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Log-Log Plots and Decibels

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


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

Doug Gingrich
Tue Jul 13 16:55:15 EDT 1999