Master Thesis

Simulation of Phased Arrays with

Rectangular Microstrip Patches on

Photonic Crystal Substrates

Supervisor: Prof. Sven-Erik Sandström

Asim Akhtar, Hassan Mateen Alahi and

Moeed Sehnan.

2012-10-12

Electrical Engineering

Advance Level

Course code: 5ED06E

Contents

Acknowledgement 5

Abstract 6

Introduction 7

Objectives 8

Thesis Overview 9

1 Microstrip Patch Antenna 101.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.2 Basic characteristics . . . . . . . . . . . . . . . . . . . . . . . 101.3 The feeding methods . . . . . . . . . . . . . . . . . . . . . . . 11

1.3.1 The microstrip line . . . . . . . . . . . . . . . . . . . . 111.3.2 The coaxial probe . . . . . . . . . . . . . . . . . . . . . 121.3.3 Proximity coupling . . . . . . . . . . . . . . . . . . . . 131.3.4 Aperture coupling . . . . . . . . . . . . . . . . . . . . . 14

1.4 Types of microstrip antennas . . . . . . . . . . . . . . . . . . 151.5 The microstrip patch antenna . . . . . . . . . . . . . . . . . . 16

2 Photonic Crystals 182.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.2 Types of photonic crystals . . . . . . . . . . . . . . . . . . . . 192.3 The difference between photonic crystals and metamaterials . 192.4 Photonic crystal substrates in antennas . . . . . . . . . . . . . 202.5 Defects in photonic crystals . . . . . . . . . . . . . . . . . . . 212.6 Basic characteristics of a 2D photonic crystal . . . . . . . . . . 22

2.6.1 Bandgap analysis of Alumina . . . . . . . . . . . . . . 232.7 Applications of photonic crystals . . . . . . . . . . . . . . . . 26

1

3 Advanced Design System (ADS) 273.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.2 Design Windows . . . . . . . . . . . . . . . . . . . . . . . . . 273.3 The Substrate . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.4 The Ports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303.5 The Mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303.6 The LineCalc . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.7 The ADS momentum . . . . . . . . . . . . . . . . . . . . . . . 323.8 The method of calculation used in ADS . . . . . . . . . . . . . 323.9 The Theory of ADS momentum . . . . . . . . . . . . . . . . . 33

4 Antenna Beam Steering 354.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.2 Beam steering techniques . . . . . . . . . . . . . . . . . . . . . 35

4.2.1 The mechanical beam steering . . . . . . . . . . . . . . 354.2.2 The electronic beam steering . . . . . . . . . . . . . . . 36

4.3 The phase shifters . . . . . . . . . . . . . . . . . . . . . . . . . 364.3.1 The phase controlled shifter . . . . . . . . . . . . . . . 374.3.2 The switched-line phase shifter . . . . . . . . . . . . . 38

5 Antenna Design and Analysis 395.1 The single patch antenna . . . . . . . . . . . . . . . . . . . . . 395.2 The 1x2 array antenna . . . . . . . . . . . . . . . . . . . . . . 445.3 The 1x4 array antenna with equal spacing . . . . . . . . . . . 495.4 The 1x4 array antenna with unequal spacing . . . . . . . . . . 505.5 Antenna beam steering . . . . . . . . . . . . . . . . . . . . . . 55

6 Conclusion 56

7 Future work 57

Bibliography 58

2

List of Figures

1.1 3-D view of a microstrip feed line. . . . . . . . . . . . . . . . . 121.2 The physical length of a rectangular microstrip patch. . . . . . 121.3 The coaxial probe feed. . . . . . . . . . . . . . . . . . . . . . . 131.4 The proximity feeding. . . . . . . . . . . . . . . . . . . . . . . 131.5 The aperture coupling feed. . . . . . . . . . . . . . . . . . . . 141.6 Shapes of microstrip antennas. (a) Microstrip patch antennas,

(b) Microstrip dipole antennas, (c) Printed slot antennas (d)Travelling wave antennas. . . . . . . . . . . . . . . . . . . . . 15

1.7 Geometry of a rectangular patch antenna. . . . . . . . . . . . 16

2.1 The bandgap in a photonic crystal. . . . . . . . . . . . . . . . 182.2 The types of photonic crystals. . . . . . . . . . . . . . . . . . . 192.3 (a) Simple and (b) photonic crystal antenna substrates. . . . . 202.4 Point defects (a) and line defects (b) in a photonic crystal. . . 212.5 A 2-D photonic crystal slab. . . . . . . . . . . . . . . . . . . . 222.6 The TE bandgap of a 2D triangular Alumina photonic crystal. 242.7 The TM bandgap of a 2D triangular Alumina photonic crystal. 252.8 The complete bandgap of a 2D triangular Alumina photonic

crystal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.1 The schematic window of ADS. . . . . . . . . . . . . . . . . . 283.2 The layout window of ADS. . . . . . . . . . . . . . . . . . . . 283.3 The substrate definition in ADS. . . . . . . . . . . . . . . . . 293.4 The mesh settings in ADS. . . . . . . . . . . . . . . . . . . . . 313.5 The LinCalc for mictrostrip feed line calculation. . . . . . . . 323.6 The mesh generation in ADS momentum. . . . . . . . . . . . . 33

4.1 The mechanical beam steered antenna. . . . . . . . . . . . . . 364.2 The electronic beam steering using phase shifters. . . . . . . . 364.3 The electronic beam steering mechanism. . . . . . . . . . . . . 374.4 The switched-line phase shifter. . . . . . . . . . . . . . . . . . 38

3

5.1 The dimensions of a feed line in the schematic window. . . . . 405.2 A single patch microstrip antenna in the ADS layout. . . . . . 405.3 The S11 simulation results for a single patch microstrip antenna. 415.4 A comparison of S11 for the photonic crystal and RT-Duroid

6010. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425.5 The simulation results for gain and directivity. . . . . . . . . . 425.6 The 3D far field radiation pattern of a single microstrip patch

antenna. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435.7 The 1x2 array antenna in ADS layout. . . . . . . . . . . . . . 455.8 The S11 simulation results for a 1x2 array antenna. . . . . . . 465.9 The S11 for a photonic crystal and RT-Duroid 6010. . . . . . . 465.10 The simulation results for gain and directivity. . . . . . . . . . 475.11 The 2D far-field radiated power of a 1x2 array antenna. . . . . 485.12 The 3D far-field radiation pattern of a 1x2 array antenna. . . 485.13 The 1x4 array antenna with equal spacing in ADS layout. . . . 495.14 The S11 simulation results of a 1x4 array antenna with equal

spacing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495.15 The 1x4 array antenna with unequal spacing in ADS layout. . 505.16 The S11 simulation results of a 1x4 array antenna with unequal

spacing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515.17 The S11 comparison for photonic crystal and RT-Duroid 6010. 525.18 The current distribution on the array antenna. . . . . . . . . . 525.19 The simulation results for Gain and Directivity. . . . . . . . . 535.20 The 2D far-field radiation power. . . . . . . . . . . . . . . . . 535.21 A 3D far-field radiation pattern of the 1x4 array antenna. . . . 545.22 The beam steering mechanism in ADS layout. . . . . . . . . . 555.23 The simulation result of beam steering. . . . . . . . . . . . . . 55

4

Acknowledgement

We would like to thank Dr. Sven-Erik Sandstrom for his advice, constantsupport and guidance throughout this thesis work and for responding to allour queries and questions so promptly and inspired us in many ways andtook a lot of interest in our thesis. We would also like to express our sinceregratitude to Mr. Imad Kassar Akeab for helping us during the completionof the thesis.

5

Abstract

This thesis describes the investigation of photonic crystals as a substrate inmicrostrip phased array antennas. Alumina with a relative dielectric con-stant of 9.6 is used as substrate to obtain miniaturization of the componentsin the high-frequency range. The proposed design consists of four rectangularpatches in a linear array configuration operating at 12 GHz. The antenna el-ements are excited by a microstrip feed line using the inset feeding techniquefor perfect impedance matching. A beam steering of 20o is achieved us-ing a switched line phase shifter. Antenna parameters, including impedancematching, bandwidth, gain, directivity and the S parameters of the proposedarray antenna are obtained. The simulation results are obtained with theAdvanced Design System (ADS) simulator.

Key words: Microstrip phased array antenna, Rectangular patch, Photoniccrystal, Beam steering and ADS Momentum.

6

Introduction

The advancement of wireless communication necessitates higher capacity,higher data rates and reduced interference. One essential component is themicrostrip patch antenna since it has a low profile and a low cost and iseasy to fabricate [1]. However, patch antenna design has some operationalconstraints such as confined bandwidth, low gain, low directivity and lowradiation power due to surface wave losses. The use of thick substrates inantennas may boost the operational bandwidth but the excitation of surfacewave modes also increases. To minimize this problem, photonic bandgapmaterials with high relative dielectric constant (εr) are used.The photonic bandgap materials originated in the late eighties and allowcontrolling the emission and propagation of electromagnetic waves inside adielectric substrate to a degree that was previously not attainable [1]. Theidea is to match the viable bandwidth of the antenna with the bandgap ofthe photonic crystal. The implementation of a photonic crystal substrate, in-stead of a conventional substrate, has been shown to minimize the excitationof surface wave modes, and hence improve bandwidth, gain and directivityas well as minimizing the mutual coupling [2]. In this thesis the photoniccrystal Alumina is used. The performance of a patch array antenna on aconventional substrate is compared to that of a patch array antenna on aphotonic crystal substrate.Beam steering has become vital in commercial wireless communication. Inbeam steering the main radiated lobe of an antenna is moved or scanned byusing several techniques. The beam steering can be achieved by mechanicallymoving the antenna or by varying the phase shift fed to the antenna elements.Usually electronic beam steering is done by means of phase shifters in phasedarray antennas [3]. In this thesis, electronic beam steering is achieved by us-ing the switched line phase shifter that provides the best results at low cost.

7

Objectives

The main objectives of the thesis are,

• To study, calculate and analyze the bandgap of photonic crystals (Alu-mina) at an operating frequency of 12 GHz.

• To design and simulate a 1x4 rectangular microstrip phased array an-tenna with photonic crystals (Alumina) as a substrate.

• Investigate different techniques to improve the antenna parameters i.e.impedance matching, bandwidth, gain and directivity.

• Compare simulation results for a photonic crystal and a conventionalsubstrate (RT-Duroid 6010).

• Steer the main beam of antenna radiation up to 20o using switched linephase shifters.

8

Thesis Overview

The thesis is organized as follows. Chapter 1 introduces the microstrip patchantenna, antenna types and feeding techniques. Chapter 2 contains a simpletheory of photonic crystals as antenna substrates and concludes with a cal-culation of the photonic bandgap. Chapter 3 deals with antenna design andsimulation in ADS momentum. Chapter 4 describes antenna beam steeringtechniques and gives an overview of phase shifters. Chapter 5 illustrates de-sign and simulation of a phased array antenna with comparison of a photoniccrystal substrate and a conventional substrate. Chapter 6 and 7 conclude andsuggest possible future work.

9

Chapter 1

Microstrip Patch Antenna

1.1 Introduction

The concept of microstrip radiators was first introduced by G.A. Deschampsin 1953 [4]. The practical implementations of microstrip antennas startedin the early 1970s when substrate materials became commonly available.Further developments were made by Robert E. Munson and John Q. Howell.Now microstrip antennas are popular in modern wireless communications be-cause of their low profile structures and extreme compatibility with MMIC(Monolithic Microwave Integrated Circuits) designs. Two major applicationareas of microstrip patch antennas are security and defense systems. Themicrostrip antennas are also flexible to use in satellites and modern mobilecommunication systems [5].The microstrip patch antennas perform very well in terms of resonant fre-quency and impedance matching [4]. The microstrip patch antennas havesome drawbacks in terms of low efficiency, low radiation power and high Qfactor. This also includes poor polarization, poor scan performance and alow bandwidth that is just a fraction of the operating frequency due to sur-face wave formation. The bandwidth of the microstrip patch antenna can beincreased somewhat by using a thick substrate or by using a low dielectricpermittivity substrate [7].

1.2 Basic characteristics

The microstrip patch antenna consists of a very thin ( t λo) metallic strip(patch) placed above the ground plane and separated by a dielectric materialcalled substrate. The microstrip patch is usually a pure conductor (copper,

10

gold) [4]. The microstrip patch can have many shapes but regular shapes aresimple in design and analysis and the prediction of their performance showsbetter results. The dielectric constant of a substrate usually lies in the rangeof 2.2 to 12. The microstrip patch antennas are preferably fabricated onhigh dielectric constant materials as they are easy to integrate with MMICRF front end circuitry. However, using high εr substrates results in low effi-ciency and narrow bandwidth [4]. The relationship between the bandwidth,substrate height and dielectric constant is [5],

BW =h√εr. (1.1)

BW = Bandwidth of antennah = Height of substrateεr = Relative dielectric constant of the substrate

1.3 The feeding methods

There are many techniques to feed a microstrip patch antenna. The mostwidely used are,

1. The microstrip line

2. The coaxial probe

3. The proximity coupling

4. The aperture coupling

1.3.1 The microstrip line

The microstrip feed line is a conducting strip that is simple to fabricateand easy to impedance match by adjusting the inset position of the patchas shown in Figure (1.1). The width of the microstrip feed line is muchsmaller than the width of the patch. However, the drawback of this feedingtechnique is that the surface wave and feed line radiation increases as thethickness of the substrate increases, therefore the bandwidth of the antennais limited. The microstrip feed line techniques are used extensively in planartransmission lines and microwave and millimeter wave circuitry [4].

11

Figure 1.1: 3-D view of a microstrip feed line.

Figure 1.2: The physical length of a rectangular microstrip patch.

1.3.2 The coaxial probe

In a coaxial probe feed the outer conductor is connected to the ground planeand the inner conductor is soldered to the patch as shown in Figure (1.3).This feeding technique has low spurious power radiation because the feedingnetwork is isolated from the patch, therefore low side lobes are produced.However, coaxial probe feeding is not easy to model especially for antennasthat has a thick substrate (h > 0.02λ) [8].The main disadvantage of this technique is the inherent asymmetry whichcreates higher order modes that cause cross polarization [4].

12

Figure 1.3: The coaxial probe feed.

1.3.3 Proximity coupling

The proximity coupling is also known as the electromagnetically coupled mi-crostrip feed. In proximity coupling, two substrates of different permittivitiesare used. The radiating patch lies on top of the substrate and a microstripline is connected between the substrate layers as shown in Figure (1.4). Inthis mechanism the link between feed line and patch is capacitive. The de-sign and analysis of such antennas is difficult compared to other antennas.This feed technique has no physical contact between feed line and patch, soit has low spurious radiation and high suppression of side lobes. The maindrawback is that it is hard to fabricate because the two dielectric substratelayers require proper alignment and this increases the antenna thickness.

Figure 1.4: The proximity feeding.

13

1.3.4 Aperture coupling

The aperture coupling technique has a ground plane that lies between twosubstrates with different permitivites as shown in Figure (1.5). A thick low εrmaterial is at the top of the ground plane to produce loosely bound fringingfields for spurious radiation. A high dielectric constant material is at thebottom of the plane for tightly coupled fields that do not produce spuriousradiations. The ground plane also separates the feed line from the radiatedpatch to minimize the interference of spurious radiation [4].Impedance matching is done by adjusting the length of the slot and thewidth of the feed line. This technique is difficult to fabricate and has narrowbandwidth [9].

Figure 1.5: The aperture coupling feed.

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1.4 Types of microstrip antennas

The microstrip antennas are divided into four categories [5],

1. Microstrip patch antennas

2. Microstrip dipole antennas

3. Printed slot antennas

4. Travelling wave antennas

Figure 1.6: Shapes of microstrip antennas. (a) Microstrip patch antennas,(b) Microstrip dipole antennas, (c) Printed slot antennas (d) Travelling waveantennas.

15

1.5 The microstrip patch antenna

In a microstrip patch antenna one side of the dielectric substrate is groundedand the other side has a conducting patch. The patch could have differentshapes such as rectangular, circular, triangular and elliptical etc, but therectangular patch is extensively used for thin substrates in the microwaveregime because of its ease of fabrication. It is easily described with both thecavity and the transmission line models [4].

Figure 1.7: Geometry of a rectangular patch antenna.

The Figure (1.7) shows a microstrip rectangular patch antenna of width (W),length (L) and thickness of substrate (h). In cartesian coordinates the patchis shown with the length along the X-axis, the width along the Y-axis andthe thickness along the Z-axis.The width (W) of the rectangular patch antenna is calculated as [4],

W =c

2fo√

εr+12

. (1.2)

c = Speed of light in free spacefo = Operating frequencyεr = Permittivity constant of dielectric substrate

For a rectangular patch antenna the length is normally chosen in the range0.333λ < L < 0.5λ. When the patch is excited by the feed line a chargedistribution is established on the ground plane and on the downside of thepatch. The ground plane is negatively charged and the patch is positivelycharged by the feed excitation. Attractive forces are generated between theground plane and the patch and this produces fringe fields. This fringingeffect is equivalent to an extension of the patch by a distance ∆L.

16

The effective length of the patch is given by [4],

L = Leff −∆L (1.3)

Leff =c

2fo√εreff

(1.4)

εreff =εr + 1

2+εr − 1

2

(1 +

12h

W

)− 12

(1.5)

∆L = 0.412h(εreff + 0.3)

(Wh

+ 0.264)

(εreff − 0.258)(Wh

+ 0.8) (1.6)

17

Chapter 2

Photonic Crystals

2.1 Introduction

Crystals are periodic structures of atoms and molecules. The pattern ofatoms and molecules is repeated in space and forms a crystal lattice. A crys-tal lattice may stop the propagation of certain electromagnetic waves becausethere is an energy gap in the crystal lattice that prevents the movement ofelectrons with certain energies in a certain direction. With a strong latticepotential the energy gap may be extended to prevent propagation in all di-rections. This energy gap of a crystal lattice is called the photonic bandgapand it exists between the dielectric bandgap and the air bandgap of a pho-tonic crystal and relates to conduction and valence bands in semiconductors[11].

Figure 2.1: The bandgap in a photonic crystal.

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2.2 Types of photonic crystals

The dielectric constant of a photonic crystal varies periodically in space inspecific directions. When the dielectric constant of the photonic crystal variesin one direction it is called a one-dimensional (1D) photonic crystal. Thesame with (2D) and (3D) photonic crystals where the dielectric constantvaries in two and three dimensions, respectively [12].

Figure 2.2: The types of photonic crystals.

2.3 The difference between photonic crystals

and metamaterials

The metamaterials have exceptional properties that are not found in natureand not discovered in other materials. The basic difference between meta-materials and photonic crystals is the existence of a photonic bandgap in thelatter. This occurs when the lattice constant a is equal to wavelength i.e,

a = λ . (2.1)

The bandgap effect stems from the periodicity of the lattice. In metamate-rials the artificial atoms (subunits) are smaller than the wavelength so thereis no bandgap since a λ [13].In photonic crystals the refractive index η =

√εr varies periodically. Meta-

materials are artificial structures having negative values of refractive index(η) and dielectric constant (εr).

19

2.4 Photonic crystal substrates in antennas

Photonic crystals are low loss periodic dielectric structures in which di-electrics of different refractive index are used to produce the photonic bandgap. This photonic band gap behaves as a stop band filter for a certain rangeof frequencies and prevents these frequencies from propagating in certain di-rections [11].The substrates with high dielectric constant have narrow bandwidth but thebandwidth can be increased by thickening the substrates. Unfortunately thisproduces strong surface waves that impair antenna efficiency. To overcomethis problem, photonic crystals can be used to block the surface waves[14].

Figure 2.3: (a) Simple and (b) photonic crystal antenna substrates.

Figure (2.3a) shows that when a microstrip patch antenna has a simple di-electric substrate, the antenna radiates electromagnetic energy into both theair and the antenna substrate. In the substrate the power is radiated in theform of surface waves and this reduces the bandwidth. Large back lobes alsolower efficiency. Total internal reflection in the substrate occurs when theincident angle is greater than the critical angle.When photonic crystals are used as a substrate and the frequency is withinthe bandgap, the total power radiates into the air. No power radiates intothe substrate because that particular frequency is blocked by the bandgap ofthe crystal as shown in Figure (2.3b). The bandgap of the photonic crystalbehaves as a stop band filter and stops transmission of power in the band.Since there is no surface wave the transmitted signal has a large bandwidthand this makes the antenna more efficient [15].

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2.5 Defects in photonic crystals

The periodicity of photonic crystals can be broken by defects in the crystal.These defects can be added or removed. When an atom is added it is a donorand the crystal will be in donor mode. Similarly a removed atom becomesan acceptor and relates to the acceptor mode. The acceptor mode in crystallattices is widely used to fabricate single mode microcavities for single modeoscillation[11].Defects in crystal structure can be produced by two techniques,

• Point defects

• Line defects

A point defect in a photonic crystal can be produced by adding or removinga single atom from the lattice. A point defect can be used to trap a certainfrequency of light in photonic crystals. In a point defect a single mode canbe localized when its frequency is in the range of photonic bandgap [11].

A line defect in a photonic crystal can be produced by adding or removing arow of atoms from the lattice. A line defect in the crystal can guide the lightfrom one location to another. By producing line defects photonic crystalscan also be used as waveguides [11].

Figure 2.4: Point defects (a) and line defects (b) in a photonic crystal.

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2.6 Basic characteristics of a 2D photonic crys-

tal

The analysis of a 2D photonic crystal fabricated by a periodic array of holesand organized in a triangular lattice shape is shown in Figure (2.5). Thetriangular lattice can provides the large element spacing that can reduce themutual coupling effects. The bandgap property in 2D photonic crystals canbe described by waves with a wave vector in the plane of periodicity. Thispropagation mode is known as Bloch waves. The mathematical form is [16].

E(r + a, t) = E(r, t) eik•a (2.2)

a = lattice vectork = wave vectort = thickness of slab

Equation (2.2) provides the solution of Maxwell’s equations for waves travel-ling in a photonic crystal. The wave vector k is a key entity in equation (2.2)and relates to frequency via the dispersion relation. The dispersion relationdetermines the stop and pass bands in the periodic structure.

Figure 2.5: A 2-D photonic crystal slab.

Various computational techniques are used for solving Maxwells equations inthe crystals. FDTD (Finite difference time domain), FEM (Finite elementmethod), and PWE (plane wave expansion) are commonly used techniquesto analyze the bandgap.

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2.6.1 Bandgap analysis of Alumina

The formation of bandgaps in a photonic crystal depends on the periodicity ofthe lattice and the refractive index ratio of the material and the impuritiesthat are added in the crystal. Usually the refractive index ratio must begreater than 2:1 (material to impurity) [17].The different types of photonic crystals are used as antenna substrates. Theproposed 2D photonic crystal Alumina is a triangular lattice of air holes withradius r and lattice constant a drilled into an Alumina slab with a relativedielectric constant of 9.6. The r/a value is chosen to maximize the photonicbandgap at the required operating frequency [18]. In a 2D photonic crystalthe bandgap exists only for propagation in the plane of periodicity [19].The Alumina has a thickness of 1.25 mm, the period a is 4.43 mm, and thefilling ratio r/a is 0.46. The width of the strip conductor has a constantvalue of 5.43 mm to fix the rejection band at 12 GHz according to the Braggcondition [20],

fmax =c

2√εreff a

. (2.3)

c = Speed of lightεreff = Effective dielectric constant of Aluminaa = Period of the lattice

As the number of periods in the Alumina substrate increases with r/a fixed,the rejection level also increases as the interference at the Bragg frequencyis reinforced.The bandgap of Alumina is shown in Figure (2.6) in the form of a bandof frequencies where the dispersion relation has no solutions. The bandgapof a photonic crystal depends upon the filling ratio r/a and the dielectricconstant (εr). The r/a ratio affects the size of the TE and TM bandgaps.The width of the bandgap increases with ε.

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The Alumina lattice with constant a and filling ratio r/a is designed so thatthe operating frequency 12 GHz falls within the photonic bandgap.The PWE technique is used to obtain the dispersion relation [21]. The realpart of the wave vector shows irregular dispersion inside the bandgap. Theimaginary part of the wave vector is small and oscillatory in the pass band,and it is identically zero inside the stop band. The dispersion diagram inFigure (2.6) shows the band structure for the TE mode with the electric fieldparallel to the plane of periodicity.

0 5 10 15 20 25 300

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

|k|

fa /

c

Figure 2.6: The TE bandgap of a 2D triangular Alumina photonic crystal.

The bandgap of a 2D Alumina crystal is calculated by using Matlab. 441plane waves are used to determine the TE bandgap to 8.8 < f <13.04 GHz.

24

The dispersion diagram of the TM mode is shown in Figure (2.7). Thepolarization of the electric field is perpendicular to the plane of periodicity.

0 5 10 15 20 25 300

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

|k|

fa /

c

Figure 2.7: The TM bandgap of a 2D triangular Alumina photonic crystal.

The TM bandgap is computed in the same way and it is found to be quitenarrow, 11.6 < f < 12.9 GHz. The filling ratio r/a can be varied to adjustthe band structure [22].

25

The resulting complete bandgap for this lattice is shown in Figure (2.8) andcoincides with the TM bandgap 11.6 ≤ f ≤ 12.9 GHz.

0 5 10 15 20 25 300

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

|k|

fa /

c

complete bandgap

Figure 2.8: The complete bandgap of a 2D triangular Alumina photoniccrystal.

2.7 Applications of photonic crystals

The applications of photonic crystals are expanding to areas such as bio pho-tonics, atomic physics, quantum computing and communication appliances[12].

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Chapter 3

Advanced Design System(ADS)

3.1 Introduction

The advanced design system is an electronic design software that is usedfor microwave and radio frequency applications. It produces design configu-rations for radio frequency electronic products, i.e. radar systems, wirelessnetworks and high-speed data links [23].Design and simulation of the antenna in ADS includes the following elements.

3.2 Design Windows

The Advance Design System has two main windows,

1. Schematic window

2. Layout window

In the schematic window, different types of component palettes are built-into design circuits. The schematic window is used for the proposed design andalso provides the microstrip feed line calculations with the help of LineCalc.The schematic design simulation is fast and provides accurate results. Designguides and real time tuning are also available in the schematic window.

27

Figure 3.1: The schematic window of ADS.

The layout window is used for the physical design of the model. The physicaldesign can be created directly in the layout window, or be designed in theschematic and then converted into the layout window [23].

Figure 3.2: The layout window of ADS.

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3.3 The Substrate

The substrate layers are specified in terms of material, dielectric constant,thickness and loss tangent. The different types of predefined substrates inADS momentum can be modified as required [23].

Figure 3.3: The substrate definition in ADS.

To use a predefined substrate in ADS, the following steps are used.

1. From the layout window of the ADS, select Momentum > Substrate >Open.

2. Select the required substrate from the opened list.

3. Add substrate layers, name them, and add.

The important steps to modify the predefined substrate are.

1. Define the substrate layers.

2. Map the metalization layers.

3. Specify the conductivity of metalization layers.

4. Solve the substrate.

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3.4 The Ports

Energy enters and leaves the substrate via the ports. At least one port isrequired for the simulation process. To define the ports in ADS, the followingsteps are used [23].

1. A port is added to a circuit either from the schematic or a layoutwindow.

2. Specify the type of port by selecting Momentum > Port > Editor.

3. The port and the circuit must be on the same layout layer.

4. The arrow head of the port at the edge of the circuit must be pointinginward to the circuit, and it must be at right angle.

5. The ports must be attached to some part of the designed circuit. Ifit is not completely attached to the circuit, momentum automaticallysnaps the port to the edge of the closet object.

6. After adding the ports, the resolution of the layout should not bechanged. If it is changed, then delete the ports and add them again.The reason for this is that the resolution change produces error in meshcalculations.

7. Do not add the ground port component, momentum does not recognizethe ground component when it is placed in the layout.

3.5 The Mesh

In the simulation, the circuit is divided into a large number of triangles andrectangles to compute the current. This grid-like pattern of triangles andrectangles is called the mesh, and each small part of the pattern is calleda cell. Every circuit has a unique mesh pattern. The mesh is applied tothe circuit to compute the current and identifies the coupling effects in thecircuit during the simulation. Finally, it calculates the S -parameters for thecircuit.To define mesh parameters in ADS, select Momentum >Mesh >Setup.The more cells, the higher the accuracy in the simulation, but too many cellswill slow down the simulation and provide little improvement in accuracy.It is better to use the default parameters for the mesh settings. The meshfrequency must be higher than the operating frequency [23].

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Figure 3.4: The mesh settings in ADS.

3.6 The LineCalc

The LineCalc is a computation module that is a built-in schematic window.It is used to calculate the dimensions of the microstrip feed line. By settingthe simulation parameters one can easily calculate the length and the widthof the feed line at the required frequency. To run LineCalc from the schematicwindow, select Tools > LineCalc > Start the LineCalc [23].

31

Figure 3.5: The LinCalc for mictrostrip feed line calculation.

3.7 The ADS momentum

The momentum is a component of Advanced Design System, and it providesthe necessary tools to design and evaluate a communication system. Theelectromagnetic simulator is known as momentum and provides a completetool kit to analyze the performance of high-frequency products such as ICs,antennas and amplifiers.The ADS momentum computes the scattering parameters (S -Parameters)for general planar circuits such as microstrip, slot line and waveguide. Mul-tilayer RF printed circuit boards, ICs, Multichip modules and hybrids canbe simulated with accurate results by using ADS momentum. The ADS mo-mentum has a capability to design automation tool that can be extended bymomentum optimization. The ADS momentum visualization provides 3Dpresentation of current flow in slots and conductors. It also provides 2D and3D views of far-field radiation pattern [23].

3.8 The method of calculation used in ADS

The simulation technique used by the ADS momentum is known as themethod of moments that is based on the integral formulation of Maxwell’sequations. Integral equations generate the matrix equations that are used

32

to obtain the accurate simulation results. In ADS Momentum, the circuit isdivided into mesh strips with triangles and rectangles. In the next step, thesurface current is linearly distributed in each current cell as shown in Figure(4.3).

Figure 3.6: The mesh generation in ADS momentum.

Finally, ADS momentum solves the mesh matrix equation and computes thescattering parameters [23].

3.9 The Theory of ADS momentum

The numerical discretization technique used to solve Maxwell’s equationsfor planar structures embedded in multilayer dielectric substrates is calledthe method of moments. The simulation modes that are available in ADSmomentum (microwave and RF) are based on this type of discretization. Themicrowave mode is also known as the full wave mode in which a frequencydependent Green function is used. This mode of simulation uses L and Celements that are complex and frequency dependent.The RF simulation mode is also called the Quasi-static mode with a frequency

33

independent Green function. It produces elements C and L that are real andfrequency independent. The RF simulation mode is used extensively forstructures that are smaller than half a wavelength [23].

34

Chapter 4

Antenna Beam Steering

4.1 Introduction

The antenna beam steering is of interest as soon as the antenna has a sub-stantial directivity. When transmission in a specific direction is required,antennas are rotated by hand to transmit the power in that particular di-rection. In modern wireless communication systems, phased array antennasare implemented to steer the main beam of radiation by shifting the phase ofeach element. The phased array antennas can steer the main beam effectivelyand minimize the side lobes but have a limited bandwidth [24].

4.2 Beam steering techniques

The main techniques for beam steering are either mechanical or electrical.

4.2.1 The mechanical beam steering

Here, the antenna elements are rotated mechanically through a circular discpivoted at the bottom of the antenna.

35

Figure 4.1: The mechanical beam steered antenna.

4.2.2 The electronic beam steering

In this case the radiated beam of the antenna is scanned electronically bymeans of switched line phase shifters. This technique has a high scanningrate but requires complex and expensive circuitry [3].

Figure 4.2: The electronic beam steering using phase shifters.

The phase variation in electronic beam steering can be obtained by changingthe operating frequency or by using electronic phase shifters [25].

4.3 The phase shifters

The phase shifters are used to change the transmission angle of the antenna.The ideal phase shifter provides no insertion loss and equal amplitude in all

36

phase states. The two main types of phase shifter are,

1. The phase controlled shifter.

2. The switched-line phase shifter.

4.3.1 The phase controlled shifter

In the phase controlled shifter, each element of the array is connected toa phase shifter. The main beam is formed by shifting the phase of thetransmitted signal from each element.

Figure 4.3: The electronic beam steering mechanism.

The phase shift between two successive elements remains fixed and is givenby [25],

∆ϕ =2π∆L

λ(4.1)

∆L = d sin Θs (4.2)

Hence

∆ϕ =2π d sin Θs

λ(4.3)

∆ϕ = Phase shift between two successive elementsd = Distance between successive radiating elementsΘs = Beam steering angle

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4.3.2 The switched-line phase shifter

In the switched-line phase shifter, phase shifting is obtained by varying thelength of the antenna feed line. The phase delay in the feed line is calculatedfrom [3],

∆L =βc

2πf√εeff

. (4.4)

∆L = Change in lengthβ = Propagation constantc = Speed of lightεeff = Effective dielectric constantf = Operating frequency

Figure 4.4: The switched-line phase shifter.

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Chapter 5

Antenna Design and Analysis

The design, simulation and analysis of a single patch, and 1x 2 and 1x 4arrays are demonstrated. The simulation results are obtained using the ADS(Advanced Design System) simulator.

5.1 The single patch antenna

In the proposed design, a rectangular microstrip patch antenna with an Alu-mina substrate is fed by a 50 Ω inset feed line. The relative dielectric constantof Alumina is 9.6 with a loss tangent of 0.0002. The height of the substrateis set to 0.05λ, that is 1.25 mm at 12 GHz operating frequency. The widthof the patch is calculated from equation (1.2) to 5.43 mm, and the length iscalculated from equation (1.3) to 4.35 mm. The effective dielectric constant7.95 is calculated from equation (1.5). The feed line dimensions are calcu-lated by the LineCalc and has a width of 1.45 mm and a length of 2.27 mm.The inset feed length is 1.27 mm as shown in Figure (5.1).

39

Figure 5.1: The dimensions of a feed line in the schematic window.

The geometry of the antenna is shown in Figure (5.2).

Figure 5.2: A single patch microstrip antenna in the ADS layout.

A single patch microstrip antenna is fed by a 50 Ω line and simulated withADS momentum.

40

The antenna resonates at 11.99 GHz with a return loss of -11.1 dB. Theresults for the scattering parameters S11 are shown in Figure (5.3).

Figure 5.3: The S11 simulation results for a single patch microstrip antenna.

The simulation results for the scattering parameters are compared with theconventional substrate (RT-Duroid 6010 with dielectric constant 10.2) at theoperating frequency of 12 GHz as shown in Figure (5.4).

41

Figure 5.4: A comparison of S11 for the photonic crystal and RT-Duroid6010.

The results show that the photonic crystal substrate provides a better returnloss than the conventional substrate RT-Duroid 6010 and also resonates ex-actly at the operating frequency.The 2D simulation results for the gain and directivity of a single patch an-tenna with photonic crystals are shown in Figure (5.5).

Figure 5.5: The simulation results for gain and directivity.

42

The top view of the 3D far-field radiation pattern of a single patch antennais shown in Figure (5.6).

Figure 5.6: The 3D far field radiation pattern of a single microstrip patchantenna.

The Figure (5.6) shows that the antenna radiates almost isotropically. Toenhance the directivity, gain and other radiation parameters, a 1x2 antennaarray is designed.

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5.2 The 1x2 array antenna

The two patches are arranged in a linear array configuration with 0.5λ interelement spacing. It is fed by a 50 Ω line using the corporate feeding techniqueaccording to the Wilkinson dividing rule, in order to obtain matching to the100 Ω patch.The self conductance of two patches is calculated using [5],

G1 =I1

120π2(5.1)

I1 =

π∫0

sin(koW2

cos)

cos

2

sin3 θ dθ (5.2)

= −2 + cos (X) +X Si (X) +sin (X)

X(5.3)

X = koW (5.4)

Si = Sine integral.The self-conductance of the patches can also be calculated asymptoticallyfrom [5],

G1 =

190

(Wλo

)2for W λo

1120

(Wλo

)for W λo

(5.5)

The mutual conductance between two patches is calculated from [5],

G12 =1

120π2

π∫0

sin(koW2

cos)

cos

2

Jo (koL sin θ) sin3 θ dθ (5.6)

Jo is the Bessel function of the first kind of order zero. In microstrip an-tennas the self-conductance is larger than the mutual conductance [5]. Themutual conductance G12 is computed by means of numerical integration inMathematica. The resonant input resistance Rin of the patches is calculatedfrom [5],

Rin =1

2 (G1 ±G12)(5.7)

44

G1 = Self conductanceG12 = Mutual conductanceThe (+) sign is used for the odd symmetry modes and the (-) sign is usedfor the even symmetry modes [5].The input resistance of the patches with mutual coupling is calculated with[5],

Rin (y = yo) =1

2 (G1 ±G12)cos2

(π

Lyo

). (5.8)

yo = Inset length of the feed line.

The layout of a 1x2 array antenna is shown in Figure (5.7).

Figure 5.7: The 1x2 array antenna in ADS layout.

The 1x2 array antenna resonates at 12.5 GHz with a return loss S11 of -24dB.The simulation results for the scattering parameters of a 1x2 array antennaare shown in Figure (5.8).

45

Figure 5.8: The S11 simulation results for a 1x2 array antenna.

In the Smith chart, simulation shows that the antenna resonates at 12 GHzhaving the minimum impedance over the straight resistance line at the res-onated frequency.The simulated S -parameters for a photonic crystal and RT-Duroid 6010 areshown in Figure (5.9).

Figure 5.9: The S11 for a photonic crystal and RT-Duroid 6010.

The comparison shows that photonic crystals are much better in terms ofimpedance matching and bandwidth.

46

The 2D simulation results for the gain and directivity of a 1x2 array antennawith photonic crystals are shown in Figure (5.10).

Figure 5.10: The simulation results for gain and directivity.

The gain and directivity of the antenna are 5 dB and 9 dB, respectively, inthe range of -20o to 20o. The power radiated by the antenna is 0.6 mW.

47

Figure 5.11: The 2D far-field radiated power of a 1x2 array antenna.

A 3D view of the far-field radiation pattern is shown in Figure (5.12).

Figure 5.12: The 3D far-field radiation pattern of a 1x2 array antenna.

The results show that a 1x2 array antenna is more directive, has larger band-width and is generally better than the single patch antenna.

48

5.3 The 1x4 array antenna with equal spacing

The proposed design consists of four microstrip patches with an equal spacingof 0.5λ. The corporate feed method is used to excite the array elements. Thewidth of the feed line of the two central elements is twice the width of theother two elements to improve the impedance matching and reduce the sidelobes. The array is fed by a 50 Ω impedance line. The layout is shown inFigure (5.13).

Figure 5.13: The 1x4 array antenna with equal spacing in ADS layout.

The scattering parameter S11 is shown in Figure (5.14).

Figure 5.14: The S11 simulation results of a 1x4 array antenna with equalspacing.

The simulation results show that a 1x4 array antenna resonates perfectly at12 GHz with a return loss of -13.2 dB.

49

5.4 The 1x4 array antenna with unequal spac-

ing

To improve the return loss and reduce the side lobes unequal inter-elementspacing is used. The separations are 0.8λ and 0.45λ, as shown in Figure(5.15). The length of the antenna feed line is also increased, and the arrayis fed by a 50 Ω line.

Figure 5.15: The 1x4 array antenna with unequal spacing in ADS layout.

The 1x4 array antenna with unequal spacing resonates at 12.03 GHz with a-41.9 dB return loss and reduced side lobes. The simulation shows that theantenna is perfectly matched to a 50 Ω feed line. The 10 dB bandwidth ofthe 1x4 array antenna is 900 MHz, that is 7.5% of the operating frequency.

50

The scattering parameter S11 is shown in Figure (5.16).

Figure 5.16: The S11 simulation results of a 1x4 array antenna with unequalspacing.

51

The simulation results compared with RT-Duroid 6010 are shown in Figure(5.17).

Figure 5.17: The S11 comparison for photonic crystal and RT-Duroid 6010.

These simulation results show that the photonic crystal provides better re-sults for the impedance matching and the resonant frequency.

Figure 5.18: The current distribution on the array antenna.

52

The 2D simulation results for the gain and directivity of a 1x4 nonuniformarray are shown in Figure (5.19).

Figure 5.19: The simulation results for Gain and Directivity.

Figure (5.19) shows that the array antenna has a maximum directivity andgain of 20 dB and 22 dB, respectively. The far-field radiated power is shownin Figure (5.20).

Figure 5.20: The 2D far-field radiation power.

53

A 3D view of the far-field radiation pattern for the nonuniform 1x4 arrayantenna is shown in Figure (5.21).

Figure 5.21: A 3D far-field radiation pattern of the 1x4 array antenna.

54

5.5 Antenna beam steering

The beam steering of a 1x4 uniform array antenna based on photonic crystalis obtained by means of switched line phase shifters. The main beam issteered about 20o by changing the phase between the array elements. Thechange in phase is obtained by altering the length of the feed line. The lengthof the delay lines for phase shifting are ∆L, 2∆L and 3∆L. The length ∆L iscomputed to steer the beam of the array antenna to 20o according to equation(4.4). The layout of the proposed design is shown in Figure (5.22).

Figure 5.22: The beam steering mechanism in ADS layout.

The simulation result is shown in Figure (5.23).

Figure 5.23: The simulation result of beam steering.

The simulated magnitude of a 1x4 array when a beam steering of 20o isapplied.

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Chapter 6

Conclusion

This thesis introduced and analyzed some simple microstrip phased array an-tennas with a design based on photonic crystals. A comparison of results forconventional substrates and photonic crystals shows that photonic crystalsoffer potential regarding bandwidth, gain and directivity. The suppressionof side lobes and a virtually perfect impedance matching is also achieved.A bandwidth of 900 MHz and a return loss of -41.9 dB are obtained. Thebandgap of photonic crystals with varying hole diameters were studied in or-der to obtain the required frequency range. The beam steering results showthat photonic crystal techniques are applicable.

56

Chapter 7

Future work

Antenna design is a vast field for researchers and engineers. Further im-provement of the 1x4 phased array antenna can be made in the followingareas,

• Design intended to minimize the surface area occupied by the photoniccrystals.

• The array size can be increased to further improve the antenna param-eters, such as bandwidth, impedance matching, directivity and gain.

• Further improvement of side lobe reduction and beam steering angle.

• More advanced simulation tools, for example CST microwave studio.

57

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