Introduction To The dB
Describing Power  
Signal stages are cascaded, so powers are multiplied by gain or loss. This yields a lot of multiplications. This suggests the need for a logarithmic representation of power. A logarithmic scale is used to
 
Logarithms  
Log(x) = power to which base must be raised to give x. The base is chosen to be 10.
Some example logarithm values:
 
The deciBel  
Represent gains or attenuations logarithmically (base 10) (the Bel) But to make numbers more convenient, scale by a factor of 10 (the deciBel or dB)
Examples:
Since Log(A x B) = Log(A) + Log(B) we can add gains and losses. P_{R} = P_{T} + 20  1 + 30  2  204 + 30 1 + 60 = P_{T}  68 dB For converting from a power ratio to dB, first work out powers of 10, e.g:
Then note the smaller factors:
Examples of converting from dB to a Ratio (or more generally, ratio = 10^{dB/10}):
 
Applying dB to Other Units  
By default, dB is a power ratio. But it can be other things, for example, dB banana = dB relative to 1 banana. dBW = dB relative to 1 watt, so:
Bandwidth in Hz can be expressed in dBHz
Similarly, Noise Temperature:
By default, with dBs we are dealing with power.
Thus a change in power (e.g. due to amplification) can be represented by:
TIP: Take care with "Voltage gain in dB" which is usually a power gain, i.e 20Log(V_{2} / V_{1})  
How Big Is A dB?  
Examples of BER vs. Eb/No in dB:
