notes 11 3317.pptx - ECE 3317 Prof Ji Chen Spring 2019 Notes 11 Transmission Lines(Standing Wave Ratio(SWR and Generalized Reflection Coefficient 1

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Prof. Ji Chen Notes 11 Transmission Lines (Standing Wave Ratio (SWR) and Generalized Reflection Coefficient) ECE 3317 1 Spring 2019
Standing Wave Ratio Consider a lossless transmission line that is terminated with a load: Z g z Sinusoidal source Z L z = 0 Z 0 S + - V( z ) I( z ) 2 0 V( ) 1 I( ) L L j z j z j z j z z A e e z A e e Z    0 2 2 V( ) 1 1 I( ) 1 L L j z j z j z j z z Ae e z Ae e Z    0 L Z C 0 0 L L L Z Z Z Z j L V ( ) j z z Ae V ( ) L j z z A e 2 V ( ) / V ( ) L j z z z e 
Denote Then we have The magnitude is Maximum voltage: Maximum voltage: Standing Wave Ratio (cont.) 3 2 V( ) 1 L j z j z z Ae e  j L L e  2 V( ) 1 L z j j z z Ae e   2 V( ) 1 L z j z A e   max max V( ) 1 L z V A   min min V( ) 1 L z V A   2 2 z m 2 2 z n , 0, 1, 2, m n   
The voltage standing wave ratio is the ratio of V max to V min . We then have For the current we have Standing Wave Ratio (cont.) 4 max min V VSWR V 1 1 L L VSWR     0 2 1 I( ) 1 L z j j z z Ae e Z   1 VSWR 
Hence we have The current standing wave ratio is thus Hence Standing Wave Ratio (cont.) 5 0 2 1 I( ) 1 L z j z A e Z   max max 0 1 I( ) 1 L I z A Z   min min 0 1 I( ) 1 L I z A Z   1 1 L L ISWR     VSWR ISWR SWR 2 2 z n 2 2 z m
6 Note: V + is not in general the same as V inc .

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