Implicit Equations
The model of the direct current of a diode demonstrates the advantage of implicit relations:
It is not possible to express this relationship as an explicit function: i = f(v)
The previous example of a diode model can also be formulated using an auxiliary variable and a second equation:
Here Vd is the voltage over the intrinsic diode,
which is the total voltage minus the voltage over the series resistance Rs.
For this simple case Vd could also have been defined as an intermediate variable,
since the second equation is explicit.