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Wed Nov 5 10:25:45 EST 2014

## Rethinking circuit representation

I'm starting to understand the spice rationale[1]. The basic model is
that of a resistive network with one node dedicated as ground node.
Equations are set up using KCL for each non-ground node. This gives a
relation between node voltages and currents flowing into each node:
G V = I
This is just a relation. It can be interpreted as currents drawn from
voltage sources, or node voltages caused by current sources.
The matrix G is symmetric, positive definite.
- symmetric: a resistor has no directionality
- positive definite: V^T G V = V^T I = P, total power is always > 0
Starting from this basic model, SPICE linearizes the equations and
performs NR iterations at a particular time instance, and uses one of
several integration methods to move forward in time.
The structure of G allows for Krylov subspace methods (conjugate
gradient, lanczos)
[1] entry://../math/20141105-000511

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