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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 steadystate. + 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 07/19/2010 for the course ECE ECE329 taught by Professor Kudeki during the Summer '10 term at University of Illinois at Urbana–Champaign.
 Summer '10
 KUDEKI
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