Question

A rectangular waveguide of width w and height h has cut-off frequencies for TE10 and TE11 modes in the ratio 1 : 2. The aspect ratio ?

Answer 1

Solution:-

Rectangular waveguides:-

Generally, electromagnetic waves when travelled from one point to another in open space, its power intensity decreases and loses energy. So, in order to guide the waves, we use waveguides which provides a hollow metallic structure and confined to a particular direction which reduces the loss of energy.

Definition: A rectangular waveguide is defined as a hollow metallic tube with rectangular cross section. This type of cross section makes the EM waves travel into the hollow structure which travels with the principle of Total Internal Reflection in the waveguide.

Aspect ratio:

The performance of a rectangular waveguide is determined by the dimensions of the waveguide which are: width (w) and height (h). So, aspect ratio is the measurement factor to choose correct waveguide. It is defined as "the ratio of height of the rectangular waveguide to the width of the rectangular waveguide". Here the aspect ratio is defined by

Aspect ratio = h/w.

Modes Of Operation :

The electromagnetic waves travel along the waveguide in different types of modes based on the direction of propagation of waves. The different modes have different properties, so we need to choose the correct mode for our purpose. There are 3 different types of modes of operation. They are: 1)TE 2)TM 3)TEM

TE_mn Mode: The electric field vector is perpendicular to the direction of propagation of waves. This mode depends upon transverse electic waves or H waves.

The integers m, n indicate the waveguide sub modes within the waveguide. The integer values range from 0,1 to infinity. But we choose the values of sub modes according to the waveguide dimensions.

Cut off frequency: fc

The waveguides propagate the electromagnetic waves only above a certain frequency below which the waves cannot be propagated. This frequency is known as cutoff frequency fc, where this frequency depends upon the dimensions of waveguide,submodes ( values of m, n) of the waveguide.

The ratio of TE₁₀ and TE₁₁ modes is given as 1:2

So, we determine the aspect ratio by the formula of the cutoff frequency of TE_mn rectangular waveguide as shown below:-

Hence by the above calculations, aspect ratio is determined and the value is

Aspect ratio = 0.577