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Solved Problems-17

Problem-17
A cubical cavity resonator made of copper Description: 42860.png is to be operated at 15 GHz. Find the dimensions of the cavity, its quality factor and the bandwidth if it is operated in the dominant mode.
Solution
The dominant mode in the resonant cavity is TE101 mode. For this mode, for a cubical cavity, the resonant frequency is given as,
 
Description: 42852.png
 
This is given as 15 GHz.
 
Description: 42844.png
 
Description: 42837.png
 
Hence, the dimensions of the cavity are: 1.414 cm × 1.414 cm × 1.414 cm.
 
The quality factor for TE101 mode is given as,
 
Description: 42829.png
 
For cubical resonator,
 
Description: 42820.png
 
where, skin depth, Description: 42810.png
 
 
Description: 42802.png
 
The bandwidth of the resonator is,
 
Description: 42793.png
 





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