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Unformatted text preview: 36 Smith Chart and VSWR Consider the general phasor expressions V ( d ) = V + e jd (1 + L e- j 2 d ) and I ( d ) = V + e jd (1- L e- j 2 d ) Z o describing the voltage and current variations on TLs in sinusoidal steady-state. +- Wire 2 Wire 1 +- F = V g Z g Z L I ( d ) V ( d ) l Transmission line Load Z o Generator d d max | V ( d ) | d min | V ( d ) | min | V ( d ) | max .2 .5 1 2 r 5 x 5 2 1 .5 .2 x 5 2 1 .5 .2 VSWR SmithChart 1 ( d ) 1 + ( d ) | 1 + ( d ) | maximizes for d = d max ( d max ) = | L | | 1 + ( d ) | minimizes for d = d min such that ( d min ) =- ( d max ) Complex addition displayed graphically superposed on a Smith Chart z ( d max ) =VSWR Unless L = 0 , these phasors contain reflected components, which means that voltage and current variations on the line contain standing waves. In that case the phasors go through cycles of magnitude variations as a function of d , and in the voltage magnitude in particular (see margin) varying as | V ( d ) | = | V + || 1 + L e- j 2 d | = | V + || 1 + ( d ) | takes maximum and minimum values of | V ( d ) | max = | V + | (1 + | L | ) and | V ( d ) | min = | V + | (1-| L | ) at locations d = d max and d min such that ( d max ) = L e- j 2 d max = | L | and ( d min ) = L e- j 2 d min =-| L | , and d max- d min is an odd multiple of 4 . 1 These results can be most easily understood and verified graphi- cally on a SC as shown in the margin. +- Wire 2 Wire 1 +- F = V g Z g Z L I ( d ) V ( d ) l Transmission line Load Z o Generator d d max | V ( d ) | d min | V ( d ) | min | V ( d ) | max .2 .5 1 2 r 5 x 5 2 1 .5 .2 x 5 2 1 .5 .2 VSWR SmithChart 1 ( d ) 1 + ( d ) | 1 + ( d ) | maximizes for d = d max (...
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This note was uploaded on 06/20/2011 for the course ECE 329 taught by Professor Kim during the Spring '08 term at University of Illinois, Urbana Champaign.
- Spring '08