# Waveguide Cutoff Frequency

### - waveguide cutoff frequency is an essential parameter for any waveguide - it does not propagate signals below this frequency. It is easy to understand an calculate with our equations.

The cutoff frequency is the frequency below which the waveguide will not operate.

Accordingly it is essential that any signals required to pass through the waveguide do not extend close to or below the cutoff frequency.

The waveguide cutoff frequency is therefore one of the major specifications associated with any waveguide product.

## Waveguide cutoff frequency basics

Waveguides will only carry or propagate signals above a certain frequency, known as the cut-off frequency. Below this the waveguide is not able to carry the signals. The cut-off frequency of the waveguide depends upon its dimensions. In view of the mechanical constraints this means that waveguides are only used for microwave frequencies. Although it is theoretically possible to build waveguides for lower frequencies the size would not make them viable to contain within normal dimensions and their cost would be prohibitive.

As a very rough guide to the dimensions required for a waveguide, the width of a waveguide needs to be of the same order of magnitude as the wavelength of the signal being carried. As a result, there is a number of standard sizes used for waveguides as detailed in another page of this tutorial. Also other forms of waveguide may be specifically designed to operate on a given band of frequencies

## What is waveguide cutoff frequency? - the concept

Although the exact mechanics for the cutoff frequency of a waveguide vary according to whether it is rectangular, circular, etc, a good visualisation can be gained from the example of a rectangular waveguide. This is also the most widely used form.

Signals can progress along a waveguide using a number of modes. However the dominant mode is the one that has the lowest cutoff frequency. For a rectangular waveguide, this is the TE10 mode.

The TE means transverse electric and indicates that the electric field is transverse to the direction of propagation.

TE modes for a rectangular waveguide

The diagram shows the electric field across the cross section of the waveguide. The lowest frequency that can be propagated by a mode equates to that were the wave can "fit into" the waveguide.

As seen by the diagram, it is possible for a number of modes to be active and this can cause significant problems and issues. All the modes propagate in slightly different ways and therefore if a number of modes are active, signal issues occur.

It is therefore best to select the waveguide dimensions so that, for a given input signal, only the energy of the dominant mode can be transmitted by the waveguide. For example: for a given frequency, the width of a rectangular guide may be too large: this would cause the TE20 mode to propagate.

As a result, for low aspect ratio rectangular waveguides the TE20 mode is the next higher order mode and it is harmonically related to the cutoff frequency of the TE10 mode. This relationship and attenuation and propagation characteristics that determine the normal operating frequency range of rectangular waveguide.

## Rectangular waveguide cutoff frequency

Although waveguides can support many modes of transmission, the one that is used, virtually exclusively is the TE10 mode. If this assumption is made, then the calculation for the lower cutoff point becomes very simple:

Where:
fc = rectangular waveguide cutoff frequency in Hz
c = speed of light within the waveguide in metres per second
a = the large internal dimension of the waveguide in metres

It is worth noting that the cutoff frequency is independent of the other dimension of the waveguide. This is because the major dimension governs the lowest frequency at which the waveguide can propagate a signal.

## Circular waveguide cutoff frequency

the equation for a circular waveguide is a little more complicated (but not a lot).

Where:
fc = circular waveguide cutoff frequency in Hz
c = speed of light within the waveguide in metres per second
a = the internal radius for the circular waveguide in metres

Although it is possible to provide more generic waveguide cutoff frequency formulae, these ones are simple, easy to use and accommodate, by far the majority of calculations needed.

By Ian Poole

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