Introduction To Modern Planar Transmission Lines. Anand K. Verma

C‐ and π‐mode excitations of the asymmetrically coupled microstr...Figure 12.8 Equivalent C‐ and π‐mode impedances.Figure 12.9 Symmetrical edge‐coupled CPW on finite thickness substrate.Figure 12.10 Characteristic impedance and effective relative permittivity of...Figure 12.11 Shielded broadside coupled CPW and its even–odd mode characteri...Figure 12.12 4‐Port symmetrical coupled transmission line section.Figure 12.13 Even and odd modes excitation of the symmetrical coupled lines....Figure 12.14 Even‐mode analysis of the symmetrical coupled lines.Figure 12.15 Ten configurations of the symmetrical coupled lines.Figure 12.16 The 4‐port network and equivalent 2‐port with terminated load a...Figure 12.17 Two‐port single conductor transmission line section.Figure 12.18 Even–odd analysis of the symmetrically coupled microstrips with...Figure 12.19 Several two‐port networks, with ABCD parameters, of coupled mic...Figure 12.20 Asymmetrical coupled lines in an inhomogeneous medium.

      12 Chapter 13Figure 13.1 Some common multilayer microstrip lines.Figure 13.2 Substrates and fabrication process of HMIC.Figure 13.3 Steps of the chemical etching process.Figure 13.4 Positive photolithography process.Figure 13.5 Physical vapor deposition (PVD) process.Figure 13.6 Schematic diagram of the thick film process using screen printin...Figure 13.7 The photo‐imageable thick film technology process.Figure 13.8 MMIC fabrication process.Figure 13.9 MIS and Schottky structures.Figure 13.10 Thin‐film microstrip.Figure 13.11 Fishbone‐type stub loaded line on PES substrate.Figure 13.12 Multilayered microstrip and coupled microstrip lines for MMIC a...Figure 13.13 Some buried microstrip lines.Figure 13.14 Electrodes of active devices as multilayer CPW lines.Figure 13.15 Wet and dry etching of Si‐substrate.Figure 13.16 Basic steps for creation of microbridge by the surface micromac...Figure 13.17 Some membrane supported microstrip type of MEMS lines.Figure 13.18 Some variants of MEMS strip lines on low and high resistivity s...Figure 13.19 Microstrip on air‐substrate.Figure 13.20 MEMS CPW on high resistivity Si‐substrate.Figure 13.21 MEMS microshielded microstrip line.Figure 13.22 Micro‐shielded MEMS CPW.Figure 13.23 MEMS CPW in CMOS technology.Figure 13.24 LIGA planar transmission lines.Figure 13.25 LIGA fabrication process.Figure 13.26 Fabrication process of MEMS waveguide.Figure 13.27 A typical LTCC structure with embedded and surface mounted comp...Figure 13.28 Casting process of green‐tape.Figure 13.29 A typical arrangement of vias, passive components, and conducto...Figure 13.30 Steps of LTCC circuit fabrication process.Figure 13.31 Some LTCC circuit fabrication processes.Figure 13.32 Microstrip lines in LTCC.Figure 13.33 Microstrip CPW transition in the LTCC.Figure 13.34 Coupler in LTCC technology.Figure 13.35 Branch line coupler in the LTCC.Figure 13.36 The embedded microstrip bandpass filter in LTCC.Figure 13.37 Bandpass filter in LTCC.Figure 13.38 Waveguide and cavity structures in the LTCC.

      13 Chapter 14Figure 14.1 Nature of variational (a and b) and nonvariational (c) functiona...Figure 14.2 Transmission lines and variational bounds.Figure 14.3 A few common charge distribution functions and potential distrib...Figure 14.4 Boxed microstrip and current distributions on its ground planes....Figure 14.5 Open microstrip line in the inhomogeneous medium.Figure 14.6 Different cases of the multilayer microstrip line with electric/...Figure 14.7 Equivalent transmission line model used in TTL technique.Figure 14.8 Equivalent transmission line model of the four‐layered microstri...Figure 14.9 TTL method for the open‐sided multilayer microstrip line.Figure 14.10 Multilayer coupled microstrip line structures.Figure 14.11 Decoupled single microstrip under even/odd mode excitation and ...Figure 14.12 Multilayer coupled microstrip line without the sidewalls.Figure 14.13 Control of phase velocities and characteristic impedances of co...Figure 14.14 Boxed microstrip and CPW structures.Figure 14.15 Galerkin's process of taking the inner product of three testing...

      14 Chapter 15Figure 15.1 Four‐layered microstrip and some special cases.Figure 15.2 The two‐step SLR‐formulation process.Figure 15.3 The virtual relative permittivity‐based SLR‐dispersion models....Figure 15.4 Validation of SLR and ISLR‐dispersion models against results of ...Figure 15.5 Flow‐chart of the synthesis process for a multilayered microstri...Figure 15.6 Dielectric loss in the shielded and composite substrate microstr...Figure 15.7 Conductor loss in the shielded and dielectric covered microstrip...Figure 15.8 Four‐layered coupled microstrip and some special cases.Figure 15.9 Even‐ and odd‐mode dispersion of the coupled microstrip lines on...Figure 15.10 Even and odd dispersion characteristics of a coupled microstrip...Figure 15.11 Dielectric loss of coupled microstrip on a composite substrate ...Figure 15.12 Conductor loss of the coupled microstrip on several types of su...Figure 15.13 Multilayer ACPW and equivalent single‐layer substrate using the...Figure 15.14 Computed and simulated line parameters of shielded CPW on the c...

      15 Chapter 16Figure 16.1 Shielded CPW and microstrip structures.Figure 16.2 Generic structure supporting hybrid mode and its two‐port circui...Figure 16.3 One‐half of the CPW structure.Figure 16.4 Hybrid modes on a microstrip line [J.15].Figure 16.5 Basis functions for current density on microstrip.Figure 16.6 Bound and leaky mode on a slot‐line.Figure 16.7 Bound and leaky mode on a CPW.Figure 16.8 Same level multiconductors and multislots.Figure 16.9 Multilayer planar transmission line structures.Figure 16.10 Spectral wave propagation.Figure 16.11 Equivalent transverse transmission line (TTL) for TE^y and TM^y –...Figure 16.12 Equivalent TTL network for two‐level strip conductors in (u, v,...Figure 16.13 Determination of the transfer (mutual) impedance of the LSE (TEFigure 16.14 Two levels coupled structures.

      16 Chapter 17Figure 17.1 Some resonating structures.Figure 17.2 Some patch and ring resonators.Figure 17.3 Behavior of series resonant circuit.Figure 17.4 Behavior of the parallel resonant circuit.Figure 17.5 Basic types of planar resonators with equivalent circuits.Figure 17.6 Input impedance variation of the one‐port reflection‐type resona...Figure 17.7 Circuit configurations of series and parallel resonators.Figure 17.8 Sketched insertion loss and phase response ∠S₂₁(f) of series/shu...Figure 17.9 Some reaction‐type resonators.Figure 17.10 Basic transmission line resonators, showing voltage and current...Figure 17.11 Reactance variation of short‐circuited line with frequency βℓ =...Figure 17.12 Equivalent circuit and higher‐order modes of both end short‐cir...Figure 17.13 Both ends short‐circuited line with an equivalent circuit.

      17 Chapter 18Figure 18.1 Some popular forms of microstrip resonators.Figure 18.2 Modeling of the open‐end and short‐circuited‐end microstrip reso...Figure 18.3 Periodically loaded microstrip λ_g/2 resonator.Figure 18.4 Transmission line model of the ring resonator.Figure 18.5 Step impedance resonators.Figure 18.6 Harmonic frequency control of the λ_g/4− SIR.Figure 18.7 Control of spurious resonance by the impedance ratio K.Figure 18.8 Control of length of the SIR by the length of line #1 and impeda...Figure 18.9 Some microstrip hairpin resonator.Figure 18.10 Control of fundamental and first spurious resonance frequencies...Figure 18.11 CPW resonators.Figure 18.12 UBPF using CPW SIR.Figure 18.13 Some simple slot line resonators.Figure 18.14 Direct‐coupled line resonator.Figure 18.15 Reactively coupled line resonators.Figure 18.16 Graphical solution of the transcendental equations.Figure 18.17 Tapped line resonator.Figure 18.18 Feeding arrangement of λ_g/2 microstrip line resonators.Figure 18.19 Feeding arrangement of CPW line resonators.Figure 18.20 Coupled microstrip line resonators.Figure 18.21 S₂₁ response of coupled microstrip resonator.Figure 18.22 Coupling arrangements between open square resonators.Figure 18.23 Coupling arrangements of bent microstrip resonators and slot li...Figure 18.24 Some microstrip patch resonators. Thickness h of the substrate ...Figure 18.25 Ez‐field distribution of a few TM_mn‐modes. (M: Magnetic current...Figure 18.26 Shielded multilayer microstrip rectangular patch resonator.Figure 18.27 Field and current patterns of a few TM_mn modes of microstrip ci...Figure 18.28 Field and current patterns of a few TM_nm‐modes of microstrip ri...Figure 18.29 Field patterns of two TM_nml‐modes of microstrip equilateral tri...Figure 18.30 Resonance frequency of the equilateral triangular patch.Figure 18.31 Creation of scaled copies of objects in Euclidean space.Figure 18.32 Creation of a Koch curve from a line segment.Figure 18.33 Creation of Koch island or Koch Snowflake from an equilateral t...Figure 18.34 Creation of square Koch island or square Koch Snowflake from a ...Figure 18.35 Generation of Minkowski curve from the 8‐sided pulse generator....Figure 18.36 Generation of Minkowski island from the 5‐sided square/rectangu...Figure 18.37 Generation of Hilbert curves using U shape generator.Figure 18.38 Generation of Sierpinski triangles.Figure 18.39 Generation of Sierpinski carpet.Figure 18.40 Resonance frequency behavior of Koch and other folded