Design of Vivaldi Antennas - Thesis

Czech Cze ch Tec Technic hnical al Univ Univers ersity ity in Pra Prague gue Facul aculty ty of Electr Electrical ical Enginee Engineering ring

DIPLOMA THESIS Design of Vivaldi Antenna

Prague, 2007

Student : Josef Nevrl´ y

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

Prohl´ aˇsen´ı Prohlaˇ Pro hlaˇsuji, suji , ˇze ze jsem dipl diplomovou omovou práci aci vypracoval samosta samostatnˇ tnˇe a pouˇzil zil k tomu literatu literaturu, ru, kterou uvád´ ad´ım v se sezn znaamu pˇrilo ri loˇˇzen´ ze ném em k pr pr´ aći. aci. Nemám am námi mitk tky y pr prot otii p˚ ujˇcov´ ujˇ cován´ı, zve veˇˇrejnˇen´ı a dalˇs´ s´ımu vyuˇzit´ı prace, aće, poku pokud d s t´ım bude souhlasit souhla sit katedra elektroma elektromagnetick´ gnetického eho 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: ˇ y, • Ing. Pe Petr tr Cern´ y, my diploma thesis advisor, for many ideas behind this work, his

patient help and support throughout the project and finally for countless hours of the processor time on his black machine

• Prof. Ing. Miloˇs Mazánek anek CSc., who has directed me to the topic of UWB antennas • Doc. Ing. Jan Macháˇ aˇc DrSc., who ignited my intere interest st in the theory of electromagnetic field some years ago

• my family and my girlfriend, for their patience, support and love

ii

Abstrakt Tato diplomov´ a práce ace se zabýv´ yv´ a návrhe av rhem m Viva Vivald ldiho iho antény eny pr proo p ouˇzit´ zit´ı v UWB pásmu asmu dle definice FCC, tedy 3.1 - 10.6 GHz. Speciál aln n´ı po pozo zorno rnost st je vˇenov´ enov ana ańa optim optimalizac alizacii pro minim´ al n´ı zkr aln zkresl eslen´ en´ı UWB pul pulsu su pˇri ri za zachov´ chován´ an´ı ma mal´ lé veli velikost kostii antény. eny. De Desig sign n antény eny je rozdˇ ro zdˇelen el en do dvo dvou u ˇc´ cást as t´ı - vy vyzaˇ zaˇrova rovacc´ı st stru rukt ktur ury y a na nap´ pájec´ aj ec´ıho ıh o obvodu obvo du.. V ˇc´ cásti asti pojedn po jedná´va j´ıc´ı o vyzaˇ vy zaˇrovac rova c´ıch st stru rukt ktur ur´ách ach jsou studovány an y ve verz rzee Vi Vival valdi diho ho an ant´ tény eny v je jedn dn´é vr vrst stvˇ vˇe (r (roozˇs´ıˇren´ re ná ˇstˇ stˇerbina) erbi na) i ve dvou vrst vrstv´ vách ach (protich˚ udné ploutve). Kapitol udn´ Kapitolaa o napájec aj ec´´ıch obvo obvodech dech je vˇenov´ enov´ ana nap´ ana ajen´ı jedn ajen´ jednost ostrann´ ranné stru struktur ktury y po pomo mocc´ı pˇrechodu recho du mikr mikrop´ opásek-ˇstˇerbinové veden vede n´ı. Pro Prostu studov´ dovány any js jsou ou ver verze ze pˇrecho re chodu du s r˚ uznými ty uzn´ typy py zako konˇ nˇcen´ı ve ved den´ı a nˇeko kollik ty typ˚ p˚ u mikrop´ as kového askov´ eh o im imp p ed edan anˇˇcn´ cn´ıho ıh o tr tran ansf sfor orm´ mátoru atoru (lineárn ar n´ı, exp expon onenc enci´ iáln´ al n´ı,ı, Kl Kloopf pfen enst stei ein˚ n˚ uv ). uv). V závˇeru er u pr pr´áce ac e jso j sou u po p o dl dlee zjiˇ z jiˇstˇ stˇen´ en ych y ćh pozn znaatk˚ u nav avrˇ rˇzeny, ze ny, se sesstro jen eny y a zm zmˇˇeˇ eˇreny re ny dv dvˇˇe ant nt´ény eny s jedn jednovrst ovrstvou vou vyzaˇrovac´ rovac´ı stru struktur kturou. ou. Vla Vlastno stnosti sti tˇechto echto antén en jso jsou u po pot´ té po porovn´ rovnány any 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.

iv

Prostudujte doporuˇcenou literaturu. Navrhnˇete, analyzujte a porovnejte dvˇe základn´ı ˇ s ohledem na struktury Vivaldiho antény bez napájec´ıch obvod˚ u. Porovn´ an´ı provedte minimalizaci zkreslen´ı vyzaˇrovan´ ych impuls˚ u v UWB pásmu dle FCC, zpˇetné vyzaˇrován´ı, rozmˇer˚ u a tvaru zakonˇcen´ı ploutv´ı. Na základˇe tohoto porovnán´ı vyberte jednu strukturu a doplˇ n te ji o napájec´ı obvod. Tuto anténu zoptimalizujte, zrealizujte a zmˇeˇrte jej´ı impedanˇcn´ı a vyzaˇrovac´ı parametry.

Study the recommended references. Design, analyze and compare two basic structures 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 it’s impedance and radiation parameters.

v

Contents Table of Figures

ix

Table of Tables

xii

1 Introduction

1

1.1 Scope of this pro ject . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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

Antipodal vivaldi antenna . . . . . . . . . . . . . . . . . . . . . .

20

2.2.5

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

3.2.1.3

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

Transition with a via connection . . . . . . . . . . . . .

39

3.2.1.3.1 3.2.1.4


40

Transition with a via connection and a real slot line open end . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1.4.1

41


41

Double Y balun . . . . . . . . . . . . . . . . . . . . . . . . . . . .

43

3.3 Conclusion, choice of transition . . . . . . . . . . . . . . . . . . . . . . .

45

3.2.2

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 it’s variables . .

20

2.14 Inner curvature profiles and signals reflected from the structure for various settings of parameter p 1 . . . . . . . . . . . . . . . . . . . . . . . . . . .

21

2.15 Return loss and fidelity factor F for various settings of parameter p 1 . . .

21

2.16 Outer curvature profiles and signals reflected from the structure for various settings of parameter p 2 . . . . . . . . . . . . . . . . . . . . . . . . . . .

22

2.17 Return loss and signals reflected from the structure for various settings of parameter L2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

ix

23

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 Ω to 200 Ω transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

27

3.2 Exemplary profiles of impedance transformers for 50 Ω to 200 Ω transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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 . . . . . . . . . . . . . . . . . . . . .

x

42

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 Vivaldi 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 r tr (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 exponentially 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 theoretically 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 equipment. 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.

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. MwS’s 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 S 11 and S 21 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 1 Gaussian pulse 0 − 11 GHz Gaussian doublet Gaussian modulated sine 3.1 − 10.6 GHz

0.8 0.6 0.4 0.2 0 −0.2 −0.4 −0.6 −0.8 −1 0

0.1

0.2

0.3

0.4

0.5 Time[ns]

0.6

0.7

0.8

0.9

1

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 don’t 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 remains approximately the same for various waveguide port sizes and meshing settings.

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 b etween 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 

∞

−∞

 

√ R 1max s1(t + τ ) √ R 1max s2(t)dt 1 2

(1.1)

Where s 1 is the excitation signal, s 2 is the received signal and R 1max and R 2 max are the maximum values of the autocorrelation function for excitation signal and received signal respectively.



∞

Rx max = max



sx (t + τ )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


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.

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 2.1.1

Overview of Vivaldi antenna designs Tapered slot Vivaldi Antenna

Tapered slot Vivaldi antenna is the original design introduced by Gibson in 1979 [4]. It’s 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 bandwidth 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 λ0 (2.1) 2 where sw is width of the slot. Therefore, the wide end of the exponential taper sw =

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 it’s 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 transition

Microstrip to slotline transition, as shown in fig. 2.1, is mostly used for tapered slot Vivaldi antenna. It’s possible to design transitions which operate over a decade of bandwidth 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 Ω 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 v ph , which has to hold to the following

8


condition

v ph ≤ 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 λ = 1+ 0 2L v ph

(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 thickness normalized to the free space wavelength λ 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

√ tef f t = ( r − 1) (2.4) λ0 λ0 where t is the actual substrate thickness. This rule should hold for any tapered structure within the length of 4 λ0 to 10 λ0. 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: 10L ) (2.5) λ0 where L is the length of the taper. This relation holds for taper lengths of 3 λ0 to 7 λ0 D = 10log(

and c/v ph ≈ 1.05. For longer antennas, the multiplicative constant is somewhat lower, Johnsson [6] presents a relation of

D = 10log(

4L ) λ0

(2.6)

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 =

 55

L λ0

; BW =

 77

L λ0

(2.7)

In general, it’s 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 Gibson’s original design. In the antipodal configuration, antenna is created on a dielectric substrate with two-sided metallization. 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 Gibson’s 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.


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 especially 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, depending 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. Nester’s patent [9] introduced a slightly different geometry of the bottom side metallization, lacking the twin line section. Hybrid exponential flare version of antipodal Vivaldi also exists, as documented in Fischer’s patent [1].


2.1.3

11

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 crosspolarization 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 groundplanes 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 construction 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 surface 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 don’t differ significantly from the antipodal design. Constant beamwidth for wide range of frequencies

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. Parameters 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

Substrate height

H

Dielectric constant (at 10 GHz)

r

Dissipation factor (at 10 GHz)

tgδ

Metallization thickness

t

Metallization (Copper) conductivity

s

Value 0.76 mm

2.52

0.0022 35 µm

15.88 · 107 Sm

−1

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) = Ae px − Ae p +

sw 2

(2.8)

13


where coefficient p is the curvature parameter, sw is the slotline width and A is defined as: aw 2

sw

− −e 2

(2.9) p e Parameter aw stands for aperture width at the end of the taper, T L is the taper A =

pT L

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 antenna’s E-field vector. Return loss was calculated automatically by the MwS, with values normalized to the calculated port impedance.

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 Ω line impedance was used as the structure’s feed.

Figure 2.5: Schema of the tapered slot Vivaldi antenna design and variables

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 .

CHAPTER CHAP TER 2. RADIA RADIATING TING STRUCT STRUCTURE URE

15

Figuree 2.6: Taper profiles and signal Figur signalss reflected from the struc structure ture for various 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 parameter p p does not influence the wide end reflection significantly. Following these observations, it can be inferred that increasing the parameter p can improve impro ve matching matching ch charact aracteris eristics tics.. The improveme improvement nt is of cour course se with within in the limit limitss giv given en by the antenna antenna aperture aperture and slot line width. width. Th This is can be seen on the return return loss plot in fig. 2.7.

Figuree 2.7: Retur Figur Return n loss and fidelity factor factor F for various settings of parameter p

Varying the value of p also p also influences the signal distortion, represented by the fidelity factor F relation on of the fidelit fidelity y fac factor tor to the p is depict depicted. ed. It can be see seen, n, F .. In fig. 2.7, relati


16

that the F the F is is the best at lower values of p, Observ rvations ations on p , as opposed to the return loss. Obse different models suggest that for a range of p of p values, fidelity factor F factor F reaches reaches maximum at the point where the curvature is most ”round”. Reason Re asonss for this behavior behavior were were not found during during the des design ign work. work. Th Thee onl only y lea lead d is the wave waveform form of the refle reflecte cted d signal signal.. If the signal reflected reflected from the structure structure has low distortion (typical for lower p, fig. 2.6), also the radiated pulse will have low distortion. That is, how howev ever, er, an expected expected resu result. lt. Ther Theree is no obv obvious ious connection connection between between the low fidelity factor and the return loss or other characteristics.

2.2.4. 2.2 .4.2 2

Using Usi ng spline spline curve curvess for taper taper definiti definition on

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 signal fidelity fidelity on the same or better level level that the exponential exponential definition. definition. For return loss properties, propert ies, the basic spline definition definition provided provided wor worse se results than the exponential. exponential... It’s however safe to say, that with more elaborate spline definition (more points), the solution is equivalent to the exponential curvature.

2.2.4. 2.2 .4.3 3

Influen Infl uence ce of the ant antenn enna a dimensi dimensions ons

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-


17

ences the return loss. Apart of that, both parameters are indirectly (through parameter p p)) connected with the taper profile, influencing the fidelity factor F F .. Changing the antenna width, while leaving the parameter p parameter p and and length of the taper T taper T L unchanged, yields results plotted in fig. 2.8. It can be seen that the matching properties improve impro ve towards towards the low lower er frequencies frequencies.. On the reflected reflected signa signall plot, higher distortion distortion of the wide end reflection can be observed. This results in lower fidelity of the transmitted signal. Changing the taper length T L, while leaving W W 22 and p parameters unchanged, has very ve ry littl littlee effec effectt on the overall overall performance. performance. It is, how howev ever, er, a wa way y to impro improve ve the directivity 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 lo low w re reflec flectio tion. n. Th Thee onl only y ph physi ysical cal lim limits its are re repre prese sent nted ed by the sma smalle llest st aper apertur turee width defined in (2.1) and the maximal taper length defined in (2.3).

2.2.4. 2.2 .4.4 4

Influen Infl uence ce of of the rou round nd corne corners rs

Rounding the taper corners, as depicted in fig. 2.9 had been explored as a way of maintaining smooth taper profile. Fig. 2.10 depicts the influence of such rounding with changing corner radius R radius R..

Figure 2.9: Round corner design and reflected signal for various settings of corner radius R

Obvious Ob viously ly,, retu return rn loss is only slightly slightly impro improve ved d for frequencie frequenciess abov abovee 7 GHz. Bett Better er


18

improve impro vemen mentt can be seen in the plots of the refle reflected cted signal. With bigger rounding, rounding, the distortion of the reflected pulse is decreased. That results in improvement of the fidelity factor F 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 corne cornerr 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 shouldn’t be considered as serious. Observations showed that rounding taper corners is a way of improving the signal fidelity fideli ty without without ch changing anging the return loss. The price paid for suc such h impro improve vemen mentt is the increase of the antenna dimensions and slightly more complicated fabrication process.

2.2.4. 2.2 .4.5 5

Comb Com b str struct ucture uress

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 Resu lts showed showed that comb structure structure can help reducing reducing the back radiation lobe. Measured 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


19

decreasing the fidelity factor F .

Figure 2.11: Two investigated comb structures - capacitive comb and resistive 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 operation. Simulations during this work however pointed out, that it is impossible to achieve


20

good reflection properties with small taper dimensions, thus rendering this solution unsuitable for antenna designed in this work.

Figure 2.13: Hybrid taper design, description of antipodal design and it’s 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 tapered 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 profile’s derivative


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 observed fig. 2.14. Reflections from the wide end of the structure are again inevitable and can’t be influenced significantly by the change of p 1.

Figure 2.14: Inner curvature profiles and signals reflected from the structure 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 parameter p1

The relation of the fidelity factor F to the p 1 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.


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 structure’s 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 p 2 , 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 structure 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


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 various 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


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, it’s 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, it’s 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


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 advisable. 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 structure’s slot line. Such transition influences signal’s 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 requirement 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 Ω and the impedance of the microstrip at the point where a SMA connector is attached must be 50 Ω, 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 Ω. To achieve minimal reflection, the connector is soldered to a 50 Ω 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 Ω, so that reflection from the transition to

26

CHAPTER 3.

FEEDING STRUCTURE

27

the 100 Ω 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 Ω to 200 Ω transformation

The simulations were concerning only one type of substrate and metallization, described already in Chapter two. Microstrip widths to achieve 50 Ω and 100 Ω 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 calculations using the CST Microwave studio.

CHAPTER 3.

28

FEEDING STRUCTURE

Z lin

w[mm]

50 Ω

2.12

100 Ω

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, simulations 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 Ω to 200 Ω 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 S 21 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 (x − ∆x)Z (x + ∆x)

Figure 3.3: Return and insertion losses of linear taper impedance transformers

(3.1)

CHAPTER 3.

30

FEEDING STRUCTURE

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) = Z 1 and Z (L) = Z 2 results in the following relation for the impedance variation along the taper:

x

Z 2 ln Z (x) = Z 1 exp L Z 1



(3.2)

In can be inferred from the relation that impedance of such transformer varies exponentially with length. Theoretical behavior of reflection coefficient vs. frequency resembles a passband with decaying ripples [12], with the highest ripple being -13.3 dB from the zero frequency reflection coefficient Γ 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 Ω 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.

31

FEEDING STRUCTURE

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

impedance transformers

losses of exponentially tapered

CHAPTER 3.

3.1.3

32

FEEDING STRUCTURE

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 freedom in the taper definition, represented by the variable A in the relation



1 Γ0 2x ln Z (x) = ln [Z 1Z 2 ] + A2 φ 2 cosh A L



− 1, A

(3.3)

Where φ(x, A) is defined as

 I A 1 − y   dy φ(x, A) = −φ(−x, A) = A 1−y x

2

1

0

2

(3.4)

I 1 is a modified Bessel function and Γ 0 is the maximum reflection coefficient at the zero frequency Z 2 − Z 1 (3.5) Z 2 − Z 1 Using parameter A, the maximum ripple in the passband characteristics can be set, Γ0 =

defined as Γ0 cosh A More details can be found in [12] and other sources. ΓM =

(3.6)

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 ΓM 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 picture’s 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

CHAPTER 3.

FEEDING STRUCTURE

33

-15 dB and doesn’t 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. That’s 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 improvement 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 improvements 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-

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 doesn’t 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

CHAPTER 3.

3.2

FEEDING STRUCTURE

35

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

CHAPTER 3.

36

FEEDING STRUCTURE

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 ). It’s ◦

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

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 . ◦

CHAPTER 3.

38

FEEDING STRUCTURE

Figure 3.12: Schematics and parameters of the microstrip to slot line transition with radial stub

With α above 70 , however, the performance worsens, as the proximity of the slot line ◦

to the stub increases. In the end, α = 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 α = 60 , indicated the optimal radius of 5.3 mm. ◦

This size (on the used substrate) roughly corresponds with the quarter-wave length of

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 termination 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 advantage of this solution is that the via is a truly wideband short, working in an unlimited

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 transition 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 transition.

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

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 border

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 further 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

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 antenna’s front-to-back ratio and limits utilization 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 radial stub and the via connection open end design

CHAPTER 3.

3.2.2

FEEDING STRUCTURE

43

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 possible 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.

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 excitation 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. It’s 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,

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 reflection 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 transition. 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

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 approximately 55 mm (including feed). Precise dimensions can be seen in the layout mask in 47

48

CHAPTER 4. FINAL ANTENNA DESIGN AND MEASUREMENTS

Figure 4.1: Designs of Via Vivaldi and Stub Vivaldi antennas

Appendix B. The taper profile is defined by the following relation: f (x) = 0.513e0.09x − 0.431

(4.1)

This definition was obtained from relations (2.8) and (2.9), using the actual dimensions as the input values. For both feeds, linear taper was used as the impedance transformer. The length was slightly increased to 28 mm, compared to the simulations in Chapter three. The geometry of the open end cut in the Via Vivaldi design was slightly changed, to provide more space for the SMA connector mount. Simulation proved this change has no significant influence to the transition performance. Other transition parameters are identical with those optimized in Chapter three.

4.2

Antipodal Vivaldi antenna

One antipodal design was prepared to provide comparison with tapered slot antennas. This design is basically the antipodal structure with rounded corners, introduced in Chapter two. Fins are defined with spline curves, and all dimensions are documented in the model available on the attached DVD.

49


To provide feeding of the antipodal structure, a simple microstrip-to-balanced stripline transformer was added to the design. Transformer was defined with spline curves and only briefly optimized. The design is depicted in fig. 4.2.

Figure 4.2: Design of the Antipodal Vivaldi antenna

4.3

Simulated results

Fig. 4.3 presents plots of return loss and radiated signals for both tapered slot and antipodal designs. It can be seen that the Via Vivaldi model provides the best matching properties. The matching for frequencies below 5 GHz is much better than the properties of the radiating structure itself. Later observations indicated that this improvement is caused by the radiation from the open end. This is noticeable in the radiation pattern plot (Appendix A) for 3 GHz. The signal reflected from the structure is not returned back to the port through the transition, but is instead radiated away in the backfire lobe, approximately 40 from the ◦

longitudinal axis. This is only happening for lower frequencies, and the pattern becomes symmetrical above 5 GHz. Such property could be undesirable for a conventional antenna, but is acceptable for UWB use.


50

From the signal fidelity point of view, a small trailing ripple can be observed for both Via and Stub Vivaldi designs. This is caused by the signal reflected from the wide end of the taper, and again from the open end (transition). Antipodal design, which does not suffer from this multiple reflection effect, has therefore the best signal fidelity.

Figure 4.3: Return loss and signal received at the far field front probe for simulated designs

Values of the fidelity factor F are also presented in tab. 4.1. The table has two sections - for excitation with Gaussian doublet, and for excitation with CST band limited pulse, which has been documented in Chapter one. The CST pulse has been originally used to confirm comparisons with the antenna introduced in the work of Piksa and Sokol [11]. There is, however, a problem with the explicit definition of the CST pulse. This definiton (unlike the one for the Gaussian doublet) has not been known during the comparisons. A generic Gaussian modulated sine pulse from Matlab Signal Processing Toolbox has been therefore used as the base for correlations. Although the waveform of the generic pulse was almost identical with the CST pulse, the correlation method is extremely sensitive to even small differences. The CST comparisons are therefore less precise than the Gaussian doublet ones. Results confirm what could be observed in fig. 4.3, that is, the best values has been achieved with the antipodal model. For tapered slot designs, it can be seen that the Via Vivaldi can achieve better results, because of the optimized feed.


4.5

52

Fabrication notes

Both Via and Stub Vivaldi designs were fabricated to enable real world measurements. Model geometries had been converted to layout masks and transferred to transparent film. Film was then used to expose the board during the photoresistive etching process. The main challenge during the exposure and etching is the proper alignment of both layout sides. As the transition performance depends gravely on the proper placement of the microstrip, the slot line and the open end, alignment of both layout sides has to be done with caution. In the end, a decision was made to leave the substrate dielectric of the Via Vivaldi open end cut part. The reason for this is due to the difficulties connected with cutting the substrate with available equipment (scalpel). There was a legitimate danger of damaging the transition during cutting. The real Via Vivaldi antenna therefore differs from the simulated model. Nevertheless, given the physical background of the transition principle and relatively low dielectric constant of the substrate, the influence should not be significant. After the layouts were etched and cleaned, via connections were riveted to the Via Vivaldi transition. As the last step, SMA connector mounts were attached together with the connectors, and the connector central wires were soldered to the microstrip feeds. Pictures of manufactured antennas can be see in the Appendix C.

4.6

Return loss measurements

Measurements were performed on the Agilent E8364A Vector Network Analyzer in a 45 MHz - 15 GHz frequency band. Each antenna was first measured for reflection losses in 1 port setup. Consequently, insertion losses of a transmission set consisting of two antennas in approximately 30 cm distance were measured in 2 port setup. Original measurement values, together with the calibration info can be found on the attached DVD. Measured values for both antennas can be seen in the fig. 4.4. Plots indicate that best matching was achieved with Via Vivaldi antenna. One of the Via Vivaldi antennas exhibited unfavorable matching properties above 12 GHz, but that does not influence operation in the UWB band. The S 21 plot demonstrates that insertion losses remain relatively stable within the UWB band, with approximately 6 dB variance.


53

Figure 4.4: Return and insertion loss plots of measured antennas

Measurements were also compared with the simulated results in fig. 4.5. It can be seen that the real antenna matching is better than the simulations within the most of the UWB frequency range. The simulations fit the measurement well for lower frequencies below 2.5 GHz. For higher frequencies however, simulations are not corresponding to the measurements very much. This can be explained with the possibility of inaccurate meshing of the simulated model and overall limited precision of the FDTD solver. Also, the real version of the Via Vivaldi differs from the model in the open end section, as mentioned before.

Figure 4.5: Comparisons of measured and simulated values of return loss for Via Vivaldi and Stub Vivaldi antennas

Nevertheless, measurements have proved both antenna designs provide sufficient match-


54

ing. Via Vivaldi antenna has return loss better than -16 dB within the whole UWB range, Stub Vivaldi design provides matching better than -13 dB for the same frequency band. Fig. 4.4 presents comparison of the return loss properties of both antennas with the antenna manufactured accordingly to the design from Piksa and Sokol [11].

4.7

Signal fidelity measurement

Analysis of the signal fidelity in a real world is more complicated measurement, requiring additional processing. The measurement setup, which can be seen in fig. 4.6, consists of fast sampling oscilloscope, Gaussian monocycle pulse generator and the pair of antennas. This way the received pulse at the antenna port can be measured.

Figure 4.6: Signal distortion measurement setup

Fig. 4.7 depicts both excitation pulse and received pulses. Waveform of the received pulse should be Gaussian doublet. According to this, it can be seen that the Via Vivaldi antenna achieved the smallest distortion. Measured pulses were used to confirm the validity of the time-domain simulated results. The real excitation pulse was covoluted with the transformation functions obtained during the simulations. Results were then compared with the measured received pulse. The transmission process can be described in the time-domain as a series of transformations: sr (t) = s e (t) ∗ ttr (t) ∗ ptr (t) ∗ rtr (t)

(4.2)


55

Figure 4.7: Excitation signal used for measurements, measured received signals

ttr (t) is the transformation function representing transmission of the excitation signal se (t) from the antenna port to the free space signal. rtr (t) is the transformation function representing transition of the free space signal to the received signal at the antenna port sr (t). ptr (t) is the transformation function representing propagation in the free space. As this transformation consists of phase shift and amplitude scaling, it can be substituted with time shift and scaling in the evaluation step. It should be noted, that this transformation was simplified for antennas oriented in their endfire directions and properly aligned with regards to the polarization. In the general form, the transformations are always function of time, distance, radiation angle and polarization angle. ttr (t) can be determined from the simulations by deconvolution of the excitation signal and the signal received in the far field probe. In the same way, rtr (t) is obtained by deconvoluting the plane wave excitation signal and the signal measured at the antenna port. Matlab procedures for convolution and deconvolution used in the postprocessing are contained in the files deconv2 *.m and Transfer *.m and can be found on the attached DVD. Both transformation functions are depicted in fig. 4.8. The ripples in the waveform are caused by the deconvolution in the frequency domain. During this process, a Fourier transform is applied to the time-limited excitation pulse without proper windowing, thus disturbing the signal spectrum.


56

Figure 4.8: Plots of transformation functions rtr (t) and ttr (t)) and an example of rtr (t) derivative for the Stub Vivaldi antenna

Once obtained, these transformation functions can be applied on the signal provided by the Gaussian monocycle generator (depicted in fig. 4.7), as described in relation (4.2). In this way, the received pulse waveform is obtained. The comparison of calculated pulse waveforms with measured pulse waveforms can be seen in fig. 4.9.

Figure 4.9: Comparisons of measured and calculated received signals

The pulses were time-shifted and scaled for the comparison purposes. It can be noted that a good match was achieved for a large part of the pulse. Small mismatch in the trailing part of the pulse can be explained with high repetition rate of the pulse generator. That may cause the initial part of the following pulse to influence the trailing part of the previous pulse during the transformation.


57

This comparison proved that the time-domain results obtained by simulations are valid and correspond to the properties of real antennas.

Chapter 5 Conclusion Parametric studies, contained in this work, indicated that special approach must be applied to design Vivaldi antennas for UWB use. To ensure high fidelity between the excitation pulse and its radiated form, both radiating and feeding parts of the antenna must be carefully optimized. The optimization for signal fidelity is not connected and sometimes even opposes the optimization for best matching. Simulations indicated the best signal fidelity results can be achieved with antipodal structure, at the cost of the antenna size. Creating smooth antipodal crossing, with wide, rounded fins can minimize the pulse distortion. If small Vivaldi antenna is desired, tapered slot structure can be used. Lowest signal distortion was observed with round taper profiles. Unfortunately, round curvature is not well matched, therefore a compromise solution must be always found with parameter sweeps. Transition from the microstrip feed to the taper slot has also fundamental influence to the signal fidelity. To suppress signal distortion in the microstrip-to-slot line transition, capacitances and inductances connected with the transition must be minimized. Capacitances are typically introduced by radial or circular stubs on the microstrip side; inductances are connected with stubs on the slot line side. This work shows that transition with via connection can perform better that transition with radial stub. In the same way, slot line circular stub can be well substituted with real open end, created by a cut out in the metallization. Following these principles, two tapered slot Vivaldi antennas were designed, fabricated and measured. Both antennas demonstrated sufficient matching properties within the UWB frequency range, with return loss smaller than -13 dB and -16 dB. 58

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Time-domain measurements confirmed that antenna with optimized feed using via connection has achieved lower signal distortion than antenna utilizing radial stub in the transition. A good match with measurements was obtained with transformation functions from simulated models. This indicates that simulation results for designed antennas are valid. The importance of careful optimization was demonstrated in comparison with antenna introduced in [11]. It turned out that antennas introduced in this work had exceeded antenna from [11] in both signal distortion and matching, that all with smaller dimensions. The only drawback is lower gain, which is ultimately connected with the taper length.

Bibliography [1] J.J. Fisher. Vivaldi antenna. US Patent Application US 2005/0012672 A1 , 2005. [2] P.G. Frayne and A.J. Leggetter. Wideband measurements on vivaldi travelling wave antennas. [3] E. Gazit. Improved design of the vivaldi antenna. IEE Proceedings , 135:89–92, 1988. [4] P.J. Gibson. The vivaldi aerial. Proceedings of the 9th European Microwave Conference , pages 101–105, 1979. [5] M.C. Greenberg, K.L. Virga, and C.L. Hammond. Performance characteristics of the dual exponentially tapered slot antenna (detsa) for wireless communications applications. IEEE Transactions on Vehicular Technology , 52:305–311, 2003. [6] R.C. Johnsson. Antenna Engineering Handbook . McGraw-Hill, 1993. [7] J.D.S. Langley, P.S. Hall, and P. Newham. Balanced antipodal vivaldi antenna for wide bandwidth phased arrays. IEE Proc. Microw. Antennas Propag. , 143:97–102, 1996. [8] V.A. Mikhnev and P. Vainikainen. A simple tapered-slot antenna with well-matched opening. Poster on EuCAP Conference, Session 3PP4A , 2006. [9] W.H. Nester. Microstrip notch antenna. US Patent No. 4,500,887 , 1985. [10] J.A.N. Noronha, T. Bielawa, C.R. Anderson, D.G. Sweeney, S. Licul, and W.A. Davis. Designing antennas for uwb systems. Microwaves&RF , 2003. [11] P. Piksa and V. Sokol. Small vivaldi antenna for uwb. Radioelektronika , 2005. [12] H. Schantz. The art and science of ultrawideband antennas . Artech House, Inc., 2005. 60

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[13] K.S. Yngvesson, T.L. Korzeniowski, Y.S. Kim, E.L. Kollberg, and J.F. Johansson. The tapered slot antenna - a new integrated element for milimeter-wave applications. IEEE Transactions on Microwave Theory and Techniques , 37:365–374, 1989. [14] K.S. Yngvesson, D.H. Schaubert, T.L. Korzeniowski, E.L. Kollberg, T. Thungren, and J.F. Johansson. Endfire tapered slot antennas on dielectric substrates. IEEETRAN , AP-33:1392–1400, 1985. [15] M.M Zinieris, R. Sloan, and L.E. Davis. A broadband microstrip-to-slot-line transition. MICROWAVE AND OPTICAL TECHNOLOGY LETTERS , 18, No. 5:339– 342, 1998.

Appendix A Radiation patterns Raditation patterns for both tapered slot antennas were obtained from simulations. Efield plane corresponds to the plane of antenna board; H-field plane corresponds to the plane perpendicular to the antenna board. Patterns were obtained for frequencies of 3, 5, 7, 9 and 11 GHz.

I

APPENDIX A. RADIATION PATTERNS

Figure A.1: Radiation patterns of the Via Vivaldi antenna

II

APPENDIX A. RADIATION PATTERNS

Figure A.2: Radiation patterns of the Stub Vivaldi antenna

III

Appendix B Layout masks

Figure B.1: Layout mask for the Via Vivaldi antenna

IV

APPENDIX B. LAYOUT MASKS

Figure B.2: Layout mask for the Stub Vivaldi antenna

V

Appendix C Photographs

Figure C.1: Front side of the Via Vivaldi antenna

VI

APPENDIX C. PHOTOGRAPHS

Figure C.2: Back side of the Via Vivaldi antenna

Figure C.3: Front side of the Stub Vivaldi antenna

VII

APPENDIX C. PHOTOGRAPHS

Figure C.4: Back side of the Stub Vivaldi antenna

Figure C.5: Size comparison with the antenna introduced by Piksa and Sokol

VIII

Design of Vivaldi Antennas - Thesis

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