### HARTLEY'S LAW – BANDWIDTH REQUIREMENTS BASIC INFORMATION

The carrier wave is a sine wave for almost any communication system. A sine wave, of course, exists at only one frequency and therefore occupies zero bandwidth.

As soon as the signal is modulated to transmit information, however, the bandwidth increases. A detailed knowledge of the bandwidth of various types of modulated signals is essential to the understanding of the communication systems.

Thorough study of signal bandwidths will have to wait until we know more about the modulation schemes referred to above. However, at this time it would be well to look at the concept of bandwidth in more general terms.

First, bandwidth in radio systems is always a scarce resource. Not all frequencies are useful for a given communication system, and there is often competition among users for the same part of the spectrum.

In addition, as we have seen, the degrading effect of noise on signals increases with bandwidth. Therefore, in most communication systems it is important to conserve bandwidth to the extent possible.

There is a general rule known as Hartley’s Law which relates bandwidth, time, and information content. We will not yet be able to use it for actual calculations, but it would be well to note it for future reference, as Hartley’s Law applies to the operation of all communication systems.

Here it is:
I = ktB; where

I = amount of information to be transmitted in bits
k = a constant that depends on the modulation scheme and the signal-to-noise ratio
t = time in seconds
B = bandwidth in hertz

Our problem thus far is that we do not have precise ways of quantifying either the amount of information I or the constant k. However, the general form of the equation is instructive.

It tells us that the rate at which information is transmitted is proportional to the bandwidth occupied by a communication system. To transmit more information in a given time requires more bandwidth (or a more efficient modulation scheme).