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Homework2

# Homework2 - ECE 3025C Electromagnetics Homework...

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ECE 3025C -- Electromagnetics Homework Assignment #2 September 6, 2007 Problem 1. Consider the following circuit consisting of a generator, transmission line, and a resistive load at the end of the transmission line: The switch is thrown at 0 t = and T is the one way propagation time in the transmission line. For times much greater than 10 reflections, the transmission line effects diminish and the resultant equivalent circuit is: For this equivalent circuit L V is related to g V , g R and L R by: L L g g L R V V R R = + (2.1) If all line reflections are considered as t → ∞ , then L V , the steady state voltage on the line and across the load, may be expressed in terms of reflection coefficients L Γ and G Γ as: 1 1 O L L g O G L G Z V V Z R + Γ = + − Γ Γ (2.2) Use equations L O L L O R Z R Z Γ = + and G O G G O R Z R Z Γ = + to show that Equation 2.2 reduces to the equivalent circuit described by Equation 2.1.

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