I am trying to understand,
Q1: What causes spice simulations to not converge specifically if the model is implemented in a piecewise fashion?
Q2: Is the problem caused to the variable time-step used in SPICE and how?
Q3: If implemented in a fixed-step solver, will the convergence problem still exist?
Few points related to this question
1. Continuity of the piecewise model is not known. (maybe discontinuous)
2. each piece is continuous and differentiable.
Can the convergence/divergence be proved mathematically?
In NGSPICE you can define the model in XSPICE, and use helper functions that will 'spline over' the discontinuities. But I am convinced something much simpler is causing the problem. (The basic PULSE and PWL sources also have discontinuities in higher derivatives but simulate just fine.)
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