**Subject :**Microwave Engineering

## Power losses in Rectangular Waveguide

There are two types of power losses in a rectangular waveguide:

**1.** Losses in the dielectric

**2**. Losses in the guide walls

First we shall consider power losses caused by dielectric attenuation. In a low-loss dielectric (that is, (σ<<με), the propagation constant for a plane wave traveling in an unbounded lossy dielectric is given by :

The attenuation caused by the low-loss dielectric in the rectangular waveguide for the TE_{mn} or TM_{mn} modes is given by

As f>>f_{c} , the attenuation constant in the guide approaches that for the unbounded dielectric. However, if the operating frequency is way below the cutoff frequency, f<<f_{c }the attenuation constant becomes very large and non-propagation occurs.

Now we shall consider power losses caused by the guide walls. When the electric and magnetic intensities propagate through a lossy waveguide, their magnitudes may be written :

where Eoz and Hoz are the field intensities at z = O. It is interesting to note that, for a low-loss guide, the time-average power flow decreases proportionally to e ^{- 2αgz} . Hence :

For Ploss <<Ptrr; and 2αgz << 1,

Finally,

where PL is the power loss per unit length. Consequently, the attenuation constant of the guide walls is equal to the ratio of the power loss per unit length to twice the power transmitted through the guide.

Since the electric and magnetic field intensities established at the surface of a low-loss guide wall decay exponentially with respect to the skin depth while the waves progress into the walls, it is better to define a surface resistance of the guide walls as :

where ρ = resistivity of the conducting wall in ohms-meter

σ= conductivity in mhos per meter

δ = skin depth or depth of penetration in meters

The power loss per unit length of guide is obtained by integrating the power density over the surface of the conductor corresponding to the unit length of the guide.This is