notes 10 3317.pptx - ECE 3317 Prof Ji Chen Spring 2019 Notes 10 Transmission Lines(Reflection and Impedance 1 Reflection Consider a transmission line

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Prof. Ji Chen Notes 10 Transmission Lines (Reflection and Impedance) ECE 3317 1 Spring 2019
Reflection Consider a transmission line that is terminated with a load: Sinusoidal source Voltage and current on the line: Z L z = 0 Z g Z 0 S z + - V( z ) I( z ) 2 V( ) z z z Ae Be 0 0 I( ) z z A B z e e Z Z 0 R j L Z G j C V z V z I z I z
Reflection (cont.) Important point: The forward-traveling and backward-traveling wave amplitudes are the amplitudes that describe the two waves in sinusoidal steady-state (after all bounces have died down and we are in steady state). Z L z = 0 Z g Z 0 S + - V( z ) I( z ) 3 A = amplitude of net forward-traveling wave B = amplitude of net backward-traveling wave V( ) z z z Ae Be 0 0 I( ) z z A B z e e Z Z
At the load ( z = 0 ): Hence we have or Reflection (cont.) Z L z = 0 Z g Z 0 S z + - V( z ) I( z ) 4 V(0) I 0 L Z 0 L Z A B A B Z 0 0 1 1 L L Z Z B A Z Z 0 R j L Z G j C
Hence We define the load reflection coefficient : or We then have Reflection Coefficient 5 V 0 V 0 L L B A 0 0 1 1 L L L Z Z Z Z 0 0 L L L Z Z Z Z V( ) z z z Ae Be V ( ) V ( ) z z z Ae z Be
We can then write Voltage and Current Note: The generator (source) will determine the unknown (complex) constant A . 6 V( ) L z z z A e e  0 1 I( ) z z L z A e e Z  
We define the input impedance at any point on the line Impedance Z L z = 0 Z g Z 0 S z + - V( z ) I( z ) Z in 7 V I in z Z z z

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