**Subject :**Microwave Engineering

## TEM modes in Circular Waveguide

The transverse electric and transverse magnetic (TEM) modes or transmission-line modes are characterized by :

This means that the electric and magnetic fields are completely transverse to the direction of wave propagation. This mode cannot exist in hollow waveguides, since it requires two conductors, such as the coaxial transmission line and two-open-wire line. Analysis of the TEM mode illustrates an excellent analogous relationship between the method of circuit theory and that of the field theory. Figure shows a coaxial line.

**Figure : coordinates of a circular waveguides
**

Maxwell's curl equations in cylindrical coordinates :

....(1)

becomes

..(2)

where ∂/ ∂r = - jβ_{g} and E_{z} = H_{z} =0 are replaced.

Solving equation (2) mutually , gives :

...(3)

which is the phase constant of the wave in a lossless transmission line with a dielectric.

In comparing the preceding equation with the characteristic equation of the Helmholtz equation in cylindrical coordinates :

..(4)

It is evident that :

...(5)