lecture21 - 1 ECE 303 – Fal 2007 – Farhan Rana –...

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Unformatted text preview: 1 ECE 303 – Fal 2007 – Farhan Rana – Cornel University Lecture 21 Transmission Lines: RF and Microwave Circuits In this lecture you will learn: • More about transmission lines • Impedance transformation in transmission lines • Transmission line circuits and systems ECE 303 – Fal 2007 – Farhan Rana – Cornel University Transmission Lines: A Review o Z + V − V ( ) z k j z k j e V e V z V + − − + + = Voltage at any point on the line can be written as: Current at any point on the line can be written as: ( ) z k j o z k j o e Z V e Z V z I + − − + − = C L Z o = The characteristic impedance of a transmission line is: The dispersion relation for a transmission line is: LC k ω = Co-axial line Wire on a ground plane Some common examples of transmission lines 2 ECE 303 – Fal 2007 – Farhan Rana – Cornel University In general, voltage on a transmission line is a superposition of forward and backward going waves: ( ) z k j z k j e V e V z V + − − + + = The corresponding current is also a superposition of forward and backward going waves: ( ) z k j o z k j o e Z V e Z V z I + − − + − = Transmission Line Circuits Consider a transmission line connected as shown below: o Z s Z s V L Z = z l − = z z = o Z Transmission line impedance ( ) [ ] t j s s e V t V ω Re = = L Z Load impedance = s Z Source impedance ECE 303 – Fal 2007 – Farhan Rana – Cornel University Load Boundary Condition o Z s Z s V L Z = z l − = z z ( ) [ ] t j s s e V t V ω Re = ( ) z k j z k j e V e V z V + − − + + = Boundary condition: At z = 0 the ratio of the total voltage to the total current must equal the load impedance : ( ) z k j o z k j o e Z V e Z V z I + − − + − = ( ) ( ) L o o Z Z V Z V V V z I z V = − + = = = − + − + This gives us the backward going wave amplitude in terms of the forward going wave amplitude Define a load reflection coefficient Γ L as: 1 1 + − = = Γ + − o L o L L Z Z Z Z V V + V − V 1 1 + − = ⇒ + − o L o L Z Z Z Z V V +- 3 ECE 303 – Fal 2007 – Farhan Rana – Cornel University Load Reflections o Z s Z s V + V − V Suppose Z L = 0 (short): + − + − − = ⇒ − = + − = = Γ V V Z Z Z Z V V o L o L L 1 1 1 ( ) = + = = − + V V z V ( ) o o o Z V Z V Z V z I + − + = − = = 2 and o Z s Z s V + V − V Suppose Z L = ∞ (open): + − + − = ⇒ + = + − = = Γ V V Z Z Z Z V V o L o L L 1 1 1 ( ) + − + = + = = V V V z V 2 ( ) = − = = − + o...
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This note was uploaded on 02/02/2008 for the course ECE 3030 taught by Professor Rana during the Fall '06 term at Cornell University (Engineering School).

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lecture21 - 1 ECE 303 – Fal 2007 – Farhan Rana –...

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