Environmental Engineering Reference
In-Depth Information
it is usually convenient to analyse the frequency response of the loop-gain
rather than that of the open-loop transfer function. This is because the loop-
gain transfer function gives
information on most of the closed-loop
properties.
The closed-loop characteristics of an amplifier can be also investigated in
the time domain, by evaluating the response, to a unitary input step
u
(t). The step response gives important specifications for applications (such
as instrumentation, control, and sample data systems) sensitive to the
amplifier's transient response.
Let us consider a closed-loop configuration comprising the single-pole
amplifier with the transfer function shown in (4.1). The step response is
easily found to be
The output steady state value is
and is reached exponentially with time
constant
The reader should know that the
settling time,
is the time interval
required for the output response to settle to some specified percentage of the
final value. For a single-pole amplifier the settling time is then proportional
to Usually, the settling time needed to reach 1% or 0.1% of the final
value is considered. In these two cases, the settling time results
and
