This document provides information about waveguides, including: 1) A rectangular waveguide with dimensions of 5cm by 3cm is operating the TM11 mode, and the cut-off frequency is calculated to be 5.83MHz. 2) Cut-off frequencies and the number of supported modes are calculated for a rectangular waveguide with dimensions of 3.5cm by 2cm operating below 15GHz. 3) Operating parameters like cut-off frequency, waveguide impedance, time delay, and frequency range are calculated for a 7.5cm by 4.5cm rectangular waveguide operating at 3GHz.

1. Waveguide
Tutorial 8
1) A rectangular waveguide has dimensions a=5cm & b=3cm. The medium within which the
waveguide has r=1,μr=1,=0 and conducting walls of waveguide are perfect conductors.
Determine cut-off frequency for TM(1,1) mode. Ans:- 5.83MHz
2) A rectangular waveguide has dimension 3.5cmx2cm & is to be operated below 15GHz. The
medium in the waveguide is air. Determine
a) Cut-off frequency.
b) Number of TEm,n and TMm,n mode that waveguide can support
3) A waveguide with dimension 7.5x4.5cm operates at 3GHz, Determine
a) Cut-off frequency of the waveguide.
b) Waveguide impedance.
c) Time delay in 1Km length of the waveguide.
d) Operating frequency range for dominant mode of operation
5) A rectangular waveguide with dimensions a=2.5cm b=1cm is to operate below 15.1GHz. How
many TE and TM modes can the waveguide transmit if the guide is filled with a medium
characterized by =0,=4o,μr=1. Calculate cut-off frequencies. Also write the expression for
instantaneous field for TE01 mode.
6) In the rectangular waveguide for which 1=1.5cm,b=0.8cm, =0,=4o,μ= μ0 and
Hx= 2 sin( )cos( )sin(x10’’t-z) A/m
Determine;
a) The mode of operation.
b) Cut-off frequency.
c) The phase constant .
d) The Propagation constant .
e) The intrinsic wave impedance .
7) An air filled rectangular waveguide has dimensions a=2cm, and b=1cm. Determine the range
of frequencies over which the guide will operate single mode.

2. 8) For rectangular waveguide with a=3cm,b=2cm. If the medium within guide , =0,r=μr=1 will
this waveguide support mode with frequencies 3.2GHz.
9) An air filled rectangular waveguide has dimensions a=6cm, and b=4cm. The signal frequency
is 34Hz. Calculate following for TE01,TE10,TE11, and TM11 modes; a) fc b) λg c)g
10) For TE10, the difference between maximum and minimum is 4.47cm, for rectangular
waveguide with dimensions 6cmx4cm. Find signal frequency for dominant mode. Ans:-
2.92GHz.
11) A rectangular waveguide with dimensions a=2.5cm b=1cm is operated at 15GHz with,
=0,=4o, μr=1, for TE10 mode and TM10 mode calculate; Phase coeffiecient,velocity, wave
impedance
Ans:- For TE10 mode;615.6rad/m;1.531x108m/s;192.4
For TM10 ,mode;529.4rad/m;1.78x108m/s;158.8
12) For rectangular waveguide with dimension a=6cm,b=4cm with TE10 mode, Power density
1HP, f=20GHz. Find peak value of electric field intensity.
13)An air filled rectangular waveguide has cross section dimension 8cmx4cm. Find
a) cut-off frequency for TE10,TE20,TE01,TE02 mode.
b) Find out the ratio of guide velocity to velocity in free space for TE10. If v=1.8Vc
Ans:- a) 1.875GHz for TE10;3.75GHz for TE20 & TE01;7.5GHz for TE02.
b) 1.2026
14) An air filled 5cm x2cm waveguide has
Ezs= 20 sin40x sin50ye-jz
V/m at 15GHz
a) What mode is being propagated.
b) Find .
C) Determine Ey/Ex.
15) Specify the minimum width a and minimum height b of an air filled rectangular waveguide
so that it will operate single mode over the frequency range 15GHz<f<20GHz.
Ans:- 1cm,0.75cm.
16) Determine the group delay between these two modes over a distance of 1cm for the
waveguide operating at 25GHz with mode m=1 and m=2 will be above cut-off.

3. 17) Determine wave angle m for the 1st
four mode (m=1,2,3,4) in parallel plate waveguide with
a=2cm,r’=1 f=30GHz.Hint Use cosm= Ans:- 76’,60’,41’,0’.
18) Parallel plate waveguide has plate spacing d=5mm and is filled with glass (=1.45). What is
maximum frequency at which the guide will operate in TEM mode only? Ans:- 20.7GHz
19) Parallel plate guide having d=1cm is filled with air. Find the cut-off wavelength for m=2
mode (TE or TM) Ans:- 1cm