The problem of a two-level device and circuit simulation is demonstrated by an
example circuit as shown in Fig. 4.1 where *V*_{S} is a
constant voltage source and *G* is a linear conductance. The non-linear
device is a diode whose characteristic is determined by the doping profile and
the physical models used in the device simulation. The DC characteristic is
shown in Fig. 4.2. In Fig. 4.1a the original
circuit is shown. When using Newton's method to solve the non-linear circuit
equations, a linear companion circuit [9] is solved at each iteration
until some convergence criterion is met. The companion circuit for arbitrary
non-linear two-terminal devices is shown in Fig. 4.1b. It
consists of a linear conductance
*G*_{eq} and a current source
*I*_{eq} which depend on the operating point. They are derived from
the non-linear characteristic as shown in Fig. 4.2 and read

with

For the calculation of the conductances an approach as proposed in [39] is well suited and will be outlined in the following section.

1999-05-31