# 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

The cut-off frequencies as calculated from the above equation for different values of

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

*TE*or*TM*mode, the cut-off frequency is given as,*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) |

TE_{10} |
0.833 |

TE_{01}, TE_{20} |
1.667 |

TE_{11}, TM_{11} |
1.863 |

TE_{21}, TM_{21} |
2.357 |

TE_{30} |
2.500 |