I'm reading Computer Networks: A Systems Approach by Peterson and Davies. One of the examples demonstrates the relationship between link capacity and the Shannon-Hartley Theorem.
We can find the channel capacity by the formula:
$$C = B \log_2 \left( 1+\frac{S}{N} \right)$$
In the example of the book, they define bandwidth of the channel to be 3000Hz and the signal to noise ratio to be 30 dB, which they say would imply that S/N = 1000.
$$C = 3000 \times \log_2 (1001)$$
However, I don't understand how a signal to noise ratio of 30 dB is equivalent to 1000? How is this worked out? It's not explained in the example.
Best Answer
In the formula, S/N is the power ratio of signal to noise. If this ratio is expressed as 30 dB, then we have 10log(S/N) = 30 which results in a value for S/N of 1000.