Simulation of Phased Arrays with Rectangular Microstrip Patches on Photonic Crystal Substrates

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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.

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List of Figures

1.1 3-D view of a microstrip feed line. . . 12

1.2 The physical length of a rectangular microstrip patch. . . 12

1.3 The coaxial probe feed. . . 13

1.4 The proximity feeding. . . 13

1.5 The aperture coupling feed. . . 14

1.6 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. . . 18

2.2 The types of photonic crystals. . . 19

2.3 (a) Simple and (b) photonic crystal antenna substrates. . . 20

2.4 Point defects (a) and line defects (b) in a photonic crystal. . . 21

2.5 A 2-D photonic crystal slab. . . 22

2.6 The TE bandgap of a 2D triangular Alumina photonic crystal. 24 2.7 The TM bandgap of a 2D triangular Alumina photonic crystal. 25 2.8 The complete bandgap of a 2D triangular Alumina photonic crystal. . . 26

3.1 The schematic window of ADS. . . 28

3.2 The layout window of ADS. . . 28

3.3 The substrate definition in ADS. . . 29

3.4 The mesh settings in ADS. . . 31

3.5 The LinCalc for mictrostrip feed line calculation. . . 32

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5.1 The dimensions of a feed line in the schematic window. . . 40

5.2 A single patch microstrip antenna in the ADS layout. . . 40

5.3 The S11 simulation results for a single patch microstrip antenna. 41 5.4 A comparison of S11 for the photonic crystal and RT-Duroid 6010. . . 42

5.5 The simulation results for gain and directivity. . . 42

5.6 The 3D far field radiation pattern of a single microstrip patch antenna. . . 43

5.7 The 1x2 array antenna in ADS layout. . . 45

5.8 The S11 simulation results for a 1x2 array antenna. . . 46

5.9 The S11 for a photonic crystal and RT-Duroid 6010. . . 46

5.10 The simulation results for gain and directivity. . . 47

5.11 The 2D far-field radiated power of a 1x2 array antenna. . . 48

5.12 The 3D far-field radiation pattern of a 1x2 array antenna. . . 48

5.13 The 1x4 array antenna with equal spacing in ADS layout. . . . 49

5.14 The S11 simulation results of a 1x4 array antenna with equal spacing. . . 49

5.15 The 1x4 array antenna with unequal spacing in ADS layout. . 50

5.16 The S11simulation results of a 1x4 array antenna with unequal spacing. . . 51

5.17 The S11 comparison for photonic crystal and RT-Duroid 6010. 52 5.18 The current distribution on the array antenna. . . 52

5.19 The simulation results for Gain and Directivity. . . 53

5.20 The 2D far-field radiation power. . . 53

5.21 A 3D far-field radiation pattern of the 1x4 array antenna. . . . 54

5.22 The beam steering mechanism in ADS layout. . . 55

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Acknowledgement

We would like to thank Dr. Sven-Erik Sandstr¨om for his advice, constant support and guidance throughout this thesis work and for responding to all our queries and questions so promptly and inspired us in many ways and took a lot of interest in our thesis. We would also like to express our sincere gratitude to Mr. Imad Kassar Akeab for helping us during the completion of the thesis.

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Abstract

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

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

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Introduction

The advancement of wireless communication necessitates higher capacity, higher data rates and reduced interference. One essential component is the microstrip patch antenna since it has a low profile and a low cost and is easy to fabricate [1]. However, patch antenna design has some operational constraints such as confined bandwidth, low gain, low directivity and low radiation power due to surface wave losses. The use of thick substrates in antennas may boost the operational bandwidth but the excitation of surface wave modes also increases. To minimize this problem, photonic bandgap materials with high relative dielectric constant (r) are used.

The photonic bandgap materials originated in the late eighties and allow controlling the emission and propagation of electromagnetic waves inside a dielectric substrate to a degree that was previously not attainable [1]. The idea is to match the viable bandwidth of the antenna with the bandgap of the photonic crystal. The implementation of a photonic crystal substrate, in-stead of a conventional substrate, has been shown to minimize the excitation of surface wave modes, and hence improve bandwidth, gain and directivity as well as minimizing the mutual coupling [2]. In this thesis the photonic crystal Alumina is used. The performance of a patch array antenna on a conventional substrate is compared to that of a patch array antenna on a photonic crystal substrate.

Beam steering has become vital in commercial wireless communication. In beam steering the main radiated lobe of an antenna is moved or scanned by using several techniques. The beam steering can be achieved by mechanically moving 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 phased array 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.

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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 conventional substrate (RT-Duroid 6010).

• Steer the main beam of antenna radiation up to 20o _{using switched line}

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Thesis Overview

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

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Chapter 1 Microstrip Patch Antenna

1.1 Introduction

The concept of microstrip radiators was first introduced by G.A. Deschamps in 1953 [4]. The practical implementations of microstrip antennas started in 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 application areas of microstrip patch antennas are security and defense systems. The microstrip antennas are also flexible to use in satellites and modern mobile communication systems [5].

The microstrip patch antennas perform very well in terms of resonant fre-quency and impedance matching [4]. The microstrip patch antennas have some drawbacks in terms of low efficiency, low radiation power and high Q factor. This also includes poor polarization, poor scan performance and a low bandwidth that is just a fraction of the operating frequency due to sur-face wave formation. The bandwidth of the microstrip patch antenna can be increased somewhat by using a thick substrate or by using a low dielectric permittivity substrate [7].

1.2 Basic characteristics

The microstrip patch antenna consists of a very thin ( t λo) metallic strip

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gold) [4]. The microstrip patch can have many shapes but regular shapes are simple in design and analysis and the prediction of their performance shows better results. The dielectric constant of a substrate usually lies in the range of 2.2 to 12. The microstrip patch antennas are preferably fabricated on high dielectric constant materials as they are easy to integrate with MMIC RF front end circuitry. However, using high r substrates results in low

effi-ciency and narrow bandwidth [4]. The relationship between the bandwidth, substrate height and dielectric constant is [5],

BW = √h r

. (1.1)

BW = Bandwidth of antenna h = Height of substrate

r = Relative dielectric constant of the substrate

1.3 The feeding methods

There are many techniques to feed a microstrip patch antenna. The most widely 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 fabricate and easy to impedance match by adjusting the inset position of the patch as shown in Figure (1.1). The width of the microstrip feed line is much

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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 plane and the inner conductor is soldered to the patch as shown in Figure (1.3). This feeding technique has low spurious power radiation because the feeding network is isolated from the patch, therefore low side lobes are produced. However, coaxial probe feeding is not easy to model especially for antennas that has a thick substrate (h > 0.02λ) [8].

The main disadvantage of this technique is the inherent asymmetry which creates higher order modes that cause cross polarization [4].

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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 permittivities are used. The radiating patch lies on top of the substrate and a microstrip line is connected between the substrate layers as shown in Figure (1.4). In this 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, so it has low spurious radiation and high suppression of side lobes. The main drawback is that it is hard to fabricate because the two dielectric substrate layers require proper alignment and this increases the antenna thickness.

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1.3.4 Aperture coupling

The aperture coupling technique has a ground plane that lies between two substrates with different permitivites as shown in Figure (1.5). A thick low r

material is at the top of the ground plane to produce loosely bound fringing fields for spurious radiation. A high dielectric constant material is at the bottom of the plane for tightly coupled fields that do not produce spurious radiations. The ground plane also separates the feed line from the radiated patch to minimize the interference of spurious radiation [4].

Impedance matching is done by adjusting the length of the slot and the width of the feed line. This technique is difficult to fabricate and has narrow bandwidth [9].

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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 wave antennas.

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1.5 The microstrip patch antenna

In a microstrip patch antenna one side of the dielectric substrate is grounded and the other side has a conducting patch. The patch could have different shapes such as rectangular, circular, triangular and elliptical etc, but the rectangular patch is extensively used for thin substrates in the microwave regime because of its ease of fabrication. It is easily described with both the cavity 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 patch is shown with the length along the X-axis, the width along the Y-axis and the thickness along the Z-axis.

The width (W) of the rectangular patch antenna is calculated as [4],

W = c 2fo q r+1 2 . (1.2)

c = Speed of light in free space fo = Operating frequency

r = Permittivity constant of dielectric substrate

For a rectangular patch antenna the length is normally chosen in the range 0.333λ < L < 0.5λ. When the patch is excited by the feed line a charge distribution is established on the ground plane and on the downside of the patch. The ground plane is negatively charged and the patch is positively charged by the feed excitation. Attractive forces are generated between the ground plane and the patch and this produces fringe fields. This fringing effect is equivalent to an extension of the patch by a distance ∆L.

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The effective length of the patch is given by [4], L = Lef f − ∆L (1.3) Lef f = c 2fo √ ref f (1.4) ref f = r+ 1 2 + r− 1 2 1 + 12h W !−1₂ (1.5) ∆L = 0.412h(ref f+ 0.3) _W h + 0.264 (ref f− 0.258) _W h + 0.8 (1.6)

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Chapter 2 Photonic Crystals

2.1 Introduction

Crystals are periodic structures of atoms and molecules. The pattern of atoms and molecules is repeated in space and forms a crystal lattice. A crys-tal lattice may stop the propagation of certain electromagnetic waves because there is an energy gap in the crystal lattice that prevents the movement of electrons with certain energies in a certain direction. With a strong lattice potential the energy gap may be extended to prevent propagation in all di-rections. This energy gap of a crystal lattice is called the photonic bandgap and 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].

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2.2 Types of photonic crystals

The dielectric constant of a photonic crystal varies periodically in space in specific directions. When the dielectric constant of the photonic crystal varies in one direction it is called a one-dimensional (1D) photonic crystal. The same with (2D) and (3D) photonic crystals where the dielectric constant varies 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 nature and not discovered in other materials. The basic difference between meta-materials and photonic crystals is the existence of a photonic bandgap in the latter. 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 there is no bandgap since a λ [13].

In photonic crystals the refractive index η = √r varies periodically.

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

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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 band gap. This photonic band gap behaves as a stop band filter for a certain range of frequencies and prevents these frequencies from propagating in certain di-rections [11].

The substrates with high dielectric constant have narrow bandwidth but the bandwidth can be increased by thickening the substrates. Unfortunately this produces strong surface waves that impair antenna efficiency. To overcome this 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 the air and the antenna substrate. In the substrate the power is radiated in the form of surface waves and this reduces the bandwidth. Large back lobes also lower efficiency. Total internal reflection in the substrate occurs when the incident angle is greater than the critical angle.

When photonic crystals are used as a substrate and the frequency is within the bandgap, the total power radiates into the air. No power radiates into the substrate because that particular frequency is blocked by the bandgap of the crystal as shown in Figure (2.3b). The bandgap of the photonic crystal behaves 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 bandwidth and 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 donor and the crystal will be in donor mode. Similarly a removed atom becomes an acceptor and relates to the acceptor mode. The acceptor mode in crystal lattices is widely used to fabricate single mode microcavities for single mode oscillation[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 removing a single atom from the lattice. A point defect can be used to trap a certain frequency of light in photonic crystals. In a point defect a single mode can be 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 a row of atoms from the lattice. A line defect in the crystal can guide the light from one location to another. By producing line defects photonic crystals can also be used as waveguides [11].

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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 holes and organized in a triangular lattice shape is shown in Figure (2.5). The triangular lattice can provides the large element spacing that can reduce the mutual coupling effects. The bandgap property in 2D photonic crystals can be described by waves with a wave vector in the plane of periodicity. This propagation mode is known as Bloch waves. The mathematical form is [16].

E(r + a, t) = E(r, t) eik•a (2.2)

a = lattice vector k = wave vector t = 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 relation determines 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 in the crystals. FDTD (Finite difference time domain), FEM (Finite element method), and PWE (plane wave expansion) are commonly used techniques to 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 of the lattice and the refractive index ratio of the material and the impurities that are added in the crystal. Usually the refractive index ratio must be greater than 2:1 (material to impurity) [17].

The different types of photonic crystals are used as antenna substrates. The proposed 2D photonic crystal Alumina is a triangular lattice of air holes with radius r and lattice constant a drilled into an Alumina slab with a relative dielectric constant of 9.6. The r/a value is chosen to maximize the photonic bandgap at the required operating frequency [18]. In a 2D photonic crystal the 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 the filling ratio r/a is 0.46. The width of the strip conductor has a constant value of 5.43 mm to fix the rejection band at 12 GHz according to the Bragg condition [20], fmax = c 2√ref fa . (2.3) c = Speed of light

ref f = Effective dielectric constant of Alumina

a = 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 frequency is reinforced.

The bandgap of Alumina is shown in Figure (2.6) in the form of a band of frequencies where the dispersion relation has no solutions. The bandgap of a photonic crystal depends upon the filling ratio r/a and the dielectric constant (r). The r/a ratio affects the size of the TE and TM bandgaps.

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The Alumina lattice with constant a and filling ratio r/a is designed so that the operating frequency 12 GHz falls within the photonic bandgap.

The PWE technique is used to obtain the dispersion relation [21]. The real part of the wave vector shows irregular dispersion inside the bandgap. The imaginary 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 in Figure (2.6) shows the band structure for the TE mode with the electric field parallel to the plane of periodicity.

0 5 10 15 20 25 30 0 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. 441 plane waves are used to determine the TE bandgap to 8.8 < f <13.04 GHz.

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

0 5 10 15 20 25 30 0 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 quite narrow, 11.6 < f < 12.9 GHz. The filling ratio r/a can be varied to adjust the band structure [22].

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

0 5 10 15 20 25 30 0 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 photonic crystal.

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 used for microwave and radio frequency applications. It produces design configu-rations for radio frequency electronic products, i.e. radar systems, wireless networks 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-in to design circuits. The schematic window is used for the proposed design and also provides the microstrip feed line calculations with the help of LineCalc. The schematic design simulation is fast and provides accurate results. Design

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Figure 3.1: The schematic window of ADS.

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

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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 in ADS 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.

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3.4 The Ports

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

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

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 pointing inward to the circuit, and it must be at right angle.

5. The ports must be attached to some part of the designed circuit. If it is not completely attached to the circuit, momentum automatically snaps the port to the edge of the closet object.

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

7. Do not add the ground port component, momentum does not recognize the 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 and rectangles to compute the current. This grid-like pattern of triangles and rectangles is called the mesh, and each small part of the pattern is called a cell. Every circuit has a unique mesh pattern. The mesh is applied to the circuit to compute the current and identifies the coupling effects in the circuit during the simulation. Finally, it calculates the S -parameters for the circuit.

To define mesh parameters in ADS, select Momentum >Mesh >Setup. The more cells, the higher the accuracy in the simulation, but too many cells will slow down the simulation and provide little improvement in accuracy. It is better to use the default parameters for the mesh settings. The mesh frequency 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 setting

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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 provides the necessary tools to design and evaluate a communication system. The electromagnetic simulator is known as momentum and provides a complete tool 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 can be simulated with accurate results by using ADS momentum. The ADS mo-mentum has a capability to design automation tool that can be extended by momentum optimization. The ADS momentum visualization provides 3D presentation of current flow in slots and conductors. It also provides 2D and 3D 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 the method of moments that is based on the integral formulation of Maxwell’s equations. Integral equations generate the matrix equations that are used

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to obtain the accurate simulation results. In ADS Momentum, the circuit is divided into mesh strips with triangles and rectangles. In the next step, the surface 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 the scattering parameters [23].

3.9 The Theory of ADS momentum

The numerical discretization technique used to solve Maxwell’s equations for planar structures embedded in multilayer dielectric substrates is called

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

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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 antennas are implemented to steer the main beam of radiation by shifting the phase of each element. The phased array antennas can steer the main beam effectively and 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 disc pivoted at the bottom of the antenna.

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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 by means of switched line phase shifters. This technique has a high scanning rate 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 changing the operating frequency or by using electronic phase shifters [25].

4.3 The phase shifters

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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 to a phase shifter. The main beam is formed by shifting the phase of the transmitted signal from each element.

Figure 4.3: The electronic beam steering mechanism.

The phase shift between two successive elements remains fixed and is given by [25], ∆ϕ = 2π ∆L λ (4.1) ∆L = d sin Θs (4.2) Hence ∆ϕ = 2π d sin Θs λ (4.3)

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4.3.2 The switched-line phase shifter

In the switched-line phase shifter, phase shifting is obtained by varying the length of the antenna feed line. The phase delay in the feed line is calculated from [3], ∆L = βc 2πf√ef f . (4.4) ∆L = Change in length β = Propagation constant c = Speed of light

ef f = Effective dielectric constant

f = Operating frequency

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Chapter 5 Antenna Design and Analysis

The design, simulation and analysis of a single patch, and 1x 2 and 1x 4 arrays 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 constant of Alumina is 9.6 with a loss tangent of 0.0002. The height of the substrate is set to 0.05λ, that is 1.25 mm at 12 GHz operating frequency. The width of the patch is calculated from equation (1.2) to 5.43 mm, and the length is calculated from equation (1.3) to 4.35 mm. The effective dielectric constant 7.95 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).

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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 with ADS momentum.

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The antenna resonates at 11.99 GHz with a return loss of -11.1 dB. The results 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 the conventional substrate (RT-Duroid 6010 with dielectric constant 10.2) at the operating frequency of 12 GHz as shown in Figure (5.4).

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

6010.

The results show that the photonic crystal substrate provides a better return loss 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).

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

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

The Figure (5.6) shows that the antenna radiates almost isotropically. To enhance the directivity, gain and other radiation parameters, a 1x2 antenna array 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 inter element spacing. It is fed by a 50 Ω line using the corporate feeding technique according to the Wilkinson dividing rule, in order to obtain matching to the 100 Ω patch.

The self conductance of two patches is calculated using [5],

G1 = I1 120π2 (5.1) I1 = π Z 0   sinkoW 2 cos cos   2 sin3θ 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 asymptotically from [5], G1 =    1 90 W λo 2 for W λo 1 120 W λo for W λo (5.5)

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

G12 = 1 120π2 π Z 0   sinkoW 2 cos cos   2 Jo(koL sin θ) sin3θ 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]. The mutual conductance G12 is computed by means of numerical integration in

Mathematica. The resonant input resistance Rin of the patches is calculated

from [5],

Rin=

1 2 (G1± G12)

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G1 = Self conductance

G12 = Mutual conductance

The (+) sign is used for the odd symmetry modes and the (-) sign is used for 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 -24

dB.

The simulation results for the scattering parameters of a 1x2 array antenna are shown in Figure (5.8).

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

In the Smith chart, simulation shows that the antenna resonates at 12 GHz having 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 are shown in Figure (5.9).

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

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The 2D simulation results for the gain and directivity of a 1x2 array antenna with 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, in the range of -20o to 20o. The power radiated by the antenna is 0.6 mW.

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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.

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5.3 The 1x4 array antenna with equal spacing

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

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

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5.4 The 1x4 array antenna with unequal

spac-ing

To improve the return loss and reduce the side lobes unequal inter-element spacing 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 array is 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 the antenna is perfectly matched to a 50 Ω feed line. The 10 dB bandwidth of the 1x4 array antenna is 900 MHz, that is 7.5% of the operating frequency.

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

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

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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.

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The 2D simulation results for the gain and directivity of a 1x4 nonuniform array 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 and gain of 20 dB and 22 dB, respectively. The far-field radiated power is shown in Figure (5.20).

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

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5.5 Antenna beam steering

The beam steering of a 1x4 uniform array antenna based on photonic crystal is obtained by means of switched line phase shifters. The main beam is steered about 20o _{by changing the phase between the array elements. The}

change in phase is obtained by altering the length of the feed line. The length of the delay lines for phase shifting are ∆L, 2∆L and 3∆L. The length ∆L is computed 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.

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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 for conventional substrates and photonic crystals shows that photonic crystals offer potential regarding bandwidth, gain and directivity. The suppression of 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. The bandgap of photonic crystals with varying hole diameters were studied in or-der to obtain the required frequency range. The beam steering results show that photonic crystal techniques are applicable.

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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 following areas,

• Design intended to minimize the surface area occupied by the photonic crystals.

• 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.

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Simulation of Phased Arrays with Rectangular Microstrip Patches on Photonic Crystal Substrates

Master Thesis