# Solved Problems-7

Problem-7

In an air-filled rectangular waveguide, the cut-off frequency of a

*TE*_{10}mode is 5 GHz, whereas that of*TE*_{01}mode is 2 GHz. Calculate- The dimension of the guide
- The cut-off frequencies of the next three higher
*TE*modes - The cut-off frequency for
*TE*_{11}mode if the guide is filled with a lossless material having*Îµ*= 2.25 and_{r}*Î¼*= 1_{r}

Solution

Here,

(a) Since the cut-off frequency is lowest in
Now, for
Also, for
So, the dimension of the rectangular waveguide is 3 cm Ã— 7.5 cm.

(b) The cut-off frequency for
Next higher order modes will be
The corresponding cut-off frequencies are given as follows.

(c) If the guide is filled with a lossless material having

(a) Since the cut-off frequency is lowest in

*TE*_{01}mode, this is the dominant mode. This implies that for the rectangular waveguide,*b*>*a*.*TE*_{01}mode, the cut-off frequency is given as,*TE*_{10}mode, the cut off frequency is given as,(b) The cut-off frequency for

*TE*_{mn}mode is given as,*TE*_{02},*TE*_{11},*TE*_{03}.*Îµ*= 2.25 and_{r}*Î¼*= 1, the cut-off frequency for_{r}*TE*_{11}mode is,