Shannon's Theorem gives an upper bound to the capacity of a link, in bits per second (bps), as a function of the available bandwidth and the signal-to-noise ratio of the link.
The Theorem can be stated as:
C = B * log2(1+ S/N)
where C is the achievable channel capacity, B is the bandwidth of the line, S is the average signal power and N is the average noise power.
The signal-to-noise ratio (S/N) is usually expressed in decibels (dB) given by the formula:
10 * log10(S/N)
so for example a signal-to-noise ratio of 1000 is commonly expressed as
10 * log10(1000) = 30 dB.
Here is a graph showing the relationship between C/B and S/N (in dB):
Here are two examples of the use of Shannon's Theorem.
For a typical telephone line with a signal-to-noise ratio of 30dB and an audio bandwidth of 3kHz, we get a maximum data rate of:
C = 3000 * log2(1001)
which is a little less than 30 kbps.
Satellite TV Channel
For a satellite TV channel with a signal-to noise ratio of 20 dB and a video bandwidth of 10MHz, we get a maximum data rate of:
C=10000000 * log2(101)
which is about 66 Mbps.
L L Peterson and B S Davie,
Computer Networks:a systems approach
(Morgan Kaufmann), 1996. ISBN: 1-55860-368-9 (Paperback ISBN: 1-55860-404-9 ) pp 94-95.