comandos matlab linha de transmissao

8/10/2019 Comandos Matlab Linha de Transmissao

1/10

ElectromagneticWaves and Antennas

Sophocles J. Orfanidis

ECE DepartmentRutgers University94 Brett RoadPiscataway, NJ 08854-8058

Tel: 732-445-5017

e-mail: [email protected]

This book is a work in progress. Anyfeedback from readers is welcome.

This text provides a broad and applications-oriented introductionto electromagnetic waves andantennas. 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,propagation, and reception of electromagnetic waves. Computer and solid-state device engineersworking on ever smaller integrated circuits and at ever higher frequencies must take into account wavepropagation effects at the chip and circuit-board levels. Communication and computer networkengineers routinely use waveguiding systems, such as transmission lines and optical fibers. Novel recentdevelopments in materials, such as photonic bandgap structures, omnidirectional dielectric mirrors, andbirefringent multilayer films, promise a revolution in the control and manipulation of light. These arejust some examples of topics discussed in this book.

The text is organized around three main topic areas:

The propagation, reflection, and transmission of plane waves, and the analysis and design ofmultilayer films.

Waveguides, transmission lines, impedance matching, and S-parameters. Linear and aperture antennas, scalar and vector diffraction theory, antenna array design, and

coupled antennas.

The text emphasizes connections to other subjects. For example, the mathematical techniques foranalyzing wave propagation in multilayer structures, multisegment transmission lines, and the design of

Page 1 of 10Electromagnetic Waves and Antennas

1/16/2007http://www.ece.rutgers.edu/~orfanidi/ewa/


2/10

multilayer optical filters are the same as those used in DSP, such as the lattice structures of linearprediction, the analysis and synthesis of speech, and geophysical signal processing. Similarly, antennaarray design is related to the problem of spectral analysis of sinusoids and to digital filter design, andButler beams are equivalent to the FFT.

Individual chapters are available below in PDF format. Please note that they are subject to continuousrevision.Initially posted online in November 2002. Last revision date - June 21, 2004.

Front Matter and PrefaceTable of Contents

Ch.1: Maxwell's EquationsReview of Maxwell's equations, Lorentz force, constitutive relations, boundary conditions, chargeand energy conservation, Poynting's theorem, simple models of dielectrics, conductors, andplasmas, relaxation time in conductors.

Ch.2: Uniform Plane WavesUniform plane waves in lossless media, monochromatic waves, wave impedance, polarization,waves in lossy media, waves in weakly lossy dielectrics, propagation in good conductors,propagation in oblique directions, complex waves, Doppler effect.

Ch.3: Propagation in Birefringent MediaLinear and circular birefringence, uniaxial and biaxial media, chiral media, natural vs. Faradayrotation, gyrotropic media, linear and circular dichroism, oblique propagation in birefringentmedia.

Ch.4: Reflection and TransmissionReflection and transmission at normal incidence, propagation and matching matrices, reflectedand transmitted power, single and double dielectric slabs, reflectionless slab, time-domainreflection response, lattice diagrams, reflection by a moving boundary, such as a moving mirror.

Ch.5: Multilayer StructuresMultiple dielectric slabs at normal incidence, antireflection coatings, dielectric mirrors,propagation bandgaps, narrow-band transmission filters, quarter-wave phase-shifted Fabry-Perotresonators, fiber Bragg gratings, equal travel-time multilayer structures, applications of layeredstructures, Chebyshev design of reflectionless multilayers.

Ch.6: Oblique Incidence

Oblique incidence and Snell's laws, transverse impedance, propagation and matching of transversefields, Fresnel reflection coefficients, total internal reflection, Brewster angle, complex waves,oblique reflection by a moving interface, geometrical optics, Fermat's principle of least time, raytracing techniques in geometrical optics illustrated by several exactly solvable examples drawnfrom several applications, such as atmospheric refraction, mirages, ionospheric refraction,propagation in a standard atmosphere and the effect of Earth's curvature, and propagation ingraded-index optical fibers.

Ch.7: Multilayer Film Applications




3/10

Multilayer dielectric structures at oblique incidence, antireflection coatings at oblique incidence,omnidirectional dielectric mirrors, polarizing beam splitters, reflection and refraction inbirefringent media, Brewster and critical angles in birefringent media, multilayer birefringentstructures, giant birefringent optics.

Ch.8: WaveguidesLongitudinal-transverse decompositions of Maxwell's equations, power transfer and attenuation in

guiding systems, TEM, TE, TM modes, rectangular waveguides, higher TE and TM modes,operating bandwidth, power transfer, energy density, and group velocity in waveguides, powerattenuation, reflection model of waveguide propagation, dielectric slab guides.

Ch.9: Transmission LinesGeneral properties of TEM transmission lines, parallel-plate, microstrip, coaxial, and two-wirelines, distributed circuit model of a transmission line, wave impedance and reflection response,two-port equivalent circuits, terminated lines, power transfer from generator to load, open- andshort-circuited lines, Thevenin and Norton equivalent circuits, standing wave ratio, determinationof unknown load impedance, Smith chart. Transient Response.

Ch.10: Coupled LinesCoupled transmission lines, even-odd mode decomposition for identical matched or unmatchedlines, crosstalk between lines, weakly coupled lines with arbitrary terminations, coupled-modetheory, co-directional couplers, fiber Bragg gratings as examples of contra-directional couplers,quarter-wave phase-shifted fiber Bragg gratings as narrow-band transmission filters, and theSchuster-Kubelka-Munk theory of diffuse reflection and transmission as an example of contra-directional coupling.

Ch.11: Impedance MatchingConjugate and reflectionless matching, multisection transmission lines, quarter-wavelengthimpedance transformers, two-section dual-band Chebyshev transformers, quarter-wavelengthtransformers with series sections and shunt stubs, two-section series impedance transformers,single-stub matching, balanced stubs, double- and triple-stub matching, L-, T-, and Pi-sectionlumped reactive matching networks and their Q-factors.

Ch.12: S-ParametersScattering parameters, power flow, parameter conversions, input and output reflectioncoefficients, stability circles, transducer, operating, and available power gains, generalized S-parameters and power waves, simultaneous conjugate matching, power gain circles, unilateralgain circles, operating and available power gain circles, noise figure circles, design examples oflow-noise high-gain microwave amplifiers and their microstrip matching circuits.

Ch.13: Radiation Fields

Currents and charges as sources of fields, retarded potentials, fields of a linear wire antenna, nearand far fields of electric and magnetic dipoles, Ewald-Oseen extinction theorem of molecularoptics, radiation fields, radiation field approximation, computing the radiation fields, radiationvector.

Ch.14: Transmitting and Receiving AntennasEnergy flux and radiation intensity from a radiating system, directivity, gain, and beamwidth of anantenna, effective area, gain-beamwidth product, antenna equivalent circuits, effective length andpolarization and load mismatches, communicating antennas, Friis formula, antenna noise




4/10

temperature, system noise temperature, limits on bit rates, satellite links, radar equation.

Ch.15: Linear and Loop AntennasLinear antennas, Hertzian dipole, standing-wave antennas, half-wave dipole, monopole antennas,traveling wave antennas, vee and rhombic antennas, loop antennas, circular and square loops,dipole and quadruple radiation.

Ch.16: Radiation from AperturesField equivalence principle, magnetic currents and duality, radiation fields from magneticcurrents, radiation fields from apertures, Kottler's formula, Huygens sources, directivity andeffective area of apertures, uniform, rectangular, and circular apertures and their gain-beamwidthproducts, Rayleigh diffraction limit, vector diffraction theory, Stratton-Chu, Kottler, Franz, andKirchhoff diffraction integral formulas, extinction theorem, vector diffraction from apertures,Fresnel diffraction, Knife-edge diffraction, geometrical theory of diffraction and Sommerfeld'ssolution for a conducting half-plane.

Ch.17: Aperture AntennasOpen-ended waveguides, horn antennas, horn radiation fields, horn directivity, optimum horn

design, microstrip antennas, parabolic reflector antennas, gain and beamwidth of reflectorantennas, aperture-field and current-distribution methods, radiation patterns of reflector antennas,dual-reflector antennas, lens antennas.

Ch.18: Antenna ArraysAntenna arrays and translational phase shift, array pattern multiplication, one-dimensional arrays,visible region, grating lobes, uniform arrays, array directivity, steering, and beamwidth.

Ch.19: Array Design MethodsSchelkunoff's zero-placement method, Fourier series design method with windowing, sector beamarray design, Woodward-Lawson frequency-sampling design, narrow-beam low-sidelobe designs,binomial arrays, Dolph-Chebyshev arrays, Taylor-Kaiser arrays, multi-beam arrays, emphasis onthe connections to DSP methods of digital filter design and spectral analysis of sinusoids.

Ch.20: Currents on Linear AntennasHallen and Pocklington integral equations, delta-gap and plane-wave sources, solving Hallen'sequation, sinusoidal current approximation, reflecting and center-loaded receiving antennas,King's three-term approximation, numerical solution of Hallen's equation, numerical solutionsusing pulse functions and for arbitrary incident field, numerical solution of Pocklington'sequation.

Ch.21: Coupled AntennasNear fields of linear antennas, self and mutual impedance, coupled two-element arrays, arrays of

parallel dipoles, Yagi-Uda antennas, Hallen equations for coupled antennas.

AppendicesPhysical constants, electromagnetic frequency bands, vector identities and integral theorems,Green's functions, coordinate systems, Fresnel integrals, Lorentz transformations, list ofMATLAB functions.

ReferencesIndex




5/10

Copyright Notice

Copyright (c) 1996-2004 by Sophocles J. Orfanidis, All Rights Reserved. The book currently exists onlyin online form through the web page www.ece.rutgers.edu/~orfanidi/ewa. Links to this page may beplaced on any web site.

Any part of this book may be downloaded and printed for personal or educational use only, as long asthe printed or photocopied pages are not altered in any way from the original PDF files posted on thebook'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 Toolbox

The text makes extensive use of MATLAB. We have developed an "Electromagnetic Waves &Antennas" toolbox containing 140 MATLAB functions for carrying out all of the computations andsimulation examples in the text. Code segments illustrating the usage of these functions are foundthroughout the book, and serve as a user manual. The functions may be grouped into the followingcategories:

Design and analysis of multilayer film structures, including antireflection coatings, polarizers,omnidirectional mirrors, narrow-band transmission filters, birefringent multilayer films and giantbirefringent optics.

Design of quarter-wavelength impedance transformers and other impedance matching methods,

such as stub matching and L-, Pi- and T-section reactive matching networks. Design and analysis of transmission lines and waveguides, such as microstrip lines and dielectric

slab guides. S-parameter functions for gain computations, Smith chart generation, stability, gain, and noise-

figure circles, conjugate matching, and microwave amplifier design. Functions for the computation of directivities and gain patterns of linear antennas, such as dipole,

vee, rhombic, and traveling-wave antennas. Aperture antenna functions, for open-ended waveguides, horn antenna design, diffraction

integrals, and knife-edge diffraction coefficients. Antenna array design functions for uniform, binomial, Dolph-Chebyshev, Taylor arrays, sector-

beam, multi-beam, Woodward-Lawson, and Butler arrays. Functions for beamwidth anddirectivity calculations, and for steering and scanning arrays.

Numerical methods for solving the Hallen and Pocklington integral equations for single andcoupled antennas and computing self and mutual impedances.

Several functions for making azimuthal and polar plots of antenna and array gain patterns indecibels and absolute units.

There are also several MATLAB movies showing the propagation of step signals and pulses onterminated transmission lines, or propagating on cascaded lines, step signals getting reflected offreactive terminations, fault location by TDR, propagating crosstalk signals on coupled lines, andtime-evolution of the field lines radiated by a dipole antenna.




6/10

Please read the license agreementbefore using the toolbox. The toolbox was developed under MATLABv5.3. The zipped file ewa.zip(revised on Feb. 28, 2004) contains all the MATLAB functions. It shouldbe uncompressed in a directory, say c: \ ant ennas\ ewa. To add this directory to the MATLAB path andto get initial help, use the following commands:

addpath c: \ ant ennas\ ewa;hel p ewa;

Note that just typing the name of any function will produce a help/usage comment for that function. Forgain plots that will eventually be exported into EPS and inserted in LaTeX files, we found it best to addthe following lines to the MATLAB startup.m file:

set ( 0, ' Def aul t AxesLi neWi dt h' , 1) ;set ( 0, ' Def aul t Li neLi neWi dt h' , 1. 5) ;

The detailed list of the MATLAB functions is as follows:

Multilayer Dielectric Structures- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

n2r - refr acti ve i ndi ces t o ref l ecti on coef f i c i ent s of M- l ayer str uctur er2n - ref l ecti on coef f i c i ent s t o ref r acti ve i ndi ces of M- l ayer str uctur e

multidiel - r ef l ecti on r esponse of i sot r opi c or bi r ef r i ngent mul t i l ayerdi el ectr i c str ucturemultidiel1 - s i mpl i f i ed ver si on of mul t i di el f or i sot ropi c l ayersmultidiel2 - ref l ecti on response of l ossy i sot ropi c mul t i l ayer di el ectr i cstructures

omniband - bandwi dt h of omni di r ect i onal mi r r or s and Br ewst er pol ar i zer somniband2 - bandwi dt h of bi r ef r i ngent mul t i l ayer mi r r or s

brewster - cal cul at es Br ewst er and cri t i cal angl es f or i sot r opi c or

bi r ef r i ngent medi afresnel - Fresnel r ef l ecti on coef f i c i ent s f or i sot ropi c or bi ref r i ngentmedi asnell - cal cul at es r ef ract i on angl es f romSnel l ' s l aw f or bi ref r i ngentmedi a

Quarter-Wavelength Transformers- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -bkwrec - order - decreasi ng backwar d l ayer r ecur si on - f r oma, b t o rfrwrec - or der - i ncreasi ng f or war d l ayer r ecur si on - f r om r t o A, B

chebtr - Chebyshev desi gn of br oadband r ef l ect i onl ess quart er - wavet r ansf ormer

chebtr2 - Chebyshev desi gn of br oadband ref l ect i onl ess quart er - wavet r ansf ormerchebtr3 - Chebyshev desi gn of br oadband ref l ect i onl ess quart er - wavet r ansf ormer

Dielectric Waveguides- - - - - - - - - - - - - - - - - - - - -dguide - TE modes i n di el ect r i c sl ab wavegui dedslab - sol ves f or t he TE- mode cut of f wavenumber s i n a di el ect r i c sl ab




7/10

Transmission Lines- - - - - - - - - - - - - - - - - -g2z - r ef l ect i on coef f i ci ent t o i mpedancez2g - i mpedance t o r ef l ect i on coef f i ci entlmin - f i nd l ocat i ons of vol t age mi ni ma and maxi ma

mstripa - mi crostr i p anal ysi s ( cal cul at es Z, ef f f r om w/ h)mstripr - mi crost r i p synt hesi s wi t h r ef i nement ( cal cul at es w/ h f r om Z)

mstrips - mi crost r i p synt hesi s ( cal cul at es w/ h f r om Z)

multiline - r ef l ect i on r esponse of mul t i - segment t r ansmi ssi on l i neswr - st andi ng wave r at i otsection - T- sect i on equi val ent of a l engt h- l t r ansmi ssi on l i ne segment

gprop - r ef l ecti on coef f i ci ent pr opagat i onvprop - vol t age and cur r ent pr opagat i onzprop - wave i mpedance pr opagat i on

Impedance Matching- - - - - - - - - - - - - - - - - -qwt1 - quart er wavel engt h t r ansf ormer wi t h ser i es segment

qwt2 - quart er wavel engt h t r ansf ormer wi t h 1/ 8- wavel engt h shunt st ubqwt3 - quart er wavel engt h t r ansf ormer wi t h shunt st ub of adj ust abl el engt h

dualband - t wo- sect i on dual - band Chebyshev t r ansf ormerdualbw - bandwi dt h of dual - band t r ansf ormer

stub1 - si ngl e- st ub mat chi ngstub2 - doubl e- st ub matchi ngstub3 - t r i pl e- st ub mat chi ng

onesect - onesect i on i mpedance t r ansf ormer

twosect - t wo- sect i on i mpedance t r ansf ormer

pi2t - Pi t o T t r ansf or mat i ont2pi - T t o Pi t r ansf or mat i onlmatch - L- sect i on r eact i ve conj ugat e mat chi ng networkpmatch - Pi - sect i on r eact i ve conj ugat e mat chi ng net work

S-Parameters- - - - - - - - - - - -gin - i nput r ef l ect i on coef f i ci ent i n t er ms of S- par amet er sgout - out put r ef l ect i on coef f i ci ent i n t er ms of S- par amet er snfcirc - const ant noi se f i gur e ci r cl enfig - noi se f i gur e of t wo- por t

sgain - t r ansducer , avai l abl e, and oper at i ng power gai ns of t wo- portsgcirc - stabi l i t y and gai n ci rcl essmat - S- par ameter s t o S- matr i xsmatch - si mul t aneous conj ugate match of a t wo- por tsmith - dr aw basi c Smi t h chartsmithcir - add st abi l i t y and const ant gai n ci r cl es on Smi t h char tsparam - st abi l i t y par amet er s of t wo- por tcircint - ci r cl e i nt er sect i on on Gamma- pl anecirctan - poi nt of t angency bet ween t he two ci r cl es

Linear Antenna Functions




8/10

- - - - - - - - - - - - - - - - - - - - - - - -dipole - gai n of cent er - f ed l i near di pol e of l engt h Ltraveling - gai n of t r avel i ng- wave ant enna of l engt h Lvee - gai n of t r avel i ng- wave vee ant ennarhombic - gai n of t r avel i ng- wave r hombi c ant ennadmax - comput es di r ect i vi t y and beam sol i d angl e of a gai n f unct i on

hallen - sol ve Hal l en' s i nt egr al equat i on wi t h del t a- gap i nput

hallen2 - sol ve Hal l en' s i nt egr al equat i on wi t h ar bi t r ar y i nci dent E-f i el dhallen3 - sol ve Hal l en' s i nt egr al equat i on f or 2D ar r ay of i dent i call i near ant ennashallen4 - sol ve Hal l en' s i nt egr al equat i on f or 2D ar r ay of non- i dent i call i near ant ennaspockling - sol ve Pockl i ngt on' s i nt egr al equat i on f or l i near ant enna

king - Ki ng' s 3- t er m si nusoi dal appr oxi mat i onkingeval - eval uat e Ki ng' s 3- t er m si nusoi dal cur r ent appr oxi mat i onkingfit - f i t s a sampl ed cur r ent t o Ki ng' s 2- t er m si nusoi dalappr oxi mat i on

gain2 - nor mal i zed gai n of ar bi t r ar y 2D ar r ay of l i near si nusoi dalant ennasgain2h - gai n of 2D ar r ay of non- i dent i cal l i near ant ennas wi t h Hal l encur r ent simped - mutual i mpedance between t wo paral l el st andi ng- wave di pol esimpedmat - mut ual i mpedance mat r i x of arr ay of paral l el di pol e ant ennasresonant - cal cul at es t he l engt h of a resonant di pol e ant ennayagi - si mpl i f i ed Yagi - Uda ar r ay desi gn

Aperture Antenna Functions- - - - - - - - - - - - - - - - - - - - - - - - - -diffint - gener al i zed Fr esnel di f f r acti on i nt egr aldiffr - kni f e- edge di f f ract i on coef f i c i ent

dsinc - t he doubl e- si nc f unct i on cos( pi *x)/ ( 1- 4*x 2)fcs - Fresnel i nt egr al s C( x) and S( x)fcs2 - t ype- 2 Fresnel i nt egr al s C2( x) and S2( x)

hband - hor n ant enna 3- dB wi dthheff - aper t ur e ef f i ci ency of horn ant ennahgain - horn antenna H- pl ane and E- pl ane gai nshopt - opt i mum horn ant enna desi gnhsigma - opt i mumsi gma paramet es f or hor n antenna

Antenna Array Functions- - - - - - - - - - - - - - - - - - - - - - -array - gai n comput at i on f or 1D equal l y- spaced i sotr opi c ar r ay

bwidth - beamwi dt h mappi ng f r om psi - space to phi - spacebinomial - bi nomi al ar r ay wei ght sdolph - Dol ph- Chebyshev arr ay wei ght sdolph2 - Ri bl et - Pri t char d ver si on of Dol ph- Chebyshevdolph3 - DuHamel versi on of endf i r e Dol ph- Chebyshevmultibeam - mul t i beam ar r ay desi gnsector - sect or beam ar r ay desi gnscan - scan arr ay wi t h gi ven scanni ng phasesteer - st eer arr ay t owards gi ven angl etaylor - Tayl or- Kai ser wi ndow ar r ay wei ght suniform - uni f or m ar r ay wei ght s




9/10

woodward - Woodwar d- Lawson- But l er beams

chebarray - Br esl er' s Chebyshev arr ay desi gn method - wr i t t en by P. Si mon( I woul d l i ke t o t hank Dr . Si mon f or per mi ssi on t o i ncl ude t hi s f unct i oni n thi s col l ect i on. )

Gain Plotting Functions- - - - - - - - - - - - - - - - - - - - - - -

abp - pol ar gai n pl ot i n absol ut e uni t sabz - azi mut hal gai n pl ot i n absol ut e uni t sab2p - pol ar gai n pl ot i n absol ut e uni t s - 2*pi angl e r angeabz2 - azi mut hal gai n pl ot i n absol ut e uni t s - 2pi angl e r ange

dbp - pol ar gai n pl ot i n dBdbz - azi mut hal gai n pl ot i n dBdbp2 - pol ar gai n pl ot i n dB - 2*pi angl e r angedbz2 - azi mut hal gai n pl ot i n dB - 2pi angl e r ange

abadd - add gai n i n absol ut e uni t sabadd2 - add gai n i n absol ut e uni t s - 2pi angl e rangedbadd - add gai n i n dB

dbadd2 - add gai n i n dB - 2pi angl e rangeaddbwp - add 3- dB angl e beamwi dt h i n pol ar pl ot saddbwz - add 3- dB angl e beamwi dt h i n azi mut hal pl ot saddcirc - add gr i d ci r cl e i n pol ar or azi mut hal pl ot saddline - add gr i d r ay l i ne i n azi mut hal or pol ar pl ot saddray - add r ay i n azi mut hal or pol ar pl ot s

Miscellaneous Utility Functions- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -ab - dB t o absol ut e power uni t sdb - absol ut e power t o dB uni t sc2p - compl ex number t o phasor f ormp2c - phasor f orm t o compl ex number

d2r - degr ees t o r adi ansr2d - r adi ans t o degr ees

dtft - DTFT of a si gnal x at a f r equency vector wI0 - modi f i ed Bessel f unct i on of 1st ki nd and 0t h or der

ellipse - pol ar i zat i on el l i pse par amet er setac - eta and cwavenum - cal cul ate wavenumber and charact eri st i c i mpedance

poly2 - speci al i zed ver si on of pol y wi t h i ncreased accur acyquadr - Gauss- Legendr e quadr atur e wei ghts and eval uat i on poi ntsquadrs - Gauss- Legendr e quadr ature wei ght s and eval uat i on poi nt s on

subi nt er val sflip - f l i p a col umn, a r ow, or bot hblockmat - mani pul at e bl ock mat r i ces

upulse - gener at es t r apezoi dal , r ect angul ar , t r i angul ar pul ses, or auni t - st epustep - uni t - step or r i s i ng uni t - step f uncti on

MATLAB Movies (in subdirectory ewa\movies)- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -




10/10

pulsemovie - st ep and pul se pr opagat i on on t er mi nat ed t r ansmi ssi on l i nespulse2movie - st ep and pul se pr opagat i on on t wo cascaded l i nesRLCmovie - st ep get t i ng r ef l ect ed f r om a r eact i ve t er mi nat i onTDRmovie - f aul t l ocat i on by t i me- domai n r ef l ect omet r yxtalkmovie - crosstal k si gnal s on coupl ed t r ansmi ssi on l i nesdipmovie - el ectr i c f i el d pat t ern of radi at i ng Hert zi an di pol e


comandos matlab linha de transmissao

Documents