ECE 447 Lecture 1 - Field Analysis of TL(2006)

8/3/2019 ECE 447 Lecture 1 - Field Analysis of TL(2006)

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ECE 447 Lecture 1:

Microwave Introduction and FieldAnalysis of Transmission Line

RF/Microwaves Education

by Prof. Milton Feng

Jan, 2006

Department of Electrical and Computer Engineering

University of Illinois at Urbana-Champaign


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2Department of Electrical and Computer Engineeringat the University of Illinois at Urbana-Champaign 2006 by Prof. Milton Feng

Purpose

Wireless Communications

Microwave (0.8 to 2.5 GHz cell phone)

WLAN (5.2 GHz to 20 GHz)

Moving toward Millimeter-wave ( 60GHz and 94GHz)

Imaging: Focal Plane Array Image

IR image

Submillimeter-Wave Image

THz Image Microelectronics:

4 GHz Signal Processing

10 to 100 GHz Signal Process ( Mix signal ICs)

RF front end (High speed, low power, high dynamic range ADC, DDS)

Optoelectronics:

Integrated Photon and electron toward 160 Gbits

Display Technology


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Research vertical scaling in Type I andType II material systems

Lateral scaling down to 0.15 um InP

DHBT enables devices with Ft & Fmax >500 GHz

Planarized device & processing methodsthat enable circuits of density > 20,000devices

4 level planarized interconnect High breakdown voltages for linear RF

circuits Demonstration of 150 GHz divider, and

other key DDS circuits

0.25m 8mInP/InGaAs SHBT beforeplanarization Ft> 550 GHz

Goals, Objectives and Main TechnicalApproach

Material and advancedHBT Research (UIUC

Lead)

Manufacturable InP DHBTResearch (Vitesse Lead)

Circuits andApplications (BAESystems Lead)Worlds Fastest FlipFlop ckt @ 152 GHz

Super-scaled InP Technology for EWApplications(DRAPA TFast $ 7M Project)

Base

Collector

Emitter

UIUC Sub-micron SHBTs

Device performance forVIP-2 device havingFt/Fmax > 330 GHz withBVceo > 4.5 Volts

Spectrum of Divider Output

-90.00

-80.00

-70.00

-60.00

-50.00

-40.00

-30.00

-20.00

-10.00

0.00

3.7450E+10 3.7500E+10 3.7550E+10

Frequency (Hz)

Amplitude(dBm)


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Microwave Theory - Overview

Microwaves Introduction

Frequency Band Designations Transmission Lines

Field Analysis of Transmission Lines


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Microwaves Introduction

Microwavesrefers to AC signals with frequencies between 300 MHz and 300GHz.

Corresponds to electrical wavelengths between 1 m and 1 mm respectively. Lumped circuit element approximations are no longer valid at microwave

frequencies.

Distributed elements must be used when the phase of a voltage or current

changes significantly across the length of a device at high frequencies.

cf =


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Frequency Band Designations

L-band 1-2 GHz

S-band 2-4 GHz

C-band 4-8 GHzX-band 8-12 GHz

Ku-band 12-18 GHz

K-band 18-26 GHz

Ka-band 26-40 GHz

U-band 40-60 GHz

V-band 60-75 GHz

W-band 75-110 GHz


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Transmission Lines

Transmission Lines

Conventional parallel conductor transmission lines such as two-wire

lines, coaxial line, and stripline are used to transmit microwaveenergy.

Modern high-frequency integrated circuits (ICs) will typically usemicrostrip transmission lines or coplanar waveguide (CPW).

In microwave network analysis, transmission line theory bridges the gapbetween field analysis and circuit theory.

Field analysis is required when the physical dimensions of a network

are larger than the electrical wavelength.

Transmission line analysis is needed when the physical dimensionsof a network are equal to a fraction of the electrical wavelength.

Circuit analysis assumes that the physical dimensions of a networkare relatively smaller than the electrical wavelength.


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Field Analysis of Transmission Lines

Parallel Plate Transmission Line (Perfect Conductor)

xx x

xx x

x

z

xEx

HyJs = Hy iz

Js

x x xx

+++++++++++++++++++++++++++

Perfect Conductor

d

w

Hy Hy Hy

xx itzEE ),(=

yy itzHH ),(=

Boundary condition in a perfect conductor:

0=tE0=nH

(Tangential component of E = 0)

(Normal component of H = 0)

Charge density produce E field : Gauss Law

[ ] [ ] xxxxxnxs EiEiDi === == )(00

[ ] [ ] xxxxdxndxs EiEiDi === == )(

[1]

[2]

[3]

[4]

[5]

[6]

y


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Field Analysis of

Transmission Lines (contd.)

Wave propagation along the transmission line is supported by charges and

currents on the plate, which vary both with time and distance along the line.

For the finite space between the two plates x=0 and x=d, the voltage

between the two conductors is equal to dEx(z,t):

Current density produced H-Field :

[ ] [ ] )()(00 zyyyxxnxs

iHiHiHiJ =====

[ ] [ ] )()()( zyyyxdxndxs iHiHiHiJ === ==

),(),(),( tzEddxtzEtzV x

dx

ox

x == =

=

For a finite-sized plate y=w, the current flow in the conductor is equal towHy(z,t):

),(),(),(),( tzHwdytzHdytzJtzI y

wy

oy

y

wy

oy

s === =

=

=

=

[7]

[8]

[9]

[10]


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Field Analysis of

Transmission Lines (contd.)

Power flow in the z-direction can be expressed in terms of the Poyntingvector, P(z,t):

( ) dStzHtzEtzPdx

x

wy

y yx =

=

=

=

=0 0 ),(),(),(

( )z

dx

x

wy

yyx dxdyitzHtzE =

=

=

=

=0 0),(),(

dxdyw

tzI

d

tzVdx

x

wy

y=

=

=

=

=

),(),(

0 0

),(),( tzItzV = Maxwell Equations for Ex and Hy propagating in the z-direction:

t

H

z

E

t

BE

y

=

=

t

EE

z

H

t

DJH xxy

=

+=

This leads to V=dEx and I=wHy in a perfect dielectric medium wherethe conductivity is equal to 0.

[11]

[12]

[13]

[14]

[15]

[16]


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Inductance and Capacitance

Transmission Lines

Inductance:

zatcurrentline

lengthunitperfluxMagnetic

m

Henry=

L

w

d

zHw

zzdH

zI

zAB

m

HL

y

ymy =

=

=

)(

)/1()(

)(

)/1(

Capacitance:

zatvoltageline

lengthunitperCharge

m

Faraday

=

C

d

w

zEd

zzwE

zV

zA

m

FC

x

xes =

=

=

)(

)/1()(

)(

)/1(

The wave propagation can be determined as follows:

2

1

p

CL

==

11==

LCp

[17]

[18]

[19]

[20]


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Field Analysis Transmission Lines Transmission line equations can be put in terms of voltage and current

by substituting Ex and Hy with I, V, L, and C. However, we should notforget about the actual phenomenon that the the conductors guide

electromagnetic wave propagation:

t

IL

z

V

t

H

z

E yx

=

=

t

VC

z

I

t

E

z

Hxy

=

=

The solution to the lossless transmission line is as follows:

)()(),( LCztBgLCztAftzV ++=

[ ])()(/

1),( LCztBgLCztAf

CLtzI ++=

directionzinwaveTraveling + :)( LCztf

directionzinwaveTraveling: + )( LCztg

Where:

[21]

[22]

[23]

[24]


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Phase Velocity & Characteristic Impedance

of Transmission Lines

In summary:

2

1

p

CL

==

11==

LCp

=

==

w

d

w

d

C

LZo

Phase velocity

Characteristic impedance

The characteristic impedance is related to the intrinsic impedance by thegeometric factor.

Any transmission line is then characterized by the phase velocity and thecharacteristic impedance Zo.

[25]


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Transmission Line

with Small Finite Conduction

Parallel Plate Conductor:

d

wC =

d

wG =

w

dL =

11==

LCp

)/()/( wdwdC

LZo

===

w

RR s

2=


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Home Work 1-1

Coaxial Cylindrical Conductor

Derive and prove that Coaxial Cylindrical Conductor (where ais theradius of the inner conductor and bis the radius of the outer conductor)

a

b

C=2

ln(b/a)

G =2

ln(b/a)

L =

2lnb

a

p 1 LC= 1

Zo =L

C={

1

2ln(b

a)}

+=

ba

RR S

11

2


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17Department of Electrical and Computer Engineeringat the University of Illinois at Urbana-Champaign

2006 by Prof. Milton Feng

Homework 1-2Parallel Cylindrical Wires Conductor

Derive and prove that Parallel Cylindrical Wires Conductor (where aisthe radius of the conductor and 2d is the separation of the two

conductors measured from the center of the lines)

2d

a a

C=1

cosh (d/a)

G =

1cosh (d/a)

L =

1cosh

d

ap 1 LC= 1

Zo =L

C={

1

1cosh (

d

a)}

a

RR S

=


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18Department of Electrical and Computer Engineeringat the University of Illinois at Urbana-Champaign

2006 by Prof. Milton Feng

Homework 1-3

Parallel Cylindrical Wire

Parallel Cylindrical Wire to the Ground Conductor (where ais the radiusof the conductor and h is the separation of the conductor and ground

plane)

h

a

C=2

1cosh (h/a)

G =2

1cosh (h/a)

L =

2

1cosh

h

a

p 1 LC= 1

Zo =L

C={

1

2

1cosh (

h

a)}

a

RR S

2=

ECE 447 Lecture 1 - Field Analysis of TL(2006)

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