Design of Vivaldi Antennas - Thesis

Czech Technical University in Prague

Faculty of Electrical Engineering

DIPLOMA THESIS

Design of Vivaldi Antenna

Prague, 2007 Student: Josef Nevrly

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

i

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

ii

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.

iii

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.

iv

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.

v

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

vi

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


3.2.1.4 Transition with a via connection and a real slot line open

end . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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

vii

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

viii

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

ix

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

x

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

xi

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

xii

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.

1

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.


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.


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


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.

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

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


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)


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.


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].


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


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)


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.


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 .


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,


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-


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


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


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


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


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.


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


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


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


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.


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


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


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.


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


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


-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-


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


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


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


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.


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


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


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.


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


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.


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


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


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.


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,


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


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

Documents

Design of Vivaldi Antennas - Thesis