ee256-08-hw3

ee256-08-hw3 - 1 EE256 Numerical Electromagnetics H.O#22...

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Unformatted text preview: 1 EE256 Numerical Electromagnetics H.O. #22 Marshall 17 July 2008 Summer 2008 HOMEWORK ASSIGNMENT #3 (due Tuesday, July 29th) 1. One dimensional wave incident on a dielectric slab. Consider the propagation of a one dimensional electromagnetic wave in a medium and its reflection from and transmission through a dielectric slab. Construct a 1-D FDTD space with a lossless dielectric slab ( r 2 = 2 , μ r 2 = 1 ) at the center of your grid, free space ( r 1 = 1 , μ r 1 = 1 ) to the left of the slab, and another dielectric ( r 3 = 4 , μ r 3 = 1 ) to the right of the slab. You should allow for the length of the slab to be adjustable. Launch a Gaussian pulse from the left boundary of your FDTD space which is given by E z n i =1 = e- ( n- 3 τ ) 2 /τ 2 where τ Δ t = 0 . 8 ns. Choose Δ x ≥ λ / 20 √ r , where λ = 0 . 3 m, Δ t = Δ x/v p , and i max Δ x = 3 m. Once the tail end of the pulse leaves the source (i.e., when n = 6 τ ), replace the source end with a simple boundary condition: E z n +1 1 = E z n 2 + v p Δ t − Δ x v p Δ t + Δ x E z n +1 2 −E z n 1 Take the rightmost end of your FDTD space to be as far away as needed so that there are no reflections from that boundary, or implement a similar radiation boundary at i = i max ....
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ee256-08-hw3 - 1 EE256 Numerical Electromagnetics H.O#22...

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