Small-signal model

The small-signal behavior describes the behavior of a system in modulation with small signals, the word " small " is not to be understood as less distance to zero but to a working point. For these small signals in a limited but essential for the task area to reach an approximately linear transfer function between input and output signal.

Linearity, for example, a prerequisite for the application of the Laplace transform in systems theory / electrical system for the purpose of analysis.

Field of application

The description by means of the small-signal behavior is applied to the non-linear components and analog electronic circuits, transistors or other non-linear semiconductor components included. The operating points of the components are chosen so that neither the limits of the control range even more non-linear regions of the transfer characteristic can be achieved. Through a small modulation around the operating point is approximated as a linear relationship between the input and the output size.

Any non- linearity produces distortion. There are harmonics, which is equivalent to an increase of the distortion factor. The limit for the small signal behavior arises from the limit on how far the distortion can be accepted.

Linear approximation

A continuously curved curve can be linearly approximated by its tangent at this point in an operating arbitrarily chosen. As long as the behavior of the component can be described by the tangent, one speaks of his small-signal behavior.

With a known transfer function can be approximated by a Taylor series this. Since only linear components taking into account the small-signal behavior, you break the series expansion about the operating point A to the linear term from.

The current-voltage characteristics of a silicon semiconductor diode in the passband (for the diode current at positive voltage) can be described by the Shockley equation substantially.

The linear Taylor approach

Results in this application

And after insertion and differentiating

For the small signal parameters and to obtain

This corresponds to the small signal behavior of a diode to a differential resistor whose value is inversely proportional to the current at the working point.