### Electromagnetic Waves and Antennas

Any feedback from readers is welcome. This book provides a broad and applications-oriented introduction to electromagnetic waves and antennas, with MATLAB examples. Current interest in these areas is driven by the growth in wireless and fiber-optic communications, information technology, and materials science. Communications, antenna, radar, and microwave engineers must deal with the generation, transmission, and

Any feedback from readers is welcome.

This book provides a broad and applications-oriented introduction to

electromagnetic waves and antennas, with MATLAB examples. Current

interest in these areas is driven by the growth in wireless and

fiber-optic communications, information technology, and materials

science.

Communications, antenna, radar, and microwave engineers must deal with

the generation, transmission, and reception of electromagnetic waves.

Device engineers working on ever-smaller integrated circuits and at ever

higher frequencies must take into account wave propagation effects at

the chip and circuit-board levels. Communication and computer network

engineers routinely use waveguiding systems, such as transmission lines

and optical fibers. Novel recent developments in materials, such as

photonic bandgap structures, omnidirectional dielectric mirrors,

birefringent multilayer films, surface plasmons, negative-index

metamaterials, slow and fast light, promise a revolution in the control

and manipulation of light and other applications. These are just some

examples of topics discussed in this book.

Please note that the book is now completed and, except for corrections, the August 1, 2016 revision

will be the last one.

The entire book is freely available in PDF 2-up

format, and in PDF 1-up format. The MATLAB

toolbox is available here . The book is also

available in printed form. Individual chapters are

available below in PDF in 2-up format.

An errata file (updated December 10, 2020) is also available here. Many thanks to all who have sent me errata and,

especially, to Lee Byeong-Yoon who found most of them.

Copyright (c) 1996-2016 by Sophocles J. Orfanidis, All Rights Reserved. The

book exists in online form through the web page www.ece.rutgers.edu/~orfanidi/ewa. Links to

this page may be placed on any web site. The book may cited as follows:

S. J. Orfanidis, “Electromagnetic Waves and Antennas”, 2016 [Online].

Available: https://www.ece.rutgers.edu/~orfanidi/ewa/.

Any part of this book may be downloaded and printed for personal or educational

use only, as long as the printed or photocopied pages are not altered in any

way from the original PDF files posted on the book’s web page.

No part of this book may be reproduced, altered in any way, or transmitted in

any form for commercial, profit, sale, or marketing purposes.

MATLAB (R) is a registered trademark of The MathWorks, Inc.

I am grateful to Mr. Davide Ramaccia, student of Prof. Alessandro

Toscano, Department of Applied Electronics, University “Roma Tre”, Rome,

Italy, for producing very detailed solutions

of the problems of Chapters 1 & 2 , and for allowing me to post them

online. Solutions to the rest of the problems are not yet available.

The book is also available in print-on-demand form. Because of printer

limitations, the book has been evenly split into two volumes, each with

its own index, but with the list of references and appendices included

only in volume two. The following versions are available:

The text makes extensive use of MATLAB. We have developed an

“Electromagnetic Waves & Antennas” toolbox containing about 200 MATLAB

functions for carrying out all of the computations and simulation

examples in the text. Code segments illustrating the usage of these

functions are found throughout the book, and serve as a user manual. Our

MATLAB-based numerical solutions are not meant to replace sophisticated

commercial field solvers. The inclusion of numerical methods was

motivated by the desire to provide the reader with some simple tools for

self-study and experimentation. We felt that it would be useful and fun

to be able to quickly carry out the computations illustrating various

waves and antenna applications, and have included enough MATLAB code in

each example (but skipping all figure annotations) that would enable the

reader to reproduce the results. The functions may be grouped into the

following categories:

Multilayer Dielectric Structures

--------------------------------

brewster - calculates Brewster and critical angles

fresnel - Fresnel reflection coefficients for isotropic or birefringent media

n2r - refractive indices to reflection coefficients of M-layer structure

r2n - reflection coefficients to refractive indices of M-layer structure

multidiel - reflection response of isotropic or birefringent multilayer structures

multidiel1 - simplified version of multidiel for isotropic layers

multidiel2 - reflection response of lossy isotropic multilayer dielectric structures

omniband - bandwidth of omnidirectional mirrors and Brewster polarizers

omniband2 - bandwidth of birefringent multilayer mirrors

snel - calculates refraction angles from Snel's law for birefringent media

Quarter-Wavelength Transformers

-------------------------------

bkwrec - order-decreasing backward layer recursion - from a,b to r

frwrec - order-increasing forward layer recursion - from r to A,B

chebtr - Chebyshev design of broadband reflectionless quarter-wave transformer

chebtr2 - Chebyshev design of broadband reflectionless quarter-wave transformer

chebtr3 - Chebyshev design of broadband reflectionless quarter-wave transformer

Dielectric Waveguides

---------------------

dguide - TE modes in dielectric slab waveguide

dslab - solves for the TE-mode cutoff wavenumbers in a dielectric slab

dguide3 - TE and TM modes in asymmetric 3-slab dielectric waveguide

Plasmonic Waveguides

---------------------

drude - Drude-Lorentz model for Silver, Gold, Copper, Aluminum

dmda - asymmetric DMD plasmonic waveguide - iterative solution

dmds - symmetric DMD plasmonic waveguide - iterative solution

dmdcut - cutoff width for asymmetric DMD guides

pwg - plasmonic waveguide solution for symmetric guides

pwga - plasmonic waveguide solution for asymmetric guides

pwgpower - transmitted power in plasmonic waveguide

Sommerfeld and Goubau Wires

----------------------------

sommer - solve characteristic equation for Sommerfeld wire

goubau - solve characteristic equation of Goubau line

goubatt - Goubau line attenuation

gcut - cutoff function for Goubau line

attw - characteristic equation of Attwood surface waveguide

attwatt - attenuation of Attwood surface waveguide

J01 - J0(z)/J1(z) approximation for large imag(z)

Transmission Lines

------------------

g2z - reflection coefficient to impedance transformation

z2g - impedance to reflection coefficient transformation

lmin - find locations of voltage minima and maxima

mstripa - microstrip analysis (calculates Z,eff from w/h)

mstripr - microstrip synthesis with refinement (calculates w/h from Z)

mstrips - microstrip synthesis (calculates w/h from Z)

multiline - reflection response of multi-segment transmission line

swr - standing wave ratio

tsection - T-section equivalent of a length-l transmission line segment

gprop - reflection coefficient propagation

vprop - voltage and current propagation

zprop - wave impedance propagation

Impedance Matching

------------------

qwt1 - quarter wavelength transformer with series segment

qwt2 - quarter wavelength transformer with 1/8-wavelength shunt stub

qwt3 - quarter wavelength transformer with shunt stub of adjustable length

dualband - two-section dual-band Chebyshev transformer

dualbw - bandwidth of dual-band transformer

stub1 - single-stub matching

stub2 - double-stub matching

stub3 - triple-stub matching

onesect - one-section impedance transformer

twosect - two-section impedance transformer

pi2t - Pi to T transformation

t2pi - T to Pi transformation

lmatch - L-section reactive conjugate matching network

pmatch - Pi-section reactive conjugate matching network

S-Parameters

------------

gin - input reflection coefficient in terms of S-parameters

gout - output reflection coefficient in terms of S-parameters

nfcirc - constant noise figure circle

nfig - noise figure of two-port

sgain - transducer, available, and operating power gains of two-port

sgcirc - stability and gain circles

smat - S-parameters to S-matrix

smatch - simultaneous conjugate match of a two-port

smith - draw basic Smith chart

smithcir - add stability and constant gain circles on Smith chart

sparam - stability parameters of two-port

circint - circle intersection on Gamma-plane

circtan - point of tangency between the two circles

Linear Antenna Functions

------------------------

dipdir - dipole directivity

dmax - computes directivity and beam solid angle of g(th) gain

dipole - gain of center-fed linear dipole of length L

traveling - gain of traveling-wave antenna of length L

vee - gain of traveling-wave vee antenna

rhombic - gain of traveling-wave rhombic antenna

king - King's 3-term sinusoidal approximation

kingeval - evaluate King's 3-term sinusoidal current approximation

kingfit - fits a sampled current to King's 2-term sinusoidal approximation

kingprime - converts King's 3-term coefficients from unprimed to primed form

hbasis - basis functions for Hallen equation

hdelta - solve Hallen's equation with delta-gap input

hfield - solve Hallen's equation with arbitrary incident E-field

hmat - Hallen impedance matrix with method of moments and point-matching

hwrap - wraps a Toeplitz impedance matrix to half its size

kernel - thin-wire kernel computation for Hallen equation

pfield - solve Pocklington's equation with arbitrary incident E-field

pmat - Pocklington impedance matrix with method of moments and point-matching

hcoupled - solve Hallen's equation for 2D array of non-identical parallel dipoles

hcoupled2 - solve Hallen's equation for 2D array of identical parallel dipoles

gain2d - normalized gain of 2D array of parallel dipoles with Hallen currents

gain2s - normalized gain of 2D array of parallel dipoles with sinusoidal currents

imped - mutual impedance between two parallel standing-wave dipoles

imped2 - mutual impedance between two parallel standing-wave dipoles

impedmat - mutual impedance matrix of array of parallel dipole antennas

resonant - calculates the length of a resonant dipole antenna

yagi - simplified Yagi-Uda array design

Aperture Antenna Functions

--------------------------

BBnum - computation of fields in Bethe-Bouwkamp model

BBfar - far fields in Bethe-Bouwkamp model

BBnear - near fields in Bethe-Bouwkamp model

diffint - generalized Fresnel diffraction integral

diffr - knife-edge diffraction coefficient

dsinc - the double-sinc function cos(pi*x)/(1-4*x^2)

fcs - Fresnel integrals C(x) and S(x)

fcs2 - type-2 Fresnel integrals C2(x) and S2(x)

jinc - jinc and "shifted" jinc function

talbot - Gauss sums for fractional Talbot effect

tbw - Taylor's one-parameter window

tnb1 - Taylor's n-bar window (1-D)

tnb2 - Taylor's n-bar window (2-D)

hband - horn antenna 3-dB width

heff - aperture efficiency of horn antenna

hgain - horn antenna H-plane and E-plane gains

hopt - optimum horn antenna design

hsigma - optimum sigma parametes for horn antenna

Antenna Array Functions

-----------------------

gain1d - normalized gain computation for 1D equally-spaced isotropic array

bwidth - beamwidth mapping from psi-space to phi-space

binomial - binomial array weights

dolph - Dolph-Chebyshev array weights

dolph2 - Riblet-Pritchard version of Dolph-Chebyshev

dolph3 - DuHamel version of endfire Dolph-Chebyshev

multibeam - multibeam array design

prol - prolate array design

prolmat - prolate matrix

scan - scan array with given scanning phase

sector - sector beam array design

steer - steer array towards given angle

taylornb - Taylor n-bar line source array design

taylor1p - Taylor 1-parameter array design

taylorbw - Taylor B-parameter and beamwidth

uniform - uniform array weights

woodward - Woodward-Lawson-Butler beams

ville - Villeneuve array design

chebarray - Bresler's Chebyshev array design method - written by P. Simon

I would like to thank Dr. Simon for premission to include

this function in this collection.

Gain Plotting Functions

-----------------------

abp - polar gain plot in absolute units

abz - azimuthal gain plot in absolute units

abp2 - polar gain plot in absolute units - 2*pi angle range

abz2 - azimuthal gain plot in absolute units - 2pi angle range

dbp - polar gain plot in dB

dbz - azimuthal gain plot in dB

dbp2 - polar gain plot in dB - 2*pi angle range

dbz2 - azimuthal gain plot in dB - 2pi angle range

abadd - add gain in absolute units

abadd2 - add gain in absolute units - 2pi angle range

dbadd - add gain in dB

dbadd2 - add gain in dB - 2pi angle range

addbwp - add 3-dB angle beamwidth in polar plots

addbwz - add 3-dB angle beamwidth in azimuthal plots

addcirc - add grid circle in polar or azimuthal plots

addline - add grid ray line in azimuthal or polar plots

addray - add ray in azimuthal or polar plots

Miscellaneous Utility Functions

--------------------------------

ab - dB to absolute power units

db - absolute power to dB units

c2p - complex number to phasor form

p2c - phasor form to complex number

d2r - degrees to radians

r2d - radians to degrees

dtft - DTFT of a signal x at a frequency vector w

I0 - modified Bessel function of 1st kind and 0th order

ellipse - polarization ellipse parameters

etac - eta and c

wavenum - calculate wavenumber and characteristic impedance

poly2 - specialized version of poly with increased accuracy

quadr - Gauss-Legendre quadrature weights and evaluation points

quadrs - quadrature weights and evaluation points on subintervals

quadr2 - Gauss-Legendre quadrature weights and evaluation points

quadrs2 - quadrature weights and evaluation points on subintervals

quadts - tanh-sinh, double-exponential, quadrature

Ci - cosine integral Ci(z)

Cin - cosine integral Cin(z)

Gi - Green's function integral

Si - sine integral Si(z)

sinhc - hyperbolic sinc function

asinhc - inverse hyperbolic sinc function

sqrte - evanescent SQRT for waves problems

pswf - prolate spheroidal wave functions

spherj - spherical Bessel functions

legpol - evaluate Legendre polynomials

flip - flip a column, a row, or both

blockmat - manipulate block matrices

upulse - generates trapezoidal, rectangular, triangular pulses, or a unit-step

ustep - unit-step or rising unit-step function

Elliptic Function Computation

--------------------------------

snv - sn elliptic function at a vector of moduli

dnv - dn elliptic function at a vector of moduli

ellipK - complete elliptic integral of first kind at a vector of moduli

ellipE - complete elliptic integral of second kind at a vector of moduli

landenv - Landen transformations of a vector of elliptic moduli

MATLAB Movies (in subdirectory ewa/movies)

------------------------------------------

grvmovie1 - pulse propagation with slow and negative group velocity (vg<0)

grvmovie2 - pulse propagation with slow and fast group velocity (vg>c)

pulsemovie - step and pulse propagation on terminated transmission lines

pulse2movie - step propagation on two cascaded lines

RLCmovie - step getting reflected off a reactive termination

TDRmovie - fault location by time-domain reflectometry

xtalkmovie - crosstalk signals on coupled transmission lines

dipmovie - electric field pattern of radiating Hertzian dipole