ECE & TCOM 590 Microwave Transmission for Telecommunications Introduction to Microwaves January 29, 2004.

ECE & TCOM 590Microwave Transmission for

Telecommunications

Introduction to Microwaves

January 29, 2004

Microwave Applications

– Wireless Applications – TV and Radio broadcast– Optical Communications– Radar– Navigation – Remote Sensing– Domestic and Industrial Applications– Medical Applications– Surveillance– Astronomy and Space Exploration

Brief Microwave History• Maxwell (1864-73)

– integrated electricity and magnetism– set of 4 coherent and self-consistent equations– predicted electromagnetic wave propagation

• Hertz (1873-91) – experimentally confirmed Maxwell’s equations – oscillating electric spark to induce similar

oscillations in a distant wire loop (=10 cm)

Brief Microwave History• Marconi (early 20th century)

– parabolic antenna to demonstrate wireless telegraphic communications

– tried to commercialize radio at low frequency

• Lord Rayleigh (1897)– showed mathematically that EM wave

propagation possible in waveguides

• George Southworth (1930)– showed waveguides capable of small

bandwidth transmission for high powers

Brief Microwave History• R.H. and S.F. Varian (1937)

– development of the klystron

• MIT Radiation Laboratory (WWII)– radiation lab series - classic writings

• Development of transistor (1950’s)

• Development of Microwave Integrated Circuits– microwave circuit on a chip– microstrip lines

• Satellites, wireless communications, ...

Ref: text by Pozar

Microwave Engr. Distinctions· 1 - Circuit Lengths:

· Low frequency ac or rf circuits· time delay, t, of a signal through a device· t = L/v « T = 1/f where T=period of ac signal· but f=v so 1/f= /v· so L «, I.e. size of circuit is generally much

smaller than the wavelength (or propagation times 0)

· Microwaves: L · propagation times not negligible

· Optics: L»

Transit Limitations

• Consider an FET

• Source to drain spacing roughly 2.5 microns

• Apply a 10 GHz signal:– T = 1/f = 10-10 = 0.10 nsec– transit time across S to D is roughly 0.025 nsec

or 1/4 of a period so the gate voltage is low and may not permit the S to D current to flow

Microwave Distinctions· 2 - Skin Depth:

· degree to which electromagnetic field penetrates a conducting material

· microwave currents tend to flow along the surface of conductors

· so resistive effect is increased, i.e.

· R RDC a / 2 , where

= skin depth = 1/ ( f o cond)1/2

– where, RDC = 1 / ( a2 cond)– a = radius of the wire• R waves in Cu >R low freq. in Cu

2

Microwave Engr. Distinctions

· 3 - Measurement Technique

· At low frequencies circuit properties measured by voltage and current

· But at microwaves frequencies, voltages and currents are not uniquely defined; so impedance and power are measured rather than voltage and current

Circuit Limitations• Simple circuit: 10V, ac driven, copper wire,

#18 guage, 1 inch long and 1 mm in diameter: dc resistance is 0.4 m and inductance is 0.027 H– f = 0; XL = 2 f L 0.18 f 10-6 =0– f = 60 Hz; XL 10-5 = 0.01 m– f = 6 MHz; XL 1 – f = 6 GHz; XL 103 = 1 k – So, wires and printed circuit boards cannot be

used to connect microwave devices; we need transmission lines

High-Frequency Resistors• Inductance and resistance of wire resistors

under high-frequency conditions (f 500 MHz): L/RDC a / (2 )– R /RDC a / (2 )– where, RDC = /( a2 cond) {the 2 here

accounts for 2 leads}– a = radius of the wire– = length of the leads = skin depth = 1/ ( f o cond)1/2

2

Reference: Ludwig & Bretchko, RF Circuit Design

High Frequency Capacitor

• Equivalent circuit consists of parasitic lead conductance L, series resistance Rs describing the losses in the the lead conductors and dielectric loss resistance Re = 1/Ge (in parallel) with the Capacitor.

• Ge = C tan s, where

– tan s = (/diel) -1 = loss tangent

Reference: Ludwig & Bretchko, RF Circuit Design

Reference: Ludwig & Bretchko, RF Circuit Design

Reference: Ludwig & Bretchko, RF Circuit Design

Reference: Ludwig & Bretchko, RF Circuit Design

Maxwell’s Equations

tDJH

tBE

B

D

/

/

0

• Gauss

• No Magnetic Poles

• Faraday’s Laws

• Ampere’s Circuit Law

Characteristics of MediumConstitutive Relationships

npropagatio ofdirection z constant, phase

constanton attentuati ,j where

z)-texp(j toalproportion HE,

plasma ferrites,except scalars,,

surfaceson sonot itself, medium in the 0,J

sAssumption

Current ConvectiveJJJJ E,J

tyPermeabili Magnetic ,H,B

yPermitivit Dielectric,ED

v v,cc

ro

,or

Fields in a Dielectric Materials

0on conservatientergy todue negative

(heat) medium in the lossfor accounts

magnitude) of orders 4or (3 dielectric goodfor ,

j)1(

EE)1(D

itysuceptibil dielectric ,E density moment dipole P

density)nt displacemeor flux electric(D 0J and

so magnetic,non and ,PED Assume

eo

eo

eoe

oo

Fields in a Conductive Materials

tan tangent loss effective

tyconductivi effective theis where

E)](j[E)jj(j

E))j(jj(E)j

(j

EjEt

EE

t

DJH

e as vary fields E where,EJJ tjc

Wave Equation

and by described mediumin

wavesofconstant n propagatio :

;H - H

;E - E

E))((

)H( E -E)(E)(

EjH H,-jE

jt/Consider

2

22

22

2

kdefine

similarly

jj

j

General Procedure to Find Fields in a Guided Structure

• 1- Use wave equations to find the z component of Ez and/or Hz

– note classifications

– TEM: Ez = Hz= 0

– TE: Ez = 0, Hz 0

– TM: Hz = 0, Ez 0

– HE or Hybrid: Ez 0, Hz 0

General Procedure to Find Fields in a Guided Structure

• 2- Use boundary conditions to solve for any constraints in our general solution for Ez and/or Hz

conductor of surface the tonormaln where

conductorperfect of surfaceon 0Hor ,0Hn

JHn

/E n

conductorperfect of surfaceon 0Eor 0,En

n

s

t

s

Plane Waves in Lossless Medium

direction z in the movingconstantkztω

))kzt(cos(E))kzt(cos(E)t,z(E

:domain timein theor

eEeE)z(E0Ekz

E

0y/x/ and E E

medium lossless ain

real are and since real is ωk where0,EkE

x

jkzjkzxx

22x

2

x

22

Phase Velocity

cfv :space freein

fvor f

vv2

k

2

k2))k(z-t(-kz)-t(

maxima successive 2between distance :Wavelength

m/sec 103c1

vspace freein

1

k)

k

constant-t(

dt

d

dt

dzv

velocityaat elspoint trav phase Fixed

p

ppp

8

oo

p

p

Wave Impedance

E/Hor k

where

)eEeE(k

H

HjejkEejkE

yz

ExEz

z so ;0

yx

Hjt

H-E :eqn sMaxwell'By

jkzjkzy

yjkzjkz

xx

Plane Waves in a Lossy Medium

k and j and

0,0 note)j1(jj

complex now,number ewav)j1(

0E)j1(E

E)E(E

)EEj(j)H(jE

EEjH and HjE

22

22

2

Wave Impedance in Lossy Medium

losses with impedance wavej

where

)eEeE(j

H

)ztcos(edomain timeeee

eEeE)z(E0Ez

E

0y/x/ and xEE before as

zzy

zzjzz

zzxx

22x

2

x

Plane Waves in a good Conductor

surface on the flow currents s,frequencie microwaveat

Au)Ag,Cu,(Al, metalsmost for m1 GHz, 10at

depth skin/2/1

2/2/)j1(

/jj/jj

case practical

s

s

2

Energy and Power

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dvHH4/dvBHRe4/1W

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loss as dissipatedor ed transmittbemay that

powercarry andenergy magnetic and electric store

thatfields up setsenergy neticelectromag of sourceA

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o

emo

s

v

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v

*m

v

*

v

*e

systems coordinateother for

Pozar of Bappendix see ;zz

yy

xx

sderivative partialx /by defined Changes

C sinBABA

other on the vector one of projection

product,dot or scalar : cosBABA

vectorsngintersecti be B and ALet

Review Math

river) adown flowing leaf twistinga (likerotation

(Russian) ROTor Curl;)y

A

x

A()A(

flow outwardnet :Divergence ; z

A

y

A

x

AA

change of rate :gradient ;zz

uy

y

ux

x

uu

spacein s variationz)y,u(x,u fieldscalar a have weif

zxy

z

zyx

theoremStokes ;ds)A(dA

theoremDivergence ;dV)A(dsA

0 curl of divor

0C)()C( ;C)BA()CB(A

0 gradient of curlor 0u ;0AA

s

vs