Introduction To Modern Planar Transmission Lines

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