Question

Describe rectangular waveguide in TE & TM mode.

Answer 1

i. Mode is defined as all possible configuration of electric and magnetic field which can exists in the waveguide.

ii. Modes in rectangular waveguides are labeled TEm,nif they are transverse electric, and TMm,nif they are transverse magnetic. In each case m and n are integers denoting the number of half wavelengths of intensity between each pair of walls.

iii. mis measured along the x axis of the waveguide (dimension a), this being the direction along the broader wall of the waveguide; n is measured along the y axis (dimension b). 

TEm,n Modes: In TE modes, electric field is transverse only, and the has a component of the magnetic field in the direction of propagation.

The equation of characteristic wave impedance is given by –

Where,

Z0= characteristic wave impedance of the waveguide

It is seen that the different TEm,0modes all have different cutoff wavelengths and therefore encounter different characteristic wave impedances.

The cut-off wavelength for TEm,nmode is given by-

In the TEm,o mode, cut off wavelength is given by

For TE1,0Mode m=1,

Which has the largest cutoff wavelength and hence TE1,0 called as dominant mode

TMm,n Modes:

In TM modes, the magnetic field is transverse only, and the electric field has a component in the direction of propagation. Since lines of magnetic force are closed loops, if a magnetic field exists and is changing in the x direction, it must also exist and be changing in the y direction. Hence TMm,0 modes cannot exist in rectangular waveguides. The formula for characteristic wave impedance for TM modes is,