/mcpRelative loss = 0.5 x 10−3
1 X 10−3
Relative loss = 0.5
Half the power that the 1004 Hz test−tone introduced at A is lost by the time
it reaches B.
This example repeats the test with the use of less test−tone power. The oscillator at demarc A is set to
generate 1004 Hz tone at a power of 0.1 mW. At demarc B, the power measurement is 0.05 mW. Then, the
absolute power loss is:
0.1 mW 0.05 mW = 0.05 mW
The relative loss, or the ratio between power out (B) and power in (A), is:
Relative Loss = Power out(B)
Power in (A)
Relative Loss = 0.05 x 10−3
1 x 10−3
Relative Loss = 0.5
The relative loss, or power ratio between B and A, is the same whether you use a test signal of 1 mW or 0.1
mw.
The Decibel
Mathematically, the decibel is a logarithmic measure. The logarithm, or log, of a particular number is the
mathematical power to which a base number must be raised in order to result in the particular number. The
base number you use when you deal with the decibel is 10. For example, what is the logarithm (log) of 100?
Another way to ask this question is 'To what power do you raise 10 to get 100?'. The answer is 2 because 10 x
10 = 100.
Similarly,
log (100)= 2
log (1000)= 3
log (10,000)= 4
and so on.
You can also use logarithms to express fractional quantities. For example, what is the logarithm of 0.001?
Another way to ask this question is 'To what power do you raise 1/10 (0.1) to get 0.001?'. The answer is 3. By
convention, the log of a fractional number is expressed as negative.
log (0.001) = −3
Logarithms of numbers that are not integral powers of 10 can be calculated when you look them up in a table
or when you use a hand calculator.