(where 
):
.
Note that since 
and 
are complex, 
is complex
In Lab 5 we measured the step response of some first order systems. Although it only describes the response to piecewise constant signals, the step response in fact completely characterizes the behavior of a linear system.
The step response is a time domain characterization. It describes what the output looks like as a function of time. We can also characterize a linear system by its frequency response, which describes its behavior in the frequency domain.
The frequency response is a special case of the transfer function
where
s
is replaced by
(where
):
.
Note that since
and
are complex,
is complex
We usually express
in polar form, in terms of its
magnitude
(
).
and
phase
(
).
For our generic first order system:
we have
so we can find the output voltage, 
by setting 
in the transfer function:
is called the
cutoff frequency
of the network.
For the magnitude of the frequency response, we have
, 
.