The dominant mode in rectangular waveguide is

Concept:

The dominant mode in a particular waveguide is the mode having the lowest cut-off frequency.

The cut-off frequency for a rectangular waveguide with dimension ‘a (length)’ and ‘b (width)’ is given as:

\(\Rightarrow {{f}_{c\left( mn \right)}}=\frac{c}{2}\sqrt{{{\left( \frac{m}{a} \right)}^{2}}+{{\left( \frac{n}{b} \right)}^{2}}}\)

'm' and 'n' represents the possible modes.

Application:

For a standard rectangular waveguide a > b;

The minimum frequency is obtained when m = 1 and n = 0,

\(i.e.~{{f}_{c\left( 10 \right)}}=\frac{c}{2}\sqrt{\frac{{{m}^{2}}}{{{a}^{2}}}}=\frac{c}{2a}\)

• For a rectangular waveguide with b > a, TE₀₁ will be the dominant mode with the lowest cut-off frequency.
• TEM mode cannot exist in Hollow conductor waveguide
• Circular and rectangular are hollow waveguides hence there is no TEM mode in them, they can support only TE or TM but not TEM mode
• The transmission line, parallel plate waveguide, coaxial cable can have TEM mode