Tue Oct 21 10:29:33 EDT 2014

A slowed-down diode

Starting from the analog circuit:

             |    C   |
       L     |        |
V1 ---OOOO---o--|>|---o--- V0
    I>       Vx   Id>

  I = Id + Ic
  L DI = V1 - V0
  Ic = C DVx
  Id = f(Vx-V0)

The transformation from analog to digital is completely captured in
the equation:

   Id/Is = e(Vx0/VT) (1 + [Vx-Vx0]/VT)

Now, what about elimiting L and C, and trusting that the global
circuit has enough inertia to make this approximation work when
applied naively?

Is this just a very roundabout way to approximating every static
nonlinearity with a linearized version around the previous set point?


The key element is to equate the iteration process necessary for
solving a non-linear equation with the temporal one necessary to solve
a differential equation.

So the point is: the previous derivation with L/C filter localizes the
effect.  In practice, this is probably not necessary if the circuit is
slow enough.