computed the correlation using autocorrelation and Pearson correlation. The results are shown in Fig. A.3. For autocorrelation, we used the lowest
frequency, 26.5 GHz. It can be seen that the only correlation above the general used 0.37 or
0.3 thresholds is the 0 lag case. However, when computing the correlation with the Pearson
approach (here we computed the correlation between the 0-degree position with all other positions), it can be seen that there are significantly correlated positions. In the autocorrelation
approach, this only translated to a higher overall correlation, which is not deemed significant
in current approaches.
While the Pearson correlation approach can provide more insight into the correlation between mode-stirring samples, the obvious downside is that it does not provide insight into the
frequency-dependent behavior. In a way, the autocorrelation approach provides the average
correlation of all mode-stirring samples per frequency. In contrast, the Pearson correlation
provides the average correlation across frequency per mode-stirring position. A workaround
for this is to compute the Pearson correlation across smaller chunks of bandwidth, similar to
the approach for computing chamber-decay time.
115
1
Pseudo-random
Original
Correlation
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
0.8
1
Normalized interval
Figure A.2: Correlation computed using the Pearson approach for data taken in a predictable
order, and that same data scrambled in a pseudo-random way. It can be seen that, while the
location of the correlated data points changes due to the scrambling, the levels of correlation
do not change.
1
Pearson
Autocorrelation
Correlation
0.8
0.6
0.4
0.2
0
0
50
100
150
200
250
300
350
Lags
Figure A.3: Correlation in the same dataset computed using the Pearson and autocorrelation
methods. It can be seen that the Pearson correlation distinguishes individual highly-correlated
datapoints, while the autocorrelation merely increases the overall level of correlation.
116
Appendix B
This Appendix shows a derivation to obtain the equation from which the one-, two- and threeantenna methods are derived in [97]. This equation is given by
1
(B.2)
ηAtot ηBtot = CRC ⟨|S21 |2 ⟩ .
Q
It can be obtained by combining two different ways of describing the mean-squared electricfield strength E02 [93]. The first one is given in [93], eq.23, as
E02 =
QPt ηatot
.
ωεV
(B.3)
The transmitted power Pt is the power that is transmitted by the antenna. Note that we included ηatot here because in [93], it is assumed that the antenna efficiency is 100 %. The
second expression is given in the paper by combining eq.44 and eq.45 as
E02 =
8π⟨Pr⟩Z
.
λ 2 ηbtot
(B.4)
Substituting (B.3) into (B.4) yields
⟨Pr ⟩
Qλ 2
.
= ηatot ηbtot
Pt
8πZωεV
(B.5)
c
2π
= √ ,
λ
λ µε
(B.6)
ω can be written as
ω = 2π f = 2π
and Z as
r
Z=
µ
.
ε
(B.7)
Substituting (B.6) and (B.7) into (B.5) gives
⟨Pr ⟩
Qλ 3
= ηatot ηbtot
.
Pt
16π 2V
117
(B.8)
118
A PPENDIX B
Introducing the constant CRC as given in Chris Holloway’s paper as eq.7 we obtain
⟨Pr ⟩
Q
= ηatot ηbtot
,
Pt
CRC
(B.9)
1
ηatot ηbtot = CRC ⟨|S21 |2 ⟩ .
Q
(B.10)
which can be rewritten as
List of Publications
Journal publications
[P1] A. Hubrechsen, S. J. Verwer, A. C. F. Reniers, L. A. Bronckers and A. B. Smolders,
“Reverberation Chamber for Over-the-Air Measurements up to 140 GHz,” in preparation.
[P2] A. Hubrechsen, A. C. F. Reniers, L. A. Bronckers, and A. B. Smolders, “Atmospheric
Loss in a mm-wave Reverberation Chamber,” in preparation.
[P3] A. Hubrechsen, M. van den Meerakker, S. J. Verwer, A. C. F. Reniers, L. A. Bronckers, and A. B. Smolders, “Unwanted Monostatic Scattering from ReverberationChamber Mode-Stirring Mechanisms,” in preparation.
[P4] E. Galesloot, A. Hubrechsen and L. A. Bronckers, “Contactless Method to Estimate
Antenna Efficiency in a Reverberation Chamber,” in IEEE Transactions on Antennas
and Propagation, vol. 71, no. 5, pp. 3797-3805, May 2023.
[P5] T. Stek, A. Hubrechsen, D. S. Prinsloo and U. Johannsen, “Over-the-Air Noise Figure Characterization of mm-Wave Active Integrated Antennas Using a Reverberation
Chamber,” in IEEE Transactions on Microwave Theory and Techniques, vol. 71, no. 3,
pp. 1093-1101, Mar. 2023.
[P6] G. Federico, A. Hubrechsen, S. L. Coenen, A. C. F. Reniers, D. Caratelli and A.
B. Smolders, “A Wide-Scanning Metasurface Antenna Array for 5G Millimeter-Wave
Communication Devices,” in IEEE Access, vol. 10, pp. 102308-102315, Sept. 2022.
[P7] A. Hubrechsen, K. A. Remley and S. Catteau, “Reverberation Chamber Metrology
for Wireless Internet of Things Devices: Flexibility in Form Factor, Rigor in Test,” in
IEEE Microwave Magazine, vol. 23, no. 2, pp. 75-85, Feb. 2022.
[P8] A. Hubrechsen, K. A. Remley, R. Jones, D. F. Williams, D. Gu, A. B. Smolders, and
L. A. Bronckers, “The Effect of Noise on Reverberation-Chamber Measurements of
119
120
L IST OF P UBLICATIONS
Antenna Efficiency,” in IEEE Transactions on Antennas and Propagation, vol. 69, no.
12, pp. 8744-8752, Dec. 2021.
[P9] A. Hubrechsen, K. A. Remley, R. Jones, R. Horansky, V. Neylon, and L. A. Bronckers, “NB-IoT Devices in Reverberation Chambers: A Comprehensive Uncertainty
Analysis,” in International Journal of Microwave and Wireless Technologies, vol. 13,
no. 6, July 2021.
[P10] D. Gu, J. A. Jargon, M. J. Ryan and A. Hubrechsen, “Influence of Noise on ScatteringParameter Measurements,” in IEEE Transactions on Microwave Theory and Techniques, vol. 68, no. 11, pp. 4925-4939, Nov. 2020.
[P11] R. Steiner, D. Ung, A. Hubrechsen, R. Jones, R. Wayth, M. J. Bentum, and A. B.
Smolders, “Optimizing Processing Time of Radio-Astronomy Antnna Simulations using FEKO,” in Applied Computational Electromagnetics Society Journal, vol. 35, no.
10, pp. 1153-1160, Oct. 2020.
Conference publications
[P12] A. Hubrechsen, T. Stek and A. B. Smolders, “Simplified Over-the-Air Noise Figure
Measurement Method for Reduced Uncertainty,” 2023 IEEE/MTT-S International Microwave Symposium - IMS 2023, San Diego, CA, USA, 2023, pp. 911-914.
[P13] A. Hubrechsen, T. Stek, R. Budé, R. van Dommele, L. A. Bronckers, A. C. F. Reniers, and A. B. Smolders, “Total Radiated Power Measurement at 100 GHz in a Reverberation Chamber,” 2023 17th European Conference on Antennas and Propagation
(EuCAP), Florence, Italy, 2023, pp. 1-4.
[P14] T. Stek, A. Hubrechsen, D. S. Prinsloo and U. Johannsen, “Over-the-Air System Noise
Temperature Measurement of Active Integrated Antennas in a Reverberation Chamber,” 2022 International Conference on Electromagnetics in Advanced Applications
(ICEAA), Cape Town, South Africa, 2022, pp. 073-073.
[P15] A. C. F. Reniers, A. Hubrechsen, G. Federico, L. A. Bronckers and A. B. Smolders,
“Spherical mm-Wave Anechoic Chamber for Accurate Far-Field Radiation Pattern
Measurements,” 2022 52nd European Microwave Conference (EuMC), Milan, Italy,
2022, pp. 318-321.
[P16] G. Federico, A. Hubrechsen, D. Caratelli and A. B. Smolders, “Relative Permittivity
Measurements With SIW Resonant Cavities at mm- Wave Frequencies,” 2022 52nd
European Microwave Conference (EuMC), Milan, Italy, 2022, pp. 103-106.
L IST OF P UBLICATIONS
121
[P17] N. Farid, A. Hubrechsen, J. Fridén, U. Johannsen, A. B. Smolders and L. A. Bronckers, “A mm-Wave Hybrid Stirring Technique for Over-the-Air Testing in Reverberation
Chambers,” 2022 52nd European Microwave Conference (EuMC), Milan, Italy, 2022,
pp. 704-707.
[P18] A. Hubrechsen, G. Federico, S. J. Verwer, A. C. F. Reniers, A. B. Smolders and L.
A. Bronckers, “De-Embedding Unwanted Radiation from Phased-Array Systems in a
Reverberation Chamber,” 2022 IEEE International Symposium on Antennas and Propagation and USNC-URSI Radio Science Meeting (AP-S/URSI), Denver, CO, USA,
2022, pp. 623-624.
[P19] S. J. Verwer, A. Hubrechsen, L. A. Bronckers, A. C. F. Reniers and A. B. Smolders,
“Coherence-Distance Estimation of Non-Linear Mode-Stirring Mechanisms,” 2022
IEEE International Symposium on Antennas and Propagation and USNC-URSI Radio Science Meeting (AP-S/URSI), Denver, CO, USA, 2022, pp. 629-630.
[P20] A. Hubrechsen, A. C. F. Reniers, A. B. Smolders and L. A. Bronckers, “ChamberDecay Time in a mm-Wave Reverberation Chamber,” 2021 IEEE International Symposium on Antennas and Propagation and USNC-URSI Radio Science Meeting
(APS/URSI), Singapore, Singapore, 2021, pp. 835-836.
[P21] A. Hubrechsen, S. J. Verwer, A. C. F. Reniers, L. A. Bronckers and A. B. Smolders,
“Pushing the Boundaries of Antenna-Efficiency Measurements towards 6G in a mmWave Reverberation Chamber,” 2021 IEEE Conference on Antenna Measurements &
Applications (CAMA), Antibes Juan-les-Pins, France, 2021, pp. 263-265.
[P22] A. Hubrechsen, A. C. F. Reniers, A. B. Smolders and L. A. Bronckers,
“Reverberation-Chamber Performance of the Oscillating-Wall Stirrer for Estimating
Antenna Efficiency,” 2021 51st European Microwave Conference (EuMC), London,
United Kingdom, 2022, pp. 506-509.
[P23] A. Hubrechsen, V. T. Neylon, K. A. Remley, R. D. Jones, R. D. Horansky and L. A.
Bronckers, “A Preliminary Study on Uncertainty of NB-IoT Measurements in Reverberation Chambers,” 2020 50th European Microwave Conference (EuMC), Utrecht,
Netherlands, 2021, pp. 1051-1054.
[P24] A. Hubrechsen, L. A. Bronckers, K. A. Remley, R. D. Jones, R. D. Horansky,
A. Roc’h, and A. B. Smolders, “The Effect of Peripheral Equipment Loading on
Reverberation-Chamber Metrics,” 2019 International Symposium on Electromagnetic
Compatibility - EMC EUROPE, Barcelona, Spain, 2019, pp. 7-12.
[P25] A. Hubrechsen, A. C. F. Reniers and A. B. Smolders, “Thick wire concept applied on a
bi-quad antenna to enlarge the bandwidth,” The Loughborough Antennas Propagation
Conference (LAPC 2018), Loughborough, 2018, pp. 1-6.
122
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Other publications
[P26] A. Hubrechsen and T. Stek “System and method for measuring EM property such as
noise figure or gain,” Patent applicationt, filed.
[P27] A. Hubrechsen and A. J. van den Biggelaar “An assembly for testing Electromagnetic
properties of a Device-Under- Test, DUT, as well as a corresponding method,” Patent
application, filed.
[P28] A. Hubrechsen, A. J. van den Biggelaar, T. Stek and R. X. F. Budé “Reverberation
chamber and measurement system comprising the same,” Patent application, filed.
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Acknowledgments
Over the past few years, I have received the help and support of many in finishing this PhD
thesis. While words cannot describe the impact these people have had on my life, I would
like to use this part of the thesis to acknowledge each of them.
First, I want to thank my promotor Bart Smolders, who has shown a tremendous amount
of trust in me over the past few years. I feel incredibly appreciative of the fact that he gave
me this PhD project in March 2021 with almost complete freedom on the topic. I would also
like to thank him for the many opportunities during my PhD and for his role in receiving
my current position within ANTENNEX. Second, I would like to thank my co-promotor Ad
Reniers, who has been the most important person in my professional and academic life in the
past decade. No one has believed in me more than Ad, and it has given me the technical and
personal self-confidence I needed to get to where I am today. On top of that, he has put my
own needs before his more times than I can count - something I will never forget. Thank you
for always standing up for what is right.
Throughout all experiences within my PhD, there has been one person in my personal life
who has been there by far the most, Rowanne Steiner, who is also my first paranymph. Her
unwavering support has helped me to stay grounded through some of the most difficult times,
and I am happy she was always there to share each and every success with me. I would also
like to thank my second paranymph, Gabriele Federico. I probably spent most of my time in
Flux at the coffee machine with him, talking about anything and everything. Thank you for
always being there.
In October 2023, I got the opportunity to take over as CEO of ANTENNEX. This has
been and still is the ride of a lifetime, and I would like to thank my co-founders Roel Budé
(roèl), Teun van den Biggelaar (anteunna), and Tim Stek (timmietek) for choosing to take
on this adventure with me, and for supporting me throughout everything. In particular, I
would also like to thank Daniel van der Weide, who came into our lives through a simple
twist of fate. My life would have not been the same without him, and I want to thank him
for his immeasurable contributions to ANTENNEX, and for his unquestionable belief in our
team. I also want to thank him for being a member of my defense committee.
I want to thank Kate Remley at NIST for hosting me as a guest researcher in 2018 and
2019, and for being on my defense committee. Most of what I know about reverberation
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ACKNOWLEDGMENTS
chambers I have learned from her and her influence is reflected in this thesis. I would also like
to thank my former colleagues who have turned into great friends: Rob Jones and Paritosh
Manurkar, and in particular Jérôme Chéron.
My TU/e colleagues have been great company throughout my PhD project. In particular,
I would like to thank Paola Escobari, Leroy Driessen, Pieter van Diepen, David Prinsloo,
Suzanne Kuijlaars, Roeland Dilz, Niels Vertegaal and Elles Raaijmakers for all their support during my PhD project. I would also like to thank Sander Bronckers, Anne Roch, and
Guus Pemen for their involvement in my first PhD project in 2020. I am thankful for the collaboration with students I supervised such as Esmé Galesloot, Menno van den Meerakker,
Jasper Beerentemfel, Oscar Appelman and Tim Stek, and current ANTENNEX students
Naila Rubab and Remco Heijs. Thank you to Steven Verwer for our always fun discussions
about reverberation chambers and for contributing to many measurement campaigns. I would
also like to thank TU/e colleagues Martijn van Beurden and Sonia Heemstra for being a
part of my (reserve) defense panel, along with Marianna Ivashina from Chalmers.
During my time at ANTENNEX, I have had the support of many people: Thank you to
Marcella Gagliardo and Sonja Vos-Poppelaars of The Gate, Frank Poort and Hans de
Penning for their advisory role and financial support, Boudewijn Docter for his advisory
role, and Nicole Tencha for creating our brand and for designing the thesis cover. I would
like to acknowledge the support of the BOM, Innovation Industries, Rabobank, NWO, and the
faculty of EE. I want to thank Kevin Hastenberg and Niels Vertegaal for performing many
measurement services and organizational activities for us. Thank you to Gert Doodeman
who is no longer with us for choosing to spend his retirement working for ANTENNEX.
Thank you Sander Verdiesen for sharing your life with me for many years and for supporting me during a difficult period in my PhD in 2020, and thank you to Max Opperman and
Jasper Beerentemfel for living together with me through all this time. Thank you Stephanie
Slee and Julie de Nooij for many nights with one too many glasses of wine and thank you
dispuut-members Michelle Borm, Laura Kollau, Julia-Alessa Mäntz and Elise Kok for all
the good times. Thank you to Daan Daverveld for all our cocktail and dinner nights. Thank
you Oscar Quevedo-Teruel for your support and for being a great friend. Thank you Jarno
Verhagen and Ymke van der Pol for our over-a-decade-long friendship that travels all across
the world. Thank you Joris van Abeelen for all the great festival experiences. Thank you to
Rik van der Hoven for many afternoons on the Eindhoven Markt. Thank you to my parents
Monique Hubrechsen and Wim Hubrechsen for always being there, and thank you to the
rest of my family. Lastly, thank you to all the people who have gone before me scientifically
and musically.
Curriculum Vitae
Anouk Hubrechsen received the B.Sc. and M.Sc. degrees in
Electrical Engineering from the Eindhoven University of Technology, Eindhoven, The Netherlands, in 2017 and 2019, respectively, after which she started as a PhD candidate in the
same department. She also received a Bachelor of Education in
Mathematics in 2018 from the Eindhoven School of Education.
She was a Guest Researcher with the National Institute of Standards and Technology at Boulder, Boulder, CO, USA, in 2018
and 2019, where she was involved in reverberation-chamber metrology for Internet-of-Things
applications. In 2021, she started working on mmWave reverberation chambers in the Electromagnetics Group in the Department of Electrical Engineering, TU/e. This thesis describes
the main findings of this project.
Based on these findings, she co-founded ANTENNEX B.V. in January 2023, a company
that develops over-the-air measurement instrumentation for mmWave integrated antennas,
where she has since been CEO. Anouk received the Regional and District Zonta Women in
Technology Awards, in 2019. From 2020 to 2021, she was the Vice-Chair of IEEE Benelux
Women in Engineering. She received the URSI Benelux Forum Best Poster Prize in 2022 and
was a finalist in the IMS 2023 Early Career Paper Competition.
145