hw7 - ECE 329 Homework 7 Due 5PM 1 TEM wave...

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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, loss-less, and source-free 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 real-valued 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.

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hw7 - ECE 329 Homework 7 Due 5PM 1 TEM wave...

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