# Solved Problems-4

Problem-4
A rectangular waveguide with dimensions of a = 2 cm and b = 1 cm filled with deionised water  operates at 3 GHz. Determine all the propagating modes and the corresponding cut-off frequencies.
Solution
For a general TE or TM mode, the cut-off frequency is given as,

The cut-off frequencies as calculated from the above equation for different values of m and n are given in the table below.

 Cut-off Frequency (in GHz) for TM Modes Cut-off Frequency (in GHz) for TE Modes n = 1 n = 2 â€¦ n = 0 n = 1 n = 2 m = 1 1.863 3.436 â€¦ m = 0 Ã— 1.667 3.333 â€¦ m = 2 2.357 3.727 â€¦ m = 1 0.833 1.863 3.436 â€¦ m = 3 3.005 m = 2 1.667 2.357 3.727 â€¦ m = 3 2.500 3.005 m = 4 3.333

Since the operating frequency is 3 GHz, all the propagating modes and their cut-off frequencies are given in the table below.

 Mode Cut-off Frequency (GHz) TE10 0.833 TE01, TE20 1.667 TE11, TM11 1.863 TE21, TM21 2.357 TE30 2.500