Design and Implementation of Advanced Microwave Filter and Antenna for Dual-band Systems

/ i.

^ h 丨 ？

YM，Ho Yan

A Thesis Submitted to Partial Fulfilment of the Requirements for the Degree of

Master of Philosophy in

Electronic Engineering

© The Chinese University of Hong Kong May 2007

The Chinese University of Hong Kong holds the copyright of this thesis. Any person(s) intending to use a part or whole of the materials in the thesis in a proposed publication must seek copyright release from the Dean of the Graduate School.

( 知 丄 M !

Abstract

Abstract of thesis entitled:

Design and Implementation of Advanced Microwave Filter and Antenna for Dual-band Systems

Submitted by Yim Ho Yan

for the degree of Master of Philosophy in Electronic Engineering

at The Chinese University of Hong Kong in December 2006

Development of compact dual-band devices has become an important research topic, particularly for wireless applications with multiple operating frequency bands. The design of multi-band, multi-mode transceiver is likely to be the ultimate goal in modem wireless system. Great effort has recently been devoted to the design of dual-band passive components, such as filter, antenna, coupler and power divider, since it can help to reduce the size and complexity of RF systems.

This thesis will cover two new types of dual-band microwave devices, namely microwave filter and circularly polarized (CP) antenna.

The filter is constructed using novel dual-band resonators and admittance inverters with closed-form design formulas. These filters also feature compact size, planar structure and low-insertion loss. For verification, the measured performance of a 900/2000 MHz, 3"* - order, band-pass filter with equal bandwidth implemented using microstrip technique is given. Insertion loss of less than 0.4dB and 0.8dB are found at the lower and upper bands, respectively. A 3dB bandwidth of 360MHz and mid-band attenuation of over 60dB have been achieved. For filter design with unequal bandwidths, another type of resonator has been proposed. A prototype with center frequencies at around 800/1900 MHz was designed and characterized. 3dB bandwidth of

ii

the two operating bands are found to be approximately 250 MHz (/} = 750 MHz) and 350 MHz (f2 = 1850 MHz). Return loss and insertion loss of 12dB (minimum) and 0.65±0.25 dB, respectively, have been achieved over both pass-bands. Excellent stop-band attenuation of more than 30 dB was also observed, particularly at frequencies close to 1.25 GHz and 2.8 GHz.

In the second part of this research, a compact dual-band CP antenna is obtained by combining two linearly-polarized dual-band antenna elements with a dual-frequency quadrature hybrid. The antenna element is basically a slotted cross patch with dual resonant frequencies. This combination can offer good isolation and substantially reduce the undesirable cross-polarization radiation. For compactness, the two antenna elements and the dual-band hybrid coupler are integrated together by using multi-layer technology. A prototype of the proposed CP patch antenna operating at 915 MHz and 2.45 GHz is implemented and characterized. The impedance bandwidth and port isolation are found to be 20.1 % (895 MHz), 8.9% (2.40 GHz), 22dB (885 MHz) and 38dB (2.46 GHz), respectively. The 3-dB AR bandwidths are measured to be 8.9% (lower band) and 1.8% (upper band).

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論文摘要

摘要題目：

基於雙波段系統的微波過濾器和天線的設計和實施

提交人： 嚴可欣

提交學位： 哲學碩士

香港中文大學二零零六年十二月

現今，設計小型化的雙頻器件已成爲硏究領域的一個重要的方向，尤其是針對多頻段的

無線通訊領域。從某種程度上來說，設計多頻段多模式的收發信機就是現代無線通信的

目標。硏究人員做了大量的工作用於設計雙頻段的無源器件例如濾波器，天線，輔合器

和功分器從而減小射頻系統的體積和複雜度。

本論文提出了一種新型雙頻段微波濾波器和圓極化天線。

該濾波器包括新穎的雙波段諧振器和倒訥變換器。這種濾波器還具有小型化，平面結構

和低差損特性°爲了驗證該爐波器性能’我們測量了該濾波器在900/2000MHZ以及3階

等帶寬處特性。插入損耗在低端和高端分別低於 0 . 4 d B和 0 . 8 d B � 3 d B帶寬爲 3 6 0 M H z �

在中間帶的抑制度大於60dB�爲了更好的分別調整兩個頻帶，我們提出並且驗證了相應

的設計公式。最終我們實現了該濾波器。該濾波器原型在兩個工作頻點處的3dB測量帶

寬爲分別爲 250MHz (/；=750 MHz)和 350MHz(/>1850 MHz) ’ 回損爲 1 2 d B �插入損耗

爲0.65±0.25 dB，阻帶抑制大於30dB，尤其在1 .25 GHz和2.8 G H z �

iv

小型化的雙頻段圓極化天線由兩部分組成一一線極化雙頻段天線和雙頻功分器。天線部

分是基本的交叉縫隙片狀雙頻天線。通過將該天線和雙頻功分器組合在一起，我們在獲

得較高隔離度的同時還減少了無用的交叉極化輻射。爲了進一步縮小尺寸，我們採用多

層結構將該天線與功分器集成在一起。最終實現並測試了該雙頻段圓極化天線。其工作

頻率爲915 MHz和2.45 GHz�阻抗帶寬和璋隔離度分別爲20.1% (895 MHz)，8.9% (2.40

GHz) ’ 22dB (885 MHz)和38dB (2.46 GHz) °在兩個頻段的3dB軸比帶寬分別爲8.9%和

1.8%。

V

Acknowledgement

First of all, I would like to express my gratitude to all the people in The Chinese University of Hong Kong, Faculty of Engineering, and Department of Electronic Engineering who promoted research policies and maintained a research environment indispensable for this project.

I would like to thank my supervisor Dr K. K. Cheng for giving me the opportunity to work on microwave and RF circuit design. I am grateful for all the given support and the essential guidance during my M.Phil study.

I wish to express my appreciation to Prof. K. L. Wu for his encouragements and the inspiring lectures on "Advanced Microwave Engineering — Microwave Filter Design".

I would like to thank Mr. K. K. Tse, Mr. Tony S. H. Cheng, Mr. Fred F. L. Wong, Mr. Alvis C. F. AuYeung, Mr. C. P. Kong, Mr. K. F. Chang, Mr. Sam K. K. Mok, Mr. D. C. Wei and Mr. H. Hu for their valuable help and discussions during this project.

I dedicate this work to my family.

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Table of Content Abstract ii 赦 腰 iv Acknowledgement vi Table of Content vii List of Figures x List of Tables xiv Chapter 1 Introduction 1

1.1 Filter 3 1.2 Antenna 4 1.3 Outline of the Thesis 6

Chapter 2 Basic Theories in Filter and Patch Antenna Design 7 2.1 Microwave Filter Design 7

2.1.1 Transfer Functions 8 2.1.2 Lowpass Prototype Filters and Elements 14 2.1.3 Filter Transformations 18 2.1.4 Admittance Inverter 21

2.2 Antenna Concepts 23 2.2.1 Microstrip Antenna 23 2.2.2 Patch Antenna Design 24 2.2.3 Polarization 28

Chapter 3 Review of Conventional Dual-band Filter Designs 33 3.1 Bandstop / bandpass Filters in a Cascade Connection 33 3.2 Stepped Impedance Resonator 34 3.3 Tunable Transmission Zero for Spurious Responses Suppression 36 3.4 Comparison 38

Chapter 4 Novel Dual-band Filter Design with Equal Bandwidth 39 4.1 Introduction 39 4.2 Frequency Behavior of Shunt Stubs 39 4.3 Dual-band Resonator with Paralleled Stubs 42 4.4 Dual-band Admittance Inverter 47 4.5 Dual-band Filter Realization 51

vii

4.5.1 Simulation Examples 54 4.5.2 Comparison of Simulation results 60 4.5.3 Experimental Results 64

Chapter 5 Novel Dual-band Filter Design with Unequal Bandwidth 70 5.1 Introduction 70 5.2 Dual-band Resonator using Step-Impedance Line 70 5.3 Dual-band Admittance Inverter 74 5.4 Dual-band Filter Realization 75

5.4.1 Comparison of Simulation Results 81 5.4.2 Experimental Results 85

Chapter 6 Review of Conventional CP Antenna Designs 91 6.1 Degenerated Mode Patch 91 6.2 CP Stacked Microstrip Patch Antenna Array 92 6.3 Coplanar Waveguide-fed Slot Antenna 93 6.4 Dual-band CP antenna fed by 2 different 90° hybrid couplers 95

Chapter 7 Novel New Dual-band CP Antenna Design 96 7.1 Introduction 96 7.2 Dual-band CP Patch Antenna 96

7.2.1 Slotted Square Patch Antenna 96 7.2.2 Slotted Cross Patch Antenna 99 7.2.3 Simulation Results: Slotted Cross Patch Antenna 101

7.3 Dual-band Quadrature Hybrid 104 7.3.1 Simulation Results: Dual-band Hybrid Coupler 107

7.4 Dual-band CP Antenna Realization 113 7.4.1 Antenna Configuration 113 7.4.2 Measurement Setup 114 7.4.3 Experimental Results 115

Chapter 8 Conclusions and Recommendations for Future Work 123 8.1 Filter 123 8.2 Antenna 123 8.3 Recommendations for future work 124

References 125 viii

Author's Publications 128 Acronyms and Abbreviations 129

ix

List of Figures Figure 1-1 Block diagram of RF receiver 1 Figure 1-2 A concurrent dual-band receiver 2 Figure 1-3 Dual-band RF front-end architecture 2 Figure 1-4 (a) The concept of satellite communication (b) CP antenna 5 Figure 2-1 Butterworth lowpass response 10 Figure 2-2 Pole distribution of Butterworth response 11 Figure 2-3 Chebyshev lowpass response 12 Figure 2-4 Graph of Chebyshev polynomial with different order n . { n = \ Brown; n = 2 Black; n = 3 Red; n = 4 Pink; n = 5 Blue; n = 6 Green) 13 Figure 2-5 Pole distribution of Chebyshev response 14 Figure 2-6 Ladder circuits for lowpass filter prototypes and their element definitions, (a) Prototype beginning with a shunt element, (b) Prototype beginning with a series element 15 Figure 2-7 Lowpass prototype to bandpass transformation 21 Figure 2-8 (a) Operation of admittance inverter; (b) Implementation as quarter-wavelength transformer 22 Figure 2-9 Microstrip antenna 23 Figure 2-10 Four feeding methods (a) microstrip line feed; (b) coaxial-line feed; (c) aperture coupled feed; (d) proximity coupled feed 25 Figure 2-11 Effective length extension 27 Figure 2-12 (a) Left-hand circular polarization; (b) right-hand circular polarization 29 Figure 2-13 Elliptical polarization 31 Figure 2-14 Different arrangements for generating CP waves 32 Figure 3-1 Block diagram showing bandpass and bandstop filters in cascade connection 33 Figure 3-2 Photo of the fabricated dual-band filter proposed by Tsai et al 34 Figure 3-3 Basic structure of SIR 35 Figure 3-4 Circuit layout of dual-band cross-coupled filter 35 Figure 3-5 Dual-band SIR filter 36 Figure 3-6 Insertion loss of the dual-band filter proposed by Ma et al (— with transmission zeros; --- without transmission zero) 37 Figure 3-7 Dual-band SIR filter with tunable transmission zeros 38 Figure 4-1 Input admittances of (a) open-circuited stub; (b) short-circuited stub 40

X

Figure 4-2 Frequency behavior of (a) open-circuited and (b) short-circuited shunt stubs 41 Figure 4-3 Proposed dual-band resonator: (a) Frequency behavior, and (b) its structure 42 Figure 4-4 Proposed dual-band resonator and its equivalent 46 Figure 4-5 Proposed structure of the dual-band quarter-wavelength branch-line and its equivalent 47 Figure 4-6 Proposed dual-band admittance inverter 51 Figure 4-7 Filter design (aP'd order bandpass filter prototype; (b) with dual-band inverters and resonators 52 Figure 4-8 Simplification of a pair of shunt stubs 53 Figure 4-9 Proposed structure of dual-band filter 53 Figure 4-10 ADS simulation results: Design 1 55 Figure 4-11 ADS simulation results: Design 2 57 Figure 4-12 ADS simulation results: Design 3 59 Figure 4-13 ADS schematic diagram for ideal simulation 60 Figure 4-14 ADS schematic diagram for simulation with junction effect 61 Figure 4-15 IE3D layout diagram for EM simulation 62 Figure 4-16 Return loss (comparison between simulations) 63 Figure 4-17 Insertion loss (comparison between simulations) 63 Figure 4-18 (a) Fabricated filter (b) its dimension 66 Figure 4-19 Return loss (simulated and measured) 67 Figure 4-20 Insertion loss (simulated and measured) 67 Figure 4-21 Insertion loss (a) lower and (b) upper pass-band 68 Figure 5-1 Proposed structure of the dual-band resonator 71 Figure 5-2 Step-impedance section (open-circuited) 72 Figure 5-3 Proposed dual-band admittance inverter and its equivalent 75 Figure 5-4 (a) Basic topology; (b) with proposed inverter; (c) with proposed resonator 76 Figure 5-5 Proposed dual-band filter structure 79 Figure 5-6 Dual-band filter design: flow chart 80 Figure 5-7 ADS schematic diagram for ideal simulation 82 Figure 5-8 ADS schematic diagram for simulation with junction effect 83 Figure 5-9 IE3D layout diagram for EM simulation 83 Figure 5-10 Return loss (comparison between simulations) 84

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Figure 5-11 Insertion loss (comparison between simulations) 85 Figure 5-12 (a) Fabricated filter (b) its dimension 87 Figure 5-13 Return loss (simulated and measured) 88 Figure 5-14 Insertion loss (simulated and measured) 88 Figure 5-15 Insertion loss (a) lower and (b) upper pass-band 89 Figure 6-1 Square-ring microstrip antenna with truncated comers 91 Figure 6-2 Stacked microstrip antenna with a crossed slot on the bottom patch 92 Figure 6-3 2x2 array using sequential rotation method 93 Figure 6-4 Layout of the coplanar waveguide-fed slot antenna 94 Figure 6-5 Dual-band dielectric resonator antenna with radiating slot 94 Figure 6-6 Geometry of dual-band CP antenna 95 Figure 7-1 Geometry of the slotted square patch antenna 97 Figure 7-2 Current distribution on the slotted square patch, (a) TMioo mode; (b) TM300 mode.. 98 Figure 7-3 Geometry of the slotted cross patch antenna 99 Figure 7-4 Current distribution at the patch corner at TM300 mode for (a) slotted square patch antenna and for (b) slotted cross patch antenna 100 Figure 7-5 Geometry of the slotted cross patch antenna 102 Figure 7-6 Simulation results - return loss and isolation factor 103 Figure 7-7 Conventional design of single-band quadrature hybrid 104 Figure 7-8 Dual-band transformer 105 Figure 7-9 Overall structure of dual-band coupler 106 Figure 7-10 Final topology of dual-band hybrid coupler 107 Figure 7-11 Layout of dual-band hybrid coupler 108 Figure 7-12 Simulation result - return loss 110 Figure 7-13 Simulation result - isolation 110 Figure 7-14 Simulation result - insertion loss I l l Figure 7-15 Simulation result - phase difference 112 Figure 7-16 Geometry of dual-band CP antenna using hybrid coupler feeding 114 Figure 7-17 Measurement setup 115 Figure 7-18 Photo of the proposed design 116 Figure 7-19 Measured return loss (a) Lower band; (b) Upper band 117 Figure 7-20 Measured isolation (a) Lower band; (b) Upper band 118

xii

Figure 7-21 Measured axial ratio (a) Lower band; (b) Upper band 119 Figure 7-22 Measured far field radiation patterns at 852 MHz (a) in XZ plane and (b) in YZ plane 121 Figure 7-23 Measured far field radiation patterns at 2.49 GHz (a) in XZ plane and (b) in YZ plane 122

xiii

List of Tables Table 3-1 Comparison between dual-band filters 38 Table 4-1 Filter parameters of Design 1 54 Table 4-2 Impedance values of Design 1 54 Table 4-3 Filter parameters of Design 2 56 Table 4-4 Filter parameters of Design 3 58 Table 4-5 Physical dimension of dual-band microstrip filter 65 Table 4-6 Simulated and experimental results 69 Table 5-1 Design values of the dual-band filter 81 Table 5-2 Physical dimension of dual-band microstrip filter 86 Table 5-3 Simulated and experimental results 90 Table 7-1 Physical dimension of slotted cross patch antenna 102 Table 7-2 Summary of the simulation result 103 Table 7-3 Impedance values of dual-band coupler 108 Table 7-4 Physical dimension of dual-band hybrid coupler 109 Table 7-5 Summary of simulation results 112 Table 7-6 Substrate details 113 Table 7-7 Summary of the experimental results 120

xiv

Chapter 1

Introduction

In the last decade, many new wireless applications and services have emerged. In order to support these new systems and to have a global coverage, the mobile terminal must be able to connect to different networks. In addition to cellular systems, other wireless systems have already found their way into mobile terminals, including proximity radios (Bluetooth and RFID, for example), wireless local area network radios (IEEE802.11a/b/g), and receivers for positioning (GPS) and broadcasting (DVB-H) [4]. As a result, multi-mode and multi-band circuits have recently received great attention. In the early year, multi-band system (e.g. GSM & PCS) was constructed by using separated circuits [2] designed for different operating bands [3]. Figure 1-1 shows the block diagram of a basic Radio Frequency (RF) receiver.

V Preselecting 丨 = M i x e r IF Filter Demodulator Output Data

A i

© Local Oscillator

Figure 1-1 Block diagram of RF receiver

Alternatively, a dual-band RF front-end may help to reduce the complexity of a multi-band, multi-mode receiver design [5] [6]. As illustrated in Figure 1-2，the basic configuration can consist of a dual-band antenna, followed by a dual-band filter and a concurrent dual-band low-noise amplifier (LNA).

1

Dual-band Antenna ¥ Dual-band Dual-band

Filter LNA ^ ； • Dual-band Image - Rejection • Base-band Signal 1 1 〜 丨 ~ I Downconvertor • Base-band Signal 2

Figure 1-2 A concurrent dual-band receiver

The proposed radio concept in [7] shows that dual-band front-end can also have two gain modes: high-gain mode and low-gain mode, to relax the linearity and gain control requirements for the IF and baseband blocks. As shown in Figure 1-3，two frequency inputs are fed separately into the dual-band LNA via a series of filter and switches.

Input 1

I 叩u t 2 V \ , Low-Noise V L^ Filter & Amplifier Mixer

1 Switches

J Filter & , n Switches ^ ^

Figure 1-3 Dual-band RF front-end architecture 2

1.1 Filter

Filter have played an important role in early stages of telecommunication and progressed steadily in accordance with the development of communication technology. The introduction of a transmission system of multiplex communication required the development of new technology to extract and detect signals contained within a specific frequency band.

Traditionally, filter design is focused on passive electrical circuits based upon lumped induction {L) and capacitor (Q. Although the above mentioned filter utilized a linear resonant system, early stages of filter development suggested the probable and likely existence of another approach that would realize filter response. The main reason behind was the general view of filters as functional devices which achieved their performances according to given transfer functions [8].

The introduction of new telecommunication systems has brought harsh constraints on either out-of-band rejection or in-band insertion loss for RF filters. Moreover, the wide range of modem wireless applications requires systems with board bandwidth and high selectivity. However, RF systems with two RF front ends working in parallel at different frequencies will lead to increased circuit complexity, which results in higher cost, circuit size and larger insertion loss.

To overcome these problems, new dual-band receiver architecture is introduced [9]. In this approach, it simultaneously operates at two separate frequency bands using a set of dual-band components, including antenna, filter and LNA. Dual-band filter has become a key component in future wireless front-end application.

3

1.2 Antenna

An antenna is a device, which radiates or receives electromagnetic waves. Antenna is the interface between a guiding device (transmission line, waveguide) and free space. Its main purpose is to effectively transfer energy from a guided structure into free-space wave, or vice versa.

Since 1970s, microstrip antennas have played an increasingly important role in the field of antenna design. Microstrip antenna is probably the simplest yet most popular planar antenna. It provides significant advantages over conventional antenna designs, namely, [10]

_ Low profile

• Reduced weight

• Relatively low manufacturing cost

• The potential to build arrays

• Polarization diversity

Microstrip antennas have matured considerably during the past 30 years. The results of the research have contributed to overcome many of the limitations and to the success of these antennas in commercial areas. In the recent years, there has been an explosion in commercial applications involving RF and microwave systems, from remote keyless entry for automobiles to RFID for animal tracking, toll collection, and supply-chain management. As customers demand smarter, smaller and cheaper products, more innovative antennas will be required. Microstrip antennas are ideal for these applications as they are very thin and are compatible with IC technology in the sense that they can be readily interfaced with IC interconnects. They can even be made part of the chip. Most importantly, microstrip antennas are manufactured using printed circuit techniques, and therefore, are very low in cost.

4

Polarization is a basic consideration in the design of any wireless communication system. In general, Linear Polarization (LP) antennas have less design constraints in compared to Circular Polarization (CP) antennas and therefore are more commonly used. However, CP antennas find application primarily in satellite communication, such as Global Positioning System (GPS), and Radio Frequency Identification (RFID) system. These applications use CP antennas in situations where precise alignment between transmit and receive antennas is impractical, or where the orientation of the transmitting antenna is unknown. It is interesting to note that, for wireless communication, CP antennas have additional advantages over LP signals in combating multipath fading environment. For example, when radio wave hits a smooth reflective surface, they may incur a 180 degree phase shift, a phenomenon known as specular or mirror image reflection. The reflected signal may then destructively or constructively affect the direct line-of-sight (LOS) signal. Circular polarization has been used to an advantage in these situations since the reflected wave would have a different sense than the direct wave and block the fading from these reflections [1].

(a) (b)

Figure 1-4 (a) The concept of satellite communication (b) CP antenna

5

1.3 Outline of the Thesis

Chapter 2 presents the basic theories in filter and patch antenna design. Low-pass prototype synthesis method is discussed briefly. Definition of polarization and axial ratio are given as they are the major performance indicator to characterize a CP antenna.

Chapter 3 gives a review of conventional dual-band filter design. Different filter structures and their main advantages and drawbacks are covered and compared.

Chapter 4 & 5 introduces the design and implementation of dual-band filter with equal or unequal bandwidth. Working principles of dual-band resonator and inverter with closed-form design formulas are described.

Chapter 6 reviews the designs of conventional dual-band CP antenna which include different methods to produce CP radiation and their limitations.

Chapter 7 presents the design of novel dual-band CP antenna using a dual-band hybrid as the feeding network. A multilayer structure is proposed for implementation to attain both compactness and high isolation.

Finally, chapter 8 concludes this work and provides recommendations for future research.

6

Chapter 2

Basic Theories in Filter and Patch Antenna Design

2.1 Microwave Filter Design

Filters designed using the image parameter method consist of a cascade of two-port filter sections to provide the desired cutoff frequencies and attenuation characteristics, but do not allow the specification of a frequency response over the complete operating range. Although the procedure is relatively simple, the design of filters by the image parameter method often must be iterated many times to achieve the desired results.

A more modem procedure, called the insertion loss method, uses network synthesis techniques to design filters with a completely specified frequency response. The design is simplified by beginning with low-pass filter prototypes that are normalized in terms of impedance and frequency. Transformations are then applied to convert the prototype designs to the desired frequency range and impedance level.

Since the image method cannot provide a clear-cut way to improve the design and the insertion loss method allows a high degree of control over the passband and stopband amplitude and phase characteristics with a systematic way to synthesize a desired response, insertion loss method is chosen in this project.

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2.1.1 Transfer Functions

2.1.1.1 Definitions

The transfer function of a two-port filter network is a mathematical description of network response characteristics, namely, a mathematical expression of S21. An amplitude-squared transfer function for a lossless passive filter network is defined as

刺 2 、 + 一 二 / ⑶ (2.1)

where e is a ripple constant, F„(Q) represents a filtering or characteristics function, and is a frequency variable. Q is in radian and the cut-off frequency in a lowpass prototype is at Q= Qc for lOc = 1 (rad/s).

For linear, time-invariant networks, the transfer function may be defined as a rational form, that is

s 善 截 ( - )

where N(p) and D(p) are polynomials in a complex frequency variable p = a+jQ.

For a given transfer function of (2.1)，the insertion loss response of the filter can be computed by

咖 鳥 (2.3)

8

2 2

Since S ” + S21 = 1 for a lossless, passive two-port network, the return loss response of

the filter can be found. Lr{n) = 10log\l -\S2i{jnf\jb ( 2 . 4 )

2.1.1.2 The poles and Zeros on the complex plane

The {a, Q) plane, where a rational transfer function is defined, is called the complex plane. The horizontal axis of this plane is called the real axis, and the vertical axis is called the imaginary axis. The values of p at which the function becomes zero are the zeros of the function, and the values of p at which the function becomes infinite are the poles of the function. Therefore, the zeros of S2i(p) are the roots of the numerator N(p) and the poles of S2i(p) are the roots of denominator D(p).

These poles are the natural frequencies of the filter whose response is described by S2i(p). For a stable filter, those natural frequencies must lie in the left hand of the imaginary axis. If it is not the case, oscillation would occur with exponentially increasing magnitude. This is impossible in a passive network. Hence, the roots of D(p) are in the left half-plane, whereas the roots of N(p) may occur anywhere on the entire complex plane. The roots of N(p) are called finite-frequency transmission zeros of the filter.

2.1.1.3 Butterworth Response

The amplitude-squared transfer function for Butterworth filters that have an insertion loss of La" = 3 dB at the cut-off frequency Qc= l i s given by

2 1 (2.5)

9

where n is the order of the filter, which corresponds to the number of elements required in the lowpass prototype filter. This type of response is also referred to as maximally flat because its amplitude-squared transfer function defined in (2.5) has the maximum number of (2«-l) zero derivatives at •Q = 0. Therefore, the maximally flat approximation to the ideal lowpass filter in the passband is best aiQ = 0.

L射 ^

" c a —

Figure 2-1 Butterworth lowpass response

A transfer function is

S21{P) = ^ n ( p - p , . ) (2.6) i=1

10

with

. � ( 2 / - : 0 ; r " | Pi =Jexp 2n (2-7)

All the zeros of S2i(p) are at infinity and the poles pi lie on the unit circle in the left half-plane at the equal angular spacings.

Jfl

�

Figure 2-2 Pole distribution of Butterworth response

2.1.1.4 Chebyshev Response

The Chebyshev response exhibits the equal-ripple passband and the response is illustrated in Figure 2-3.The amplitude-squared transfer function of Chebyshev response is

糾、+ 乂咖 (2.8)

11

where the ripple constant s is related to a given passband ripple Lak in dB by

e = (2.9)

T„(Q) is a Chebyshev function of order n, which is defined as

_ . X f coslncos''' Hi n <1 咖 = 口 伞 7 (2.10)

Figure 2-4 shows the response of Chebyshev polynomial with different order.

I X Figure 2-3 Chebyshev lowpass response

12

I ] I I .

-3-

Figure 2-4 Graph of Chebyshev polynomial with different order n. (n = 1 Brown; n = 2 Black; n = 3 Red; n = 4 Pink; n = 5 Blue; n = 6 Green)

All the transmission zeros of S2i(p) are located at infinity. However, the pole locations for Chebyshev filter are different from Butterworth one. They lie on an ellipse in the left half-plane. The pole distribution is shown, for « = 5，in Figure 2-5.

13

j a

/ I

\

• 一

Figure 2-5 Pole distribution of Chebyshev response

2.1.2 Lowpass Prototype Filters and Elements

If we have to realize the transfer function discuss before, we are going to synthesise by lowpass filter prototype.

For a normalized lowpass design, the source impedance is IQ and the cut-off frequency is Qc = 1 (rad/s). The element values are numbered from go at the generator impedance to g„+i at the load impedance, for a filter with n order; therefore, n is also the number of reactive elements.

14

o rnJfxmL^ m m ^ ©

《 。 途 ： 。 j S ^ or t s . _ “

o • p — 一 • - 0 画—一 • A o (w even) odd)

(a)

gi _ gi

G ~ Q RRHRRJI_Q

ZZS2 Of

G • — — — — O — — — Q (Steven) odd)

(b)

Figure 2-6 Ladder circuits for lowpass filter prototypes and their element definitions, (a) Prototype beginning with a shunt element, (b) Prototype beginning with a series

element

15

The elements alternate between series and shunt connections, and gk has the following definition:

‘generator resistance On = <

[generator conductance

n _ f inductance for series inductors yk —

{k=i to n) [capacitance for shunt capacitors ‘load resistance if g" is a shunt capacitor

q .= < [load conductance if g" is a series inductor

Then the circuit of Figure 2-6 can be considered as the dual of each other, and both will give the same response.

2.1.2.1 Butterworth Lowpass Prototype Filters

For Butterworth filters having resistor terminations at both ends, a response of the form of that in

Figure 2-1 with 丄如=3 dB，go = 1，and i^c = 1，the element values may be computed as follows [11]:

广 9 0 = 1

� � ( 2 / c - 7 > r 1 , ^ � < Qk =2sin 2门 'k = 1’2,…’ n (2.11)

� S i n n 二 1

16

To determine the degree of a Butterworth lowpass prototype, the minimum stopband attenuation Las dB at Q =Qs for Qs>\ is usually given.

(2.12)

2.1.2.2 Chebyshev Lowpass Prototype Filters

For Chebyshev filters having resistor terminators at both ends, with response of the form shown in Figure 2-3 having La” dB passband ripple, go = 1’ and Qc = 1, the element values may be computed as follows [11]:

f i_ \ r p = ln coth—^

y = sink — • {2n)

< � / � n (2.13) a, = ’k = 1 , 2 n

L �

bk +sm2 —— ,l< = 1,2,…’ n ^ I n j

and

2ai 9i= —

r

,/c = 2 , 3 n

bk-i9k-i (2.14) Y , � for n odd

—J f _ 1 coth^ — for n even

17

For the required passband ripple La” dB, the minimum stopband attenuation Las dB at Q =Qs should meet the specification of the degree of Chebyshev lowpass prototype.

I川O.ILas cosh . ~—

n t h o O i L A r - 1 (2.15)

cosh—i n^

2.1.3 Filter Transformations

The lowpass filter prototypes mentioned were normalized design having a source impedance of go = \Q and a cut-off frequency of Qq = 1. Hence, we have to scale these designs in term of impedance and frequency, and convert to give bandpass characteristics.

2.1.3.1 Impedance Scaling

We aim at adjusting the filter to work for source impedance Zq and we have the new filter component values given by

L'=ZoL

C ' = f

R'=Z:R (2.16)

Zo

where L, C, R and G are the component values for the original prototype.

18

2.1.3.2 Bandpass Transformation

Lowpass prototype filter designs can also be transformed to have the bandpass response. If wi and C02 denote the edges of the passband, a bandpass response can be obtained using the following frequency substitution:

^ 1 CO COq Q = n 17) F B W [ o ) o 0) J ^ ^

where

,-dia/ ①2 一①1 F B W = - ^ _ I (2.18) 份0

is the fractional bandwidth of the passband. The center frequency,�()could be chosen as the arithmetic mean of coi and CO2, but the equations are simpler if it is chosen as the geometric mean:

COq =如 2①1 (2.19)

The new filter elements are determined by using (2.17) in the expression for the series reactance and shunt susceptance. Thus,

JX, (2.20)

which shows that a series inductor Ls, is transformed to a series LC circuit with element values,

19

L ' = 乙 s s FBW 6)0

(2.21)

Ls①0

Similarly,

y s 厂 M V 云吉 (2.22)

which shows that a shunt capacitor, Cp, is transformed to a shunt LC circuit with element values,

_FBW P—Cp cOo

(2.23)

C = � p P FBW 0)0

The lowpass filter elements are thus converted to series resonant circuit (low impedance at resonance) in the series arms, and to parallel resonant circuits (high impedance at resonance) in the shunt arms. Both series and parallel resonator elements have a resonant frequency of coo.

20

g L C o ~ n J U O T l _ o _ • o-HTORH

o

o

o 6

Figure 2-7 Lowpass prototype to bandpass transformation

2.1.4 Admittance Inverter

The conceptual operation of admittance inverter is illustrated in Figure 2-8. An ideal admittance inverter is a two-port network that if an admittance Y is connected at one port, the admittance Yin seen looking in the other port is

(2.24)

where J is real and called the characteristic admittance of the inverter. Because of the inverting action, a series inductance with an inverter on each side looks like a shunt capacitance form it exterior terminals.

21

One of the simplest forms of inverters is a quarter-wavelength transmission line. Observes that such a line obeys the basic admittance inverter definition in (2.24), and that it will have an admittance parameter of J = Yq where Yq is the characteristics admittance of the line.

土 90� L _ • ^

(a)

^ A^ ^ • •

Yo = J • •

(b)

Figure 2-8 (a) Operation of admittance inverter; (b) Implementation as quarter-wavelength transformer

22

2.2 Antenna Concepts

2.2.1 Microstrip Antenna

As shown in Figure 2-9，the patch antenna consists of a very thin {h « Xo where Xo is the free-space wavelength) metallic strip placed a small fraction of a wavelength (h «Xo, usually 0.003^ <h< 0.05/lo) above the ground.

For a rectangular patch, the length L of the element is usually 义 f/3 <L< XoH. And the patch and the ground plane are separated by the dielectric substrate. The dielectric constants are usually in the range of 2.2 12. The most popular choice is thick substrate whose dielectric constant is in the lower end of the range because it provides better efficiency, larger bandwidth, loosely bound fields for radiation, but at the expense of large size [12].

Substrate ( g Ground plane

Figure 2-9 Microstrip antenna

23

2.2.2 Patch Antenna Design

2.2.2.1 Feeding Methods

There are many different ways to feed microstrip antenna. The most popular one, are the microstrip line, coaxial probe, aperture coupling and proximity coupling (Figure 2-10).

The microstrip line feed is easy to fabricate, simple to match by controlling the inset position and rather simple to model. However, surface waves and spurious feed radiation increase with thicker substrate, which limit the bandwidth of the antenna.

Coaxial-line feed, where the inner conductor of the coax is attached to the radiation patch while the outer conductor is connected to the ground plane, is also widely used. The coaxial probe feed is easy to fabricate and match, and it has low spurious radiation. However, it also has narrow bandwidth for thick substrate due to the presence of long feeding inductance.

Aperture coupling feed can overcome the cross-radiation problem which is commonly found in microstrip line and coaxial-line feeds. The aperture coupling consists of two substrates separated by a ground plane. On the bottom side of the lower substrate there is a microstrip feed line whose energy is coupled to the patch through a slot on the ground plane at the middle. The ground plane isolates the feed from the radiating element and minimizes interference of spurious radiation for pattern formation and polarization purity.

Proximity coupling feed has the largest bandwidth among these four feeding methods. However its fabrication is somewhat more difficult.

24

� - j - ^ ^ ^

(a) (b)

^ microstrip patch

^ 始 ^ ^ > a n t e n n a substrate

Z coupling aperture

^ ^ ^ ~ ground plane

^ ^ ^ ^ -少： feed substrate

^ ^ S w j ^ ^ microstrip feed line

(C) ^ ^ ^ ^ ^ ^ ^ Z microstrip patch

^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ antenna substrate

^^^^^^^^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ feed substrate

^^^：：^^^ ^ ^ ^ ground plane microstrip feed line

(d)

Figure 2-10 Four feeding methods (a) microstrip line feed; (b) coaxial-line feed; (c) aperture coupled feed; (d) proximity coupled feed

25

2.2.2.2 Fringing Effects

Because the dimensions of the patch are finite along the width and length, the fields at the edges of the patch undergo fringing. The amount of fringing is a function of the dimensions of the patch and the height of the substrate. For the principal E-plane, the fringing is the function of the ratio of the length of the patch L and the height h of the substrate {L/h) and the dielectric constant of the substrate. Since for microstrip antenna L/h » 1 , fringing is reduced. However, it must be taken into account because it influences the resonant frequency of the antenna.

As L/h » 1 and Sr » 1, the electric field lines mostly concentrate inside the substrate. Fringing in this case makes the microstrip line look wider electrically compared to its physical dimensions. Since some of the wave travel in the substrate and some in air, an effective dielectric constant Sre/ S introduced to account for fringing and wave propagation in the line.

The effective dielectric constant is a function of frequency. As the frequency of operation increases, most of the electric field lines concentrate in the substrate. Therefore, the microstrip line behaves more like a homogeneous line of one dielectric (only the substrate), and the effective dielectric constant approaches the value of the dielectric constant of the substrate.

W/h > 1，

〜+1广1「 叫-"2 ^ . . - — + — 1 + 1 2 - (2.25)

2.2.2.3 Effective Length and Effective Width

Because of the fringing effects, electrically the patch of the microstrip antenna looks greater than it physical. For the principal E-plane, this is demonstrated in Figure 2-11’ where the dimensions

26

of the patch along its length have been extended on each end by AL, which is the function of the effective dielectric constant e^^^and the width-to-height ratio {W/h).

“ 0 . 3 ( 5 +0.264�

¥ = 0 .412 { (2.26) ( ‘ , - 0 . 2 5 8 ( i + 0 .8

AL L AL ^ •

m m Figure 2-11 Effective length extension

Since the length of the patch has been extended by AL on each side, the effective length of the patch is now

l-eff =L + 2AL (2.27)

27

Ideally, the length of the patch L is depended on the resonant frequency,

/_ = • (2.28)

fr = 7 ^ (2.29)

By including the fringing effect, the actual length of the patch can now be determined by

L = --2AL (2.30) 2 r Vq r = 7 7 = (2.31)

^yl^reff

A practical width that leads to good radiation efficiencies is

M/ 1 2 Uo 2 W = . = — ^ (2 37)

where fr is the resonant frequency Xq is the guided wavelength in dielectric e, and v � i s the free-space velocity of light.

2.2.3 Polarization

Polarization of the electric field (E) is an important property of electromagnetic wave propagation, which is defined by the orientation of the E vector as it varies in time. In linearly polarized systems, the E vector is fixed in a plane containing the direction of propagation and is defined as vertically polarized when the E vector is orientated perpendicular to the ground. For

28

circular polarization, the trajectory of the tip of the E vector rotates about the propagation axis as a function of time.

A perfect circularly polarized wave is generated by an antenna that simultaneously excites two orthogonal E vectors {Ex and E^ of equal amplitude and with quadrature phase. The sense of polarization is given by the direction of the rotation of the E vector describing a circle for an observer looking in the direction of propagation (Figure 2-12).

z Propagation Direction

(c>v f 7 � � � “ (a)

z Propagation Direction

、、卞、JO� f (b) Figure 2-12 (a) Left-hand circular polarization; (b) right-hand circular polarization 29

For reference, polarization is defined from an observation point at the source looking in the direction of propagation in the +z axis. The sense of a circularly polarized wave is determined by the rotation direction of the E vector as it describes a circle; a right-hand circularly polarized (RHCP) signal is generated when the rotation is clockwise, and for a left-hand circularly polarized (LHCP) wave, the E vector rotates counterclockwise.

2.2.3.1 Axial Ratio

A practical antenna usually generates an imperfect circularly polarized wave; therefore, the E vector traces out an ellipse, instead of a circle, as shown in Figure 2-13. The ratio of the major to minor axes defined the Axial Ratio (AR) of the polarized wave [13], and it is equal to

^ „ major 3xis OA . . _ 尺二 ^ ^ ^ - = — , ^ < A R < ^ (2.33)

minor axis OB

For perfect CP wave propagation, where only one hand of polarization is generated, the AR should have the value of 1. In the extreme case where the magnitude of the RHCP and LHCP components are the same, the circle formed by the tip of the E vector degenerates into a line and the polarization becomes linear, and the AR becomes infinite. To provide maximum power transfer in the wireless system, the two antennas should be polarization-matched and their tilt angles aligned. The orientation of the ellipse is given by the tilt angle of the major axis of the ellipse relative to the axis (i//) as shown in Figure 2-13.

30

Major A x i s ^ " ^ ^

Figure 2-13 Elliptical polarization

2.2.3.2 Formation of CP wave

As mentioned previously, CP is harder to achieve than LP, and CP antennas are generally more complex. There are two general methods to produce CP radiation.

Type I CP antennas are those antennas that produce CP by virtue of their unique physical structure. Helix and spiral antennas are examples and the sense of polarization rotation is determined by the sense of the windings of the helix and the spiral.

Type II CP antenna usually uses two LP and orthogonal waves with phase quadrature feeding to generate CP. This can be accomplished by adjusting the physical dimensions of the patch and using either single, or dual feeds. Simple single-band CP patch antennas may be constructed by feeding the adjacent sides of a square patch with signal of equal magnitude and quadrature phase difference using power splitter or hybrid coupler (Figure 2-14).

31

Power splitter with ^ ^ Hybrid coupler ^ ^ quarter-wavelength difference between output ports

(a) (b)

Figure 2-14 Different arrangements for generating CP waves

In the case of the patch fed by a normal power splitter, the two feed ports are not isolated; the reflected power from one feed port will transmit to the other port and result in radiation of opposite hand of polarization, so good AR performance cannot be achieved. Hybrid coupler can give isolation between the two feed ports, since it is designed so that power reflected from a mismatched antenna on one port is transferred to the absorbing load. Therefore, this isolated feeding geometry is preferable because it allows only the wanted hand of radiation.

32

Chapter 3

Review of Conventional Dual-band Filter Designs

Researchers have put much effort in dual-band filter design in planar form. Some of the published works are shown here with different circuit topologies or implementation technologies for comparison,

3.1 Bandstop I bandpass Filters in a Cascade Connection

A synthesizing method is presented in [14] which designs and implements digital dual-band filters in microwave frequency range. A dual-band filter consists of a bandstop filter and wide-band bandpass filter in a cascade connection, wherein filters are expressed in the Z domain. A prototype has been built with short-circuited stubs in bandpass filter and lowpass parallel-coupled lines in band-stop filter in [14] and has close agreement between theoretical values and experimental results.

Figure 3-1 Block diagram showing bandpass and bandstop filters in cascade connection 33

Bandpass filter Bandstop filter

Figure 3-2 Photo of the fabricated dual-band filter proposed by Tsai et al

The bandwidth of each passband is controllable by changing both the bandwidth of the bandpass filter and the center frequency of the bandstop filter. Nonetheless, by using this approach, the circuit size is increased substantially (Figure 3-2), which will lead to higher cost as well.

3.2 Stepped Impedance Resonator

Hairpin resonators used in cross-coupled filter can offer high compactness which is highly desirable in modem wireless systems. The hairpin resonator can be treated as a Stepped Impedance Resonator (SIR) in analysis.

Compact miniaturized hairpin resonators have been used as the building block of a planar filter with a dual-band elliptic function response [15]. In order to establish appropriate couplings among the resonators at the two center frequencies, the resonators have to be designed to have different geometric dimensions (Figure 3-4). To analyze stepped impedance resonator, it may be considered as a cascade of three transmission line sections with open-circuited end (Figure 3-3).

34

、 ， ） . r " � - ‘ u ‘ * * j-；：：；：--：'

：：

" j � ‘

I ' . . " :【 : : :：：

Figure 3-3 Basic structure of SIR

1 3 CJ I I j w n 1 1 m ^

Figure 3-4 Circuit layout of dual-band cross-coupled filter In order to achieve dual frequencies performance, couplings between resonators are adjusted

so as to obtain same element values (g t) and admittance inverters ( / � ) o f low-pass prototype filter for both operating frequencies. As some of the couplings have to be very strong in this design, it will increase the difficulty in realizing the filter.

35

Dual-band SIR can also be used in coupled filter structure. The dual-band filter is realized by cascaded connection of resonators with appropriate coupling [16] [17]. By making use of SIR, the spurious response of the filter can be controlled, that means the filter can have high out-of-band suppression. However, high insertion loss appeared due to the inter-stage coupling loss. To achieve the required coupling strength, the spacings of the parallel coupling have to be reduced to allow more power to be coupled to the next stage. In practice, there are limitations in fabrication. Furthermore, it may be difficult to maintain the same coupling coefficient for two widely separated frequency bands, and hence to control bandwidth and passband flatness.

i n r ^ ^ p ir 1 f 11 j j u ^ ~ — a-" eljJ L_

Figure 3-5 Dual-band SIR filter

3.3 Tunable Transmission Zero for Spurious Responses Suppression

As the frequency bands become narrower, there is increasing demand for higher selectivity and higher rejection level which implies the use of high Q resonator and high-order filter. By adding transmission zero in dual-band filter response, high out-of-band suppression can be obtained [18]. A dual-band filter has been purposed, which has two passbands at desired frequencies and can generate two transmission zeros at any desired frequencies. The location of

36

transmission zeros can be tuned independently by incorporating special input/output ports (Figure 3-7) and does not affect the passband performance of the dual-band filter. The out-of-band suppression is excellent with more that 120dB where the transmission zero located (Figure 3-6). However, this design can only offer narrow bandwidth with limited control.

^ 1 1 - 2 0 - j

-140 一 I I I I I I I I I I I I I I [‘ M I i I M I I I M I I I 1 I I I

1 2 3 4 5 6 7 frequency (GHz)

Figure 3-6 Insertion loss of the dual-band filter proposed by Ma et al ( ~ with transmission zeros; --- without transmission zero)

37

J r - i L ^ Figure 3-7 Dual-band SIR filter with tunable transmission zeros

3.4 Comparison

After going through three different types of dual-band filter, they all have satisfactory performance in certain aspects. Some of the key factors are listed in Table 3-1.

Filter Advantages Drawbacks

Bandstop / bandpass filters - Passbands with different - Large in size in a cascade connection bandwidths Filter with SIR - High out-of-band suppression - High insertion loss

-Some of the coupling coefficient may not be realizable

Filter with tunable -Transmission zero can be - Narrow bandwidth transmission zero tuned independently without

affecting the passband

-Spurious suppression

Table 3-1 Comparison between dual-band filters

38

Chapter 4

Novel Dual-band Filter Design with Equal Bandwidth

4.1 Introduction

In chapter 2，the design of a generalized single-band filter has been formulated by using resonators and •/-inverter. This approach can be extended to the development of a dual-band filter as well. In this section, dual-band resonator and dual-band /-inverter are proposed with closed-form design equations. Based on these two building blocks, a planar and low-loss dual-band filter can be realized by using the classical synthesis procedure.

4.2 Frequency Behavior of Shunt Stubs

The frequency behavior of shunt stubs (open-circuited or short-circuited) will be first revised as they are the building blocks of dual-band resonator

Let Zb be the characteristic impedance of a lossless transmission line and I be its length. If the transmission line is terminated in a short circuit, the input impedance is

f I \ Z s c = j Z B t a n a ) l (4.1) V ^ B )

where co is the angular frequency and Vb is the phase velocity of propagating wave. And its admittance is given by the following equation.

f I \ ^sc = -JYb cot CO丄 (4.2)

V Vb J

39

Similarly, the input impedance and admittance of an open-circuited transmission line are

f I \ Zoc=-jZACOt c o - ^ (4.3)

V ^ A

( I \ Yoc=jYAtan CO丄 (4.4)

V ^ A j

'�� i i 1 咖

x

(a) (b)

Figure 4-1 Input admittances of (a) open-circuited stub; (b) short-circuited stub

Figure 4-2 shows that susceptance has an infinite number of poles and zeros at frequencies at which the length of the line is an odd or even number of quarter wavelengths. Also, the location of pole and zero appeared alternatively between open-circuited stub and short-circuited stub. In the next session, the resonator will make use of this nature to achieve dual-band performance.

40

� J \ \ z ” y

4 / . 4 / , (a)

2/b Ib

(b)

Figure 4-2 Frequency behavior of (a) open-circuited and (b) short-circuited shunt stubs

41

4.3 Dual-band Resonator with Paralleled Stubs

By connecting a short-circuited stub and an open-circuited stub together, two resonances {fi&力）

are created with appropriate choice of line impedance and length (Z丄 Zb, Ia and Ig), as illustrated in Figure 4-3. In addition, transmission zeros are found in between the two resonant frequencies and above力，which can help to increase rejection level.

j\ j\ [ 4 �

广 � 1 1 4 / . 2/e

� W

Figure 4-3 Proposed dual-band resonator: (a) Frequency behavior, and (b) its structure

42

Suppose the two shunt stubs are chosen to have an electrical length of 90° {6a = 办 = t t /2)

evaluated at/m, where

平 (4.5)

^ = = (4.6) 4 / . 41b “

By using equations (4.2) and (4.4), the input admittance of the proposed structure can be written

as:

丄 （4-7)

UmJ

At resonance (7/„ = 0)，we have

� Y丨n (fi ) = JY, f f ] - J = 0

[ ^ f J < ” “ � = y v “ { f y - ( 4 . 9 )

In filter design, the susceptance slope parameter b is another important factor (bandwidth

control) where [11]:

, cOo dB b = (4.10) 2 cf 〜，

43

where B is the susceptance of the input admittance of the resonator. For a LC tank circuit, we

have

B = c o C - — (4.11) coL

= (4.12) P (OqL

⑴。二去 （4.13)

As the two passbands are equal, the slope parameters at the two resonant frequencies (/} and/：)

can be written as follows:

) r / - \ r f r \ 1 、，fp TT 2 冗 h . w ' 2 ^ 2 ^ ' 2 u

汽 r 制 + 口 c - b d , � （4.15) L

44

(4.8), (4.9), (4.14) and (4.15) can be represented as:

/ \ / \ r � � c sj - Vsc 如{營 = 0 (4.16)

/ \ / \ -Yoc ^ot]^^ £j + Vsc _[^營 = 0 (4.17)

"N y r ^ / \ 兀 /

2 ^oc f - ^J + ^ C f - ^ h e c ' l ^ ^ S j = b p (4.18)

y 「 冗 / \ 几 / \-|

、 2 ^ o c f + ^J + ^ C f + [j^J =bp (4.19)

where

尸 2 - 尸 1 " = 7 7 7 (4.20) '2 十'1

The impedance values, Z^ and Zb, can be obtained by solving the above simultaneous equations to give:

/ \ -7 71 2 ^

刊 (4.21)

/ \ -7 冗 2 ^ 1 I r j (4.22)

45

According to classical filter theory (single-band), bp can be expressed in terms of filter coefficients and bandwidth as:

bp = 0)0�

= c o , _ ^ — ^ F B W ' ( D o - Z q (4.23)

9k ~ F B W - Z q

where FBW'is the filter bandwidth.

Finally, the design equations of the dual-band resonator may be rewritten as:

= i r j (4.24)

(4.25)

where

Ck = �( 严 w (4.26) Mfu -kVo

； , . K l 2 @ f M I •

— ^ 三 &

y wm

Figure 4-4 Proposed dual-band resonator and its equivalent 46

4.4 Dual-band Admittance Inverter

As discussed in the previous section, a quarter-wavelength transmission line is often used as admittance inverter in filter design. However, this element is only suitable for single band operation. Figure 4-5 shows the structure of a dual-band admittance inverter [19] which consists of a transmission line section with an electrical length of 6m and characteristic impedance of Za, and a pair of open-circuited shunt stubs (JY).

Zc，9m

• ~ _ I I � ~ l ~ n = • • — " 1 — •

气 一 /

單 •

Figure 4-5 Proposed structure of the dual-band quarter-wavelength branch-line and its equivalent

By applying matrix formulation, the ABCD - parameters of the proposed structure (Figure 4-5) can be derived as

“ 1 O i r cose jZcSinOJ 1 O l y y 1 j V c s i n e cose j y i (斗之乃

— �L- � —II—*' _

which leads to

cos O-Z^y sin 6 jZ�sin 6 ]

yYc sinOi^-ZcY^ +2ZcYco�) cosO-Z^Ysino] (4.28)

47

Moreover, the above expression can be further reduced to

_ 0, 厂c • "叫 � 0 " J " ! y — i - 0 = J J 0 (4.29)

_ Zc sine L" u �

by making

1 Zc sinO = — (4.30)

%J

、/ cote

� = (4.31)

Equation (4.29) implies that the proposed structure is equivalent to a section of transmission line with characteristic impedance of lU and electrical length of n 12. Accordingly, for dual-band operation, the necessary conditions can be simply stated as

1 Zc sine, = - (4.32)

u

1 Zc sinO^ = - (4.33)

where 6i and 62 are electrical lengths of the branch-line evaluated at the lower (/}) and upper (/}) frequencies. The general solution of (4.32) and (4.33) can be expressed as

02 = n 7 r - 0 ^ (4.34) where n=\,2, 3, ... With the fact that

v r r , (4.35) 102

We get

(4.36)

+ (4.37)

f2—fi ^ = 7—7 (4.38)

' 2 + 厂，

The electrical length (Om) of the transmission-line section evaluated at the mid-frequency may, therefore, be determined as

〜 = 乎 = 〒 (4.39)

By substituting (4.36) and (4.37) into (4.30) and (4.31), we have

, f riTT ] (4.40) J cos ——£ ^ ‘

I 2 J r (nn \

tan ——£

^ / = / / < ,c (4.41)

f nn 1 tan ——£

- f = f2

f o r n = 1，3，5，…，and

102

Jsini'-^s] (4.42) I 2 )

r (nn: \ cot ——s f = f ,

y= J c (4.43) (nTt \ cot ——e V )’ f = f2

for « = 2, 4, 6 , . . .

The results indicate that there exist multiple solutions, which include the choice of n and the different ways in realizing the shunt element with its input admittance (Y), as defined by (4.41) and (4.43). For compact design, the topology with « = 1 is considered which results in quarter-wavelength structure.

By setting 6m = ；r/2，equations (4.36) and (4.37) can be reduced to:

Z c = — ^ “ 4 J cos —E ^ ‘‘ U J ^ / \

= = (4.45)

Finally, the shunt element may be implemented using a quarter-wavelength open-circuited stub (Zd) with input admittance given by:

102

- / \ r K cot —€

— ， / = / /

Voc= < ] � (4.46) f TT ]

cot —€

^ ， f = f2

Consequently, by combining (4.45) and (4.46), we obtain

Z - 1 , \ 1 (4.47)

J sin —£ tan —s U ) U J

Zc, mi @fM

• j H I I •

Zd, mimM I , Z o , 7r/2@fM

Figure 4-6 Proposed dual-band admittance inverter

4.5 Dual-band Filter Realization

For a bandpass filter with desired bandwidth and attenuation response, a ladder circuit with lumped-elements can be obtained by using corresponding normalized element values gx [H].

102

Without loss of generality, a 3'* -order filter design is chosen here for illustration. A dual-band design is obtained using the proposed resonator and admittance inverter to replace the lumped-elements in the basic circuit (Figure 4-7). s s s

(a)

r Za’[ 1 ZA_ i | z d Z o l i l i I z o Z o | I I z a lyiy； Z B | KB' Izb

m ^ mmm — • • _ _ (b)

Figure 4-7 Filter design (3)3"* order bandpass filter prototype; (b) with dual-band inverters and resonators

For compact layout, the quarter-wavelength open-circuited stubs associated with the resonator and inverter are merged into a single design with line impedance given by (Figure 4-8)，

(4.48)

102

z. j ^ Z 丨n ^

Zr, Till Zj , nil Z s , nil

Figure 4-8 Simplification of a pair of shunt stubs

Therefore, the final circuit layout is presented as in Figure 4-9.

！ 丄 r二 I I Zb I Z / I z ^

mm mm wm

nil @fM

Figure 4-9 Proposed structure of dual-band filter

102

4.5.1 Simulation Examples

In this session, three simulation examples with different frequency ratios {f2/fi) are presented. In practice, filter implementation is also constrained by the range of impedance that can be realized using a given fabrication technology.

4.5.1.1 Design 1 (S'^^-order Butterworth, fi = 0.9 GHz, = 2 GHz, BW = 630 MHz) A lowpass prototype with 3' ''-order Butterworth response is chosen, the element values are

go= 1 gi = 1 g2 = 2 g3= 1 g4= 1

According to the equations (4.24)，(4.25), (4.44) and (4.47), the design parameters are:

、 … 誉 ” … z a — � . ^ ~ ~ T ^ ~ n ^ � … " ^ r i i u d加、々？… I I

0.3793 108.1 a 49.9 a 54.1 Q. 24.9 a

^ ^ ^ ^ ^ ^ 60.45 1 3 0 . 9 a 0 . 0 2 0 . 0 2

Table 4-1 Filter parameters of Design 1 And by using (4.48), the impedance values of the merged open-circuited stubs are listed as in

Table 4-2.

”.、乂a�w，：〜、“、 - 、

Impedance (H) 29.69 59.39

Table 4-2 Impedance values of Design 1 102

Circuit simulation is carried out using Advanced Design System (ADS) from 0.1 to 3 GHz. Figure 4-10 shows the computed performance of the filter. Note that there are three transmission zeros (DC,/w and I/m) introduced by the two shunt stubs (open-circuited and short-circuited) to enhance stopband rejection.

A / \ f I

， - I I II' S -2�— — — CD TJ

I I ""“~1 ~I~I~I1~I~j—1~I~r—1~pi~II~II1—1~II~m~r~ 0.0 0.5 1.0 1.5 2.0 2.5 3.0

freq, GHz r ^ freq=669.0MHz m1 m2 m3 m4 dB(S(2.1))=-3.Q2：^ On ^ ― T — — ： y — T m2 10� / i i / \ freq=1.038GHz • 7 i"\ I——7 \ dB(S(2,1))=-3.028| p 20� / i \ i / \

^ I 备 - 7 ' V \ j \ 男-3。: T 1 \ I j \

m4 -40- i \ . i . . . . . . . / ....../ freq=2.231GHz - \ i j dB(S(2,1))=-3.Q23| -so |…丨丨，丨丨，|…丨丨丨“ V

0.0 0.5 1.0 1.5 2.0 2.5 3.0

freq, GHz

Figure 4-10 ADS simulation results: Design 1

102

4.5.1.2 Design 2 (3'^-order Butterworth, fi = 0.9 GHz, fz = 2.4 GHz, BW = 630 MHz)

In this design, they}//} ratio is slightly increased and the design parameters changed accordingly (Table 4-3).

e Za ZB ZA' ZB'

0.4545 69.9 Q 52.5 Q 34.9 H 26.3 ^ ‘ c Zc S ^ Zs

-

^ ^ 66.2 a 88.1 n 19.49 38.99

Table 4-3 Filter parameters of Design 2

It can be seen that, all impedance values are realizable using microstrip with impedance level ranged between 20 and 90 The simulated results are given in Figure 4-11.

102

t T ^ ^ ^ \ \ ！ - - /

x— i

i - 2 � - ： 1 j CQ 1 ！ -a

i ‘

_40 II~I~I~II~Ii' I~~I~rn~r-j~i~i~i~i[—iii 丨丨 l|~rn”i—r— 0.0 0.5 1.0 1.5 2.0 2.5 3.0

m _ ’ GHZ freq=672.0MHz m1 m2 m3 m4 dB(S(2,1))=-3.013 0-1 J Y J ^ ^ 1 0 � / \ I \ freq=1.045GHz / \ / \ dB(S(2,1))=-3.0Q9|g _2o: / \ i / \ r ^ I 结 - / \ I \ freq=2.255GHz 忌 _3。— / \ ! dB(S(2,1))=-3.009|^ _ / \ m4 -40- \ I / freq=2.628GHz - I \ I / dB(S(2,1))=-3.013| -50 I I I I I I I I I I I I I J I I I I I , , , , I , , , ,

0.0 0.5 1.0 1.5 2.0 2.5 3.0

freq, GHz

Figure 4-11 ADS simulation results: Design 2

102

4.5.1.3 Design 3 (S' -order Chebyshev, fi = 0.9 GHz, fz = 2.4 GHz, BW = 630 MHz)

3rd-order Chebyshev response with 0,5dB ripple is chosen with the following element values:

go= 1 g, = 1.5963 g2= 1.0967 g3 = 1.5963 g4= 1 The impedance values calculated by (4.24), (4.25), (4.44) and (4.47) are listed in Table 4-4.

,J二 � � " 7 " ! ^ ^ ^ ^ … � C 么 , 命 水 、 � 0.4545 43.8 n 32.9 Q 63.8 Q 47.9 Q

^ — 66.2 88.1 n 26.05 29.26

Table 4-4 Filter parameters of Design 3

102

The simulation results indicate that there are ripple in the two passbands and three distinct poles (return loss), as expected for a Chebyshev response.

r -N 7 — n

I I� - i ！

一 1 ‘

5 A A) g - 2 � - in /I'll!

I \ • i

尝 I ; _40 1 ~I~1~I~I I I 1~1I~rnI~[—1~IH~I I I~n—

0.0 0,5 1.0 1.5 2.0 2.5 3.0 freq, GHz

m1 freq=6630MHz ^ _ m l m2 m3 m4 dB(S(2,1))=-2.98^ ^ I 7 • T •： • 1 f req=1.056GHz 卜- J \ I I \ dB(S(2,1))=-2.970^ / \ / ！ \

I 敎 - \ / \

dB(S(2 ^ = - 2 . 9 7 0 f f . I T j \ m4 I / -40-......L I \ / I freq=2.637GHz / \ / dB(S(2,1))=-2.982|/ -50 | …丨 j i…丨丨丨丨）丨丨，i (丨丨丨，丨丨丨…

/ 0.0 0.5 1.0 1.5 2.0 2.5 3.0

I freq, GHz 0 " 1 1 ；

1 丨 - i

泛 _ 2 _ i C i - I CO 一 —……———i——……I 石-3 - "T•““………—t ——…厂 “‘'."."'"1 XJ

• 丨 丨 i ！ i i i

C I i I i -5 1 I I I I i_ I I I I 丨I I I I j I I I I I I 丨‘I I I I 丨I I I

0.0 0.5 1.0 1.5 2.0 2.5 3.0 freq, GHz

Figure 4-12 ADS simulation results: Design 3 102

4.5.2 Comparison of Simulation results

It is well-known that, the performance of filter may vary when the effect of junction, open-end, short-end and substrate loss are taken into account. To illustrate these, the frequency responses of a three-pole dual-band filter (Design 1) have been simulated by using ADS (with and without discontinuity effects) and IE3D platforms.

Figure 4-13 shows the schematic of the ideal filter based upon ideal transmission line elements with line impedance obtained from Table 4-1 and Table 4-2.

X TLIN X 几丨N I TUN |TL6 [ | T L 7 plTLS

認⑶m Z二 Ohm | gg^ | S-PARAMETERs"| 丫 F=fO _ 丁 F=fO _ • ^tZ

^ I “ 1 I SP\ TUN TUN Start=0.1 GHz

丁erm TL1 TL2 j t ^ Term stop=3 GHz < Term1 Z=Za Ohm i Z=Za Ohm C Term2 step=1 MHz > NumF=1 rn e=90 门 e=90 f i S NurTF2

2=50 Ohm F=fOHz F=fO Hz ] 2=50 Ohm - T T T J _ TUN TUN TUN J _ = TL3 TL4 TL5 =

Z=Z1 Ohm Z=23 Ohm Z=Z1 Ohm E=90 E=90 E=90 F=fO F=fO F=fO m VAR E l VAR E l VAR ra VAR

VAR4 VAR8 VAR6 VAR1 Z1=59.2 Z3=29.6 Za=60.45 f1=0.9G VAR VAR 12=2.0 G VAR5 VAR9 f0=(f1+f2)/2 Z2=49.9 Z4=24.9

Figure 4-13 ADS schematic diagram for ideal simulation

In Figure 4-14，discontinuity effect and substrate information have been included in the simulation using the library models provided by ADS.

102

USS S-PARAMETERS \ • I • ^ MLSC ^ MLSC ^ MLSC S Raram r^ TL14 rh TL15 rh TL16 Sn MCROSO Subst="MSut|)tROSO Subst="MSubfOiCTOSO Subst="MSubr' Start=0.1 GHz cros3 LJ V\W2 mm cros1 LJ \AA=W4 mm cros2 LJ W=VV2 mm

Stop=3 GHz Subst="MSub1" l-=L2 mm Subst="MSub1 L=L4 mm Subst="MSub1 L=L2 mm Step=10 MHz VV1 =WStd mm W1 =V\fei rm W1 =Wa mm

W2=VV2 mm W2=W4 mm VV2=W2 mm W3=\Afe mm W3=Wa mm W3=Wstd mm W4=W1 mm I I . m=W3 nTirJ"h W4=W1

MLIN LfJ MLIN LtT MLIN i-f MLIN 本，T^rm TL17 TL9 TL10 TL18 X ' errn ^ Subst="MSub1" Subst=”MSubr Subst="MSub1" Subst="MSub1" < Term2 5 : � r n i W=VVstdmm V\A=Wa nnm W=W&mm W=VVtetd mm > < mm r ^ L=La mm i-*! L=Lannm L=Lstd mm L � Z = 5 0 0hm

Mia； M1..0C Mi..OC J -i TL11 TL12 TL13 ~ 一 Subst="MSub1" Subst="MSub1" Subst="MSub1"

W=W1 mm V\ W3 rrni W=W1 mm L=L1 mm L=L3 mm L=L1 mm

MSub I 1 E]VAR 03VAR E]VAR EJVAR MSUB ^ ^ VAR1 VAR4 ^ ^ VAR6 VAR13 MSubl f 1=0.9 GHz W1 =1.08081 {o} W3=3.62696 {o} 輪=1.96184 {o} H=0.813nrm 固 VAR 固 VAR 固 VAR m VAR Er=3.38 VAR2 VAR5 VAR10 VAR14 Mur=1 f2=2 GHz U =31.8846 {o} 13=29.7596 {o} La=30.0919 {o} Cond=1.0E+50 VAR VAR VJ VAR Ppi VAR Hu=1.0e+033mm VAR3 VAR8 ^ VAR15 T=10 um f0=(f1+f2)/2 W2=1.98194 {o} W4=5.9624 {o} Wstcl=l .81044 {o} TanD=0.002 旧 V A R V A R [ | n V A R Rough=35 um VAR9 ^ ^ VAR12 VAR16

L2=31.988 {0} 14=30.9235 {0} Lstd=5.30044 {o}

Figure 4-14 ADS schematic diagram for simulation with junction effect

Finally, Zeland's IE3D (EM simulator) was used to obtain the response of the filter in a 3D structure (Figure 4-15).

102

• B h i m h m^^^U L

Figure 4-15IE3D layout diagram for EM simulation

In the ideal case, the 3 poles are clearly shown in both upper and lower passbands (Figure 4-16). However, with the inclusion of junction effects, the locations of the poles are slightly shifted and only two distinct poles are seen within the upper passband. Lastly, the results obtained by IE3D and ADS are found to be similar (Figure 4-17).

102

i i i l ‘ 4 � 1 1

- 5 0 1 -60 I I -——ADS (ideal) " • "ADS (with junction effect)

-70 l：： ! on I I HII 1 liU I 0.5 1 1.5 2 2.5 3

Frequency (GHz) Figure 4-16 Return loss (comparison between simulations) i i i l -80 [ - \ ——ADS (ideal)

1 I ^ A D S (with junction effect) „„ 1 I -^IE3D -90

•1。％ 0.5 1 1.5 2 2.5 3

Frequency (GHz)

Figure 4-17 Insertion loss (comparison between simulations) 63

4.5.3 Experimental Results

For experimental demonstration, a three-pole dual-band filter (Design 1) is designed, fabricated and characterized. The specifications of the filter under consideration are:

Center frequencies f, &力： 900 MHz and 2 GHz

Bandwidth: 630 MHz

Type: Butterworth filter

Order of the filter: n = 3

Source / load impedance: 50 Q

The impedance values are listed in Table 4-2. The physical dimensions of the microstrip filter are summarized in Table 4-5. The photograph of the fabricated filter with structural parameters is shown in Figure 4-18.

Substrate information

Type: Duriod R04003C

Dielectric constant ⑷： 3.38

Tangent loss (tan S): 0.002

Thickness: 0.813 mm

102

% F t U i I Ui

1.96 mm 31.99 mm 1.98 mm 31.88 mm 1.08 mm / Lj r Ls2 WS2 LO2 WO2

A -- - -I

30.09 m m 3 0 . 9 2 mm 5.96 mm 29.76 mm 3.63 mm

Table 4-5 Physical dimension of dual-band microstrip filter

RF measurements are conducted using Agilent E5071A Network Analyzer over the frequency range from 0.1 GHz to 3 GHz

For comparison purposes, Figure 4-19 and Figure 4-20 show the simulated (IE3D) and measured performance. The center frequencies of the two pass-bands are found to be 860 MHz and 1910 MHz. Insertion loss of 0.3 dB and 0.6 dB are observed at the lower and upper pass-band respectively. It has a measured 3dB bandwidths of 420 MHz (lower band) and 340 MHz (upper band). Also, stop-band attenuation (/m) of over 60 dB is achieved at 1.45 GHz.

102

E H MK •- : 、 通

(a)

Wsi— — VVs2- — W s i — —

I 11 I: I

Wol— — Wo2-^ — W o i — —

(b)

Figure 4-18 (a) Fabricated filter (b) its dimension 66

. , R : R F 1 —y—y— L………眷………—if

-40 - I \ • IE3D I

I Measured I caI I 1 1 i 1 - � � 0 0.5 1 1.5 2 2.5 3

Frequency (GHz)

Figure 4-19 Return loss (simulated and measured)

_

• IE3D �

Measured -801 1 1 1 1 1 0 0.5 1 1.5 2 2.5 3

Frequency (GHz) Figure 4-20 Insertion loss (simulated and measured)

102

Q�

Z ~ I — 旧 3D

, 一一〜〜 Measured I

rj I I I I I I 1_il 0.6 0.7 0.8 0.9 1.0 1.1

Frequency (GHz)

(a)

o �

I — I E 3 D Measured

_ -5 I__I 1 I LJ \ 1.7 1.8 1.9 2 2.1 2.2

Frequency (GHz)

(b)

Figure 4-21 Insertion loss (a) lower and (b) upper pass-band 68

Table 4-6 summarized all the simulated and experimental results. The schematic simulation is performed by ADS with discontinuity models such as cross junction and substrate effect.

K ：/ 、：嚇fef�::�I , > : , � a d s � " � • : � ^ I E 3 D Measured result~~ ； . ' V v： / '二 :: -.、、’、…\ -

^ 多、乂、\ w. X 、、脅 I 、 、、：、々、’、<‘、

/ � ‘ ，"A/“ (Schematic � (Layout Simulation) 、：镇舊口、： S i n m l a t i o n ) ,

、、一,、，^^ - 、 丨 Return loss 0 .78- 1.07 GHz 0 .77- 1.03 GHz 0.75-1.01 GHz (S,i<-20dB) 1.88-2.11 GHz 1.83 —2.04GHz 1.81-2.00 GHz Lower pass-band 0.11 dB 0.69 dB 0.26 dB

ripple Lower pass-band 0.68-1.13 GHz 0 .68- 1.09 GHz 0 .65- 1.07 G H z ^ bandwidth (3-dB) (450 MHz) (410 MHz) (420 MHz)

Upper pass-band 0.23 dB 0.91 dB 0.61 dB ripple

Upper pass-band 1.82-2.20 GHz 1.79-2.15 GHz 1.74-2.08 GHz bandwidth (3-dB) (380 MHz) (360 MHz) (340 MHz)

Table 4-6 Simulated and experimental results

102

Chapter 5

Novel Dual-band Filter Design with Unequal Bandwidth

5.1 Introduction

By using the newly dual-band resonator and inverter developed in the previous chapter, a dual-band filter with equal bandwidth has been constructed. For filter design with unequal bandwidths, (lower and upper bands), another new design of dual-band resonator is proposed. This structure can also help to suppress undesirable spurious within the stopband.

5.2 Dual-band Resonator using Step-Impedance Line

A resonator is characterized by its resonant frequency and slope parameter. Therefore, a resonator with controllable dual-band characteristics should fulfill at least four criteria. The dual-band resonator shown in Figure 5-1, which consists of a quarter-wavelength short-circuited stub and a step-impedance line, should satisfy the following conditions:

8 ( O = B ( f J = 0 (5.1) 尸 1 dB Uf \ 〜 = 晰 ） (3.2)

fi dB ( � 化 = 广 ( 2 ) (5.3)

102

• Z …

j B ( f ) • T I I 。 = 毕

Figure 5-1 Proposed structure of the dual-band resonator

The input impedance and admittance of the short-circuited stub is given by

f ^ f \ (5.4)

w (^ f ySO cot -— (5.5)

J

For the step-impedance line, the input impedance is determined as

( n Zoc = Z 肩 7 j-T (5.6)

Z a + J Z … � x t a n a — V 'm

1\

where

f f] cot a— (5.7)

V 'm

By combining (5.6) and (5.7), we have,

f o , n o (5.8) tan a— -Kcot a —

� J � >

Za, a Ic'Za, a

Zoc Zinl

Figure 5-2 Step-impedance section (open-circuited)

Subsequently, the total input susceptance of the proposed structure is given by

_ = 一 Yb cot Yf r n � ) f f � ,5 tan\a^\-kcot\aL] (5.9)

102

At resonance, we have

r B(fi) = —Yb cot[i - i l - , � + � � = 0 �2fM) f A , f O (5.10) � M 夕 tan a-——kcot a —

V 'm J V 'MJ

I B { f , ) = - y , J - , Y � ( i + ' ) , � = 0 � 2 f … f 2 ] , f f 2 ] (5.11) � M 乂 tan a—~ 一kcot a —

\ ^M ) \ ^M ,

With the following identities,

a ^ = a { ^ - £ ) (5.12) 'M

a ^ = a(^ + £) (5.13) 'm

f 2 - f l (5.14)

Expression (5.10) and (5.11) can be simplified as.

r 二 + ; i “ ) = o (5.13)

By combining (5.15) and (5.16)，the value of k can be derived as

k = tan a{l - e)tan a{l + (5.17)

102

In addition, the slope parameter b is defined by,

fi^o dB ^ = (5.18) 2 do)⑴，

where B is the susceptance of the input admittance of the resonator.

From (5.15) to (5.18), one can obtain

/ \

B(fi) = B(f2) = -Ye tany^ ej + Y^ cot 2ae (5.19)

響 = Y b + y , df f=fi 2fM \2 ； fM sm2aM[1-£)-sm2aM£

碰 = Y b ^ s e A ^ X y , ^ . — • 产 从 )

df f=f^ V2 J fM sin2aM[1 + £)-sin2aM£ •

5.3 Dual-band Admittance Inverter

Figure 5-3 shows the proposed dual-band admittance inverter which composes of a quarter-wavelength transmission line (characteristic impedance, Zc) and a pair of shunt element (JY). It functions as an admittance inverter with coefficient, J, and operates at two distinct frequency values {fi and fi) with the following design equations,

J cosine] (5.22) U J

广 f \

< (5.23) -J-sin\^s , f = f 2

102

Zc, m i @fM

jY rt ,

mm mm

• •

J • •

Figure 5-3 Proposed dual-band admittance inverter and its equivalent

5.4 Dual-band Filter Realization

Figure 5-4 shows the configuration of the proposed dual-band filter based upon cascaded connection of /-inverter and shunt resonators. A direct-coupled topology is used in order to avoid the need of capacitive coupling (end- and edge-coupling) often encountered in filter design. And for reduced complexity, the first and the last admittance inverters were removed by simply making J=\IZo. It is also well known that the filter characteristics (e.g. pass-band ripple, bandwidth, etc) are defined by the proper choice of J-value and slope parameter of each resonator. By following the transformation steps shown in Figure 5-4, the shunt, Bk'(/), ( ^ 1 to n) can be expressed as

102

Suppose Ai and A2 are the bandwidths of the lower (/}) and upper {fi) frequency bands respectively. From the filter synthesis method mentioned before, the slope parameters of the k-th resonator can be expressed as:

〜 ⑴ = ， 寺 （ 5 2 8 )

2 do)似=如 1 A i Z Q

1 . u \ 0)2 dBk ( f ) CO. 9k = (5.29) L 2 d o ) 似 A 2 Zq

Consequently, the impedance values {Za and Zb), and the electrical length (a) of the A:-th resonator may be obtained by solving equations (5.19)，(5.20), (5.21), (5.24), (5.25), (5.26) and (5.27). In summary, for resonator k=2 to n-l, we have

A丨力

= p 尺

Z �一 k . g k 僅 (5.31)

1

Zo (5.32) Z a 2 2

102

B[n{f2) = B U f 2 ) + Y{f,) = Y{f,) (5.24)

B]{f,) = Bj{f,) + 2Y{f,) = 2Y{f,) (5.25)

B [ M = -y{ f2 ) (5.26)

B'j{f,) = -2Y{f,) (5.27)

- n — "pcp -p：—-piT 人 B, J � 馬 J , B, B„ Jo

^ ^ ―

(a)

J0^0 ~ 1 = 1 r . r ；

' 1 1 • I I I • I p=® 4 Y Y \ B,\Y Y i B„

• � z c L p z l p n : : Iznii (b)

• I • ^ • H p z p i ? B[ B[ B：

^ V i n : b z ! = q i (c)

Figure 5-4 (a) Basic topology; (b) with proposed inverter; (c) with proposed resonator

102

And resonator k = lorn

Q + B R2M+A = ( � ” (5 33) 尺丨⑷+/\ fj^

A , � , n

A = p 尺2(仅)+4 z 一 L r. (5.34)

八2 1

p l ^ c o t ^ . - c o s ^ s (5.35) Z片 2 2

where

A - —coseCKE (5.36) 2

B = -sec-e (5.37) 4 2

/ X a sin 2a R.(a) = 7——r (5.38) ) s i n 2 a { \ - e ) - s m 2 a £

r W � a sin 2a ^ … = 7——X (5.39) sin 2 a (1 + e j -s in las

P = co\{2as) (5.40)

The schematic diagram of the filter is illustrated as in Figure 5-5. Figure 5-6 shows the

procedure to compute the impedance values in the filter structure,

102

ki-Z3, a J _k2.Z5，a2 | k , -Z3 , a,

Z3, ai • | Z s , a2 •Z3 , ai • ~ T — T — T — — • I Zi, nil I Zi, nil _

Z 2 , niim MLA, mi fc, mi — —

• • •

Figure 5-5 Proposed dual-band filter structure

102

Filter specification 7

Filter type, operating / frequencies (fi & f2)’ / bandwidths (Ai &A2) /

1 91 . . . . 9 n

bl, ... bn i=1

Calculate Zc •

For i-th re^pnator,

Solve (5.30) or (5.33) for a

i=i+1

I

Calculate Za and Zb

No ^ ^ A l l r e s o n a t o r " \ ^

Yes

( F i n i s h )

Figure 5-6 Dual-band filter design: flow chart

102

5.4.1 Comparison of Simulation Results

For comparison purposes, the frequency responses of the following dual-band filter were obtained by using both ADS and IE3D platforms.

Center frequencies/； &/ : : 850 MHz and 1.95 GHz

Bandwidth J； &山： 250 MHz and 360 MHz

Type: Chebyshev filter (0.1 dB ripple)

Order of the filter: « = 3

Source / load impedance: 50 Q

Chebyshev response is chosen with the following element values: go= 1 gi = 1.0315 g2= 1.1474 g3= 1.0315 g4= 1

According to the procedure described in Figure 5-6, the line impedance of resonator can be found (Table 5-1):

. -Z , ； I h ^ z , z , • 、 好 。 .

61.3n ~ 2 8 . 0 Q 83.9 n 30.6 Q 54.9 Q

^ ^ ^ ^ ^ ^ ^ ^ ^ ^ 0.1524 0.2328 22.8° 27.3°

Table 5-1 Design values of the dual-band filter

102

In the first simulation filter design based upon ideal transmission line was employed (Figure

5-7).

T TUN T TLIN T TLIN S-PARAMETERS I r TLQ rhTLi3 rnTLi2 I Z=ZB Ohm Z=ZB_2 Ohm Z=ZB Ohm S Param proi ^ ^ I E=90 M E=90" M E=90 SP1 LlaJ ^^^ 丫 F=fO Hz 丫 F=fO Hz 丫 F=fO Hz Start=0.1 GHz f1 =�35 Q

TLIN TLIN f2=1:95G TL1 TL2 Step=1 MHz fO=(fUf2)/2 Z=Za Ohm Z=Za Ohm E=90 E=90

A Designed BW1 = 250 MHz ‘ ‘ . ‘ ‘ T| (M Designed BW2 = 360 MHz TLIN r ^ TLIN r ^ I l s ^ i _ Term j, o ti 4 ilo i _, Term raTermI z=MOhm Z=ZA 2 Ohm � _ = m ^ Temi2 > Num=1 E=alpha -r E=alp-ha_2 丁 > Num=2 Z=50 0hm F=fO Hz F=fO Hz F-fO Hz jj Z=50 Ohm

r i , TLIN A TUN “

门 ST 厂 TL8 |TL7 _ _ I Z=(ZA 2*k 2) Ohm Z=(ZA*k) Ohm 丄 - T f ( ， ) O h m 丁 E=alpha 2" 丁 E=alpha = i E=alpha 4 F=fOHz" i F=fO Hz

F=fO Hz • • 回 職 回 職 EJvar

VAR4 � VAR7 VAR11 山 VAR15 ^ VAR13 Z/^83.8829 ZB=28.0253 alpha=22.7923 k=0.1524 Za=61.3075 • VAR 岡 vm E l 二 „ 口 侧 VAR5 VAR6 VAR10 VAR14 ZA_2=54.9499 ZB_2=30.6254 alpha_2=27.3014 k_2=0.2328

Figure 5-7 ADS schematic diagram for ideal simulation

In the second simulation, schematic diagram of the same filter with models of discontinuity

effects were adopted (Figure 5-8).

102

mun mlin mum TL20 TL22 TL21 Subst="MSub1" Subst="MSubr Subst="MSub1" W=WB mm W=WB_2 mm W=WB mm I ^ I c PARAMETERS I

關 — 町 们 卿 一 MC細。 丄吐日關 1 ^ 1 SP站履花RS I 手 Cro8l � Cros3 � S_Param pri yp^ i Subst="MSub1" i Subst«"MSubr i SP1 VARI I Wl=Wstd mm f | mm Start=0.1 GHz fi=0 85 G W2=WB mm W2=WB mm Stop=6 GHz f2=l 95 G

I mm M W3=Wstd mm M Step-1 MHz f0=(f1+f2)/2 丁 W4=WAmm T W4.WAmm Chebychev Filter mun mlin mun mun O.ldB ripple TL25 TL23 TL24 TL26 Designed 8W1 = 260 MHz Subst="MSub1" Subst="MSub1" Subd="MSubr Subst="MSubr designed BW2 = 360 MHz mm W=\A/J mm W=V\ mm 伸V\«d mm L=Lsld mm n L-Lj mm fH L'Lj mm JTl L=Ldd mm

. Y V Y ^Torm 歸 Term |>1 MCROSO < Tenm2 Term1 > Cros2 > Num=2 二 Num=1 < mlin mun Subat="MSub1" ^ MUN 1 Z=50 Ohm " q 813 mm Z=50 0hm。」TL16 p i TUB f l W1=叫 mm f l TL27 M-J L 3 38 X Subst="MSub1" Subst="MSub1" W2=\A«_2 mm Subst="MSubr - i

— W=WA mm M W=WA„2 mm M W3=V^ mm M 伸WA mm 一 cond=1 OE+50 L=LA mm T L=LA_2 mm T W4=WA—2 mm T" L=LA mm hu=1 .Oe+033 mm MLOC rn MLOC rn j | MLOC T=10 urn 丁 L31 TL33 TL32 TanD=0.002 Subst="MSubr 1—1 Subst="MSubrJ I I Subst="MSub1" Rough=35 urn W=WAk mm W=WAk_2 mm VWAkmm U n VA f LAkmm ^ VAR L'LAkJZ VAR VAR ["LMmm 職 [WJ VAR VAR2 VAR3 VAR4 VAR5 VAR6 VAR7 WA=0.7117 WB=4.2826 WA一2=1.5998 WB一2=3.8079 州=1.3243 Wstd=1.8670 LA«8.5915 LB=31.6248 LA_2=9.9996 163=31.7834 Lj=30.6 Lstd=6 WAIo=11.1137 WAk.2=11.1052 LAI7.7228 LAk_2=9.2509

Figure 5-8 ADS schematic diagram for simulation with junction effect

Finally the physical layout of the dual-band filter in a 3D environment was simulated by using

IE3D (Figure 5-9).

ilWIBP Figure 5-9 IE3D layout diagram for EM simulation

83

All three simulation results agree well in terms of return loss and insertion loss performance (Figure 5-10 and Figure 5-11). Three distinct poles are seen in lower and upper passbands with similar 3-dB bandwidths and center frequencies.

—-40 w

-50

-60

_ __ — A D S ( i d ^ I -70 — A D S (with junction effect)‘ |~^IE3D on I 1 1 I I

-8�o 1 2 3 4 5 6 Frequency (GHz)

Figure 5-10 Return loss (comparison between simulations)

102

_ I ADS (ide^ | | 丨 I - ^ A D S (with junction effect). S _ - Ij I L^iii^p r F ••

-8�o ^ 2 i ^——L- ；

Frequency (GHz)

Figure 5-11 Insertion loss (comparison between simulations)

5.4.2 Experimental Results

For experimental demonstration, the proposed dual-band filter is designed with the previous listed specifications. And the physical dimensions (in mm) of the microstrip filter are listed in Table 5-2. The photograph of the fabricated filter and structural details are shown in Figure 5-12.

Substrate information Type: Duriod R04003C

Dielectric constant ⑷： 3.38

Tangent loss {tan S): 0.002

Thickness: 0.813 mm

102

The measurements are conducted using Agilent E5071A Network Analyzer over the frequency range from 0.1 GHz to 5 GHz.

0 i n f \ - � -10 ‘ I

CD J A /

W - ' " '

1 M -30 一 E M Simulation j —Measurement -40o 1 2 3 4 5

Frequency (GHz) Figure 5-13 Return loss (simulated and measured)

-60

U - ^ E M Simulation —Measurement

-80' "-J ‘ ‘ 1 0 1 2 3 4 5

Frequency (GHz)

Figure 5-14 Insertion loss (simulated and measured)

102

P P I i l (a)

I 1 h t J -g I ^ J

1 1 1 m 譯Q (b) Figure 5-12 (a) Fabricated filter (b) its dimension 87

w ~ ^ L ^ w ； ； L ^ I

1.32 3 1 . 6 2 4 . 2 8 8.59 ^ T t I 1 1 . 1 1

. L j Ls2 Ws2 Lo2 Wo2 Lok2 Wok2

30.60 31.78 3.81 10.00 L^O ^ 1 1 . 1 1

Table 5-2 Physical dimension of dual-band microstrip filter

Figure 5-13 and Figure 5-14 compare the simulated and prototype's performance with satisfactory agreement. The measured center frequencies of the two pass-bands are found to be 761 MHz and 1855 MHz. The insertion loss of 0.9 dB and 1.0 dB are observed in lower and upper pass-band respectively. It has 3dB bandwidths of 250 MHz and 350 MHz in lower and upper pass-band respectively. Also, the stop-band has little spurious and the next passband appeared at about 4 GHz.

102

Chapter 6

Review of Conventional CP Antenna Designs

In recent years, there has been considerable interest in the development of CP microstrip antennas. There are different ways to generate CP radiation, such as degenerated mode and dual fed linear antenna with quadrature hybrid.

6.1 Degenerated Mode Patch

The technique of truncating the patch comers of a square microstrip patch to obtain single-feed CP operation of microstrip antennas is well-known. In [20], it demonstrates that such a technique can also be applied to a single-feed square-ring microstrip antenna to achieve CP operation.

The CP is obtained with a single-input port (Figure 6-1)，which excites two orthogonal modes of a patch resonating at slightly different frequencies. The feed must be carefully and accurately positioned so that the two radiating modes are excited with the same amplitude. Then 90° phase shift is obtained at a particular frequency located between the resonant frequencies of the two resonant modes. Although this method appears to be technically quite simple, the physical advantage is offset by the very limited frequency bandwidth over which a CP is effectively achieved.

_ 一 � (b) Figure 6-1 Square-ring microstrip antenna with truncated corners 91

‘ ~~~~ f , � � > “ ADS IE3D Measured result � �� � >� f~>� ���� ^ �

%�‘ ： \ ； (Schematic 'xf ‘� (Layou t Simulation) � � � � … / v 令 v . y < � …

• ： � � ‘ n f : : : ' � � \ S imula t ion)� V � “ ‘、： V、： 、 •

- ‘ » • , � � � � •K�"A� �' < j� � ，广- 、•_、、、-*

Return loss 730 - 936 MHz 695-861 MHz 671 - 8 5 1 MHz (Sn<-20dB) 1.88-2.10 GHz 1.77-2.01 GHz 1.74- 1.97 GHz

~~Lower pass-band 0.26 dB 0.44 dB 0.90 dB ripple

Lower pass-band 669 - 967 MHz 643 - 880 MHz 623 - 873 MHz bandwidth (3-dB) (298 MHz) (237 MHz) (250 MHz) Upper pass-band 0.33 dB 0.56 dB 1.00 dB

ripple Upper pass-band 1.80-2.17 GHz 1.70-2.09 GHz 1.67-2.02 G H z ^ bandwidth (3-dB) (370 MHz) (390 MHz) (350 MHz)

Table 5-3 Simulated and experimental results

102

i l l / / — E M Simulation \ 1 / / —Measurement \ \

"B.6 0.65 0.7 0.75 0.8 0.85 0.9 Frequency (GHz)

(a)

Q / / — E M Simulation \ \ 1 / —Measurement \ \

••^65 1.7 1.75 1.8 1.85 1.9 1.95 2 2.05 2.1 2.1! Frequency (GHz)

(b)

Figure 5-15 Insertion loss (a) lower and (b) upper pass-band 89

n Figure 6-4 Layout of the coplanar waveguide-fed slot antenna

Although this design can achieve dual-frequency operation, the impedance bandwidth is relatively small ( � S � / � ) . However, the field patterns at two frequencies do not fully match each other due to different operating modes at the two frequencies.

. 1 , / dielectric resonator ring slot y /

..尤’ 'k :；，'灣；；丨买知 : :—eccentr ic ring slot

* ‘ , ,、、「’，* _i1l j||l ' lFi l |) l | ' | | i i l l iiT\iin p i II III

’ ‘ � v^^v � > f^W.办• • • r i - microstrip feed

Figure 6-5 Dual-band dielectric resonator antenna with radiating slot 94

Figure 6-3 2x2 array using sequential rotation method

6.3 Coplanar Waveguide-fed Slot Antenna

A rectangular coplanar waveguide patch is surrounded by a second loop antenna which is used to generate two resonant modes [22]. With this approach, there is a first resonant frequency and two close resonant frequencies which give a wide second bandwidth.

In the layout (Figure 6-4)，the smaller patch located at the center part is responsible for the upper frequency band and the outer slot is designed to cover the lower frequency band.

In order to have a CP wave, the geometry has be slightly modified. It consists of a dielectric resonator, a ring slot and an eccentric ring slot [23]. The slot is used to feed the dielectric resonator antenna and the ring slot acts as a second radiator (Figure 6-5). This arrangement can be described as placing two resonant circuits in the same plane, one is dielectric resonator and another is the ring slot.

102

6.2 CP Stacked Microstrip Patch Antenna Array

As mentioned before, the main disadvantage of circularly polarized microstrip antennas is their limited axial ratio and impedance bandwidth. A commonly used method to achieve broadband axial ratio is to employ sequential rotation feed technique together with stacked patches [21]. The antenna geometry (Figure 6-2) consists of a microstrip line feed, crossed slot in the ground plane and stacked microstrip patches. The AR bandwidth is 19% and impedance bandwidth is 35% which are considerably improved by inserting a cross slot on the bottom patch. This can also reduce the size of the antenna. The 2x2 sequentially rotated array (Figure 6-3) has been designed to further improve the of AR and impedance bandwidths. However, the feeding network to achieve proper phase excitation of patch elements will become very complex.

. 一 l i l ^ 【 辦 均 — ：

Top Patch Ground -^^iil^mmmmmmimmmimmmmmmmmm4~~ mm wam X Bottom Patch

Figure 6-2 Stacked microstrip antenna with a crossed slot on the bottom patch

102

6.4 Dual-band CP antenna fed by 2 different 90° hybrid couplers

Microstrip antenna usually uses two orthogonal patch modes in phase quadrature to achieve circular polarization. Most CP patch antennas are on the two adjacent sides of a square patch with signals of equal magnitude and 90° phase different using a power splitting network. Using hybrid coupler as feeding network can help the reflected power from a mismatched antenna to be transferred to the absorbing load. Therefore, this geometry can give a good isolation between input port and output port.

For on dual-band operation, a dual-band CP antenna has been adopted with hybrid feeding technique [24]. Both patches are printed on the same substrate layer and electromagnetically fed through two perpendicular slots etched in the ground plane. Two single-band couplers are printed onto the stacked lower substrate layer (Figure 6-6). The bandwidths for VSWR <2.0 are about 1.5% and 8.6% at lower and upper frequencies respectively. The 3dB AR bandwidths are 3.8% and 7.4% at lower and upper frequencies respectively. The isolation between the two antennas is more than 30dB, which allows simultaneous dual-band operations. However, this structure occupies large substrate area and the two hybrids may lead to strong prohibitive coupling effects.

遷 : ： # Slot IIP y ^ Hybrid 人 J I ^

I Port 1 Portl >

Figure 6-6 Geometry of dual-band CP antenna 95

闕纖 • 圖

(a) (b) Figure 7-2 Current distribution on the slotted square patch,

(a) TMioo mode; (b) TM300 mode

Figure 7-2 shows the current lines distribution of a slotted square patch antenna at the TMioo and TM300 respectively. The electric current distribution of the TMioo has a null at the radiating edges of the patch. The current distribution of this mode is slightly perturbed if slots are added close to the edges (Figure 7-2a).

On the other hand, the current distribution of the TM300 mode is strongly modified since the slots are located where the current of the unperturbed TM300 mode is significant. As noticed in Figure 7-2b, the currents circulate around the slots and find a resonant condition with nulls close to the two edges of each slot. This makes the center part of the current distribution to be broader than that corresponding to the unperturbed TM300 mode. As a consequence, the resonant frequency decreases due to the increase in the current-lines path length. For both TMioo and TM300 modes, the slots orthogonal to the radiating edges do not perturb the current distribution since they are parallel to the current-lines.

102

精V、.？ \ 〜 ： \ • '署獄 "、、 … -

奢 � C t r : … ？ 、 ：

；：繁麵 a 藝、絲》•、 • ：“

‘‘總厂"-•— … 一 � … I ‘ -

II II ~

Figure 7-1 Geometry of the slotted square patch antenna

7.2.1.1 Dual-Feed Structure

A CP (LHCP or RHCP) radiation is produced by the sum of two linearly polarized signals that exhibit equal amplitude and 90° phase difference. It can be obtained with a dual-polarized antenna in which two signals of equal amplitudes are fed to the two input ports in quadrature by using either offsets transmission lines or a hybrid coupler.

7.2.1.2 Slot Excitation

Both the TM遍 and T M _ {n = 1, 3) can be excited in the patch cavity. For evident reasons of symmetry, the TM„^ modes behave as the T M _ modes. For the sake of simplicity, only TM— will be considered in the following discussion.

102

Chapter 7

Novel New Dual-band CP Antenna Design

7.1 Introduction

CP has been extensively used to match the enquiry signal regardless of the physical orientation of the object. Much research has been devoted to the generation of CP radiation. Degenerated mode patch antennas, antenna arrays with sequentially rotated patch and microstrip antenna fed by quadrature hybrid are just a few examples. Their merits are determined by the size, impedance bandwidth, AR bandwidth and ease of fabrication. Some applications may demand antenna with both CP radiation and dual-band operation.

7.2 Dua卜band CP Patch Antenna

Dual-band operation can be obtained by loading the antenna with reactive elements and this can be done by etching slots on a patch. This loading strongly modifies the resonant modes of the patch particularly when the slots are such to cut the current flux lines of the unperturbed mode.

7.2.1 Slotted Square Patch Antenna

The geometry of the slotted square patch antenna is shown in Figure 7-1. The patch is loaded by four narrow slots located close to its edges. In this configuration, the distance of the slots from the patch edges and the slot width are comparable with the substrate thickness.

102

7.2.2 Slotted Cross Patch Antenna

By removing the portion of metallization close to the slot ends, a cross-shape structure appears and the geometry of the antenna is shown in Figure 7-3. In this antenna, both the slot length and the patch length (W/) can be simultaneously reduced, thus eliminating the currents which are the main cause of pattern distortion, as shown in Figure 7-4.

^ . n n '

i i •

Ls • Wj W2 -

• � / . " - : • � ” ” j 丨

1 r I 1 • ‘ I ^ ”

^ �

• ‘， I ”

4 4 I Figure 7-3 Geometry of the slotted cross patch antenna

102

^ w^ • W A

• •

P

Figure 7-5 Geometry of the slotted cross patch antenna

I wp I 丨 d

Physical length (mm) 150 51 110.4 55.7 36 1

Table 7-1 Physical dimension of slotted cross patch antenna

102

7.2.3 Simulation Results: Slotted Cross Patch Antenna

Based upon the previous discussion, a slotted cross patch antenna with operating frequencies j ) = 915 MHz and f � = 2 . 4 5 GHz has been simulated with physical dimensions listed in Table 7-1.

Substrate information

Type: Duriod CGP-500

Dielectric constant (s》： 2.6

Tangent loss {tan §)\ 0.0018

Thickness: 3.974 mm

102

_ M (a) (b)

Figure 7-4 Current distribution at the patch corner at TM300 mode for (a) slotted square patch antenna and for (b) slotted cross patch antenna

7.2.2.1 Frequency Ratio (厂/,2) Consideration

As discussed in slotted square patch antenna session, locating slots close to the radiating edges only gives little perturbation to the TMioo mode. Therefore, its resonant frequency (at TMioo mode) is only slightly different from the standard patch one [25].

Also, the slot length Ls is the way to change the frequency ratio of the two modes by adjusting the resonant frequency at TM300 mode. On the other hand, decreasing L provides wider counterphase currents at the slot ends, which produce deformation of the TM300 radiation pattern. Therefore, Ls cannot be too short, thus limiting the boundary of frequency ratio.

In contrast to the slotted square patch antenna, this structure can give additional degree of freedom in frequency ratio.

102

7.2.3.1 Simulation Results

By fine tuning the critical dimensions mentioned above, the antenna is designed to operate at 915 MHz and 2.45 GHz, as shown in Figure 7-6. It should be noted that apart from the return loss (Sii), isolation factor (S21) should remain as large as possible at the resonant frequencies. This is to ensure that the power is radiating but not transmitted from one port to another port.

Ors.

I 20 \ \ 呈 \ f\

i ---A/…-一……Hi…� y a -40 V .45I 1 1 1 1 1

0 0.5 1 1.5 2 2.5 3 Frequency (GHz) Figure 7-6 Simulation results - return loss and isolation factor

， … � ‘ � '、 二 t Impedance Bandwidth :、於改、：工<、r奢‘；、、 (S1 ,<-1 OdB)

Lower Frequency band 913 MHz — 924 MHz Upper Frequency band 2.43 GHz - 2.46 GHz

Table 7-2 Summary of the simulation result 103

Zq Till @fM

�它

Zz), 7 : / 2 @ f M 、 ； Z z 5 ， 7 r / 2 @ / M

、：姿、、

Figure 7-8 Dual-band transformer

The design formulas for the dual-band transformer are given by [19]:

Z - Zr c — 「；r ) (7.1) cos —e

U J

z z 丁

. { TV f 71 \ (7.2) Sin —e tan —e

2 2 V ^ / v ^ /

where

f 2 - f l (7.3)

Subsequently, the overall structure and parameters are illustrated in Figure 7-9 with the following design equations:

102

7.3 Dual-band Quadrature Hybrid

Since a feeding network is required to provide signals of equal magnitude and 90° phase difference to CP antenna, a hybrid coupler has been chosen. This structure can transfer the reflected power from a mismatched antenna to the absorbing load. A dual-band hybrid coupler is developed and used as the feeding network for the dual-band CP patch antenna.

A conventional single-band hybrid coupler is shown in Figure 7-7. For dual-band operation, each quarter-wavelength branch-line in the design has to be replaced by the dual-band transformer as depicted in Figure 7-8.

. I

Zo.7iI2 ZO,7II2

Zf严

Figure 7-7 Conventional design of single-band quadrature hybrid

102

Finally, the two open stubs may be combined to form a single quarter-wavelength open stubs with characteristic of Zs (Figure 7-10):

(7.8)

IZs , ; r/2

Vn— • Z^.7r/2 輪 •

Figure 7-10 Final topology of dual-band hybrid coupler

7.3.1 Simulation Results: Dual-band Hybrid Coupler

For a given operating frequencies (/) = 915 MHz and 力=2.45 GHz), the dimensions of the coupler can be calculated by using equations (7.4) - (7.8) and the impedance values and physical dimensions are listed in Table 7-3 and Table 7-4 respectively.

107

I Z2,7iI2 @ / "画

Z „ ; r / 2 甲

/m=(/}+/2)/2 Z 3 ’ ; r / 2 @/M

Figure 7-9 Overall structure of dual-band coupler

广 Z - Zo f — Z ^ [7： [ tz \ (7.4) 4 2 COS — e

U J Z - Zo L2 一 ( \ ( \ m

rr . ( TT n (7.5) V2sin —E tan —e

U J U J \ Z - 丄 f ; r ) (7.6) COS —e U J Z - Zo 4 ~ f ^ \ / \ tn n\

.{ 71 71 (7.7) ： Sin —e tan —s V [2 ) [2 )

102

： , Bimejision j- Ls -- W； U W^ U - . •� ‘ ！ 、.知、'>•；;''•'、、》>-. <、 ，'‘-<i ,

Physical length (mm) 3.3 25.2 2,1 25.7 1.1 25.5

Table 7-4 Physical dimension of dual-band hybrid coupler

7.3.1.1 Simulation Results

To characterize the performance of a hybrid coupler, the measured return loss, isolation, insertion loss and phase difference between two output ports are plotted in Figure 7-12 - Figure 7-15. Table 7-5 summarizes the results evaluated at the center frequency of the two operating bands.

Apart from return loss and isolation, amplitude and phase difference between two output ports are also critical parameters as they could affect the purity of CP radiation produced by the antenna. Ideally, the coupler should have 3 dB insertion loss and 90° phase difference at both operating frequencies. According to EM simulation, the amplitude mismatch are 0.48 dB and 0.37 dB at/； and f i respectively. And the phase differences between two output ports are 96.30° and 99.71° respectively.

102

Transmission line Zi Z3 Zs

Impedance (Ohm) 473 ^ m

Table 7-3 Impedance values of dual-band coupler

Substrate information

Type: Duriod R04003C

Dielectric constant ⑷： 3.38

Tangent loss (tan S): 0.002

Thickness: 0.813 mm

W i . Figure 7-11 Layout of dual-band hybrid coupler

108

f^FVl -20 I-I j on' • • ‘ • ~ I • ‘ — - — — 1 _ 1 _ i _ I — — I _ i — I _ i I . . I _ I 1 i I I I I . _ I _

0 0.5 1 1.5 2 2.5 3 Frequency (GHz) Figure 7-12 Simulation result - return loss

P P - 6 0

. 7 0 1 ‘ ~ ‘ ~ ‘ ~ ‘ ~ I ‘ ‘ ~ ‘ ~ ‘ ~ ~ I ~ ‘ ~ ‘ ~ ‘ ~ ‘ ~ I ~ ‘ ~ ‘ ~ i ~ . ~ I _ . _ i _ . _ . _ _ I ~ i ~ i ~ ^ i ~ % 0.5 1 1.5 2 2.5 3

Frequency (GHz)

Figure 7-13 Simulation result - isolation 110

0|

-25 I — S H -

on I . _ . _ _ . _ i _ I _ 1 I ~ I ~ I ~ I ~ ‘ I _ . _ I — L i _ _ J L _ , _ _ , _ _ l J i _ , _ _ , _ , _ I _ . _ _ , _ _ , _ , _ -du� 0.5 1 1.5 2 2.5 3

Frequency (GHz)

Figure 7-14 Simulation result - insertion loss

111

欄_ l i l l npol .__I_I_I__I——L__,__,__,__I__,_,__,__,__1__,__,_,_. INN_ ,_ . . I , _ _ , _ , _

0 0.5 1 1.5 2 2.5 3 Frequency (GHz) Figure 7-15 Simulation result - phase difference

“ ~ ‘ Lower frequency band Upper frequency band . ~ ^::�::纖；;多驳；�‘《：(^30 MHz) ： (2.55 GHz) it > ！ ‘ - „ „ >

Return loss (dB) 28.26 25.80 Amplitude imbalance (dB) ^ Phase difference (degree) 96.30 99.71

Table 7-5 Summary of simulation results

102

Wo Wo

Figure 7-16 Geometry of dual-band CP antenna using hybrid coupler feeding

7.4.2 Measurement Setup

To performance antenna field pattern measurement, the Antenna Under Test (AUT) should be placed in anechoic chamber. The chamber is shielded by metal to avoid RF interference from external source. Moreover, the inner walls, floor and ceiling are covered with RF absorbing material to eliminate the reflection caused by the chamber wall. By using this setup, the anechoic chamber can simulate an open and isolated free space.

In this far field antenna measurement system (Figure 7-17), the AUT is mounted on the turning table which rotates horizontally. The source antenna is a conical log spiral antenna which can generate either LHCP or RHCP. When the wave hits the reflector, the hand of polarization will change. Hence, if the AUT is receiving LHCP, an transmit antenna with RHCP radiation

102

7.4 Dual-band CP Antenna Realization

In [26], a compact dual-band CP antenna is presented. This antenna is fed by 2 single frequency hybrid couplers. By using this feeding geometry, there is a trade-off between dimension, impedance bandwidth and AR bandwidth. In order to further reduce its size, the proposed dual-band hybrid coupler has been applied to replace the feeding network.

7.4.1 Antenna Configuration

The configuration of the proposed antenna is shown in Figure 7-16. The dual-band hybrid coupler is etched on the back of the lower substrate (Table 7-6). In between the two substrates, a ground plane is placed with dimension of 150 mm (Wq) x 150 mm (Wo). By using probe feeding method, the output ports of the hybrid are connected to the dual-band slotted cross-patch antenna through vias.

The feeding points are located in the axes of patch symmetry in order to obtain a strong decoupling between two ports at both operating frequencies. For the configuration shown in Figure 7-16，the proposed antenna will radiated a right-hand circular polarization wave (RHCP) while using port 1 as transmitted port and port 2 as received port; left-hand circular polarization wave (LHCP) will be radiated while port 1 and port 2 interchanged.

~ "： ^ : Upper substrate Lower substrate

Material Duriod R04003C Duriod CGP-500

Thickness (mm) 0.813 3.974 l ^ d 0.002 0.0018

Table 7-6 Substrate details

102

should be used. The use of the reflector is to make sure the transmitting wave is close to a plane wave suitable for far-field measurement.

>vvvvvvvvvvvvvvvvvvvvvvvvvvvv< > r Y > ^ / Reflector r^ % > N < ^ ^ < ^ ^ — — 關

^ Turning T a b l e � 1 L_J \ \ Network Analyzer

I V \> \ ^ Conical Log Spiral ^ A A A A A A A A A A八入穴 TAAAAAAAAAA八八八八；

p s H O Signal Generator

Figure 7-17 Measurement setup

7.4.3 Experimental Results

To verify the performance of the proposed design, a prototype is realized and shown in Figure 7-18. Return loss is measured using Agilent E5071A Network Analyzer over the frequency range from 0.1 GHz to 3 GHz and plotted in Figure 7-19 (a) - (b).

Figure 7-19 (a) — (b) show the measured Sn, and an impedance bandwidth (defined by SI 1 < -lOdB), of 20.1 % (805 to 985 MHz) and 8.9% (2.290 to 2.504 GHz) are obtained. Figure 7-20 (a) - (b) show the isolation performance between the two input ports. An isolation factor of 22.1dB at 885 MHz and 37.4dB at 2.46 GHz is observed.

102

Figure 7-21 (a) - (b) show the measured axial ratio versus frequency for the proposed CP antenna design. The 3-dB AR bandwidth is 76.8 MHz or about 8.9% (860 MHz); 43.8 MHz or about 1.8% (2.48 GHz).

Figure 7-18 Photo of the proposed design

102

0|

自阔 -30 Y ' ^ . 7 0.75 0.8 0.85 0.9 0.95 1

Frequency (GHz)

(a)

-20' ‘ ‘ 1 1 i —I 1 2.2 2.25 2.3 2.35 2.4 2.45 2.5 2.55 2.6

Frequency (GHz)

(b)

Figure 7-19 Measured return loss (a) Lower band; (b) Upper band 117

0|

- 20

pel X 1 I 1 I ' 1 l 7 0.75 0.8 0.85 0.9 0.95 1

Frequency (GHz)

(a)

-15 \"T

-30

-35

-401 ‘ ‘ 1 1 I 1 1 2.2 2.25 2.3 2.35 2.4 2.45 2.5 2.55 2.6

Frequency (GHz)

(b)

Figure 7-20 Measured isolation (a) Lower band; (b) Upper band 118

1] 0 4——I—I—I 1—I—I—I—I—I 1 1 1—I—I—

0.80 0.85 0.90 0.95

Frequency (GHz) (a)

5 :r

X ：：

< 0 二 1 1 1 1 1 1 1 1 1

2.40 2.45 2.50

Frequency (GHz)

(b)

Figure 7-21 Measured axial ratio (a) Lower band; (b) Upper band

102

Far field measurements in an anechoic chamber have been performed to determine radiation patterns. The 3-dB beamwidths are 84° and 79° for the XZ plane and YZ plane, respectively, at 852 MHz (Figure 7-22). At 2.49 GHz, the 3-dB beamwidths are 3 2 � a n d 35° correspondingly (Figure 7-23). The maximum cross-polarization is about -20dB.

: � ( “ � ‘ ；、- Lower band Upper band

Impedance bandwidth 805 - 985 MHz 2.290 - 2.504 GHz (Sii<-10dB) AR bandwidth 821 - 899 MHz 2.458-2.504 GHz

(AR < 3dB) XZ plane ^

b隱width YZ plane W> ^

Maximum XP suppression 20 dB 25 dB

Table 7-7 Summary of the experimental results

In Table 7-7，it shows that the impedance bandwidth and the AR bandwidth are not aligned very well. This discrepancy is mainly caused by the construction error in manufacturing process. Since the dual-band patch antenna and the dual-band hybrid coupler are fabricated separately and aligned manually, thus frequency mismatch is unavoidable which leads to poor impedance and AR bandwidths.

102

21 一•一 Cross-polarization

180

(a)

0

\ / ^ 一#一 Co-polarization — Cross-polarization

180

(b)

Figure 7-22 Measured far field radiation patterns at 852 MHz (a) in XZ plane and (b) in YZ plane

121

—X— Co-polarization 21 ^ ^ 1 5 0 r 一•— Cross-polarization

fa)

•

-•-Co-polar izat ion 18� Cross-polarization (b)

Figure 7-23 Measured far field radiation patterns at 2.49 GHz (a) in XZ plane and (b) in YZ plane

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Chapter 8

Conclusions and Recommendations for Future Work

Antennas and filters play an important role in many RF applications. In this thesis, the design of dual-band microstrip filter and dual-band circularly polarized patch antenna are proposed and verified.

8.1 Filter

Filters are used to separate signals of different frequencies. Owing to various standards available, filter with multiple operating bands will become more popular. Depending on the requirements, filter can be realized by different technologies including microstrip line, waveguide and coaxial line.

A novel dual-band microwave filter structure has been introduced with derived closed-form design equations. This filter offers planar structure, compact size and low loss performance. Excellent insertion loss (less than IdB) has been achieved experimentally. Due to the presence of transmission zero, spurious rejection more than 30dB has been obtained. In practice, realization of filter is mainly limited by the line impedance range and the operating bandwidth required.

8.2 Antenna

Planar antenna, such as patch antenna has recently attracted much attention due to the tremendous benefits that they can offer to modem wireless systems.

The design of a circularly polarized microstrip antenna operating at two frequency bands has been proposed and implemented. CP wave is generated by dual-feed approach. The use of dual-band hybrid coupler and multi-layer structure allow both compact size and good spurious

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suppression to be achieved. It is shown that by proper design of the radiating element and the feeding network, high performance can be achieved with simple configuration.

8.3 Recommendations for future work

Dual-band filter with unequal bandwidth and spurious suppression have been investigated. It is worth to explore other structures which can offer similar performance but more compact in size. Miniaturization is important since this filter is targeted for RF front-end and size is one of the major concerns. Realization of this filter using LTCC technology may provide further size reduction, particularly for circuit operating at C-band or above.

The performance of the proposed dual-band CP antenna is only marginally acceptable due to the fact that the dual-band coupler and the dual-band patch antenna have been etched and combined manually. During processing, alignment errors have occurred and the operating frequencies of the parts have been deviated from the ideal case. As a result, the impedance and AR bandwidths have been corrupted. Therefore, a more accurate fabrication technology would be advantageous to improve the performance of the antenna.

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References

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[18] W. Ma, Q.-X. Chu, "A novel dual-band step-impedance filter with tunable transmission zeros," Proceedings of Asia-Pacific Microwave Conference 2005, vol. 5, Dec. 2005.

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[23] T.A. Denidni, Q.J. Rao, "Hybrid dielectric resonator antennas with radiating slot for dual-frequency operation," Antennas and Wireless Propagation Letters, vol. 3，no. 1, pp. 321 -323 , 2004.

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Author's Publications

1. H.-Y.A. Yim, K.-K.M. Cheng, "Novel dual-band planar resonator and admittance inverter for filter design and applications," 2005 IEEE MTT-S Int. Microwave Symp.

Dig., pp. 2187 - 2190，12-17 June 2005.

2. H.-Y.A. Yim, C.-P. Kong and K.-K.M. Cheng, "Compact circularly polarised microstrip antenna design for dual-band applications," Electronics Letters, vol. 42, no. 7, pp. 380 -381, March 2006.

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Acronyms and Abbreviations

ADS Advanced Design System

AR Axial Ratio

AUT Antenna Under Test

BPP Bandpass Filter

BSF Bandstop Filter

(^p Circular Polarization

GPS Global Positioning System

J4PP Highpass Filter

LHCP Left-hand Circular Polarization

LNA Low-noise Amplifier

LOS Line-of-sight

LP Linear Polarization

LPF Lowpass Filter

RP Radio Frequency

r F I D Radio Frequency Identification

RHCP Right-hand Circular Polarization

SIR Stepped Impedance Resonator

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