lecture 5 Ch 2_9

# lecture 5 Ch 2_9 - EE 4002 RF Circuit Design Transmission...

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Unformatted text preview: EE 4002 RF Circuit Design Transmission Lines Part 3 Terminated Lossless TL Load Impedance connected to a finite lossless TL. A voltage wave is coupled into the line at z = - l o V V- + Γ = ( ) kz kz V z V e V e +-- + = + ( ) kz kz I z I e I e +-- + = + Forward Waves Reflected Waves from the terminating load impedance for z<0 Let’s now define a voltage reflection coefficient: Which is the ratio of reflected to incident wave. Terminated Lossless TL ( ) ( ) kz kz o V z V e e +- + = + Γ Traveling wave equations now become: ( ) ( ) kz kz o o V I z e e Z +- + =- Γ ( ) ( ) ( ) ( ) kz kz o o kz kz o e e V z Z z Z I z e e- +- + + Γ = =- Γ The generalized impedance eqn At any location on the TL: At the input impedance can be found. z l = - in Z At the load impedance can be found. z = L Z Solving for the reflection coefficient yields: L o o L o Z Z Z Z- Γ = + 1 ( ) (0) 1 o o z o Z z Z Z = + Γ = =- Γ Terminated Lossless TL This is a very useful way to calculate the reflection coefficient in terms of known circuit quantities, (TL and load impedances). Propagation Constant and Phase Velocity...
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lecture 5 Ch 2_9 - EE 4002 RF Circuit Design Transmission...

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