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Tue Jan 5 16:39:00 CET 2016

## Circuit: simulation and impedance tuning

I'd like to approach circuit design as a programming problem. Meaning:
- Formalize circuit capture in a data structure (initial) or program (final).
- Perform DC / AC analysis
- Find a way to tune for impedance
First step is to compute the conductivity matrix, as is used in SPICE.
Compute it as code, to perform simulation through automatic
differentiation.
Questions:
- Why does spice use constant current source, conductivity matrix,
node voltages as unknown, instead of the dual?
- Does it really matter? Does it make sense to use a representation
that has both primal and dual representations?
What is a circuit? It is related to a nonlinear manifold. Its affine
approximation is either:
- conductivity matrix + constant current sources
- resistance matrix + constant voltage sources
Until it is clear what the reason is to pick one of these, work with
the dual representation. Is there a mathematical object that uses
this? Projective geometry?

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