SYNTHESIS OF
INFINITE IMPULSE RESPONSE FILTERS USING
SURFACE ACOUSTIC WAVE TECHNOLOGY
by
PRIYANKA
Centre for Applied Research in Electronics (CARE)
Submitted
in fulfillment of the requirements of the degree of Doctor of Philosophy to the
INDIAN INSTITUTE OF TECHNOLOGY, DELHI HAUZ KHAS, NEW DELHI - 110016, INDIA
DECEMBER' 2005
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CERTIFICATE
This is to certify that the thesis entitled "Synthesis of Infinite Impulse Response Filters Using Surface Acoustic Wave Technology" being submitted by Mrs. Priyanka for the award of the degree of Doctor of Philosophy in the Center for Applied Research in Electronics, Indian Institute of Technology, Delhi, is a record of bonafide work done by her under our joint supervision and guidance. The matter embodied in this thesis has not been submitted for the award of any other degree or diploma.
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Prof. S. D. Joshi Dr. B. S. Panwar
Department of Electrical Engineering Centre for Applied Research in Electronics Indian Institute of Technology, Delhi Indian Institute of Technology, Delhi New Delhi — 110016 (INDIA) New Delhi — 110016 (INDIA)
December' 2005 New Delhi
Acknowledgement
It is great pleasure to express my deepest gratitude to Dr. B. S. Panwar for his valuable supervision of my research work. I am indebted for his useful discussions and suggestions that provided a base and direction to my research work. I am obliged for his hard work and devoting time to examine my thesis.
I want to express my best regards to Prof. S. D. Joshi for his constant support and motivation throughout my research work. I am really thankful to him for devoting time to technical discussions and providing me creative ideas that really helped in research work.
I want to thank authorities of TIT Delhi, my department- Centre for Applied Research in Electronics for providing me the research facilities of CARE Computing Lab.
I am thankful to my friends and colleagues, who supported me. I am also thankful to CARE staff Mrs Sneh Kapoor, Mr. Pradeep and all others who helped me when I need.
I am grateful to my husband for being supportive during the period of my distress and anxiety. He always inspired me to work better and not to give up the research work.
My parents deserve the utmost gratitude for looking after my daughter in a lovable manner, and for their inspiration to concentrate on my research work. Without their love and help it was just impossible to complete my research. I am also obliged for my little daughter Somya' for adjusting according to time and to sacrifice the most during my research work.
December' 2005
Abstract
A Surface Acoustic Wave (SAW) filter consists of two metal Inter Digital Transducers (IDTs) deposited on a piezoelectric substrate. When electrical signal is applied on input IDT Surface Acoustic Waves (SAWs) generate due to piezoelectricity of the substrate and these SAWs are detected by the output IDT. Response of this SAW filter is primarily governed by the geometry of input IDT and output IDT.
In order to design a SAW filter, the desired frequency response is first approximated by a Finite Impulse Response (FIR) filter. The desired response is then split between two IDTs by zero separation method. One is required to find the zeros of the transfer function before splitting. A new technique to find the zeros of the real, linear phase, FIR filter is presented in the thesis. This zero finding technique uses the properties of Z-transform and constraints on the location of zeros for a real, linear phase FIR system. After finding all the zeros and splitting these between two IDTs, one is required to realize two IDTs with desired response. Thesis presents an iterative approach to design a SAW filter having desired response. This iterative approach can be used to design SAW filters with reflections as well as without reflections. In case reflections are used in the SAW filter design (for different advantages) then it comes under Infinite Impulse Response (IIR) filter category. One cannot use conventional FIR filter design techniques to design a SAW filter when using reflections. Furthermore, analysis of SAW filters using reflections is relatively complex. A new 3-port Reflecting Cell Model (RCM) is presented in the thesis to analyze SAW filters with reflections. This model can be used to give p-parameters of a SAW structure utilizing strong electrode reflections. Finally, realization of IIR filters on SAW devices using reflections is presented.
Table of contents
Page No.
List of Symbols and Abbreviations used List of Figures
1 Synthesis of Infinite Impulse Response Filters Using Surface Acoustic Wave Technology
1.0 Introduction 2
1.1 Scope of the Work 7
1.1.1 Root Finding Algorithm for Linear Phase SAW Filters 7 1.1.2 Splitting the Impulse Response and Synthesizing the Desired p-
Matrix 8
1.1.3 3-Port Model of Reflecting Unit Cells 9 1.1.4 IIR Implementation of Filter in SAW Technology 10 1.1.5 Derivation of Cascading formulas for two p-matrices utilizing
internal reflections 11
1.1.6 Test Structures and Validation 12
1.2 Layout of the Thesis 12
2 Brief overview of SAW Technology and Zeros of Transfer function
of a Linear Phase FIR LTI Filter 15
2.0 Brief overview of SAW Technology 16
2.1 Low Loss SAW Filter Design Tools and Techniques 20
2.1.1 Low Loss SAW Filter Technology 21
2.1.2 Low Loss SAW Filter Design Techniques 23 2.1.3 Limitations of Existing Design Techniques 25 2.1.4 Splitting the Impulse Response and Root Finding Techniques 25
2.1.4.1 Techniques for Splitting the Impulse Response 25 2.1.4.2 Techniques of Finding the Zeros of a Polynomial 29 2.2 Use of Z-Transform Properties in Finding the Zeros of
Transfer function of Real, Linear phase FIR System 30
2.3 The WDK Formulas 35
2.4 Test for Convergence 37
2.5 Problem Solving and Simulation Results 38
2.6 Benchmarking of Root Finding Algorithm 45
2.6 Conclusion 46
3 An Iterative Approach for Synthesizing the Desired p — Matrix of a
SAW filter 48
3.1 Introduction and background 49
3.2 Models for a SAW Filter and Definition of a Unit Cell 51 3.3 Single Phase Unidirectional SAW Filter Design Techniques 55
3.4 Preliminaries and Problem Formulation 63
3.4.1 COM Parameters and Definition of p-Matrix 63 3.4.2 Obtaining Desired p-Matrix of a SAW Filter 66
3.4.3 p-matrices for the Unit Cells for Withdrawal Weighted Structure 67 3.4.4 Cascading Formulas for Unit Cells with Reflecting Structures 69 3.4.5 Application of Frobenious Norm for p-Matrix Synthesis 70 3.5 An Iterative Approach for Synthesizing the Desired p-Matrix 71 3.5.1 Initial Guess of the P-Matrix Parameters 73 3.5.2 Iterative Technique for Converging to the Desired p-Matrix 74
3.6 Simulation results on Filter Design 76
3.7 Conclusion 82
4 3-Port Reflecting Cell Model for the Synthesis of SAW Structures
with Reflectors 83
4.1 Introduction 84
4.2 Preliminaries and Basic Assumptions 85
4.3 Reflection, Transduction and Transmission Strengths of a Unit Cell 91
4.4 Three-port Reflecting Cell Model 95
4.5 Prediction of Insertion Loss, Bi-directionality and Triple Transit Signals 99
4.6 Simulation and Validation of Results 106
4.7 Conclusion 122
5 Realization of Infinite Impulse Response filters on SAW
Devices 123
5.1 Introduction 124
5.2 Design Requirements of Low Loss Low Cost SAW Filters 126
5.3 Realization of Poles in SAW Structure 127
5.4 SAW Unit cells for IIR realization 129
5.5 Realization of IIR transfer function on SAW Structure 133 5.5.1 Computation of p-matrices for Combinations of Two
Cascaded Unit Cells 136
5.5.2 Realization of Proper Second Order Denominator Polynomial 140 5.6 IIR Approximation of Causal, FIR Specifications Using Second Order
Information 142
5.7 IIR Implementation in SAW Technology 150
5.8 Conclusion 153
6 Summary and Discussions 154
7 References 159
8 Appendix-1: Roots/ Zeros obtained by Technique Proposed in Chapter 2, and obtained by MATLAB for the Polynomial, as discussed in Chapter 2,
Section 2.6 171
9 Appendix-2: Derivation of Cascading Formulas for
p-matrices with Internal Reflections 179
10 Appendix-3: Brief Report on Design and Development of Test Structures 187
11 List of Publications 197
12 Bio -data 199
