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Unformatted text preview: ECE 329 Homework 7 Due: Oct 21, 2010, 5PM 1. ( TEM wave characteristics )The following electric or magnetic field vectors are associated with uniform plane waves propagating in linear, isotropic, lossless, and sourcefree media of magnetic permeability that of free space. For each case find the following: • The direction of propagation of the plane wave; • The speed of light in the medium; • The permittivity of the medium; • The associated magnetic or electric field vector. (a) ⃗ E ( x, t ) = ˆ y sin(2 π · 10 8 ( t + 10 1 x 1 . 5 )) ( V/m) (b) ⃗ H ( y, t ) = ˆ x △ (10 3 ( t + 10 8 z 2 )) ( A/m) (c) ⃗ H ( z, t ) = ˆ y cos( π 10 8 t − π 2 z ) − ˆ x sin( π 10 8 t − π 2 z ) ( A/m) 2. ( TEM waves visualization ) We have on x = 0 plane a pulse of sheet current ⃗ J s ( t ) = − ˆ y 2 t rect ( t τ ) A/m, where τ = 2 µ s. (a) Determine and plot E y ( x, t ) and H z ( x, t ) vs t for x = ± 1200 m. (b) Determine and plot E y ( x, t ) and H z ( x, t ) vs x for t = 5 µ s. (c) Determine the TEM wave energy radiated per unit area (in J/m 2 units) by the current pulse ⃗ J s ( t ) = − ˆ y 2 t rect ( t τ ) A/m. Hint: inte grate the power injected per unit area, − ⃗ J s · ⃗ E , over the duration of pulse ⃗ J s ( t ) . 3. ( TEM wave energy transfer ) Consider an infinite surface current den sity ⃗ J s = − ˆ xJ so cos( ωt ) ﬂowing on z = 0 surface, where J so > is realvalued amplitude of the monochromatic surface current measured in A/m units. It is found that ⃗ J s injects field energy into propagating transverse electromagnetic (TEM) waves away from the z = 0 plane at an average rate of 1 W/m 2 — that is, the magnitude of the average Poynting vector ⟨ ¯ P⟩ is 1 2 W/m 2 for the waves excited by the surface current....
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This note was uploaded on 11/06/2011 for the course ECE 329 taught by Professor Kim during the Spring '08 term at University of Illinois, Urbana Champaign.
 Spring '08
 Kim

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