2.3.3.4 Non-linear Capacitor

The constitutive relation for a non-linear capacitor is I = dQ/dt. Using the backward Euler discretization scheme to discretize dQ/dt one obtains

$${\frac{Q - Q_o}{\Delta t}}$$ I = (2.37)

$$\approx {\frac{C_o \cdot V_o}{\Delta t}}$$ (2.38)

$${\frac{C}{\Delta t}}$$ G = (2.39)

Equation (2.38) is a commonly used approximation which, however, does not guarantee charge conservation [66,67]. For constant C (2.38) of course simplifies to (2.35). The stamp is given as

yx, y	$\varphi_{1}^{}$	$\varphi_{2}^{}$	f
n1	G	- G	- I
n2	- G	G	I