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Introduction To Modern Planar Transmission Lines

Physical, Analytical, and Circuit Models Approach

Verma, Anand K.

Wiley - IEEE


1. Edition August 2021
944 Pages, Hardcover
Wiley & Sons Ltd

ISBN: 978-1-119-63227-6
John Wiley & Sons

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Provides a comprehensive discussion of planar transmission lines and their applications, focusing on physical understanding, analytical approach, and circuit models

Planar transmission lines form the core of the modern high-frequency communication, computer, and other related technology. This advanced text gives a complete overview of the technology and acts as a comprehensive tool for radio frequency (RF) engineers that reflects a linear discussion of the subject from fundamentals to more complex arguments.

Introduction to Modern Planar Transmission Lines: Physical, Analytical, and Circuit Models Approach begins with a discussion of waves on transmission lines and waves in material medium, including a large number of illustrative examples from published results. After explaining the electrical properties of dielectric media, the book moves on to the details of various transmission lines including waveguide, microstrip line, co-planar waveguide, strip line, slot line, and coupled transmission lines. A number of special and advanced topics are discussed in later chapters, such as fabrication of planar transmission lines, static variational methods for planar transmission lines, multilayer planar transmission lines, spectral domain analysis, resonators, periodic lines and surfaces, and metamaterial realization and circuit models.
* Emphasizes modeling using physical concepts, circuit-models, closed-form expressions, and full derivation of a large number of expressions
* Explains advanced mathematical treatment, such as the variation method, conformal mapping method, and SDA
* Connects each section of the text with forward and backward cross-referencing to aid in personalized self-study
Introduction to Modern Planar Transmission Lines is an ideal book for senior undergraduate and graduate students of the subject. It will also appeal to new researchers with the inter-disciplinary background, as well as to engineers and professionals in industries utilizing RF/microwave technologies.

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


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


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


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)


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


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)


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.


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


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


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


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


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


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


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


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


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


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


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


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


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

ANAND K. VERMA, PhD, is an Adjunct Professor in the School of Engineering, Macquarie University, Sydney. Formerly, he was Professor and Head of the Department of Electronic Science, South Campus, University of Delhi. He has been Visiting Professor at Otto-Van-Guericke University, Magdeburg, Germany (2002, 2002-2003), 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.