ee256-08-hw1

# ee256-08-hw1 - 1 EE256 Numerical Electromagnetics Marshall...

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1 EE256 Numerical Electromagnetics H.O. #5 Marshall 24 June 2008 Summer 2008 HOMEWORK ASSIGNMENT #1 (due Tuesday, July 8th) 1. First-order Euler method for an ODE. Consider using the first-order Euler method for the solution of equation [2.31] of the Lecture #2 Notes. Find and plot solutions for Δ t =0 . 1 τ , 2 . 0 τ , and 2 . 5 τ and compare your numerical results with the exact solution. Your plots should cover the time range 0 <t< 10 τ . Comment on your results. How small does Δ t have to be in order for the normalized mean squared error (averaged over 0 10 τ ) between your solution and the exact one to be less than 1% ? 2. Pulse propagation on a lossless microstrip line. Consider the transmission line equations [2.4] and the voltage wave equation [2.11] for a lossless transmission line as given in Lecture #2 Notes. Write a computer program (using any language you want, but MATLAB or C/C+ are preferred) to implement the following algorithm to solve the voltage wave equation [2.11]: V n +1 i = ± v p Δ t Δ z ² 2 ³ V n i +1 2 V n i + V n i - 1 ´ +2 V n i −V n - 1 i where v p =( LC ) - 1 2 . Note that this is the same algorithm as described by equation [2.16] on page 25 of the textbook, A. Taflove and S. Hagness,

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## This note was uploaded on 01/24/2011 for the course EE 256 at Stanford.

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ee256-08-hw1 - 1 EE256 Numerical Electromagnetics Marshall...

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