design of vivaldi antennas - thesis
DESCRIPTION
DESIGN OF VIVALDI ANTENNAS - THESISTRANSCRIPT
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Czech Technical University in Prague
Faculty of Electrical Engineering
DIPLOMA THESIS
Design of Vivaldi Antenna
Prague, 2007 Student: Josef Nevrly
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Declaration
I hereby declare that I have created my diploma thesis independently and that I have
used only literature listed in the attached bibliography.
I have no objection to lending, publication and other use of the work as agreed by the
Department of Electromagnetic Field.
Prague
signature
Prohlasen
Prohlasuji, ze jsem diplomovou praci vypracoval samostatne a pouzil k tomu literaturu,
kterou uvadm v seznamu prilozenem k praci.
Nemam namitky proti pujcovan, zverejnen a dalsmu vyuzit prace, pokud s tm bude
souhlasit katedra elektromagnetickeho pole.
V Praze dne
podpis
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Acknowledgements
I would like to express my thanks to many people, without whom this thesis would have
never been started nor finished. To name the most important, I thank to:
Ing. Petr Cerny, my diploma thesis advisor, for many ideas behind this work, hispatient help and support throughout the project and finally for countless hours of
the processor time on his black machine
Prof. Ing. Milos Mazanek CSc., who has directed me to the topic of UWB antennas
Doc. Ing. Jan Machac DrSc., who ignited my interest in the theory of electromag-netic field some years ago
my family and my girlfriend, for their patience, support and love
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Abstrakt
Tato diplomova prace se zabyva navrhem Vivaldiho anteny pro pouzit v UWB pasmu
dle definice FCC, tedy 3.1 - 10.6 GHz. Specialn pozornost je venovana optimalizaci pro
minimaln zkreslen UWB pulsu pri zachovan male velikosti anteny. Design anteny je
rozdelen do dvou cast - vyzarovac struktury a napajecho obvodu. V casti pojednavajc o
vyzarovacch strukturach jsou studovany verze Vivaldiho anteny v jedne vrstve (rozsrena
sterbina) i ve dvou vrstvach (protichudne ploutve). Kapitola o napajecch obvodech
je venovana napajen jednostranne struktury pomoc prechodu mikropasek-sterbinove
veden. Prostudovany jsou verze prechodu s ruznymi typy zakoncen veden a nekolik typu
mikropaskoveho impedancnho transformatoru (linearn, exponencialn, Klopfensteinuv).
V zaveru prace jsou podle zjistenych poznatku navrzeny, sestrojeny a zmereny dve anteny
s jednovrstvou vyzarovac strukturou. Vlastnosti techto anten jsou pote porovnany se
simulacemi.
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Abstract
This diploma thesis discusses design of Vivaldi antenna for the UWB frequency range
specified by FCC (3.1 - 10.6 GHz). Special attention is paid to the minimization of
pulse distortion for small antenna dimensions. The work is divided into two parts -
design of the radiating structure and design of the antenna feed. Section dealing with the
radiating structure discusses tapered slot Vivaldi antenna and antipodal Vivaldi antenna
designs. In chapter about feeding section, various feeds utilizing microstrip-to-slot line
transition are investigated. Different versions of microstrip and slot line terminations are
explored and evaluated together with three types of microstrip impedance transformer
(linear, exponential, Klopfenstein). In the last part of this work, two tapered slot Vivaldi
antennas are designed, fabricated and measured. Measured results are then compared
with results obtained from simulations.
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Prostudujte doporucenou literaturu. Navrhnete, analyzujte a porovnejte dve zakladn
struktury Vivaldiho anteny bez napajecch obvodu. Porovnan provedte s ohledem na
minimalizaci zkreslen vyzarovanych impulsu v UWB pasmu dle FCC, zpetne vyzarovan,
rozmeru a tvaru zakoncen ploutv. Na zaklade tohoto porovnan vyberte jednu strukturu
a doplnte ji o napajec obvod. Tuto antenu zoptimalizujte, zrealizujte a zmerte jej
impedancn a vyzarovac parametry.
Study the recommended references. Design, analyze and compare two basic struc-
tures of Vivaldi antenna without feeding part. The comparison should be based on the
minimization of the pulse distortion, given the UWB band pulses according to the FCC
specifications. Attention should be paid to backfire radiation, size of the antenna and
shape of the fin termination. Choose one structure based on the previous comparisons and
implement the antenna feed. Optimize this antenna, build it and measure its impedance
and radiation parameters.
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Contents
Table of Figures ix
Table of Tables xii
1 Introduction 1
1.1 Scope of this project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Simulation and modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Signal distortion in the time domain . . . . . . . . . . . . . . . . . . . . 4
1.4 Structure of this document . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2 Radiating structure 6
2.1 Overview of Vivaldi antenna designs . . . . . . . . . . . . . . . . . . . . 6
2.1.1 Tapered slot Vivaldi Antenna . . . . . . . . . . . . . . . . . . . . 6
2.1.2 Antipodal Vivaldi Antenna . . . . . . . . . . . . . . . . . . . . . . 9
2.1.3 Balanced antipodal Vivaldi antenna . . . . . . . . . . . . . . . . . 11
2.2 Simulated designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2.1 Used substrate . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2.2 Design notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2.3 Evaluation notes . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2.4 Tapered slot Vivaldi Antenna . . . . . . . . . . . . . . . . . . . . 14
2.2.4.1 Influence of the exponential curvature . . . . . . . . . . 14
2.2.4.2 Using spline curves for taper definition . . . . . . . . . . 16
2.2.4.3 Influence of the antenna dimensions . . . . . . . . . . . . 16
2.2.4.4 Influence of the round corners . . . . . . . . . . . . . . . 17
2.2.4.5 Comb structures . . . . . . . . . . . . . . . . . . . . . . 18
2.2.4.6 Hybrid exponential model . . . . . . . . . . . . . . . . . 19
2.2.5 Antipodal vivaldi antenna . . . . . . . . . . . . . . . . . . . . . . 20
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2.2.5.1 Influence of the inner curvature profile . . . . . . . . . . 20
2.2.5.2 Using spline curves for inner profile . . . . . . . . . . . . 22
2.2.5.3 Influence of the outer curvature profile . . . . . . . . . . 22
2.2.5.4 Influence of the fin width . . . . . . . . . . . . . . . . . 22
2.2.5.5 Influence of the round corners . . . . . . . . . . . . . . . 23
2.3 Choice of radiating structure . . . . . . . . . . . . . . . . . . . . . . . . . 24
3 Feeding structure 26
3.1 Impedance transformer . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.1.1 Linear taper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.1.2 Exponential taper . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.1.3 Klopfenstein taper . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.1.4 Choice of taper . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.2 Microstrip to slot line transition . . . . . . . . . . . . . . . . . . . . . . . 35
3.2.1 Marchand balun (orthogonal transition) . . . . . . . . . . . . . . 35
3.2.1.1 Slot line circular stub termination . . . . . . . . . . . . . 36
3.2.1.2 Transition with a microstrip radial stub . . . . . . . . . 37
3.2.1.2.1 Influence of the Stub angle . . . . . . . . . . . . 37
3.2.1.2.2 Influence of the stub radius . . . . . . . . . . . 38
3.2.1.2.3 Signal distortion . . . . . . . . . . . . . . . . . 39
3.2.1.3 Transition with a via connection . . . . . . . . . . . . . 39
3.2.1.3.1 Signal distortion . . . . . . . . . . . . . . . . . 40
3.2.1.4 Transition with a via connection and a real slot line open
end . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.2.1.4.1 Signal distortion . . . . . . . . . . . . . . . . . 41
3.2.2 Double Y balun . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.3 Conclusion, choice of transition . . . . . . . . . . . . . . . . . . . . . . . 45
4 Final antenna design and measurements 47
4.1 Tapered slot Vivaldi antennas . . . . . . . . . . . . . . . . . . . . . . . . 47
4.2 Antipodal Vivaldi antenna . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.3 Simulated results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.4 Radiation patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.5 Fabrication notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.6 Return loss measurements . . . . . . . . . . . . . . . . . . . . . . . . . . 52
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4.7 Signal fidelity measurement . . . . . . . . . . . . . . . . . . . . . . . . . 54
5 Conclusion 58
References 61
A Radiation patterns I
B Layout masks IV
C Photographs VI
D Content of the attached DVD IX
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List of Figures
1.1 Typical designs of Vivaldi antennas and feeding structures . . . . . . . . 2
1.2 Excitation signals for the FDTD solver used for simulations . . . . . . . 3
2.1 Tapered slot Vivaldi antenna with microstrip to slotline transition . . . . 7
2.2 Antipodal Vivaldi antenna . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3 Balanced antipodal Vivaldi antenna . . . . . . . . . . . . . . . . . . . . . 11
2.4 Examples of radiation structure designs and the waveguide port placement 13
2.5 Schema of the tapered slot Vivaldi antenna design and variables . . . . . 14
2.6 Taper profiles and signals reflected from the structure for various settings
of parameter p . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.7 Return loss and fidelity factor F for various settings of parameter p . . . 15
2.8 Return loss and reflected signal for various settings of aperture width aw 16
2.9 Round corner design and reflected signal for various settings of corner
radius R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.10 Return loss and signal level received at the back probe for various settings
of corner radius R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.11 Two investigated comb structures - capacitive comb and resistive comb . 19
2.12 Return loss and signal level received at the front probe for both comb
structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.13 Hybrid taper design, description of antipodal design and its variables . . 20
2.14 Inner curvature profiles and signals reflected from the structure for various
settings of parameter p1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.15 Return loss and fidelity factor F for various settings of parameter p1 . . . 21
2.16 Outer curvature profiles and signals reflected from the structure for various
settings of parameter p2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.17 Return loss and signals reflected from the structure for various settings of
parameter L2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
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2.18 Antipodal round corner design and reflected signal for various settings of
corner radius R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.19 Return loss and fidelity factor F for various settings of corner radius R . 24
3.1 Exemplary designs of impedance transformers for 50 to 200 transfor-
mation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.2 Exemplary profiles of impedance transformers for 50 to 200 transfor-
mation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.3 Return and insertion losses of linear taper impedance transformers . . . . 29
3.4 Designs of the curved linear taper - 1 turn and 2 turn impedance transformer 30
3.5 Return and insertion losses of curved linear taper impedance transformers
compared to the straight design . . . . . . . . . . . . . . . . . . . . . . . 31
3.6 Return and insertion losses of exponentially tapered impedance transformers 31
3.7 Return and insertion losses of Klopfenstein taper impedance transformers 33
3.8 Return and insertion losses of impedance transformers with short tapers . 34
3.9 Return and insertion losses of impedance transformers with long tapers . 34
3.10 Return and insertion losses of a transition with variable slot line circular
stub radius . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.11 Return and insertion losses of a transition with variable slot line circular
stub distance from the transition reference plane . . . . . . . . . . . . . . 37
3.12 Schematics and parameters of the microstrip to slot line transition with
radial stub . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.13 Return and insertion losses of a radial stub transition with variable stub
angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.14 Return and insertion losses of a radial stub transition with variable stub
radius . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.15 Schematics and parameters of the microstrip to slot line transition with a
via connection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.16 Return and insertion losses of a via connection transition with variable
distance of the via placement from the slot line border . . . . . . . . . . 41
3.17 Schema of the real slot line open end via transition, signal distortion of
the transitions with a via connection . . . . . . . . . . . . . . . . . . . . 42
3.18 Comparisons of the signal distortion and radiation of the radial stub and
the via connection open end design . . . . . . . . . . . . . . . . . . . . . 42
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3.19 Schema of the double Y balun; signals reflected from all possible signal
paths in the balun . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.20 Return and insertion losses of the double Y balun. CST band limited
(3.1 GHz - 10.6 GHz) excitation was used to obtain the plots. . . . . . . 44
3.21 Return and insertion losses of the radial stub and the via real open end
transition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.1 Designs of Via Vivaldi and Stub Vivaldi antennas . . . . . . . . . . . . . 48
4.2 Design of the Antipodal Vivaldi antenna . . . . . . . . . . . . . . . . . . 49
4.3 Return loss and signal received at the far field front probe for simulated
designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.4 Return and insertion loss plots of measured antennas . . . . . . . . . . . 53
4.5 Comparisons of measured and simulated values of return loss for Via Vi-
valdi and Stub Vivaldi antennas . . . . . . . . . . . . . . . . . . . . . . . 53
4.6 Signal distortion measurement setup . . . . . . . . . . . . . . . . . . . . 54
4.7 Excitation signal used for measurements, measured received signals . . . 55
4.8 Plots of transformation functions rtr(t) and ttr(t)) and an example of rtr(t)
derivative for the Stub Vivaldi antenna . . . . . . . . . . . . . . . . . . . 56
4.9 Comparisons of measured and calculated received signals . . . . . . . . . 56
A.1 Radiation patterns of the Via Vivaldi antenna . . . . . . . . . . . . . . . II
A.2 Radiation patterns of the Stub Vivaldi antenna . . . . . . . . . . . . . . III
B.1 Layout mask for the Via Vivaldi antenna . . . . . . . . . . . . . . . . . . IV
B.2 Layout mask for the Stub Vivaldi antenna . . . . . . . . . . . . . . . . . V
C.1 Front side of the Via Vivaldi antenna . . . . . . . . . . . . . . . . . . . . VI
C.2 Back side of the Via Vivaldi antenna . . . . . . . . . . . . . . . . . . . . VII
C.3 Front side of the Stub Vivaldi antenna . . . . . . . . . . . . . . . . . . . VII
C.4 Back side of the Stub Vivaldi antenna . . . . . . . . . . . . . . . . . . . . VIII
C.5 Size comparison with the antenna introduced by Piksa and Sokol . . . . . VIII
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List of Tables
2.1 Parameters of the used substrate . . . . . . . . . . . . . . . . . . . . . . 12
3.1 Microstrip widths for line impedances on the selected substrate . . . . . . 28
4.1 Values of the fidelty factor F for simulated designs . . . . . . . . . . . . 51
4.2 Pattern parameters of simulated tapered slot antennas . . . . . . . . . . 51
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Chapter 1
Introduction
Vivaldi antenna, sometimes also called Vivaldi notch antenna, is a planar travelling wave
antenna with endfire radiation. It was first investigated by P.Gibson in 1979 [4] and many
improvements to the initial design came later, namely in the works of E. Gazit in 1988 [3]
and Langley, Hall and Newham [7] in 1996.
The basic shape of the antenna can be seen in fig. 1.1. Antenna consists of a feed
line, which is usually microstrip or stripline, transition from the feedline to the slotline
or balanced stripline and the radiating structure. Radiating structure is usually expo-
nentially tapered, however, examples of parabolic, hyperbolic or elliptical curves can be
found in [12].
The continuous scaling and gradual curvature of the radiating structure ensures theo-
retically unlimited bandwidth, which is, in practice, constrained by the taper dimensions,
the slot line width and the transition from the feed line. The limitation introduced by
transition was later partially overcame in the antipodal design investigated in [3].
Vivaldi antennas provide medium gain depending on the length of the taper and
the shape of the curvature. The gain also changes with frequency, with values ranging
typically from 4 dBi to 8 dBi [12]. Because of the exponential shape of the tapered
radiating structure, antenna maintains approximately constant beamwidth over the range
of operating frequencies [4] [3].
From the time-domain point of view, the principle of radiation through the tapered
slot is lacking any resonant parts, which results in very low distortion of radiated pulses.
This aspect, together with large bandwidth of the antenna, makes Vivaldi very good
UWB radiator in cases when directional antenna is desired.
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CHAPTER 1. INTRODUCTION 2
Figure 1.1: Typical designs of Vivaldi antennas and feeding structures
1.1 Scope of this project
The scope of this work is to design, fabricate and measure a Vivaldi antenna which can be
used for UWB applications according to the FCC specifications. That requires operating
frequency band ranging from 3.1 to 10.6 GHz and the smallest possible distortion of the
UWB pulse
The antenna should be small and easy-to-manufacture with available laboratory equip-
ment. The return loss should be less than -10 dB within the UWB range. Other aspects,
such as beamwidth, side lobes and directivity, were not considered during the design
stage, however, they were evaluated for the final design.
Special attention had been paid to the influence of the taper and feed parameters on
the pulse distortion in the time domain and on the matching properties of the antenna.
Several strategies on how to increase the time-domain pulse fidelity were then suggested
and utilized in the final design.
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CHAPTER 1. INTRODUCTION 3
1.2 Simulation and modeling
CST Microwave Studio (MwS) was used throughout the whole design process and all plots
within this document were obtained by this software, if not stated otherwise. MwSs
Finite-Difference Time-Domain (FDTD) solver was used for simulations, with various
excitation pulses according to the purpose of the simulation.
For fast, preliminary parameter sweeps, a default Gaussian pulse had been utilized.
Then, when the basic model parameters had been established, Gaussian doublet was used
for its favorable properties (zero DC component, short duration). This pulse has good
spectral properties for frequencies above approximately 1 GHz. Below this frequency,
however, simulation results tend to be inaccurate or even physically impossible. This can
be observed as a distinct peak above 0 dB around 100 MHz in some S11 and S21 plots
(e.g. fig. 3.21). For the final design, a Gaussian modulated sine pulse (default MwS signal
for frequency limited excitation) was used with spectrum corresponding to the 3.1 GHz
- 10.6 GHz frequency range. All pulses can be seen in fig. 1.2
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 11
0.8
0.6
0.4
0.2
0
0.2
0.4
0.6
0.8
1
Time[ns]
Gaussian pulse 0 11 GHzGaussian doubletGaussian modulated sine 3.1 10.6 GHz
Figure 1.2: Excitation signals for the FDTD solver used for simulations
MwS enables user to define the input port for microstrip and slot line transmission
lines as a waveguide port. As both microstrip and slot lines dont have exactly defined
boundaries, the size of the port can seriously influence simulated port impedance. In
accordance with the MwS documentation, port size was defined large enough to contain
the electromagnetic field of the basic mode.
This strategy works well for the microstrip line port, where the port impedance re-
mains approximately the same for various waveguide port sizes and meshing settings.
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CHAPTER 1. INTRODUCTION 4
For a slot line port, the situation differs dramatically. The port impedance varies
significantly even with small changes of the port size and meshing settings and there is
no MwS documentation on port design for a slot line structure. In the end, slot line
impedance values obtained by the TX Line tool from the AWR Microwave Office package
were used as a reference for setting the waveguide port in the MwS.
1.3 Signal distortion in the time domain
Observation of the signal distortion in the time-domain was one of the main scopes of this
work. For numerical evaluation of the difference between excitation and received signal,
following comparative technique had been adopted from [11]. This technique, based on
mutual correlation, represents the fidelity of the received pulse to the excitation pulse as
a fidelity factor F :
F = max
(
1R1max
s1(t+ )1
R2maxs2(t)dt
)
(1.1)
Where s1 is the excitation signal, s2 is the received signal and R1max and R2max are
the maximum values of the autocorrelation function for excitation signal and received
signal respectively.
Rxmax = max
(
sx(t+ )sx(t)dt
)(1.2)
If the received signal had been obtained from a far field E probe, a derivative of the
excitation pulse was used for comparison, as the pulse radiated from the Vivaldi antenna
is derivative of the pulse at the feeding point.
In this way, fidelity factor F ranges from 1 (identical signals) to 0. Using this sort of
evaluation also enabled designs explored in this work to be compared with the antenna
introduced by [11].
1.4 Structure of this document
This document consists of three main parts following this introduction. Second chapter is
dedicated to the choice of a radiating structure from the variety of known Vivaldi antenna
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CHAPTER 1. INTRODUCTION 5
designs. The best option is then selected according to the criteria mentioned before.
Third chapter is dealing with the feeding part including the impedance transformer
and the transition to the radiating structure selected in Chapter two.
Last part of this work, contained in Chapter four, is describing the final optimization
of the antenna, fabrication process and tools and technologies used to obtain prototype of
the designed antenna. Prototype antenna is then measured and evaluated in comparison
with the simulations and the antennas introduced in different works.
The work is concluded in the last chapter with comments on different strategies for
the UWB Vivaldi antenna design.
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Chapter 2
Radiating structure
There are three fundamental types of Vivaldi antenna, which can be used to design the
radiating structure. These types are:
1. Tapered slot Vivaldi antenna
2. Antipodal Vivaldi Antenna
3. Balanced Antipodal Vivaldi Antenna
In the beginning of this chapter, properties and features of each particular design are
discussed shortly. Consequently, these design types are simulated and their properties
investigated with regard to the criteria set for the desired antenna. In the end of the
chapter, the most suitable design is chosen for the further work.
2.1 Overview of Vivaldi antenna designs
2.1.1 Tapered slot Vivaldi Antenna
Tapered slot Vivaldi antenna is the original design introduced by Gibson in 1979 [4]. Its
basically a flared slotline, fabricated on a single metallization layer and supported by a
substrate dielectric.
The taper profile is exponentially curved, creating smooth transition from the slot
line to the open space. This structure introduces two limits for the operational band-
width of the antenna, following the rule for slotline radiation. Slot line starts to radiate
6
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CHAPTER 2. RADIATING STRUCTURE 7
significantly under the condition of
sw =02
(2.1)
where sw is width of the slot. Therefore, the wide end of the exponential taper
approximately defines the lowest possible frequency which is radiated by the structure,
while the width of slotline at the taper throat is introducing the high frequency cutoff [2].
Other limitations come with the slotline itself. First of all, slotline is a balanced
transmission line, thus its necessary to incorporate a balun (transition), if the feeding
line should be coaxial or generally unbalanced. Creating a wideband balun is usually
complicated task, rendering this solution somewhat unconvenient. The use of baluns was
therefore common in the early designs [10] and has been surpassed by antipodal designs
in later years.
Figure 2.1: Tapered slot Vivaldi antenna with microstrip to slotline tran-
sition
Microstrip to slotline transition, as shown in fig. 2.1, is mostly used for tapered slot
Vivaldi antenna. Its possible to design transitions which operate over a decade of band-
width or more [12]. Problems may be caused by the fact that on thin substrates with
low dielectric constant, it is difficult to fabricate non-radiative, narrow 50 slotline. A
slotline with higher line impedance is then used instead. In such case, an impedance
transformer must be incorporated before the microstrip to slotline transition [11], which
requires additional space on the board and makes the whole design more complex.
Vivaldi antenna, as any tapered slot structure, is utilizing a traveling wave, which
propagates along the taper with phase velocity vph, which has to hold to the following
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CHAPTER 2. RADIATING STRUCTURE 8
condition
vph c (2.2)
in order to achieve endfire radiation. If the phase velocity exceeds c, the main beam in
the radiation pattern is split and the radiation is no longer endfire. An optimum velocity
ratio has been defined in [13], resulting in the maximum directivity
p =c
vph= 1 +
02L
(2.3)
We can equally say that the maximum directivity occurs in the case of a total phase
increase of 180 along the antenna structure, caused by the dielectric slowing down the
traveling wave. If the phase shift is any bigger than 180, main beam moves off the endfire
direction.
From the above mentioned observations, an optimum range of effective dielectric thick-
ness normalized to the free space wavelength 0 has been identified in [13]. The optimum
range is about 0.005 to 0.03, and the normalized effective dielectric thickness is defined
in the relation
teff0
= (r 1)
t
0(2.4)
where t is the actual substrate thickness. This rule should hold for any tapered
structure within the length of 4 0 to 10 0. Making dielectric substrate thinner than
the optimal value results in a wider beam, thicker-than-optimum substrate causes the
pattern to split up with a null in the endfire direction.
In case of the optimum range, directivity of the radiation structure is generally defined
by the length of taper. An empirical rule derived by Yngvesson et al. in [14] defines a
general relation between the taper length and directivity of an arbitrary tapered slot
antenna as follows:
D = 10log(10L
0) (2.5)
where L is the length of the taper. This relation holds for taper lengths of 3 0 to 7 0
and c/vph 1.05. For longer antennas, the multiplicative constant is somewhat lower,Johnsson [6] presents a relation of
D = 10log(4L
0) (2.6)
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CHAPTER 2. RADIATING STRUCTURE 9
As for the beamwidth in degrees, similar empirical rules were developed and mentioned
in [6], for both optimum structures and long structures respectively
BW =55L0
; BW =77L0
(2.7)
In general, its safe to say that long structures can achieve over 10 dB directivity in the
endfire direction. Main limit is the aforementioned phase difference breaking up the main
beam. A diffraction occurring on the sharp corners of wide taper end has also impact on
the pattern fragmentation [3]. This can be treated by curving the corners appropriately.
Several variations of the original design were introduced to improve properties of the
structure. Documentation shows attempts to improve both the E and H plane pattern
and front to back ratio by introducing geometries on the outer edges of the antenna [5]
or incorporating a resistive loading [8]. Another improvements deal with the bandwidth
limitations by changing geometry of the taper to hybrid exponential flares [1].
2.1.2 Antipodal Vivaldi Antenna
Antipodal Vivaldi antenna was investigated by W. Nester in 1985 and E. Gazit in 1988 [3]
as a solution of the feeding problems associated with Gibsons original design. In the
antipodal configuration, antenna is created on a dielectric substrate with two-sided met-
allization.
Feeding part is a microstrip line, followed by a microstrip to balanced strip line (twin
line) transition. This strip line serves as a feed to the antipodal exponentially tapered
fins. Fins are arranged in such a way, that from a point of view perpendicular to the
substrate plane, they create a flared shape. Unlike the original Gibsons design, antipodal
fins also have an outer edge which can influence return loss and radiation pattern of the
antenna. Usually, an exponential curvature is used to define the outer edges; however the
parameters of the curvature can differ from the inner taper. The antipodal design can be
seen on fig. 2.2.
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CHAPTER 2. RADIATING STRUCTURE 10
Figure 2.2: Antipodal Vivaldi antenna
This design holds several advantages compared to the single sided Vivaldi antenna.
First of all, the microstrip to twin line transition is fairly easy to design and manufacture.
The twin line feed also increases the high frequency cutoff, since there is no slotline width
limitation as observed in the single sided taper [2].
Main disadvantage of the antipodal configuration is cross-polarization, observed es-
pecially for higher frequencies. This is caused by the skew of the slot fields. The skew is
changing along the length of the taper, being highest in the closed end of the antenna,
where high frequencies are being radiated; while at the open end is usually negligible, de-
pending on the substrate thickness. Result is a cross-polarization which can reach values
higher than -5 dB [7] and which is significantly frequency dependent.
Apart of the polarization issues, the pattern parameters are similar to the original
Vivaldi design in the end fire direction. However, there is usually a higher level back
lobe, caused by the creeping wave following the edges of the antipodal fin and leaking to
the outer tapers. This flaw is especially significant when corners of the radiating flares
are curved to minimize the reflection and diffraction.
Various improvements and variations of the antipodal design have been documented.
Nesters patent [9] introduced a slightly different geometry of the bottom side metalliza-
tion, lacking the twin line section. Hybrid exponential flare version of antipodal Vivaldi
also exists, as documented in Fischers patent [1].
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CHAPTER 2. RADIATING STRUCTURE 11
2.1.3 Balanced antipodal Vivaldi antenna
One of the latest improvements of the original design was presented by Langley, Hall
and Newham in 1996 [7]. This design evolves from the antipodal version. The cross-
polarization is reduced by adding another layer of metallization, creating a balanced
stripline structure.
Such configuration is depicted on fig. 2.3 and describes the function of the third
metallization layer - two E-field vectors in the direction from the central plate to ground-
planes sum up to give a resulting E-field vector which is parallel to the metallization.
This gives balanced antipodal Vivaldi antenna a typical crosspolarization of -20 dB.
Figure 2.3: Balanced antipodal Vivaldi antenna
Another positive aspect of this design is the fact that the feeding line is created by a
triplate stripline. This is reducing the radiation of the antenna feed, which could occur in
case of open feed lines of the antipodal and tapered slot Vivaldi. This solution suppresses
perturbances of the radiation pattern caused by the open feed lines.
There are also some disadvantages of the balanced design. Naturally, the construc-
tion of such antenna is more complicated due to the triplate structure, preventing it
from fabrication in some lab environments. Furthermore, the different geometries of the
groundplanes and central plane are causing an unequal propagation velocity for the sur-
face currents, which results in a squint in the E-plane radiation pattern [7]. This squint
is documented to be independent of frequency and substrate dielectric permittivity.
Apart of the crosspolarization, both pattern and matching properties dont differ
significantly from the antipodal design. Constant beamwidth for wide range of frequencies
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CHAPTER 2. RADIATING STRUCTURE 12
has been achieved, together with a directivity over 10 dB.
2.2 Simulated designs
Two aforementioned Vivaldi antenna designs were examined during this work - Tapered
slot Vivaldi Antenna and Antipodal Vivaldi antenna. Balanced Vivaldi antenna was
excluded from the simulations, as it had been known from the beginning that it would
be difficult to fabricate such structure with the available equipment.
2.2.1 Used substrate
Both types were designed with regards to the substrate available for production. Param-
eters of this substrate are described in tab. 2.1. As the substrate had been chosen in
advance, design parameters were investigated only with regards to the shape and size of
the antenna and not to the substrate parameters.
Parameter Symbol Value
Substrate height H 0.76 mm
Dielectric constant (at 10 GHz) r 2.52
Dissipation factor (at 10 GHz) tg 0.0022
Metallization thickness t 35 m
Metallization (Copper) conductivity s 15.88 107 Sm1
Table 2.1: Parameters of the used substrate
2.2.2 Design notes
Antenna tapers for both design types were defined as exponential curves in the x-y plane.
To comply with the antenna board dimensions and slot line parameters, following curve
definition was used:
f(x) = Aepx Aep + sw2
(2.8)
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CHAPTER 2. RADIATING STRUCTURE 13
where coefficient p is the curvature parameter, sw is the slotline width and A is defined
as:
A =aw2 sw
2
epTL ep (2.9)
Parameter aw stands for aperture width at the end of the taper, TL is the taper
length. Graphical representation of these variables can be seen in fig. 2.5. With this
definition, one half of the taper could be obtained. Full taper was then designed using
mirror symmetry along the x axis.
In the case of antipodal design, parameter sw was used for the balanced stripline
width. Outer tapers of the antipodal fins were obtained in a similar fashion.
Both design types were simulated without feeding section, using waveguide port as
the source of excitation. Examples of such arrangement can be seen in fig. 2.4.
Figure 2.4: Examples of radiation structure designs and the waveguide
port placement
2.2.3 Evaluation notes
To capture far field signal values, a far field E probe was used for each design. The probe
was placed 1 m from the antenna aperture in the endfire direction. To evaluate radiation
in the backfire direction, another far field E probe was placed 1 m from the antenna
back side. Probes were oriented in parallel with the antennas E-field vector. Return loss
was calculated automatically by the MwS, with values normalized to the calculated port
impedance.
-
CHAPTER 2. RADIATING STRUCTURE 14
2.2.4 Tapered slot Vivaldi Antenna
Model of the radiating part had been designed accordingly to fig. 2.5. The figure also
shows basic design variables, which can be changed in order to achieve desired antenna
performance. These variables are inspected in details in the following text. Furthermore,
advanced improvements to the basic design are introduced.
The models for parameter sweeps are generally of size 5 5 or 5 6 cm. These di-mensions were determined by the relation (2.1), together with several preliminary sweeps
performed on models with different sizes. It was convenient to test the variables on the
smallest possible model, as the final goal was to design a small UWB Vivaldi antenna.
Slot line with 100 line impedance was used as the structures feed.
Figure 2.5: Schema of the tapered slot Vivaldi antenna design and vari-
ables
2.2.4.1 Influence of the exponential curvature
Exponential curvature can be changed with the value of parameter p, as described in the
section 2.2.2. Fig. 2.6 shows the fin profile for several values of p.
The shape of the curvature influences the traveling wave in two main areas. First is
the beginning of the taper, marked as neck in fig. 2.5, the second is the wide end of
the taper. On both places, a reflection of the traveling wave is likely to occur. These
reflections can be seen on the plot of the reflected signal in fig. 2.6.
In the case of the neck, reflection occurs with the initial change of the slot line width.
Therefore, smoother taper in the neck minimizes the reflection there. This can be achieved
with higher values of p, as can be seen in fig. 2.6 .
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CHAPTER 2. RADIATING STRUCTURE 15
Figure 2.6: Taper profiles and signals reflected from the structure for var-
ious settings of parameter p
Reflection at the wide end of the taper is connected to the fin termination, and cannot
be completely avoided. Changing parameter p does not influence the wide end reflection
significantly.
Following these observations, it can be inferred that increasing the parameter p can
improve matching characteristics. The improvement is of course within the limits given
by the antenna aperture and slot line width. This can be seen on the return loss plot
in fig. 2.7.
Figure 2.7: Return loss and fidelity factor F for various settings of param-
eter p
Varying the value of p also influences the signal distortion, represented by the fidelity
factor F . In fig. 2.7, relation of the fidelity factor to the p is depicted. It can be seen,
-
CHAPTER 2. RADIATING STRUCTURE 16
that the F is the best at lower values of p, as opposed to the return loss. Observations on
different models suggest that for a range of p values, fidelity factor F reaches maximum
at the point where the curvature is most round.
Reasons for this behavior were not found during the design work. The only lead is
the waveform of the reflected signal. If the signal reflected from the structure has low
distortion (typical for lower p, fig. 2.6), also the radiated pulse will have low distortion.
That is, however, an expected result. There is no obvious connection between the low
fidelity factor and the return loss or other characteristics.
2.2.4.2 Using spline curves for taper definition
An alternative model using spline curves was briefly inspected during the design works.
Spline curves allow to achieve proper round profile easily, and thus provide good sig-
nal fidelity on the same or better level that the exponential definition. For return loss
properties, the basic spline definition provided worse results than the exponential.. Its
however safe to say, that with more elaborate spline definition (more points), the solution
is equivalent to the exponential curvature.
2.2.4.3 Influence of the antenna dimensions
Width and length of the antenna are two fundamental parameters, which can directly or
indirectly influence the overall antenna performance.
Figure 2.8: Return loss and reflected signal for various settings of aperture
width aw
Width (aperture width) determines the low frequency cutoff and thus greatly influ-
-
CHAPTER 2. RADIATING STRUCTURE 17
ences the return loss. Apart of that, both parameters are indirectly (through parameter p)
connected with the taper profile, influencing the fidelity factor F .
Changing the antenna width, while leaving the parameter p and length of the taper TL
unchanged, yields results plotted in fig. 2.8. It can be seen that the matching properties
improve towards the lower frequencies. On the reflected signal plot, higher distortion of
the wide end reflection can be observed. This results in lower fidelity of the transmitted
signal.
Changing the taper length TL, while leaving W2 and p parameters unchanged, has
very little effect on the overall performance. It is, however, a way to improve the direc-
tivity of the antenna.
From the signal fidelity point of view, changing dimensions of the radiating part can be
always translated into changing shape of the taper profile. Both width and length of the
taper should be set in such way, that the curvature has favorable distortion properties
and low reflection. The only physical limits are represented by the smallest aperture
width defined in (2.1) and the maximal taper length defined in (2.3).
2.2.4.4 Influence of the round corners
Rounding the taper corners, as depicted in fig. 2.9 had been explored as a way of maintain-
ing smooth taper profile. Fig. 2.10 depicts the influence of such rounding with changing
corner radius R.
Figure 2.9: Round corner design and reflected signal for various settings
of corner radius R
Obviously, return loss is only slightly improved for frequencies above 7 GHz. Better
-
CHAPTER 2. RADIATING STRUCTURE 18
improvement can be seen in the plots of the reflected signal. With bigger rounding, the
distortion of the reflected pulse is decreased. That results in improvement of the fidelity
factor F , with approximately 0.0025 increase for every 1 mm of the corner radius.
Figure 2.10: Return loss and signal level received at the back probe for
various settings of corner radius R
Round corners allow the creeping wave to travel to the outer edges of the antenna
more easily, thus increasing the backfire radiation. Nevertheless, fig. 2.10 shows the signal
level received at the back probe increases very little, so this factor shouldnt be considered
as serious.
Observations showed that rounding taper corners is a way of improving the signal
fidelity without changing the return loss. The price paid for such improvement is the
increase of the antenna dimensions and slightly more complicated fabrication process.
2.2.4.5 Comb structures
Utilization of comb structures on the outer edges was explored, as a way of reducing the
backfire radiation [8]. Two models were designed and tested, as depicted in fig. 2.11. One
is utilizing simple comb structure (capacitive loading), the second use resistive loading
between the comb cuts, simulated with discrete resistors.
Results showed that comb structure can help reducing the back radiation lobe. Mea-
sured as a signal level at the back far field probe, usage of both combs decreases the signal
level by 30%. This improvement however comes at the cost of other parameters. Combs
on the outer edges have significant influence on the return loss, as depicted in fig. 2.12.
More importantly, capacitive comb causes large distortion of the radiated signal, thus
-
CHAPTER 2. RADIATING STRUCTURE 19
decreasing the fidelity factor F .
Figure 2.11: Two investigated comb structures - capacitive comb and re-
sistive comb
Figure 2.12: Return loss and signal level received at the front probe for
both comb structures
2.2.4.6 Hybrid exponential model
The hybrid exponential taper, introduced in [1], was briefly explored. The design is
depicted in fig. 2.13.
Such structure is supposed to have better matching properties for a wideband opera-
tion. Simulations during this work however pointed out, that it is impossible to achieve
-
CHAPTER 2. RADIATING STRUCTURE 20
good reflection properties with small taper dimensions, thus rendering this solution un-
suitable for antenna designed in this work.
Figure 2.13: Hybrid taper design, description of antipodal design and its
variables
2.2.5 Antipodal vivaldi antenna
Model of the radiating part had been designed accordingly to fig. 2.13 and inspected in
regard to the depicted variables.
Preliminary sweeps showed that the antipodal design has to be larger than the ta-
pered slot design, in order to achieve similar return loss. The simulations were therefore
performed on a structure with dimensions 9 6 cm.
2.2.5.1 Influence of the inner curvature profile
Inner curvature profile is defined with parameter p1. Choice of p1 fundamentally influences
both return loss and signal distortion of the structure.
Similarly to the tapered slot design, there are two areas where the main reflections
occur. The first is the fin crossing depicted in fig. 2.13, the second is the wide end of
the structure.
Unlike the slot neck, the reflection from the crossing increases with the value of
p1. For bigger p1 with smoother initial part of the curve, crossing is moving towards
the knee of the exponential curvature. In this area, value of the profiles derivative
-
CHAPTER 2. RADIATING STRUCTURE 21
increases rapidly, and presents a corner-like obstacle for the traveling wave. Lower values
of p1 represents smoother crossing, and therefore lower reflection. This can be ob-
served fig. 2.14. Reflections from the wide end of the structure are again inevitable and
cant be influenced significantly by the change of p1.
Figure 2.14: Inner curvature profiles and signals reflected from the struc-
ture for various settings of parameter p1
Description of the reflection mechanisms also explains the rise of return loss with
increased p1, as opposed to the case with tapered slot Vivaldi antenna. Plots of return
losses can be seen in fig. 2.15.
Figure 2.15: Return loss and fidelity factor F for various settings of pa-
rameter p1
The relation of the fidelity factor F to the p1 value is the same as for the tapered slot
Vivaldi antenna. Signal fidelity is higher for lower values of p1, as depicted in fig. 2.15.
-
CHAPTER 2. RADIATING STRUCTURE 22
Maximum of the fidelity factor F was not found during the p1 sweeps presented in this
text.
2.2.5.2 Using spline curves for inner profile
Use of spline curves is again a functional alternative to the exponentially defined profile.
In case of the Antipodal structure, it was faster to achieve better results with spline curves
than with the exponential ones. Generally speaking, both solutions should be equivalent.
2.2.5.3 Influence of the outer curvature profile
Change of the outer profile, defined either exponentially or with splines, has (expectedly)
very little influence on the structures return loss or fidelity factor F . Plots of these
parameters were therefore not included. Slight changes of the reflected signal can be
observed with the lower values of p2, when the fast change of the strip line width causes
minor reflections before the crossing. This is depicted in fig. 2.16.
Figure 2.16: Outer curvature profiles and signals reflected from the struc-
ture for various settings of parameter p2
2.2.5.4 Influence of the fin width
Changing the fin width, represented by the parameter L2, has generally small impact
on the overall performance. Observations however pointed out, that there is a certain
minimal suitable value (1 cm in the case of the inspected design). For values of L2
smaller that this minimum the return loss worsens, and so does the fidelity factor F . The
-
CHAPTER 2. RADIATING STRUCTURE 23
value of L2 generally influences the reflection from wide end of the structure, as depicted
in fig. 2.17.
Figure 2.17: Return loss and signals reflected from the structure for vari-
ous settings of parameter L2
2.2.5.5 Influence of the round corners
Rounding the fin corners proved to be as beneficial to the overall performance as in the
case of the tapered slot design. Again, the return loss parameter changes slightly for
higher frequencies (above 5 GHz).
Figure 2.18: Antipodal round corner design and reflected signal for various
settings of corner radius R
Fidelity factor F of the transmitted signal improves with the higher corner radius.
This can be connected to the lower distortion of the signal reflected from the wide end
-
CHAPTER 2. RADIATING STRUCTURE 24
of the structure. Change of the signal level at the back probe was not observed in case
of the antipodal structure.
Figure 2.19: Return loss and fidelity factor F for various settings of corner
radius R
2.3 Choice of radiating structure
Simulations presented some basic factors influencing performance of both tapered slot
and antipodal designs.
It seems that for small structures, its easier to achieve good return loss using the
tapered slot design. Antipodal designs must be larger and wider to have the same return
loss properties.
For both designs, curvature profile is the essential parameter for achieving small return
loss and signal distortion. It was shown that the definition of the profile can be either
exponential or spline.
Once the best profile is found, its possible to improve parameters of the structure by
introducing additional geometries. Rounding the corners proved to be beneficial for the
signal distortion, without influencing any other parameters. Use of a resistive comb is
a way of improving the front-to-back ratio of the antenna, at the cost of the return loss
properties and overall structure complexity.
Some other improvements appeared to be somewhat troublesome. Hybrid tapers are
unsuitable for small structures, because of their high return losses. Use of the capacitive
-
CHAPTER 2. RADIATING STRUCTURE 25
comb is not advisable due to the signal distortion.
Finally, two basic strategies can be concluded for Vivaldi radiating structures for
UWB:
1. If minimal signal distortion is the primary goal, then antipodal design is the most
suitable solution. A high fidelity factor F can be achieved with proper profile,
wide fins and round corners. Most importantly, the transition from microstrip to
balanced stripline is very simple and does not influence the UWB pulse shape.
Disadvantage of this design is the size of the structure, because both transition
and fins need to be long, and the aperture together with the corners has to be
significantly wider than the minimal aperture width for UWB frequency range.
2. When antenna dimensions are important, use of the tapered slot structure is advis-
able. This structure provides good return loss properties and sufficient fidelity factor
F , while maintaining compact length and minimal width of the antenna. The main
disadvantage of this design is hidden in the transition from the microstrip feed to
structures slot line. Such transition influences signals waveform and also increases
the overall complexity of the design.
In the end, a simple tapered slot design without any additional structures has been
chosen for further development. The choice of simple structure was determined by the re-
quirement for easy fabrication and small size. Various strategies for feeding this structure
are described in the following chapter.
As an illustrative case, one antipodal design was also designed with feeding section,
to provide comparison in Chapter four.
-
Chapter 3
Feeding structure
Tapered slot Vivaldi antenna has been chosen in the previous chapter. Such structure is
implemented in one metallization layer. In order to feed the taper slot line, the feeding
section must implement a transition from the coaxial (SMA) connector to a microstrip
line and from a microstrip line to a slot line. As the slot line impedance is 100 and the
impedance of the microstrip at the point where a SMA connector is attached must be
50 , the feeding structure must also incorporate an impedance transformer. Therefore,
the feeding structure consists of two main parts:
Impedance transformer
Microstrip to slot line transition
Given the fact that the antenna is designed for UWB use, both parts must be wideband
and the whole feeding section should have minimal distortion of the input pulse in the
time domain. Both parts will be dealt separately in this chapter, and final solution
combining two best choices will be introduced in the end.
3.1 Impedance transformer
Antenna feed begins with the SMA connector with nominal impedance of 50 . To
achieve minimal reflection, the connector is soldered to a 50 microstrip line at the
border of the antenna board. Before signal reaches the microstrip to slot line transition,
impedance of the microstrip line must be 100 , so that reflection from the transition to
26
-
CHAPTER 3. FEEDING STRUCTURE 27
the 100 slot line is minimized in the whole UWB frequency range. To achieve such, a
wideband impedance transformer is needed.
There are several designs of wideband impedance transformer, which can be used for
such application. Unlike the narrowband quarter wave transformers, the wideband types
are typical for their smooth and continuous change of microstrip width along the line.
Particular types differ mostly in the shape of the microstrip taper, which influences the
return loss of such transformer. During the design process, three following types were
explored:
Linear taper
Exponential taper
Klopfenstein taper
All types were designed and simulated using CST Microwave Studio, for linear taper,
AWR Microwave office was also used to back-up the results. The performance of those
tapers had been examined for two different lengths to show the influence of the taper
length on the return loss.
Figure 3.1: Exemplary designs of impedance transformers for 50 to
200 transformation
The simulations were concerning only one type of substrate and metallization, de-
scribed already in Chapter two. Microstrip widths to achieve 50 and 100 line
impedance on such substrate are listed in tab. 3.1. These values had been obtained
using the TX lines tool from the AWR Microwave office and later confirmed by calcula-
tions using the CST Microwave studio.
-
CHAPTER 3. FEEDING STRUCTURE 28
Zlin w[mm]
50 2.12
100 0.56
Table 3.1: Microstrip widths for line impedances on the selected substrate
3.1.1 Linear taper
Linear taper is very simple and obvious structure, changing the width of the microstrip
in a linear fashion, as depicted in fig. 3.2. The original intention was to use the linear
transformer mostly for a comparison with the more advanced shapes. Nevertheless, simu-
lations had revealed this simple structure can achieve very similar performance compared
with the Exponential or Klopfenstein taper, given that the taper length is small.
Figure 3.2: Exemplary profiles of impedance transformers for 50 to
200 transformation
Three different lengths of the linear taper were simulated and examined and the results
can be seen in fig. 3.3. It can be seen that for all lengths, it is possible to achieve a return
loss better than -15 dB in the entire UWB range, and better than -20 dB for large parts
of the frequency band. The long 50 mm taper can perform better at the lower parts of
the UWB range. At the higher frequencies above 6 GHz, both return and insertion loss
values degrade and the performance is inferior to the short tapers. This can be partially
explained with the radiation of the structure at higher frequencies, which increases the
insertion loss when the structure is larger and the radiating area longer.
One way to extend the length of the taper on the limited space of the antenna board is
to create a curved structure. Two different designs of such structure were examined, one
with single turn, second with a meander like shape and right-angle turn. Both designs
-
CHAPTER 3. FEEDING STRUCTURE 29
can be seen in fig. 3.4. Apart of the extended length, these shapes hold an advantage in
placing the SMA connector to the back of the antenna board, thus avoiding any possible
effects connected with the wave traveling on the outer edges of the antenna.
Simulation results of curved structures performance can be seen in fig. 3.5, compared
with the straight taper. Bad performance of such structures is caused mainly by the
radiation from the curves, which occurs at higher frequencies. That can be seen in the
S21 plot. Such radiation constitutes a serious problem, because the feeding structure is
located near the radiating part of the antenna and may disturb the radiation pattern of
the antenna. However, reflection from the curved parts is also a problem, probably due
to the small diameter of the turn. The overall performance of simulated curved linear
tapers appeared to be worse than the performance of the short taper.
3.1.2 Exponential taper
The idea of exponential taper is based on the principle of quarter wave transformer,
where the quarter wave segments have infinitesimal length. Full theoretical explanation
can be found in [12] or elsewhere. Basically, we can look at the line impedance of the
continuously tapered microstrip at the distance x from the beginning as if it was the
geometrical average of the adjacent infinitesimal segments.
Z(x) =Z(xx)Z(x+x) (3.1)
Figure 3.3: Return and insertion losses of linear taper impedance trans-
formers
-
CHAPTER 3. FEEDING STRUCTURE 30
Figure 3.4: Designs of the curved linear taper - 1 turn and 2 turn
impedance transformer
By expanding this form in a Taylor series and ignoring the higher order terms [12],
we can obtain a differential equation. Solving this equation for boundary conditions
Z(0) = Z1 and Z(L) = Z2 results in the following relation for the impedance variation
along the taper:
Z(x) = Z1 exp
[x
LlnZ2Z1
](3.2)
In can be inferred from the relation that impedance of such transformer varies expo-
nentially with length. Theoretical behavior of reflection coefficient vs. frequency resem-
bles a passband with decaying ripples [12], with the highest ripple being -13.3 dB from
the zero frequency reflection coefficient 0.
Two exponential tapers with different lengths were designed using the formula (3.2).
Short taper (L = 23.7 mm) had been defined in 20 equidistant points by the line
impedance. Consequently, actual values of the microstrip width were obtained using
the TX lines tool. Long taper (L = 50 mm) was designed in the same fashion, using 50
equidistant points.
Fig. 3.1 gives a good idea of the main aspect of the short exponential tapers - for
only 50 impedance difference, the exponential curvature is too small. For that reason,
both shape and the overall performance are very similar to the linear transformer.
-
CHAPTER 3. FEEDING STRUCTURE 31
Figure 3.5: Return and insertion losses of curved linear taper impedance
transformers compared to the straight design
The performance of both lengths of the exponential taper can be seen in the fig. 3.6.
Very good values of the return loss can be achieved with longer taper, better than -20 dB
in the whole UWB range. Previously mentioned passband behavior of the reflection
coefficient can be also observed in the return loss plot. Passband ripples are approximately
10-11 dB below the zero frequency return loss, they are, however, not decaying with the
frequency. Problem of the longer structure is again connected to the radiation. The
effect can be observed on the insertion loss plot, where the loss increases significantly for
frequencies above 6 GHz.
Figure 3.6: Return and insertion losses of exponentially tapered
impedance transformers
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CHAPTER 3. FEEDING STRUCTURE 32
3.1.3 Klopfenstein taper
Klopfenstein taper represents an improved alternative to the exponential taper. This
structure can either achieve better match on the same length, or comparable match on
the shorter length than the exponential taper [12].
Compared to the exponential taper, Klopfenstein design has one more degree of free-
dom in the taper definition, represented by the variable A in the relation
lnZ(x) =1
2ln [Z1Z2] +
0coshA
A2
(2x
L 1, A
)(3.3)
Where (x,A) is defined as
(x,A) = (x,A) = x
0
I1
[A1 y2
]A1 y2
dy (3.4)
I1 is a modified Bessel function and 0 is the maximum reflection coefficient at the
zero frequency
0 =Z2 Z1Z2 Z1
(3.5)
Using parameter A, the maximum ripple in the passband characteristics can be set,
defined as
M =0
coshA(3.6)
More details can be found in [12] and other sources.
As in the previous case, two Klopfenstein tapers with different lengths were designed.
Short taper (L = 23.7 mm) had been defined again in 20 equidistant points by the line
impedance and then the TX lines tool was utilized to obtain the actual microstrip widths.
The same holds for the long taper (L = 50 mm), defined again in 50 equidistant points.
The maximum passband ripple M was set to -40 dB. As some Bessel functions are
required for the calculation, MathCad software was used to simplify the process.
Exemplary design is depicted in fig. 3.1, the characteristic element of the Klopfenstein
taper, which is the impedance discontinuity at the both ends of the taper, is not visible
due to the pictures small resolution
Fig. 3.7 shows results for return loss and insertion loss for both taper lengths. It can
be seen that the long Klopfenstein taper achieves an excellent return loss properties below
-23 dB in the whole UWB range. The short taper can achieve return loss better than
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CHAPTER 3. FEEDING STRUCTURE 33
-15 dB and doesnt differ much from the exponential or linear taper. On the insertion
loss plot, the influence of high frequency radiation can be observed again for the longer
taper.
Figure 3.7: Return and insertion losses of Klopfenstein taper impedance
transformers
3.1.4 Choice of taper
It can be inferred from the observations that the crucial factor for taper performance is
its length.
For short tapers (L = 23.7 mm), which are required for selected antenna board, the
shape does not matter significantly, as can be seen in fig. 3.8. Linear, exponential and
Klopfenstein taper achieve very similar performance, with return loss better than -15 dB
and insertion loss approximately -0.1 dB within the UWB range. Antenna designer can
therefore simplify the design and use a linear taper, without any significant degradation
of the overall feed performance. Thats why the linear taper has been chosen for the
antenna realization in this project.
Longer tapers can exploit the shape properties better, and there is a significant im-
provement with the exponential and especially with the Klopfenstein design, as can be
seen in fig. 3.9 . Paying attention to the taper shape can therefore yield great improve-
ments in the overall antenna feed performance.
Main problem, which arises with the longer taper, is the radiation along the structure,
which is inevitable effect for any microstrip structure. This takes its toll on the inser-
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CHAPTER 3. FEEDING STRUCTURE 34
Figure 3.8: Return and insertion losses of impedance transformers with
short tapers
tion loss properties, which degrade for higher frequencies in the UWB band and cause
variations of the insertion loss within the band of interest.
The observations also indicated that the use of curved tapers to increase the total
length is not advisable, due to increased radiation from the curved parts. Use of curved
tapers doesnt yield any improvement to the overall feed performance. Furthermore, the
radiation from the curves can influence the radiation pattern of the antenna. That is
especially dangerous for compact structures where the feed is located near the radiating
part of the antenna.
Figure 3.9: Return and insertion losses of impedance transformers with
long tapers
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CHAPTER 3. FEEDING STRUCTURE 35
3.2 Microstrip to slot line transition
Any Vivaldi antenna on a single metallization layer must be fed from a slot line. In
order to couple the field from the microstrip feed to the slot line, a microstrip to slot
line transition must be incorporated into the feeding structure. Since the slot line is a
balanced transmission line, while microstrip is generally unbalanced, these transitions fall
within the category of balun transformers, or shortly baluns. Two basic balun principles
exist for a microstrip to slot line transition:
Marchand balun (orthogonal transition)
Double Y, or YY balun
Marchand baluns constitute a large group of transitions with various designs. Their
common denominator is an orthogonal placement of microstrip and slot lines and generally
passband characteristics of return and insertion losses. Designs discussed in this chapter
are wideband transitions using a radial microstrip stub and a circular slot line stub.
Another design with transition using a via connection is also investigated.
Designs of both Marchand and double Y baluns will be described and explored during
the next part of this chapter and the most suitable solution will be selected in the end.
3.2.1 Marchand balun (orthogonal transition)
In a Marchand balun, the microstrip and the slot line meet in orthogonal directions on
the opposite sides of the substrate. Microstrip line ground plane is in this case created
by one side of the slot line metallization. Microstrip line is terminated by a stub, which
creates a virtual short at the point of crossing, virtually shunting the microstrip to the
other side of slot line metallization. That enables the propagating field to couple into the
slot line on the opposite metallization layer. As the slot line is terminated by an open
end at the point of transition, the field can propagate through such transition without
any reflection and insertion losses (in an ideal case) [11].
To assure conditions for a microstrip virtual short wide frequency range, a wideband
radial stub or via must be used for the microstrip termination. Similarly, a radial or
circular stub must be utilized for the slot line termination, to create an open end. Three
different designs of the transition were investigated. First two are utilizing radial stub or
via for the microstrip termination, while having the slot line terminated with a circular
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CHAPTER 3. FEEDING STRUCTURE 36
stub. The last one is using via connection and real open end of the slot line. A research
on the transition with a radial stub slot line termination can be found in [15].
An impedance transformer selected in the previous section of this chapter (short linear
taper) had been already incorporated into the designs of Marchand baluns, to speed up
the design process. Before dealing with particular designs, the properties of the circular
open end termination of the slot line had been explored, as this part is common for both
via and radial stub versions of the transition.
3.2.1.1 Slot line circular stub termination
In order to assure the field propagation through the transition, the slot line must be
terminated with an open end at the point of line crossing. Such wideband open end
can be created by a circular slot line stub. Performance of the transition is therefore
influenced by the radius of the circular stub. The impact of stub radius on the overall
transition performance in the UWB range can be seen in fig. 3.10. These results were
obtained from a transition with microstrip radial stub (R = 5.3 mm, Angle = 70). Its
obvious that radius of the circular stub must be optimized with regards to the used
substrate and the frequency band of interest.
Figure 3.10: Return and insertion losses of a transition with variable slot
line circular stub radius
The need to cut out metallization in order to create the circular stub limits the ground
plane of the microstrip line in the proximity of the transition. This has an effect on the
microstrip line impedance, causing mismatch and subsequently degrading the overall
performance. Moving the circular stub further from the transition reference plane can
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CHAPTER 3. FEEDING STRUCTURE 37
suppress this problem. In that case however, another problem arises, as the open end is
moved away from the transition point and conditions for the transition operation are not
fulfilled completely.
An optimization of the circular stub distance from the crossing is therefore necessary.
That way we can balance problems, which are arising from the impedance mismatch and
problems, which are caused by the open end distance. Plots of transition performance
vs. circular stub distance from the line crossing can be found in fig. 3.11. It can be seen
that for the distance d = 0.5 mm, which roughly corresponds to a microstrip width, the
impedance mismatch is improved (return loss plot), while a sufficient transition operation
is maintained (insertion loss plot).
Figure 3.11: Return and insertion losses of a transition with variable slot
line circular stub distance from the transition reference plane
3.2.1.2 Transition with a microstrip radial stub
This design, depicted in fig. 3.12 exploits wideband properties of the radial stub. In this
configuration, there are two variables which can influence the overall performance of such
transition - the radius and the opening angle of the stub. Influences of both variables
were inspected, using circular slot line stub with radius R = 4 mm and distance of the
stub from the transition d = 0.5 mm.
3.2.1.2.1 Influence of the Stub angle
In order to maintain wideband performance, a radial stub must be flared in a wide
angle. As depicted in fig. 3.13, the optimal performance occurs with angles above 50.
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CHAPTER 3. FEEDING STRUCTURE 38
Figure 3.12: Schematics and parameters of the microstrip to slot line tran-
sition with radial stub
With above 70, however, the performance worsens, as the proximity of the slot line
to the stub increases. In the end, = 60 has been found as the best value on the used
substrate. These observations were made with radial stub radius R = 5.3 mm.
Figure 3.13: Return and insertion losses of a radial stub transition with
variable stub angle
3.2.1.2.2 Influence of the stub radius
Stub radius is determining the operating band of the radial stub, and therefore is
a crucial factor in the overall transition performance. Parameter sweeps, performed on
the transition model with stub angle = 60, indicated the optimal radius of 5.3 mm.
This size (on the used substrate) roughly corresponds with the quarter-wave length of
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CHAPTER 3. FEEDING STRUCTURE 39
the geometrical center frequency of the FCC UWB band. This parameter is obviously
strongly substrate dependent. Influence of the stub radius on the overall performance
can be seen in fig. 3.14.
Figure 3.14: Return and insertion losses of a radial stub transition with
variable stub radius
3.2.1.2.3 Signal distortion
Time-domain observations of the signal waveform distortion showed that the signal
distortion is largely caused by the transition structure itself. That means the distortion
does not depend much on the actual value of stub radius or stub angle. As long as the
microstrip radial stub capacitance and the slot line circular stub inductance are part of
the transition, the excitation signal will be distorted at the output.
This microstrip radial stub capacity and slot line circular stub inductance tend to
accumulate some of the field energy during the initial part of the pulse. Consequently,
the later parts of the excitation pulse woud gain this energy, as the accumulated energy
is being discharged. This can be observed in fig. 3.18.
3.2.1.3 Transition with a via connection
This transition uses via connection instead of a radial stub to create a real short termi-
nation of the microstrip line. A rivet via with 0.8 mm outer diameter, 0.1 mm metal
thickness and 1.3 mm top cap had been used for design and simulations. The main ad-
vantage of this solution is that the via is a truly wideband short, working in an unlimited
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CHAPTER 3. FEEDING STRUCTURE 40
frequency range. There are, however, physical limitations, which make the use of via
connection somewhat troublesome.
The short, required for proper operation of the transition, is supposed to be localized
at the transition point. Requirement like that cannot be fulfilled with a real world via
with defined diameter. That is because the via connection must not interfere with the slot
line border. For the same reason, the via cap should not disturb the microstrip geometry
at the transition point.
Figure 3.15: Schematics and parameters of the microstrip to slot line tran-
sition with a via connection
Fig. 3.16 demonstrates the influence of via placement with regards to the slot line
border. The 0 mm distance is impossible to manufacture without disturbing the slot line,
values closer to zero would still impose serious problems for fabrication of such transition.
During the design phase, the distance of 0.4 mm was chosen as a compromise between
the transition performance and the fabrication feasibility.
With via placed with some offset from the slot line, a considerate reflection occurs.
This causes the transition to have matching properties inferior to the radial stub transi-
tion.
3.2.1.3.1 Signal distortion
Although the matching properties of a transition with via connection cannot be on
par with the radial stub transition, the signal distortion is significantly smaller when via
connection is used. Without capacitive effect of the radial stub, excitation pulse passing
trough the transition is distorted because of the via connection inductance, which is
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CHAPTER 3. FEEDING STRUCTURE 41
Figure 3.16: Return and insertion losses of a via connection transition with
variable distance of the via placement from the slot line bor-
der
rather small. The slot line circular stub inductance remains as another source of the
pulse ditortion.
3.2.1.4 Transition with a via connection and a real slot line open end
This structure is derived from the above mentioned transition using via hole. To fur-
ther suppress the signal distortion caused by the slot line stub inductance, the slot line
circular stub had been substituted with a real open end, implemented by cutting away
the substrate at the slot line termination point. A schema is depicted in fig. 3.17. Some
substrate was left on the transformer side, to keep the ground plane for the microstrip
line.
3.2.1.4.1 Signal distortion
Without both microstrip and slot line stubs, the signal distortion is very low, with the
fidelity factor F = 0.9989, which is the best result out of all feed design options explored
in this chapter. The comparison of the excitation pulse and its distorted waveform can
be seen in fig. 3.17 and fig. 3.18. While signal distortion had been significantly improved,
matching properties remained the same as in the case of transition with a via connection
and slot line circular stub.
A problem connected with this design is the slot line open end radiation. Fig. 3.18
demonstrates the radiation measured using the far field probe placed 30 cm from the
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CHAPTER 3. FEEDING STRUCTURE 42
Figure 3.17: Schema of the real slot line open end via transition, signal
distortion of the transitions with a via connection
transition, oriented in the slot line E-field direction.
Such radiation can seriously decrease antennas front-to-back ratio and limits utiliza-
tion of this transition structure only to such cases when back radiation is not considered
important.
Figure 3.18: Comparisons of the signal distortion and radiation of the ra-
dial stub and the via connection open end design
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CHAPTER 3. FEEDING STRUCTURE 43
3.2.2 Double Y balun
Double Y, or YY balun is another type of the microstrip to slot line transition. Double Y
balun is a broadband transition in principle. The structure of double Y balun is depicted
on fig. 3.19.
Figure 3.19: Schema of the double Y balun; signals reflected from all pos-
sible signal paths in the balun
It can be seen, that the microstrip line input divides at the junction point into two
equally long microstrip branches, creating shape of letter Y. One branch is terminated
with an open end, the second branch is shorted using via connection to the ground plane.
On the opposite metallization, a similar structure can be seen, implemented with a slot
lin. One branch is terminated with a circular stub, creating an open end; the second
branch is terminated with a short. Junction point is the same as for the microstrip lines
and the whole slot line structure constitutes mirror symmetry to the microstrip Y.
The basic principle for both microstrip and slot line part is that signals are reflected
with the opposite phase in each branch; therefore cancel each other out when they reach
the junction point. This suppresses reflection and forces the field to couple from the
microstrip to the slot-line and vice versa [12]. According to this principle, double Y
balun should work for any frequency.
In the real world, there are several difficulties in achieving good wideband performance
with the Double Y microstrip to slot line transition. At first, the range of frequencies
is restricted by the open end on the slot line side, which is realized as circular stub and
therefore it works as open only in a limited band.
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CHAPTER 3. FEEDING STRUCTURE 44
Figure 3.20: Return and insertion losses of the double Y balun. CST band
limited (3.1 GHz - 10.6 GHz) excitation was used to obtain
the plots.
The requirement of signals meeting each other at the junction point with the opposite
phase is also very strict, and even a small phase difference can cause a large performance
degradation. This makes realization of such balun very difficult. Designer must carefully
compensate the different electric lengths of slot-line and microstrip line on the selected
substrate. Attention must be also paid to the length differences caused by the circular
stub on the slot line side.
Even when the signals are meeting with perfectly opposite phase and the band limit
introduced by the circular slot-line stub is acceptable, there is another limitation caused
by the radiation from the branches. Such radiation causes the signals are indeed reflected
with an opposite phase, but their amplitude is reduced. When signals meet at the junction
point, they cannot cancel each other out completely due to the different amplitudes,
and the residual reflected signal causes degradation of the return loss and the overall
performance. The radiation is especially significant with the slot-line structures, both
open and short circuit.
Plots of such reflected signals from each particular termination of the double Y balun
can be found in fig. 3.19. A Gaussian modulated sine waveform was used to create exci-
tation pulse within the FCC UWB band and each path of the signal had been simulated
separately to obtain the separate reflections. To maintain simplicity and clearness of the
plot, phase of signals reflected from short had been reversed. Its obvious the amplitude
difference is significant, especially for the slot line structures.
Due to the reasons explained above, matching of the double Y balun is relatively poor,
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CHAPTER 3. FEEDING STRUCTURE 45
as can be seen in fig. 3.19 and so is the insertion loss. Such properties are rendering this
transition unsuitable for antenna feed, although the signal distortion is relatively low,
with the fidelity factor F = 0.9833.
3.3 Conclusion, choice of transition
Out of all feeding possibilities explored in this section, there are two solutions which
seem plausible for implementation as the UWB Vivaldi antenna feed. These solutions
are representing the opposite trends in requirements which every UWB feeding structure
must comply. First requirement is that the feeding structure must cause minimal signal
distortion on the UWB pulse, so that the pulse can be properly detected on the receiving
side. Second requirement is the general need for antenna to be properly matched, so it
can be used in any UWB system.
The transition utilizing radial stub provides very good matching properties with re-
flection loss better than -17 dB within the UWB range. Insertion loss is -1.3 dB in the
worst case, which occurs at the higher frequencies due to the radiation from the transi-
tion. Matching properties of this transition are however balanced with not so good signal
distortion (F = 0.9663), which occurs due to the capacitive effect of the radial microstrip
and the inductive effect of the slot line circular stub.
Figure 3.21: Return and insertion losses of the radial stub and the via real
open end transition
Using via connection instead of the microstrip radial stub, and real open end instead
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CHAPTER 3. FEEDING STRUCTURE 46
of the slot line circular stub is a way to achieve significant suppression of the pulse
distortion. Improper placement of the via connection due to the fabrication purposes
unfortunately causes degradation of the matching properties. The open end slot line
termination also radiates the coupled signal away in a backfire direction, which disturbs
the antenna pattern.
In the end, the decision was made to implement both types of feeding structure with
the radiating structure selected in the previous chapter, so that the properties of the feed
can be evaluated within the scope of the overall antenna performance.
-
Chapter 4
Final antenna design and
measurements
Both radiating and feeding structures have been chosen in previous chapters. In this
chapter, final antenna designs are presented, simulated and measured.
The work focuses mainly on the tapered slot Vivaldi antennas with feeding structures
from Chapter three. Results of these designs are compared with the antipodal antenna
suggested in the end of Chapter two. Another comparisons are made with the antenna
introduced by Piksa and Sokol in [11].
4.1 Tapered slot Vivaldi antennas
Two versions of tapered slot Vivaldi antennas were designed and fabricated. In the
following text, these antennas are called as Via Vivaldi and Stub Vivaldi, accordingly
to the feeding structures presented in Chapter three. Both designs are depicted in fig. 4.1.
Via Vivaldi contains feeding section with Via connection in the microstrip-to-slot line
transition. Stub Vivaldi uses radial stub for the same transition type. Both designs are
utilizing transitions, which have been inspected and optimized during the previous work.
Additional parameter sweeps were necessary after both feed and radiating structures had
been put together, to optimize both return loss and signal fidelity.
In the end, a tapered slot with 60 mm aperture width was chosen as a compromise
between the return loss and the signal fidelity. The length of the structure is approxi-
mately 55 mm (including feed). Precise dimensions can be seen in th