and 
are two powers, we define the decibel as
A log-log plot of a circuit's transfer function can be a useful qualitative tool to allow us to understand most of the important features of filter and amplifier circuits. The commonly used decibel unit will be defined. Although unappealing to the physicist this unit is still in wide spread use in electronics. Lets start.
If and are two powers, we define the decibel as
where we have used 
.
The decibel is a property of the network and not the signals.
Hence we can make use of any convenient signals in defining decibel.
If two constant equal amplitude sources, 
, are applied to a four-terminal
network we may write
Therefore
Using the approximation procedure of a previous lecture
and if 
and 
are not too different
By definition an octave interval is when 
and hence
Likewise for a decade interval 
and
