HW6 - for the TM cuto f frequency c , that is, the lowest...

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Assignment 6 Physics U603 Summer 1 2005 Due Tuesday, June 13 For the TM modes of a rectangular metal waveguide, the magnetic f eld is transverse to the propagation direction z ,soth a t B z =0 ,bu tth e z - component E z of the electric f eld is nonzero. x y a b z 1. Show that the expression E z = p k 2 x + k 2 y k 0 E 0 sin k x x sin k y ye i ( k z z ωt ) solves the wave equation 2 E z = 1 c 2 2 E z ∂t 2 if k 2 x + k 2 y + k 2 z = k 2 0 =( ω/c
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2. Con f rm that this solution satis f es the boundary conditions E z ( x =0)= E z ( x = a )=0 and E z ( y =0)= E z ( y = b )=0 if k x = a and k y = b , where m and n are integers. 3. Use the appropriate component of the appropriate Maxwell’s Equation to determine an expression for B x . 4. Identify the lowest frequency TM mode for b>a . (Be careful: the answer is di f erent than for the TE modes. Why?) Find an expression
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Unformatted text preview: for the TM cuto f frequency c , that is, the lowest frequency at which electromagnetic waves can propagate down the wave guide. 5. The following table lists the (inside) dimensions of waveguides used in some standard microwave frequency bands. In each case, determine the range of frequencies ( not angular frequencies) over which the the waveguide will operate in a single mode ( either TM or TE), so that all energy entering one end of the waveguide arrives at the other end at the same time. a (in) b (in) frequency range (GHz) X band 0.400 0.900 Q band 0.112 0.224 W band 0.050 0.100 2...
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This note was uploaded on 08/26/2008 for the course PHYSICS 603 taught by Professor Sage during the Summer '06 term at Northwestern.

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HW6 - for the TM cuto f frequency c , that is, the lowest...

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