Everything about The Step Response totally explained
The
step response of a system in a given initial state consists of the time evolution of its
outputs when its
control inputs are
Heaviside step functions. In
electronic engineering and
control theory, step response is the time behaviour of the outputs of a general
system when its inputs change from zero to one in a very short time. The concept can be extended to the abstract mathematical notion of a
dynamical system using an
evolution parameter.
From a practical standpoint, knowing how the system responds to a sudden input is important because large and possibly fast deviations from the long term steady state may have extreme effects on the component itself and on other portions of the overall system dependent on this component. In addition, the overall system can't act until the component's output settles down to some vicinity of its final state, delaying the overall system response. Formally, knowing the step response of a dynamical system gives information on the
stability of such a system, and on its ability to reach one stationary state when starting from another.
Time domain versus frequency domain
Depending on the application, instead of frequency response, system performance may be specified in terms of parameters describing time-dependence of response. The step response can be described by the following quantities related to its
time behavior,
In the case of
linear dynamic systems, much can be inferred about the system from these characteristics.
Below the step response of a simple two-pole amplifier is presented, and some of these terms are illustrated.
Step response of feedback amplifiers
This section describes the step response of a simple
negative feedback amplifier shown in Figure 1. The feedback amplifier consists of a main
open-loop amplifier of gain
AOL and a feedback loop governed by a
feedback factor β. This feedback amplifier is analyzed to determine how its step response depends upon the time constants governing the response of the main amplifier, and upon the amount of feedback used.
Analysis
A negative feedback amplifier has gain given by (see
negative feedback amplifier):
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