**Subject :**Microwave Engineering

## Power transmission in Circular waveguides

In general, the power transmitted through circular waveguides and coaxial lines can be calculated by means of the complex Poynting theorem. For a lossless dielectric, the time-average power transmitted through a circular guide can be given by

..(1)

Substitution of Z, for a particular mode in Eq. (1) yields the power transmitted by that mode through the guide.

For TEnp modes, the average power transmitted through a circular guide is given by :

..(2)

For TMnp modes, the average power transmitted through a circular guide is given by

....(3)

For TEM modes in coaxial lines, the average power transmitted through a coaxial line or two-open-wire line is given by

....(4)

If the current carried by the center conductor of a coaxial line is assumed to be :

..(5)

the magnetic intensity induced by the current around the center conductor is given by Ampere's law as :

....(6)

The potential rise from the outer conductor to the center conductor is given by :

....(7)

The characteristic impedance of a coaxial line is :

...(8)

The power transmitted by TEM modes in a coaxial line can be expressed from Eq. (3) as :

..(9)