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Work out the theory of TM modes for a rectangular wave
Chapter 9, Problem 31P(choose chapter or problem)
Problem 31P
Work out the theory of TM modes for a rectangular wave guide. In particular, find the longitudinal electric field, the cutoff frequencies, and the wave and group velocities. Find the ratio of the lowest TM cutoff frequency to the lowest TE cutoff frequency, for a given wave guide. [Caution: What is the lowest TM mode?]
Questions & Answers
QUESTION:
Problem 31P
Work out the theory of TM modes for a rectangular wave guide. In particular, find the longitudinal electric field, the cutoff frequencies, and the wave and group velocities. Find the ratio of the lowest TM cutoff frequency to the lowest TE cutoff frequency, for a given wave guide. [Caution: What is the lowest TM mode?]
ANSWER:
Step 1 of 5
We have to work out the theory of modes for a rectangular waveguide.
Suppose we have a waveguide of rectangular shape (as shown in the fig below), with height
and width , and we are interested in the propagation of (transverse magnetic) waves.
The problem is to solve the below equations with and subjected to the boundary conditions and