{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

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

This preview shows pages 1–2. Sign up to view the full content.

Assignment 6 Physics U603 Summer 1 2005 Due Tuesday, June 13 For the TM modes of a rectangular metal waveguide, the magnetic fi eld is transverse to the propagation direction z , so that B z = 0 , but the z - component E z of the electric fi 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 ) 2 . 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
2. Con fi rm that this solution satis fi 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 ff erent than for the TE modes. Why?) Find an expression
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

{[ snackBarMessage ]}

### Page1 / 2

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online