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Tue Oct 21 10:29:33 EDT 2014

## A slowed-down diode

Starting from the analog circuit:
Ic>
/---||---\
| 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?
YES.
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.

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