Asymptotes
Certain parts of the magnitude curves can be approximated by straight lines. It can be useful to calculate the slopes of these lines. The slopes are generally expressed in
per octave or in
per decade.
An octave and a decade are the intervals separating two frequencies. The former corresponds to twice the frequency, and the latter ten times the frequency. Example:
One octave above 1000 Hz is 2000 Hz.
One decade above 1000 Hz is 10000 Hz.
In a range of frequencies where the response is proportional to
, the magnitude difference between
and
is given by
.
So, for example, the Bode magnitude plot of an
system (i.e a system whose transfer function is proportional to
) will have a slope of
.
By the same reasoning, the magnitude difference over a decade is proportional to
. Generally, only the value of
is expressed for the frequency interval. For example,
for a slope of
, or
