Tel: 848-445-5017
e-mail: orfanidi@rci.rutgers.edu
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.
The book is organized around three main topic areas:
Initially posted online in November 2002. Latest revision date - August 1, 2016.
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.
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:
addpath c:\antennas\ewa;Note that just typing the name of any function will produce a help/usage comment for that function. For gain plots that will eventually be exported into EPS and inserted in LaTeX files, we found it best to add the following lines to the MATLAB startup.m file:
help ewa;
set(0,'DefaultAxesLineWidth', 1);The detailed list of the MATLAB functions is as follows:
set(0,'DefaultLineLineWidth', 1.5);
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