ID/VD
Often it is desired to get an approximate solution to a problem involving a nonlinear electrical device. A case in point is a circuit with a diode or several diodes in a configuration like an AND gate. To solve the problem quickly, we can approximate the actual characteristic curve by a series of straight lines, and we can represent each straight line as a simple electrical network.
The figure shows the curve for a diode with a straight line drawn in to represent an approximate linear characteristic. The straight line hits the horizontal axis at VD = VON, and has a slope of 1/Rf. We can get an equation for this line by choosing the two points (VD1, ID1), and (VON, 0).
ID/VD
This equation can be represented by an electrical circuit as shown. Since VD1 and ID1 are arbitrary, we can just replace them by VD and ID. We do have to make sure that the circuit does not let current go below the horizontal axis - that is, when ID is negative. Therefore we stick a perfect diode in series. This has no voltage drop across it while allowing current to flow in the positive direction, but will shut off if current tries to reverse. That means the second region of operation is also covered by this model: the region for VD less than VON. Here the original model predicts the current tries to reverse. If we said that the perfect diode stays on,
ID = (VD - VON)/Rf < 0 if VD < VON
so the perfect diode, in fact, switches off because it sees a negative current. Thus the line representing operation below VON is just the horizontal axis.
Note that the model is not very good for low diode currents, because when VD < VON it predicts zero current when there actually is some flowing. However, for many circuits this error is not critical, and the time saved and insight gained is worth the small error created.