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Solved Problems-4

Problem-4
A rectangular waveguide with dimensions of a = 2 cm and b = 1 cm filled with deionised water Description: 44322.png 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,
 
Description: 44314.png
 
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   n = 0 n = 1 n = 2  
m = 1 1.863 3.436 m = 0 × 1.667 3.333
m = 2 2.357 3.727 m = 1 0.833 1.863 3.436
m = 3 3.005 Description: 65714.png    m = 2 1.667 2.357 3.727
      m = 3 2.500 3.005 Description: 65724.png   
        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
TE01TE20 1.667
TE11TM11 1.863
TE21TM21 2.357
TE30 2.500





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