**Subject :**Microwave Engineering

## Circular waveguide and solutions of wave equations for circular waveguides

**CIRCULAR WAVEGUIDES :-
**

A circular waveguide is a tubular, circular conductor. A plane wave propagating through a circular waveguide results in a transverse electric (TE) or transerse magnetic (TM) mode. Several other types of waveguides, such as elliptical and reentrant guides, also propagate electromagnetic waves.

**Solution of Wave equations :-
**

A circular waveguide is shown in the following figure

**Figure : Circular Waveguide (Cylindrical coordinates)
**

The scalar Helmholtz equation in cylindrical coordinates is given by

...(1)

Using the method of separation of variables, the solution is assumed in the form of :

.......(2)

where R (r) = a function of the r coordinate only

Φ(φ) = a function of the φ coordinate only

Z(z) = a function of the z coordinate only

Substitution of Eq. (2) in (1) and division of the resultant by (2) yield :

......(3)

Since the sum of the three independent terms is a constant, each of the three terms must be a constant. The third term may be set equal to a constant

........(4)

The solutions of this equation are given by

............(5)