Electromagnetic simulation and analysis for novel filter design

... convergence and accuracy have been achieved through our method The MoM algorithm is next used to design and analyze novel bandpass filters Several miniaturization techniques for bandpass filter design. .. made of filter structures, there is a need to investigate miniaturization of the filters Filters can be categorized into bandpass filters, bandstop filters, lowpass filter and highpass filters... Various novel bandpass filter designs are investigated in Chapter As the design of compact, lowloss and good performance bandpass filter has attracted a lot of attention recently, all the filters

Acknowledgement

I would like to express my most sincere gratitude to my supervisors Associate Professor Ooi Ban Leong, Professor Prof Leong Mook Seng and Dr Guo Li Hui for their invaluable guidance, suggestions, and constructive criticisms during the investigation of the project and the preparation of this thesis

At the same time, I would like to thank my friends and colleagues from our microwave group and Institute of Microelectronics (IME), Singapore for their support and kind assistance

Finally, I would like to express my appreciation to my family and friends, from whom

I received much encouragement in the Ph.D process

Table of Contents

Acknowledgement i

Table of Contents ii

List of Figures vi

List of Tables xi

List of Symbols xii

Summary xiii

Chapter 1 Introduction 1

1.1 Literature Review 1

1.2 Scope of Work 10

1.3 Achievements and Contributions 11

1.3.1 List of Journal Publications 12

1.3.2 List of Conference Publications 13

Chapter 2 Bi-complex Algebra and Quaternion Electromagnetics 15

2.1 Introduction 15

2.2 Network Quaternion Integral Equation Formulation 16

2.3 Mixed Potential Integral Equation Formulation 31

Chapter 3 A Useful Multilayered Microstrip Pole Extraction Technique 41

3.1 Introduction 41

3.2 Pole Extraction for Two Layered Structures 44

3.2.1 Introduction 44

3.2.2 Two-layered Microstrip Geometry in TM Mode 44

3.2.3 Two-layered Microstrip Geometry in TE Mode 50

3.2.4 Numerical Results and Discussions 53

3.3.1 Extraction of Surface Wave Poles 58

3.3.2 Extraction of Leaky Wave Poles for N-layered Microstrip Geometry 65 3.3.3 Extraction of Lossy Improper Poles for N-layered Microstrip Geometry 68 3.3.4 Extraction Algorithm 68

3.3.5 Numerical Results and Discussions 70

Chapter 4 Bandpass Filters Miniaturization 76

4.1 Introduction 76

4.1.1 Method of Moment with developed DCIM algorithm 76

4.1.2 Bandpass filters Miniaturization 82

4.2 Basic Structures for Filter Design 84

4.2.1 Resonator 84

4.2.2 Basic Types of Microstrip Bandpass Filters 86

4.2.2.1 End-coupled, Half-wavelength Resonator Filters 86

4.2.2.2 Parallel-coupled, Half-wavelength Resonator Filters 87

4.2.2.3 Hairpin-line Bandpass Filters 87

4.2.2.4 Interdigital Bandpass Filters 88

4.2.2.5 Stepped Impedance Resonator (SIR) Filters 89

4.2.2.6 Dual Mode Resonator Filters 89

4.2.2.7 Other Types of Bandpass Filters 90

4.3 Bandpass Filter Miniaturization for Microstrip Structures 91

4.3.1 Bandpass Filter Miniaturization Using PBG 91

4.3.1.1 Design Structure of a SIR Bandpass Filter 93

4.3.1.2 Design Structure of a SIR Bandpass Filter using PBG 95

4.3.1.3 Experimental Results and Discussions 100

4.3.2 New Planar Filter without Using Cross-Coupled Effect 103

4.3.2.1 Intermediate, Dual Mode Microstrip Resonator 104

4.3.2.2 The Proposed Filters 109

4.3.2.3 Numerical and Experimental Results 110

4.3.3 Miniaturized Open-Loop Resonator with Wide Frequency Perturbation 116 4.3.3.1 Preliminary Analysis and Design 117

4.3.3.2 Novel Resonator Implementation 125

4.3.3.3 Novel Resonator Design 131

4.4 Coplanar Filter Miniaturization Using Advanced Technologies 134

4.4.1 Novel Miniaturized Coplanar Filter Design Using WTT 134

4.4.1.1 Introduction 134

4.4.1.2 Fabrication technology 136

4.4.1.3 Coplanar Bandpass Filter Design 139

4.4.1.4 Experimental Results and Discussions 151

4.4.2 A Modified Miniaturized LTCC Hairpin-combline Resonator 155

4.4.2.1 Introduction 155

4.4.2.2 LTCC Materials and Structures Used in This Thesis 155

4.4.2.3 Preliminary Analysis and Design 157

4.4.2.4 Two Proposed Designs Using LTCC 166

4.4.2.5 Experimental Results and Discussions 171

Chapter 5 Conclusions and Future Work 177

5.1 Conclusions 177

5.2 Recommendations for Future Work 180

Definition of Quaternions 182

Some Properties of Bi-complex Numbers 183

Non-commutative multiplication of Quaternions 183

Associativity of Multiplication of Quaternions 184

Conjugation of Quaternions 184

Quaternion Fourier Transform 185

Basic Quaternion Electromagnetics 187

Source-free, Homogeneous, Lossless TEM Case 187

Source-free, Inhomogeneous, Lossless TEM Case 191

References 196

List of Figures

Fig 1 Rotation of the axis 22

Fig 2 Transmission line models 26

Fig 3 Initial guess evaluation .47

Fig 4 Two-layered microstrip topology 48

Fig 5 A numerical comparisons of the various classical methods in terms of the residue of the function and the number of iterations (a)-(b) For the first TM root of the two-layered microstrip geometry under the case εr1 <εr2 and 1 r o o k k k ≤ ρ ≤ ε (c)-(d) For the second TM root of the two-layered microstrip geometry under the case εr1 <εr2 and k o ≤kρ ≤k o εr1 55

Fig 6 A numerical comparisons of the various classical methods in terms of the residue of the function and the number of iterations (a)-(b) For the first TM root of the two-layered microstrip geometry under the case εr1 <εr2 and 2 1 o r r o k k k ε < ρ ≤ ε (c)-(d) For the first TE root of the two-layered microstrip geometry for the case εr1 <εr2 and k o ≤kρ ≤k o εr1 56

Fig 7 A numerical comparisons of the various classical methods in terms of the residue of the function and the number of iterations (a)-(b) For the second TE root of the two-layered microstrip geometry under the case εr1 <εr2 and 1 r o o k k k ≤ ρ ≤ ε (c)-(d) For the first TE root of the two-layered microstrip geometry under the case of εr1 <εr2 and k o εr1 <kρ ≤k o εr2 57

Fig 8 N-layered microstrip topology 59

Fig 9 Initial guess evaluation .64

Fig 10 Graphic solution for TM and TE surface and leaky wave modes, where the semicircles represent 2 2 B x ± − (a) TM: 2 2 tan( ) r x B x x ε ± − = (b) TE: ( ) 2 2 cot B x x ± − = − x 67

Fig 11 A numerical comparisons of the two methods in terms of the residue of the function and the number of iterations (a)-(b) For the first TM root of the four-layered microstrip geometry under the case of εr1 <εr2 <εr3 <εr4 and 1 r o o k k k ≤ ρ ≤ ε 71

Fig 13 Barycentric subdivision of the primary triangle The triangle’s midpoint is

shown by a white circle .78

Fig 14 Photograph of the bandpass filter with SIR 81

Fig 15 Comparison of measured and simulated results 82

Fig 16 Distributed line resonators 84

Fig 17 Ring resonator 85

Fig 18 Patch resonator 86

Fig 19 General configuration of end-coupled microstrip bandpass filter 87

Fig 20 General structure of parallel (edge)-coupled microstrip bandpass filter 87

Fig 21 Layout of a hairpin-line microstrip bandpass filter 88

Fig 22 General configuration of interdigital bandpass filter 89

Fig 23 Bandpass filter with SIR 93

Fig 24 Structural variation of λg / 2 type SIRs .94

Fig 25 Bandpass filter with SIR and PBG 96

Fig 26 Dimension of one unit PBG structure 96

Fig 27 An EBG unit 97

Fig 28 Lossless equivalent circuit 97

Fig 29 Equivalent circuit of an EBG unit 97

Fig 30 Photographs of the proposed bandpass filters 101

Fig 31 Simulated (MoM) and measured results for the filter with SIR 101

Fig 32 Simulated (MoM) and measured results for the filter with SIR and PBG 102 Fig 33 A typical measured response of a squared open-loop resonator 104

Fig 34 Comparison of shifted feed lines 106

Fig 35 Equivalent circuit for the parallel direct feed structure 106

Fig 36 Physical dimensions of the proposed structure 111

Fig 37 A photograph of the prototype 112

Fig 38 (a) Comparison of S11 on the effect of the meander loop with and without the presence of the open-circuit stub; (b) Comparison of S21 on the effect of the meander loop with and without the presence of the open-circuit stub 113

Fig 39 Comparison between the simulated (MoM) and measured response of the proposed filter 114

Fig 40 The proposed miniaturized resonator with its physical dimension 115

Fig 41 The measured and simulated (MoM) responses of the structure in Fig 40115 Fig 42 Preliminary structure 118

Fig 43 Simulated responses of the preliminary structure .118

Fig 44 Equivalent circuit of the preliminary structure 119

Fig 45 (a) Even-mode and (b) odd-mode equivalent circuit 119

Fig 46 Lumped element equivalent circuit for even- and odd-mode 120

Fig 47 Various resonator implementations and their S21 responses .127

Fig 48 The dimension of the preliminary structure .128

Fig 49 (a) Comparison of measured and simulated (MoM) results and (b) A closed-up view of the response .129

Fig 50 Comparison of S-parameters withεr =9.95, εr =10.2 and εr =10.45 130

Fig 51 A novel elliptic filter .132

Fig 52 Photograph showing (i) the fabricated prototype (parallel feed): area = 49.7 mm2 (ii) the fabricated prototype (orthogonal feed): area = 60.84 mm2, (iii) the loop resonator [167]: area = 144 mm2 All filters are designed centered at 2.5 GHz 132

Fig 53 Comparison of the simulated (MoM) and measured responses for Fig 52 (ii) .133

Fig 54 Frequency response for the loop resonator for Fig 52 (iii) 133

Fig 55 Substrate structures using WTT 137

Fig 56 WTT process flow 138

Fig 58 Proposed filter design in reference [181] 142

Fig 59 CPW resonator with additional grounded meander lines 143

Fig 60 Equivalent circuit of the CPW resonator with additional grounded meander lines 144

Fig 61 Equivalent circuit of the meander lines 145

Fig 62 Novel bandpass filter design using WTT 149

Fig 63 Proposed filter structure and simulated results 151

Fig 64 Photograph of the wafer 152

Fig 65 Photograph of the coplanar bandpass filter 153

Fig 66 Simulated (IE3D) and measured results 153

Fig 67 Cross section view of the LTCC substrate 156

Fig 68 Preliminary structure I All the other lines and space is 0.1 mm 158

Fig 69 Simulated (IE3D) results for preliminary structure I for Fig 68 159

Fig 70 Approximated equivalent circuit for preliminary structure for Fig 68 159

Fig 71 Preliminary structure II 165

Fig 72 Simulated (IE3D) results for preliminary structure II 166

Fig 73 Proposed coplanar bandpass filter 168

Fig 74 Simulated (IE3D) results for the structure in Fig 73 168

Fig 75 Dimensions of the proposed two-layered filter design 170

Fig 76 Simulated (IE3D) results for the proposed two-layered design 171

Fig 77 Photographs for the proposed designs: (i) Single-layered CPW bandpass filter as shown in Fig 73, (ii) Two-layered CPW bandpass filter with via as shown in 173

Fig 78 Simulated (IE3D) and measured results for Design (i) in Fig 77 173

Fig 79 Comparison of S-parameters withεr =5.7, εr =5.9 and εr =6.1 174

Fig 80 Simulated (IE3D) and measured results for Design (ii) in Fig 77 175

Fig 81 Comparison of S-parameters withεr =5.7, εr =5.9 and εr =6.1 176 Fig 82 Properties of the three fundamental elements 182

List of Tables

Table 1 Equations for the transmission line model 27

Table 2 Two sets of Maxwell equations for electric current-source free and

magnetic current-source free 31Table 3 Two possible forms for both A

G and G in the M ( )u v, plane 35

Table 4 Comparison of the proposed approach and the Davidenko’s method [126] for leaky-wave poles extraction in TM mode The parameters adopted are

List of Symbols

o

ε Permittivity of free space (8.854 10× − 12F/m)

o

µ Permeability of free space (4π×10− 7H/m)

η Free space wave impedance (Ω)

o

k Free space wave number (rad/m)

λ Wavelength (m)

E Electric field (V/m)

H Magnetic field (A/m)

A Magnetic vector potential (Wb/m)

J Electric current density (A/m2)

Summary

Various numerical techniques have been developed to efficiently and accurately calculate the fields of a layered medium Traditionally the electric and magnetic fields are derived separately With the concept of quaternion algebra, a novel and compact quaternion formulation is derived for EM analysis The resultant formulation is subsequently utilized in the Method of Moments (MoM), which is a powerful technique to analyze planar passive circuits The MoM used herein requires the Green’s function in the spatial domain The closed-form Green’s function can be obtained using the Discrete Complex Image Method (DCIM), which needs the accurate evaluation of the poles of the Green’s function in the spectral domain The extraction of the poles of the Green’s function is one of the bottlenecks for the analysis

of multilayered structures due to the complexity of the multilayered Green’s function Although several methods have been introduced for pole extraction, they are not efficient and accurate enough Thus, a fast, stable and efficient multilayered pole extraction technique for fast evaluation of DCIM is introduced in this thesis Suitable initial guesses, good convergence and accuracy have been achieved through our method The MoM algorithm is next used to design and analyze novel bandpass filters Several miniaturization techniques for bandpass filter design have been explored for the first time These include the Photonic Bandgap (PBG) structure, dual mode resonator without cross coupling effect, novel miniaturized open-loop resonator with wide frequency perturbation, novel coplanar filter design with Wafer Transfer Technology (WTT) and a modified miniaturized LTCC hairpin-combline resonator

Chapter 1 Introduction

1.1 Literature Review

The electromagnetic field computation in layered media plays a crucial role in certain applications, such as geophysical prospecting [1]–[3], remote sensing [4], wave propagation [5]-[6], and microstrip circuits and antennas [7]–[9] Researchers have developed many computationally efficient and accurate numerical techniques for the field computation of layered media To name a few, these include the method of moments (MoM) and its variants [10], the finite-element method (FEM) [11], and the finite-difference time-domain (FDTD) method [12]

In general, the FEM and the FDTD method solve differential equations, whereas MoM deals with the integral equations MoM is a more powerful and efficient method for solving problems with simple planar geometry compared to FEM and FDTD FEM [13] and FDTD [14] are more suitable for arbitrarily shaped, inhomogeneously filled and anisotropic scatterers, but are not particularly efficient at modelling the finite source region, especially when it is necessary to describe it in details In here, the source cannot be easily described as dirac function

For solving planar layered microstrip and coplanar waveguide (CPW) structures, the MoM is regarded as one of the most popular techniques [15]-[16] For the MoM formulation, an integral equation describing the electromagnetic problem can be formulated as the mixed potential integral equation (MPIE) or the electric field integral equation (EFIE) These integral equations require the evaluation of problem-

and scalar potentials based on MPIE formulation or the electric fields based on EFIE formulation In general, the MPIE equation provides a less singular kernel compared with the EFIE equation for analyzing multilayered structure

The MoM analysis can be carried out either in the spectral domain [17]-[18] or in the spatial domain [19]–[22] In the spectral domain formulation, the MoM matrix elements involve two-dimensional (2-D) integrals of complex, oscillatory, and slow-

converging functions over an infinite domain [23] Therefore, the numerical evaluation

of these elements is quite time consuming, rendering the technique computationally inefficient Although acceleration techniques and approximations can improve the computational efficiency of the spectral-domain MoM, they may impose some restrictions The basis and testing functions are restricted to those that have analytical Fourier transforms, such as the rooftop [24] and piecewise sinusoidal basis functions [25] On the other hand, the application of the spatial-domain MoM to the mixed-potential integral equation (MPIE) requires the evaluation of Green’s functions in the spatial domain [15] The spatial-domain Green’s functions can be obtained from their spectral domain counterparts, which can be derived analytically for planar multilayered media, via the Hankel transformation, also called Sommerfeld integral [26]- [27] Since the kernel of the transformation is the Bessel function of the first kind and the function to be transformed is the spectral-domain Green’s function, the integrand is often an oscillatory and slow-converging function Therefore, the calculation of the spatial domain Green’s function, i.e., the numerical implementation

of the Hankel transformation, is the main computational bottleneck of the domain MoM The spatial-domain MoM has no restriction on the basis and testing

spatial-functions [28] In this thesis, a spatial-domain MoM is used to analyze planar structures

In modeling microstrip structures using the MoM, much effort has been devoted to the computation of the Green’s functions because the computation of Sommerfeld integrals (SIs) is very time consuming There are three methods that can be found in the literature for the evaluation of these SIs: (1) numerical integration method; (2) asymptotic method; (3) discrete complex image method The numerical integration method in [29]-[30] is suitable only when the field points are very close to the source points Generally, this method requires the largest computation time because the integrands are oscillatory The asymptotic method [31] is the fastest, but it is also the least accurate, especially when the field points are close to the source points They are also complicated and cannot be directly used for multilayered microstrip structures To address these limitations, a method based on the Sommerfeld identity, called the discrete image method (DCIM) [33]–[48], has been developed The DCIM approximates the spectral-domain Green’s functions in terms of complex exponentials and casts the integral representation into closed-form expressions via an integral identity, namely the Sommerfeld identity [49]

The DCIM divides the Green’s function into three main parts [34] They are namely: (1) extraction of the quasi-static terms dominating in the near-field region, (2) contributions of the surface wave poles (SWP) dominating in the far-field region of the substrate surface, and their extraction, and (3) the remaining terms, which are related

to leaky waves and are very important in the intermediate field region The quasi-static

surface wave contribution comes from the poles in the spectral Green’s functions The surface wave poles are extracted, and subsequently the contribution of surface waves

is evaluated through the residue calculus The remaining portion in the spectral representation is expanded into a series of exponentials using either the Prony [34] or generalized pencil-of-functions method (GPOF) methods [38], [50]

Conventionally, both the vector magnetic potential A and the vector electric potential are evaluated separately through the mixed potential formulation To achieve more compactness in the derivation, a novel quaternion mixed potential formulation is presented in the thesis In reference [51], concepts of quaternion Fourier transform (QFT), quaternion convolution (QCV), and quaternion correlation, which are based on quaternion algebra, have been found useful in the solution of Maxwell’s equations It has been shown that the derivation of regular TEM waves in homogeneous medium can be given in a very compact way, yielding all possible polarization cases simultaneously In this thesis, a new way of representing the dyadic Green’s function

in a compact form has been introduced based on the concepts of quaternion algebra in [51]

F

Several issues need to be considered when applying DCIM method for multilayered structures One of them is the difficulty of extracting the surface wave poles for the multilayered structures In applying DCIM to general multilayered media, there is a lack of a reliable procedure for the extraction of surface wave components[41] In [52] and [53], a Newton–Raphson root-searching procedure is applied to find the TE- and TM-mode surface wave poles of a grounded dielectric slab However, due to the existence of branch cuts, the initial values close to the roots are needed In this

connection, reliable and suitable initial values need to be investigated for the grounded dielectric slab, but such initial values for general multilayered media are not available

In [54] a contour integral method is used for seeking the zeros of an analytical function, which are the surface wave poles of three-layered media grounded both at the top and bottom In [55] the same method is applied to a three-layered medium which is grounded only at the bottom by eliminating the branch points associated with the semi-infinite top layer through a variable transform However, this method requires evaluation of the first-order derivative of the function, the zeros of which are to be sought, which is difficult to derive for general multilayered media When the number

of zeros in the contour is greater than four, the contour should be replaced by several smaller contours so that each contains no more than four zeros This process is generally rather tedious In [56], a two-stage root-searching procedure is proposed for seeking the roots of these denominators The residuals associated with the surface wave poles are calculated through contour integration To find all the roots automatically, the interval between the minimum and maximum wave number of all media is divided uniformly into a number of sections For each section, the golden search procedure is first applied to find the minimum of F k( )ρ [56], which is then used as the starting point for the Newton– Raphson procedure In general, this method is not very efficient since it cannot find the total number of the roots automatically and it has difficulties to seek the initial values for the surface wave poles Also, this method suffers from local minimum termination In [57], an efficient and robust iterative algorithm is introduced based on contraction mapping, which can locate all the proper and improper solutions of the characteristics equations of the grounded dielectric slab However, this method will become extremely complex when

the accurate evaluation of the overall spatial Green’s function, is difficult to find As a result, there is a need to devise an efficient, accurate and fast poles extraction algorithm for multilayered structures Our earlier success in deriving fast but efficient pole extraction procedure for a single-layered structure [58] provided a good starting point for deriving a generalized approach for multilayered microstrip pole extraction

In this thesis, a general and fast algorithm is introduced for surface wave, leaky wave and lossy pole extraction for multilayered structures

Another difficulty associated with the DCIM method is the approximation method for the complex image terms The original derivation of the closed-form Green’s functions,

as proposed in [34], employed the original Prony method for complex image terms It was limited in use to thick and single layer structures, which was due to inadequacy of the original Prony method This problem was eliminated by employing the least squares Prony method [35] Then the approximation was further improved by using the generalized pencil-of-functions method (GPOF) [38], which is less noise sensitive and more robust compared to the Prony methods However, the algorithm for the exponential approximation is still computationally expensive, because Prony’s methods and the GPOF method require uniform sampling of the function to be approximated along the range of approximation This, in turn, makes it necessary to take a large number of samples for functions with local oscillations and fast variations, like spectral-domain Green’s functions in general, rendering the algorithm computationally expensive and not robust Recently, a two-level approach that requires piecewise uniform sampling has been introduced to eliminate this problem, and is demonstrated to be much more efficient and robust [40] Hence, the spatial-

domain closed-form Green’s functions can be employed efficiently in the solution of MPIE for planar, multilayered geometries

With the appropriate spatial-domain Green’s function and boundary conditions, the surface current of a specified problem can be calculated Based on the appropriate integral equation, we need to expand the unknown function in terms of some known basis functions with unknown coefficients The preferred choice of basis functions is

the one developed by Rao et al [59], which is now commonly known as the Rao–

Wilton–Glisson (RWG) basis function This basis function provides a great capability

to model arbitrarily shaped microstrip structures The boundary conditions are then implemented in an integral sense through the testing procedure The integral equation

is next transformed into a matrix equation, whose entries are double integrals for the general 2-D geometries However, for planar 2-D geometries, the MoM matrix entries can be reduced to single integrals by transforming the convolution integrals onto the basis and testing functions and by evaluating the resulting integrals analytically [60]

In either domain, for moderate-size geometries the computational efficiency of the MoM lies in the evaluation of the MoM matrix entries In the spectral-domain application of the MoM, since the Green’s functions are known in closed form, the matrix entries become single integrals over an infinite domain For a geometry requiring a large number of unknowns, the matrix solution time dominates the overall performance of the technique, and therefore, the efficiency of the method is defined by the efficiency of the linear system solver [61]

The MoM is a powerful technique to analyze planar passive circuits, such as antennas

miniaturization for personal communications equipment has become one of the most fundamental requirements Since many of the passive circuits are made of filter structures, there is a need to investigate miniaturization of the filters Filters can be categorized into bandpass filters, bandstop filters, lowpass filter and highpass filters Among them, the bandpass filter plays a pivotal role in wireless communications systems such as satellite and mobile communications systems

In general, bandpass filters can be designed based on single- or multiple-resonator structures Microstrip resonators for filter designs may be classified as lumped-element

or quasilumped-element resonators, distributed line resonators or patch resonators Conventional bandpass filters include stepped-impedance filters [62]-[66], open-stub filters [67]-[68], semi-lumped element filters [69], end- [70] and parallel-coupled [71]-[72] half-wavelength resonator filters, hairpin-line filters [73]-[75], interdigital [76]-[79], combline filters [80]-[81], pseudo-combline filters, and stub-line filters [82] Recently some research has been conducted on designing compact, low-loss bandpass filters with good performance In view of this, we will focus on miniaturization of microstrip and coplanar bandpass filters in this thesis To minimize the size of the bandpass filter, several structures have been demonstrated including the stepped-impedance resonators (SIR) [62]-[66], the dual mode resonators [83]- [85], meandered open loop resonators [86]-[88], and the photonic bandgap structures [89]

Conventionally, filters using uniform impedance resonators (UIRs) [91] were first used in microwave communication systems They suffer from poor harmonic suppression To alleviate the problem, the stepped impedance resonator (SIR) was developed to solve the problem Stepped impedance resonators (SIR) are composed of

transmission lines with different characteristic impedances They provide an effective way to minimize circuit space and push spurious resonant frequencies away from the passband [62]

Dual-mode resonators are one of the most effective means for miniaturizing a bandpass filter (BPF) Dual-mode [90] means that two degenerate resonant modes are excited by asymmetric feed lines and by the addition of notches or stubs on the ring or patch resonators Therefore, the perturbed resonator may be used as a doubly-tuned

resonant circuit Consequently, the number of resonators for a n -degree filter can be

reduced by half, and the overall size of the filter can be compacted [91]-[92] A mode square patch resonator has been used to build Chebyshev and Elliptic filters [93] Conventional square patches suffer from large size As a result of this, several novel dual-mode structures have been introduced in this thesis for filter miniaturization

dual-Photonic bandgap (PBG) structures are specific periodic structures artificially created

in materials such as metals or substrates to influence or even change the electromagnetic properties of materials These PBG structures can be integrated in many microstrip filters so as to increase the maximum attenuation at the stopband, suppress the spurious transmission and reduce the overall circuit area

For filter implementation, the available technologies include the microstrip line and coplanar waveguide (CPW) Microstrip bandpass filters are finding wide range of applications in many RF/microwave circuits and systems owing to their low-cost, light weight and ease of integration with other components on printed circuit boards (PCBs)

through the substrate or else a wrap-around metallization at the edge of the substrate Both of these techniques increase the meanufacturing complexity and hence the cost Unlike microstrip or stripline, coplanar waveguide has the ready access to the ground plane on the topside of the substrate and permits easy parallel and series insertion of circuit components Its circuit parameters are also less sensitive to the substrate thickness, but sensitive to other parameters For filter miniaturization, the available techniques include using slow wave structures [94], meander line structures [95]- [96],

or slot-loaded CPW structures [97]- [98]

Besides the above-mentioned novel structures for filter design, there are also many advanced materials and technologies currently available for filter fabrication They include the high-temperature superconductors (HTS) [99]-[102], ferroelectrics, micromachining or microelectromechanical systems (MEMS) [103]-[105], hybrid or monolithic microwave integrated circuits (MMIC) [106]- [107], active filters, photonic bandgap (PBG) materials/structures, low-temperature cofired ceramics (LTCC) [108]-[109] and wafer transfer technology (WTT) These technologies have stimulated the rapid development of new bandpass filters In this thesis, we will introduce several novel structures of bandpass filters for microstrip structure and CPW using conventional and advanced fabrication technologies

1.2 Scope of Work

In Chapter 1, an introduction to the history and current research concerning EM modeling for multilayered structures is presented Different numerical techniques have been investigated to efficiently and accurately calculate the fields of layered medium

It is noted that the Method of Moments is a powerful technique to analyze planar passive circuits In general, MoM requires the Green’s function in spatial and spectral

domains In this research, the development of closed-form spatial-domain Green’s function are investigated using EM simulation Various techniques of filter miniaturization are introduced

Chapter 2 introduces a novel and compact quaternion analysis for EM analysis Normally, the electric and magnetic fields are derived separately With the concept of quaternion algebra, it is possible to give a compact formulation for DCIM analysis

A multilayered pole extraction technique for fast evaluation of DCIM is introduced in Chapter 3 Extracting the poles of the Green’s function is one of the difficulties for the analysis of multilayered structures due to the complexity of the multilayered Green’s function Although several authors provide some techniques for pole extraction, these methods are not very efficient and accurate Thus, there is a need to investigate a new general and fast algorithm for pole extraction in multilayered structures

MoM can be used to design and analyze different planar circuits Various novel bandpass filter designs are investigated in Chapter 4 As the design of compact, low-loss and good performance bandpass filter has attracted a lot of attention recently, all the filters introduced in this chapter focus on miniaturization, which provide low cost and good performance Several advanced design and fabrication techniques are applied for further miniaturization of bandpass filters compared to the conventional PCB technology

1.3 Achievements and Contributions

a) A novel and compact quaternion analysis has been derived Without separately deriving the electric and magnetic field, the quaternion MPIE provides a faster formulation method for the DCIM analysis

b) A multilayer pole extraction technique for fast evaluation of DCIM has been developed during the project work Suitable initial guesses and good functional expressions with fast convergence have first been derived Compared to the conventional methods, good convergence and accuracy are achieved The method is noted to be fast and stable, and does not suffer from local minimum termination

c) Several miniaturization techniques for bandpass filter design have been explored for the first time These includes the PBG structure, dual mode resonator without cross coupling effect, novel miniaturized open-loop resonator with wide frequency perturbation, novel coplanar filter design with Wafer Transfer Technology (WTT) and miniaturized two-layered LTCC coplanar filter using modified hairpin-combline resonator

As a result of these investigations, the following publications have been produced:

1.3.1 List of Journal Publications

z Y Wang and B L Ooi, “Useful multilayered microstrip pole extraction technique”,

IEE Proceedings Microwaves, Antennas and Propagation, Vol 152, Issue 3, pp

149 – 154, June 2005

z Y Wang, B L Ooi, M S Leong, “Efficient and fast approach for surface wave

poles extraction in two-layered microstrip geometry”, Microwave and Optical

Technology Letters, pp 253-258, May 2004

z H Y Fong, Y Wang, B L Ooi, “A novel microstrip loop filter”, Microwave and

Optical Technology Letters, Volume 47, Issue 3, pp 279-281, Nov 2005

z B L Ooi, D X Xu, Y Wang, B Chen and M S Leong , “A novel LTCC power

combiner”, Microwave and Optical Technology Letters, Vol 42, Issue 3, pp

255-257, Aug 2004

z B L Ooi, Y Wang, and H Y Fong, “Experimental Study of New Planar Filter without Using Cross-Coupled Effect”, IEE Proceedings Microwaves, Antennas and

Propagation, Vol 153, No 3, pp 226 – 230, June 2006

z Ban-Leong Ooi and Ying Wang, “Novel Miniaturized Open-Square-Loop

Resonator with Inner Split Rings Loading”, IEEE Trans on Microwave Theory and

Techniques, Vol 54 No 7, pp 3098-3103, July 2006

z Ying Wang, Ban Leong Ooi, Li Hui Guo and Mook Seng Leong, “Implementation

of Novel Millimeter-Wave Filter Using Wafer Transfer Technology”, Accepted by

IEEE Electronics Letters

1.3.2 List of Conference Publications

z Ying Wang, B L Ooi and M S Leong, “Fast and efficient approach N-layered

microstrip poles extraction”, International Union of Radio Science National Radio

Science Meeting, (URSI) Colorado, USA, Jan 5-8, 2004

z Ying Wang, B L Ooi and M S Leong, “Novel multi-layered poles’ extraction

technique”, Progress in Electromagnetics Research Symposium, Pisa, Italy,

28-31 March 2004

z Ying Wang, B L Ooi and M S Leong, “Comparison of various methods for poles'

extraction in microstrip problem”, International Symposium on Antennas and

Propagation, Sendai, Japan, Aug 17-21, 2004 (Invited)

z Y Wang, B L Ooi, Y J Fan, M S Leong, Y Q Zhang and L H Guo,

“Implementation of a novel millimeter-wave filter using wafer transfer technology”,

submitted to 2006 IEEE Radio Frequency Integrated Circuits Symposium

(RFIC-2006), San Francisco, California on June 11-13, 2006

z Y Wang, B L Ooi, Albert Lu, K M Chua, and M S Leong, “A modified

miniaturized LTCC hairpin-combline resonator”, submitted to 2006 IEEE Radio

Frequency Integrated Circuits Symposium (RFIC-2006), San Francisco, California

on June 11-13, 2006

Chapter 2 Bi-complex Algebra and Quaternion

Electromagnetics

2.1 Introduction

The recently developed concepts of quaternion Fourier transform (QFT), quaternion convolution (QCV), and quaternion correlation, which are based on quaternion algebra, have been found to be useful for color image processing [110]-[114] This concept has also been found useful in the solution of Maxwell’s equations [51] It has been shown that the derivation of regular TEM waves in homogeneous media can be given in a very compact way, yielding all possible polarization cases simultaneously using quaternion algebra From a physical point of view, the implication is that the electric and magnetic fields are not really separate entities, but they merely constitute components of a composite field with bicomplex mathematical nature, satisfying only one (instead of two) Maxwell-like equation In all these cases, the number of the unknown quantities has been reduced by half, compared to conventional techniques [51]

EFIE and MFIE are traditionally derived separately In this chapter, based on the concept in [51], a compact and elegant way has been introduced to derive both the EFIE and MIFE simultaneously A dyadic Green’s function in spectral domain based

on the quaternion Fourier transform [115] has been derived to theoretically verify the validity of this method The adopted approach is an extension of the work found in [115] and differs greatly from [115] through the dyadic analysis The efficiency of this

propagation in two directions, as compared to the conventional second order complex equations [51]

Following the approach in [115] and [51], this chapter will introduce a novel and compact quaternion analysis in spectral domain has been derived Without separately deriving the electric and magnetic field, the quaternion MPIE provides a faster formulation method for the DCIM analysis

2.2 Network Quaternion Integral Equation Formulation

Based on the detailed derivation shown in Appendix, with reference of [51] and applying the concept of quaternion Fourier transform in [115], we extend the concept

of quaternion analysis into transmission line models in spectral domain for the first time In the next two sections, the derivation of the Green’s function in spectral would

be used for poles extraction and MoM algorithm in the subsequent chapters

Consider a uniaxially anisotropic medium, where the general complex-valued permeability and permittivity dyadics are given as

To easily remove the exponential term in the Fourier transform integral, we apply the

right-side Fourier transform pair, namely,

F r

Thus, from eqn (2.2), we have

Extracting the last eqn from eqns (2.8) and (2.11),

µ

η η

ε

+ +

ηε

ηε

M M

+

+ + +

( ) ( 2 ) ( ) 2 2

ˆ

t t

o z e

ευε

ηµ

+

+ +

i dz

k

ηµ

ηµ

2

2 2

t t

z h

z e

t

z h

t

J k dE

M k dH

kρ = + The inverse of this rotation is given as

ˆ1

η

ηε

e o o

h h h h t o

o t e e

ηε

z h

e u

The subscripts e and h represent the fields that are respectively the TM and TE wave

Grouping eqn (2.42), we arrive at a set of transmission line equations, namely:

p

p p p p z

V

P v

Table 1 Equations for the transmission line model

Summing along similar rows and integrate along z, we have

,