# Rectangular Waveguides

Waveguides are just rectangular tubes full of air for transmission of power waves at high frequencies. Waveguides with a single conductor support either TE or TM waves, but not TEM waves.

• Modes define the properties of how a wave propagates through a guide
• Modes are defined by and
• Obtained through solving the wave equations for different boundary conditions
• Mode with lowest cutoff frequency is the dominant mode
• Dominant TM mode is
• Dominant TE mode is

## TM Modes

### Phase Constant

A wave is travelling inside the guide along the z-direction. It's phase factor is with:

### Cutoff Frequency

Corresponding to each mode there is a cutoff frequency at which . A mode can only propagate if , as only then is real.

is the phase velocity of a TEM wave in an unbounded medium with parameters and .

### Wave Impedance

is the intrinsic impedance of the lossless medium.

## TE Mode

All the parameters are the same as for TM mode, except for wave impedance

The TE dominant mode, assuming where and are the width and height of the waveguide ,is with

### Zigzag Reflections

For the mode, the field component can be expressed as the sum of two TEM plane waves, both travelling in the direction, but zigzagging between opposite walls of the waveguide. The phase velocity of these waves is and their direction is at angles. The phase velocity of their combination is that of the mode.