Small-signal diode models

The idea of small-signal modelling is that the short-cut part of the current-voltage characteristic of the semiconductor diode is not precise enough in an exact approximation and it is logical to represent the diode as a resistor at the short-cut. Using the circuit analysis technique we can find the small-signal resistance of the diode. Kirchhof equations with a diode as a load will help to calculate the $I_{diode}$ and  $V_{diode}$. These values of voltage and current for the diode are called the operating point of the diode.

Piecewise linear diode model: In this model the diode is considered as an open circuit when it is off, and as a linear resistor with the offset voltage in series, when the diode is on. And close to the operating point, discussed above, the diode behaves as a small-signal resistance with: $r_{diode}=\frac{{{\partial }^i}_{diode}}{{{\partial }^v}_{diode}}$ calculated in the operating point.  This method helps to use the semiconductor diode more accurately in its states.