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Transmission Line Analysis

• Propagating electric field

• Phase velocity

• Traveling voltage wave

)cos(0 kztEE XX −= ω

Time factor

Space factor

r

p

cfv

εεµλ ===

1

k

kztEtzV X

)sin(),( 0

−=

ω

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High frequency implies spatial voltage distribution

• Voltage has a time andspace behavior

• Space is neglected for lowfrequency applications

• For RF there can be a largespatial variation

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Generic way to measure spatial voltage variations

• For low frequency (1MHz)Kirchhoff’s laws apply

• For high frequency (1GHz)Kirchhoff’s laws do notapply anymore

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Kirchhoff’s laws on a microscopic level

• Over a differential sectionwe can again use basiccircuit theory

• Model takes into accountline losses and dielectriclosses

• Ideal line involves only Land C

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Example of transmission line: Two-wire line

• Alternating electric fieldbetween conductors

• alternating magnetic fieldsurrounding conductors

• dielectric medium tendsto confine field insidematerial

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Example of transmission line: Coaxial cable

• Electric field iscompletely containedwithin both conductors

• Perfect shielding ofmagnetic field

• TEM modes up to acertain cut-off frequency

E

H

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Example of transmission line: Microstip line

Cross-sectional view

Low dielectric medium High dielectric medium

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Triple-layer transmission line

Conductor is completely shielded between twoground planes

Cross-sectional view