# Lowest & Maximum Usable Frequency, Critical Frequency

### - Critical Frequency, Lowest Useable Frequency, LUF, and Maximum Usable Frequency, MUF and Optimum Working Frequency, OWF used in radio communications & signal propagation

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There are a number of frequencies that are of importance when working with ionospheric radio propagation. Frequencies including the Critical Frequency; Lowest Usable Frequency, LUF; Maximum usable frequency, MUF; and the Optimum Working Frequency, OWF are all of great importance when determining which frequencies will provide the best performance for a short wave radio, HF radio communications link.

These frequencies are often mentioned in radio communications propagation predictions. As such an overview of these terms is of importance to anyone using HF radio communications.

## Critical Frequency

The critical frequency is an important figure that gives an indication of the state of the ionosphere and the resulting HF propagation. It is obtained by sending a signal pulse directly upwards. This is reflected back and can be received by a receiver on the same site as the transmitter. The pulse may be reflected back to earth, and the time measured to give an indication of the height of the layer. As the frequency is increased a point is reached where the signal will pass right through the layer, and on to the next one, or into outer space. The frequency at which this occurs is called the critical frequency.

The equipment used to measure the critical frequency is called an ionosonde. In many respects it resembles a small radar set, but for the HF bands. Using these sets a plot of the reflections against frequency can be generated. This will give an indication of the state of the ionosphere for that area of the world

## Maximum Usable Frequency, MUF

When a signal is transmitted using HF propagation, over a given path there is a maximum frequency that can be used. This results from the fact that as the signal frequency increases it will pass through more layers and eventually travelling into outer space. As it passes through one layer it may be that communication is lost because the signal then propagates over a greater distance than is required. Also when the signal passes through all the layers communication will be lost.

The frequency at which radio communications just starts to fail is known as the Maximum Usable Frequency (MUF). As a rule of thumb it is generally three (for the F region) to five (for the E region) times the critical and it is true for low angles of incidence, although more exact methods are available for determining this figure.

It is possible to calculate the relationship more exactly:

$MUF=\frac{\mathrm{CF}}{\mathrm{cos}\theta }$

Where:
MUF = Maximum Usable Frequency
CF = critical frequency
θ = the angle of incidence.

The factor sec θ is called the MUF factor and it is a function of the path length if the height layer is known. By using typical figures for the heights of the different ionospheric regions the factors may be determined.

Region or layer Distance
1000 km 2000 km 3000 km 4000 km
E 3.2 4.8
F1 2.0 3.2 3.9
F2 Winter 1.8 3.2 3.7 4.0
F2 Summer 1.5 2.4 3.0 3.3

MUF factors for various distances
assuming representative heights for the principle ionospheric regions

An "operational" format for the maximum usable frequency may also be seen on occasions. This is the maximum usable frequency, MUF that would permit acceptable operation of a radio service between given terminals under specific working conditions. This form of MUF has the emphasis on the operational acceptability of the circuit. It means that factors such as the antenna, power levels and such like are considered and gives an indication regarding the possibility of real communication at a given station.

## Lowest Usable Frequency, LUF

As the frequency of a transmission is reduced further reflections from the ionosphere may be needed, and the losses from the D layer increase. These two effects mean that there is a frequency below which radio communications between two stations will be lost. In fact the Lowest Usable Frequency (LUF) is defined as the frequency at below which the signal falls below the minimum strength required for satisfactory reception.

From this it can be seen that the LUF is dependent upon the stations at either end of the path. Their antennas, receivers, transmitter powers, the level of noise in the vicinity, and so forth all affect the LUF. The type of modulation used also has an effect, because some types of modulation can be copied at lower strengths than others. In other words the LUF is the practical limit below which communication cannot be maintained between two particular radio communications stations.

If it is necessary to use a frequency below the LUF then as a rough guide a gain of 10dB must be made to decrease the LUF by 2 MHz. This can be achieved by methods including increasing the transmitter powers, improving the antennas, etc..

It is found that the LUF actually increases in periods of high solar activity. This is arises because of the increased levels of solar radiation that give rise to higher levels of ionisation in the D layer. This in turn increases the level of attenuation introduced by this layer. This means that at the peak of the sunspot cycle there is degradation in the performance of the low frequency bands for long distance communications.

## Optimum working frequency

To be able to send signals to a given location there are likely to be several different paths that can be used. Sometimes it may be possible to use the either the E or the F layers, and sometimes a signal may be reflected first off one and then the other. In fact the picture is rarely as well defined as it may appear from the textbooks. However it is still possible to choose a frequency from a variety of options to help making contact with a given area.

In general the higher the frequency, the better. This is because the attenuation caused by the D layer is less. Although signals may be able to travel through the D layer they may still suffer significant levels of attenuation. As the attenuation reduces by a factor of four for doubling the frequency in use this shows how significant this can be.

Also by increasing the frequency it is likely that a higher layer in the ionosphere will be used. This may result in fewer reflections being required. As losses are incurred at each reflection and each time the signal passes through the D layer, using a higher frequency obviously helps.

When using the higher frequencies it is necessary to ensure that communications are still reliable. In view of the ever-changing state of the ionosphere a general rule of thumb is to use a frequency that is about 20% below the MUF. This should ensure that the signal remains below the MUF despite the short-term changes. However it should be remembered that the MUF will change significantly according to the time of day, and therefore it will be necessary alter the frequency periodically to take account of this.

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