Settling time

Settling time

Discussion

Encyclopedia
The settling time of an amplifier
Amplifier
Generally, an amplifier or simply amp, is a device for increasing the power of a signal.In popular use, the term usually describes an electronic amplifier, in which the input "signal" is usually a voltage or a current. In audio applications, amplifiers drive the loudspeakers used in PA systems to...

or other output device is the time elapsed from the application of an ideal instantaneous step input to the time at which the amplifier output has entered and remained within a specified error
Error
The word error entails different meanings and usages relative to how it is conceptually applied. The concrete meaning of the Latin word "error" is "wandering" or "straying". Unlike an illusion, an error or a mistake can sometimes be dispelled through knowledge...

band, usually symmetrical about the final value.
Settling time includes a very brief propagation delay
Propagation delay
Propagation delay is a technical term that can have a different meaning depending on the context. It can relate to networking, electronics or physics...

, plus the time required for the output to slew to the vicinity of the final value, recover from the overload condition associated with slew
Slew rate
In electronics, the slew rate represents the maximum rate of change of a signal at any point in a circuit.Limitations in slew rate capability can give rise to non linear effects in electronic amplifiers...

, and finally settle to within the specified error.

Systems with energy storage cannot respond instantaneously and will exhibit transient responses when they are subjected to inputs or disturbances.

Definition

Tay, Mareels and Moore (1997) defined settling time as "the time required for the response curve to reach and stay within a range of certain percentage (usually 5% or 2%) of the final value."

Mathematical detail

Settling time depends on the system response and time constant
Time constant
In physics and engineering, the time constant, usually denoted by the Greek letter \tau , is the risetime characterizing the response to a time-varying input of a first-order, linear time-invariant system.Concretely, a first-order LTI system is a system that can be modeled by a single first order...

.

The settling time for a 2nd order, underdamped system responding to a step response
Step response
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...

can be approximated if the damping ratio by

Thus, settling time to within 2%=0.02 is: