Introduction To Modern Planar Transmission Lines

Anand K. Verma, PhD, is an Adjunct Professor in the School of Engineering, Macquarie University, Sydney. Formerly, he was Professor and Head Department of Electronic Science, South Campus, University of Delhi. He has been Visiting Professor at Otto-Van-Guericke University, Magdeburg, Germany (202-2003), and Nanyang Technological University, Singapore as a Tan Chin Tuan Scholar (2001). He holds a German Patent on microstrip antenna. He has organized and attended many International Symposia and Workshops and conducted short-term courses and delivered invited lectures at the research institutes in India and in several countries. He was also chairman of the TPC, APMC-2004, Delhi. Professor Verma has published over 250 papers in international journals and in the proceedings of international and national symposia.

Chapter 1: Overview of Transmission Lines (Historial Perspective, Overview of Present Book)
1.1 Overview of the classical transmission lines
1.1.1 Telegraph line
1.1.2 Development of theoretical concepts in EM-Theory
1.1.3 Development of the transmission line equations
1.1.4 Waveguides as propagation medium
1.2. Planar transmission lines
1.2.1 Development of planar transmission lines
1.2.2 Analytical methods applied to planar transmission lines
1.3 Overview of present book
1.3.1 The organization of chapters in this book
1.3.2 Key features, intended audience, and some suggestions

Chapter 2: Waves on Transmission Lines- I (Basic Equations, Multisection transmission lines)
2.1 Uniform transmission lines
2.1.1 Wave motion
2.1.2 Circuit model of transmission line
2.1.3 Kelvin - Heaviside transmission line equations in time domain
2.1.4 Kelvin - Heaviside transmission line equations in frequency domain
2.1.5 Characteristic of lossy transmission line
2.1.6 Wave equation with source
2.1.7 Solution of voltage and current -wave equation
2.1.8 Application of Thevenin's theorem to transmission line
2.1.9 Power relation on transmission line
2.2 Multi-section transmission lines and source excitation
2.2.1 Multisection transmission lines
2.2.2 Location of sources
2.3 Non-uniform transmission lines
2.3.1 Wave equation for non-uniform Transmission line
2.3.2 Lossless exponential transmission line
References

Chapter 3: Waves on Transmission Lines- II (Network parameters, Wave velocities, Loaded lines)
3.1 Matrix description of microwave network
3.1.1 [Z] parameters
3.1.2 Admittance matrix
3.1.3 Transmission [ABCD] parameters
3.1.4 Scattering [S] parameters
3.2 Conversion and extraction of parameters
3.2.1 Relation between matrix parameters
3.2.2 De-Embedding of true S-parameters
3.2.3 Extraction of propagation characteristics
3.3 Wave velocity on transmission line
3.3.1 Phase velocity
3.3.2 Group velocity
3.4 Linear dispersive transmission lines
3.4.1 Wave equation of dispersive transmission lines
3.4.2 Circuit models of dispersive transmission lines
References

Chapter 4: Waves in Material Medium- I (Waves in isotropic and anisotropic media, Polarization of waves)
4.1 Basic electrical quantities and parameters
4.1.1 Flux field and force field
4.1.2 Constitutive relations
4.1.3 Category of materials
4.2 Electrical property of medium
4.2.1 Linear and non-linear medium
4.2.2 Homogeneous and nonhomogeneous medium
4.2.3 Isotropic and anisotropic medium
4.2.4 Non-dispersive and dispersive medium
4.2.5 Non-lossy and lossy medium
4.2.6 Static conductivity of materials
4.3 Circuit model of medium
4.3.1 RC circuit model of lossy dielectric medium
4.3.2 Circuit model of lossy magnetic medium
4.4 Maxwell equations and power relation
4.4.1 Maxwell's equations
4.4.2 Power and energy relation from Maxwell equations
4.5 EM-waves in unbounded isotropic Medium
4.5.1 EM-wave equation
4.5.2 1D wave equation
4.5.3 Uniform plane waves in linear lossless homogeneous isotropic medium
4.5.4 Vector algebraic form of Maxwell equations
4.5.5 Uniform plane waves in lossy conducting medium
4.6 Polarization of EM-waves
4.6.1 Linear polarization
4.6.2 Circular polarization
4.6.3 Elliptical polarization
4.6.4 Jones matrix description of polarization states
4.7 EM-waves propagation in unbounded anisotropic medium
4.7.1 Wave propagation in uniaxial medium
4.7.2 Wave propagation in uniaxial gyroelectric medium
4.7.3 Dispersion relations in biaxial medium
4.7.4 Concept of isofrequency contours and isofrequency surfaces
4.7.5 Dispersion relations in uniaxial medium
References

Chapter 5: Waves in Material Medium- II (Reflection and transmission of waves, Introduction to metamaterials
5.1 EM-waves at interface of two different media
5.1.1 Normal incidence of plane waves
5.1.2 The interface of a dielectric and perfect conductor
5.1.3 Transmission line model of composite medium
5.2 Oblique incidence of plane waves
5.2.1 TE (Perpendicular) polarization case
5.2.2 TM (Parallel) polarization case
5.2.3 Dispersion diagrams of refracted waves in isotropic and uniaxial anisotropic media
5.2.4 Wave impedance and equivalent transmission line model
5.3 Special Cases of Angle of Incidence
5.3.1 Brewster angle
5.3.2 Critical angle
5.4 EM-waves incident at dielectric slab
5.4.1 Oblique incidence
5.4.2 Normal incidence
5.5 EM-waves in metamaterial medium
5.5.1 General introduction of metamaterials and their classifications
5.5.2 EM-waves in DNG medium
5.5.3 Basic transmission line model of the DNG medium
5.5.4 Lossy DPS and DNG media
5.5.5 Wave propagation in DNG slab
5.5.6 DNG flat lens and superlens
5.5.7 Doppler and Cerenkov radiation in DNG medium
5.5.8 Metamaterial perfect absorber (MPA)
References

Chapter 6: Electrical Properties of Dielectric Medium
6.1. Modeling of dielectric medium
6.1.1 Dielectric polarization
6.1.2 Susceptibility, relative permittivity and Clausius - Mossotti model
6.1.3 Models of polarizability
6.1.4 Magnetization of materials
6.2 Static dielectric constants of materials
6.2.1 Natural Dielectric Materials
6.2.2 Artificial Dielectric Materials
6.3 Dielectric mixtures
6.3.1 General description of dielectric mixture medium
6.3.2 Limiting values of equivalent relative permittivity
6.3.3 Additional equivalent permittivity models of mixture
6.4 Frequency response of dielectric materials
6.4.1 Relaxation in material and decay law
6.4.2 Polarization law of linear dielectric medium
6.4.3 Debye dispersion relation
6.5 Resonance response of the dielectric medium
6.5.1 Lorentz oscillator model
6.5.2 Drude model for conductor and plasma
6.5.3 Dispersion models of dielectric mixture medium
6.5.4 Kramers - Kronig relation
6.6 Interfacial polarization
6.6.1 Interfacial polarization in two-layered capacitor medium
6.7 Circuit models of dielectric materials
6.7.1 Series RC circuit model
6.7.2 Parallel RC circuit model
6.7.3 Parallel series combined circuit model
6.7.4 Series combination of RC parallel circuit
6.7.5 Series RLC resonant circuit model
6.8 Substrate materials for microwave planar technology
6.8.1 Evaluation of parameters of single term Debye and Lorentz models
6.8.2 Multi-term and wideband Debye models
6.8.3 Metasubstrates
References

Chapter 7: Waves in Waveguide Medium
7.1 Classification of EM-fields
7.1.1 Maxwell equations and vector potentials
7.1.2 Magnetic vector potential
7.1.3 Electric vector potential
7.1.4 Generation of EM-field by electric and magnetic vector potentials
7.2 Boundary surface and boundary conditions
7.2.1 Perfect Electric Conductor (PEC)
7.2.2 Perfect magnetic conductor (PMC)
7.2.3 Interface of two media
7.3 TEM-mode parallel-plate waveguide
7.3.1 TEM field in parallel plate waveguide
7.3.2 Circuit relations
7.3.3 Kelvin- Heaviside transmission line equations from Maxwell equations
7.4 Rectangular waveguides
7.4.1 Rectangular waveguide with four electric walls
7.4.2 Rectangular waveguide with four magnetic walls
7.4.3 Rectangular waveguide with composite electric and magnetic walls
7.5 Conductor backed dielectric sheet surface wave waveguide
7.5.1 TMz surface wave mode
7.5.2 TEz surface wave Mode
7.6 Equivalent circuit model of waveguide
7.6.1 Relation between wave impedance and characteristic impedance.
7.6.2 Transmission line model of waveguide
7.7 Transverse resonance method (TRM)
7.7.1 Standard rectangular waveguide
7.7.2 Dielectric loaded waveguide
7.7.3 Slab waveguide
7.7.4 Conductor backed multilayer dielectric sheet
7.8 Substrate integrated waveguide (SIW)
7.8.1 Complete mode substrate integrated waveguide (SIW)
7.8.2 Half -mode substrate integrated waveguide (SIW)
References

Chapter 8: Microstrip Line: Basic Characteristics
8.1 General description
8.1.1 Conceptual evolution of microstrip lines
8.1.2 Non-TEM nature of microstrip line
8.1.3 Quasi-TEM mode of microstrip line
8.1.4 Basic parameters of microstrip line
8.2 Static closed-form models of microstrip line
8.2.1 Homogeneous medium model of microstrip line (Wheeler's Transformation)
8.2.2 Static characteristic impedance of microstrip line
8.2.3 Results on static parameters of microstrip line
8.2.4 Effect of conductor thickness on static parameters of microstrip line
8.2.5 Effect of shield on static parameters of microstrip line
8.2.6 Microstrip line on anisotropic substrate
8.3 Dispersion in microstrip line
8.3.1 Nature of dispersion in microstrip
8.3.2 Waveguide model of microstrip
8.3.3 Logistic dispersion model of microstrip (Dispersion Law of Microstrip)
8.3.4 Kirschning - Jansen dispersion model
8.3.5 Improved model of frequency dependent characteristic impedance
8.3.6 Synthesis of microstrip line
8.4 Losses in microstrip line
8.4.1 Dielectric loss in microstrip
8.4.2 Conductor loss in microstrip
8.5 Circuit model of lossy microstrip line.
References

Chapter 9: Coplanar Waveguide & Coplanar Strip Line: Basic Characteristics
9.1 General description
9.2 Fundamentals of conformal mapping method
9.2.1 Complex variable
9.2.2 Analytic function
9.2.3 Properties of conformal transformation
9.2.4 Schwarz- Christoffel (SC) - Transformation
9.2.5 Elliptic sine function
9.3 Conformal mapping analysis of coplanar waveguide
9.3.1 Infinite extent CPW
9.3.2 CPW on finite thickness substrate and infinite ground plane
9.3.3 CPW with finite ground planes
9.3.4 Static characteristics of CPW
9.3.5 Top shielded CPW
9.3.6 Conductor-backed CPW
9.4 Coplanar strip line
9.4.1 Symmetrical CPS on infinitely thick substrate
9.4.2 Asymmetrical CPS (ACPS) on infinitely thick substrate
9.4.3 Symmetrical CPS on finite thickness substrate
9.4.4 Asymmetrical CPW (ACPW) and asymmetrical CPS (ACPS) on finite thickness substrate
9.4.5 Asymmetric CPS line with infinitely wide ground plane
9.4.6 CPS with coplanar ground plane [CPS-CGP]
9.4.7 Discussion on results for CPS
9.5 Effect of conductor thickness on characteristics of CPW and CPS structures
9.5.1 CPW structure
9.5.2 CPS structure
9.6 Modal field and dispersion of CPW and CPS structures
9.6.1 Modal field structure of CPW
9.6.2 Modal field structure of CPS
9.6.3 Closed-form dispersion model of CPW
9.6.4 Dispersion in CPS line
9.7 Losses in CPW and CPS structures
9.7.1 Conductor loss
9.7.2 Dielectric loss
9.7.3 Substrate radiation loss
9.8 Circuit models & synthesis of CPW and CPS
9.8.1 Circuit model
9.8.2 Synthesis of CPW
9.8.3 Synthesis of CPS
References

Chapter 10: Slot Line: Basic Characteristics
10.1 Slot line structures
10.1.1 Structures of open slot line
10.1.2 Shielded slot line structures
10.2 Analysis and modelling of slot line
10.2.1 Magnetic current mode
10.3 Waveguide model
10.3.1 Standard slot line
10.3.2 Sandwich slot line
10.3.3 Shielded slot line
10.3.4 Characteristics of slot line
10.4 Closed-form models
10.4.1 Conformal mapping method
10.4.2 Krowne model
10.4.3 Integrated model
References

Chapter 11: Coupled Transmission Lines: Basic Characteristics
11.1 Some coupled line structures
11.2 Basic concepts of coupled transmission lines
11.2.1 Forward and reverse directional coupling
11.2.2 Basic definitions
11.3 Circuit models of coupling
11.3.1 Capacitive coupling- Even and odd mode basics
11.3.2 Forms of capacitive coupling
11.3.3 Forms of inductive coupling
11.4 Even -Odd mode analysis of symmetrical coupled lines
11.4.1 Analysis method
11.4.2 Coupling coefficients
11.5. Wave equation for coupled transmission lines
11.5.1 Kelvin-Heaviside coupled transmission line equations
11.5.2 Solution of coupled wave equation
11.5.3 Modal characteristic impedance and admittance
References

Chapter 12: Planar Coupled Transmission Lines
12.1 Line parameters of symmetric edge coupled microstrips
12.1.1 Static models for even and odd mode relative permittivity and characteristic mpedances of edge coupled microstrips
12.1.2 Frequency-dependent models of edge coupled microstrip lines
12.2 Line parameters of asymmetric coupled microstrips
12.2.1 Static parameters of asymmetricallycoupled microstrips
12.2.2 Frequency dependent line parameters of asymmetrically coupled microstrips
12.3 Line parameters of coupled CPW
12.3.1 Symmetric edge coupled CPW
12.3.2 Shielded broadside coupled CPW
12.4 Network parameters of coupled line section
12.4.1. Symmetrical coupled line in homogeneous medium
12.4.2 Symmetrical coupled microstrip line in inhomogeneous medium
12.4.3 ABCD matrix of symmetrical coupled transmission lines
12.5 Asymmetrical coupled lines network parameters
12.5.1 [ABCD] - parameters of the 4-port network
References

Chapter 13: Fabrication of Planar Transmission Lines
13.1 Element of hybrid MIC (HMIC) technology
13.1.1 Substrates
13.1.2 Hybrid, MIC fabrication process
13.1.3 Thin film process
13.1.4 Thick film process
13.2 Elements of monolithic MIC (MMIC) technology
13.2.1 Fabrication process
13.2.2 Planar transmission lines in MMIC
13.3 Micromachined transmission line technology
13.3.1 MEMS fabrication process
13.3.2 MEMS transmission line structures
13.4 Elements of LTCC
13.4.1 LTCC materials and process
13.4.2 LTCC circuit fabrication
13.4.3 LTCC Planar transmission line and some components
13.4.4 LTCC waveguide and cavity resonators

Chapter 14: Static Variational Methods for Planar Transmission Lines
14.1 Variational formulation of transmission line
14.1.1 Basic concepts of variation
14.1.2. Energy method based variational expression
14.1.3 Green's function method based variational expression
14.2 Variational expression of line capacitance in Fourier Domain
14.2.1 Transformation of Poisson equation in Fourier Domain
14.2.2 Transformation of variational expression of line capacitance in Fourier Domain
14.2.3 Fourier Transform of Some Charge Distribution Functions
14. 3 Analysis of microstrip line by variational method
14.3.1 Boxed microstrip line (Green's function method in Space Domain)
14.3.2 Open microstrip line (Green's function method in Fourier Domain)
14.3.3 Open microstrip line (Energy method in Fourier Domain)
14.4 Analysis of multilayer microstrip line
14.4.1 Space Domain analysis of multilayer microstrip structure
14.4.2 Static Spectral Domain analysis of multilayer microstrip
14.5 Analysis of coupled microstrip line in multilayer dielectric medium
14.5.1 Space Domain analysis
14.5.2 Spectral Domain analysis
14.6 Discrete Fourier Transform method
14.6.1 Discrete Fourier Transform
14.6.2 Boxed microstrip line
14.6.3 Boxed coplanar waveguide
References

Chapter 15: Multilayer Planar Transmission lines: SLR Formulation
15.1 SLR process for multilayer microstrip lines
15.1.1 SLR- process for lossy multilayer microstrip lines
15.1.2 Dispersion model of multilayer microstrip lines
15.1.3 Characteristic impedance and synthesis of multilayer microstrip lines
15.1.4 Models of losses in multilayer microstrip lines
15.1.5 Circuit model of multilayer microstrip lines
15.2 SLR process for multilayer coupled microstrip lines
15.2.1 Equivalent single layer substrate
15.2.2 Dispersion model of multilayer coupled microstrips lines
15.2.3 Characteristic impedance and synthesis of multilayer coupled microstrips
15.2.4 Losses models of multilayer coupled microstrip lines
15.3 SLR process for multilayer ACPW/CPW
15.3.1 Single Layer Reduction (SLR) process for multilayer ACPW/CPW
15.3.2 Static SDA of multilayer ACPW/CPW using two-conductor model
15.3.3 Dispersion models of multilayer ACPW/CPW
15.3.4 Loss models of multilayer ACPW/CPW
15.4 Further consideration of SLR formulation
References

Chapter 16: Dynamic Spectral Domain Analysis
16.1 General discussion of SDA
16.2 Green's function of single layer planar line
16.2.1 Formulation of field problem
16.2.2 Case #1: CPW and microstrip structures
16.2.3 Case II- Sides : MW - EW, Bottom : MW, Top : EW
16.3 Solution of hybrid mode field equations
(Galerkin's Method in Fourier Domain)
16.4 Basis functions for surface current density and slot field
16.4.1 Nature of the field and current densities:
16.4.2 Basis functions and nature of hybrid modes
16.5 Coplanar multistrip structure
16.6 Multilayer planar transmission lines
16.6.1 Immittance approach for single level strip conductors
16.6.2 Immittance approach for multilevel strip conductors
References

Chapter 17: Lumped and Line Resonators: Basic Characteristics
17.1 Basic resonating structures
17.2 Zero dimensional lumped resonator
17.2.1 Lumped series resonant circuit
17.2.2 Lumped parallel resonant circuit
17.2.3 Resonator with external circuit
17.2.4 One-port reflection type resonator
17.2.5 Two-port transmission type resonator
17.2.6 Two-port reaction type resonator
17.3 Transmission line resonator
17.3.1 Lumped resonator modeling of transmission line resonator
17.3.2 Modal description of short-circuited line resonator
References

Chapter 18: Planar Resonating Structures
18.1 Microstrip Line Resonator
18.1.1 Open-ends microstrip resonator
18.1.2 and Short-circuited ends microstrip resonator
18.1.3 Microstrip ring resonator
18.1.4 Microstrip step impedance resonator
18.1.5 Microstrip hairpin resonator
18.2 CPW resonator
18.3 Slot line resonator
18.4 Coupling of line resonator to source and load
18.4.1 Direct-coupled resonator
18.4.2 Reactively coupled line resonator
18.4.3 Tapped line resonator
18.4.4 Feed to planar transmission line resonator
18.5 Coupled resonators
18.5.1 Coupled microstrip line resonator
18.5.2 Circuit model of coupled microstrip line resonator
18.5.3 Some structures of coupled microstrip line resonator
18.6 Microstrip patch resonators
18.6.1 Rectangular patch
18.6.2 Modified Wolff Model (MWM)
18.6.3 Circular patch
18.6.4 Ring patch
18.6.5 Equilateral triangular patch
18.7 2D Fractal resonators
18.7.1 Fractal geometry
18.7.2 Fractal resonator antenna
18.7.3 Fractal resonators
18.8 Dual mode resonators
18.8.1 Dual mode patch resonators
18.8.2 Dual mode ring resonators
References

Chapter 19: Planar Periodic Transmission Lines
19.1 1D and 2D lattice structures
19.1.1 Bragg's law of diffraction
19.1.2 Crystal lattice structures
19.1.3 Concept of Brillouin zone
19.2 Space harmonics of periodic structures
19.2.1 Floquet - Bloch theorem and space harmonics
19.3 Circuit models of 1D periodic transmission line
19.3.1 Periodically loaded artificial lines
19.3.2 [ABCD] parameters of unit cell
19.3.3 Dispersion in periodic lines
19.3.4 Characteristics of 1D periodic lines
19.3.5 Some loading elements of 1D periodic lines
19.3.6 Realization of planar loading elements
19.4 1D planar EBG structures
19.4.1 1D Microstrip EBG line
19.4.2 1D CPW EBG line
References

Chapter 20: Planar Periodic Surfaces
20.1 2D planar EBG surfaces
20.1.1 General introduction of EBG surfaces
20.1.2 Characteristics of EBG surface
20.1.3 Horizontal wire dipole near EBG surface
20.2 Circuit models of mushroom type EBG
20.2.1 Basic circuit model
20.2.2 Dynamic circuit model
20.3 Uniplanar EBG structures
20.4 2D circuit models of EBG structures
20.4.1 Shunt connected 2D planar EBG circuit model
20.4.2 Series connected 2D planar EBG circuit model
References

Chapter 21: Metamaterials Realization and circuit models- I (Basic structural elements & bulk metamaterials)
21.1 Artificial electric medium
21.1.1 Polarization in the wire medium
21.1.2 Equivalent parallel plate waveguide model of wire medium
21. 1.3 Reactance loaded Wire Medium
21.2 Artificial magnetic medium
21.2.1 Characteristics of the SRR
21.2.2 Circuit model of the SRR
21.2.3 Computation of equivalent circuit parameters of SRR
21.2.4 Bi-anisotropy in the SRR medium
21.2.5 Variations in SRR structure
21.3 Double negative metamaterials
21.3.1 Composite permittivity-permeability functions
21.3.2 Realization of composite DNG metamaterials
21.3.3 Realization of single structure DNG metamaterials
21.4 Homogenization and parameter extraction
21.4.1 Nicolson - Ross - Weir (NRW) method
21.4.2 Dynamic Maxwell Garnett model
References

Chapter 22: Metamaterials Realization and circuit models- II (Metalines and Metasurfaces)
22.1 Circuit models of 1D - metamaterials
22.1.1 Homogenization of the 1D-medium
22.1.2 Circuit equivalence of material medium
22.1.3 Single reactive loading of host medium
22.1.4 Single reactive loading of host medium with coupling
22.1.5 Circuit models of 1D metalines
22.2 Non-resonant microstrip metalines
22.2.1 Series-parallel (CRLH) metalines
22.2.2 Cascaded MNG-ENG (CRLH) metalines
22.2.3 Parallel-series (D-CRLH) metalines
22.3 Resonant metalines
22.3.1 Resonant inclusions
22.3.2 Microstrip resonant metalines
22.3.3 CPW resonant metalines
22.4 Some application of metalines
22.4.1 Backfire to endfire leaky wave antenna
22.4.2 Metaline based microstrip directional coupler
22.4.3 Multiband metaline based components
22.5 Modelling and characterization of metasurfaces
22.5.1 Characterization of metasurface
22.5.2 Reflection and transmission coefficients of isotropic metasurfaces
22.5.3 Phase control of metasurface
22.5.4 Generalized Snell's laws of metasurfaces
22.5.5 Surface waves on metasurface
22.6 Applications of metasurfaces
22.6.1 Demonstration of anomalous reflection and refraction of metasurfaces
22.6.2 Reflectionless transmission of metasurfaces
22.6.3 Polarization conversion of incident plane wave
References