Mathemetical modeling and computer simulation of analog electronic circuits
The overriding assumptions are that “good programs” already exist to solve any given problem of basic circuit simulation, and to some extent, they do [1][2][3][4].
First-order systems of ordinary differential equations
Analog electronic circuit simulation problems are first-order systems of ordinary differential equations to be solved numerically or approximately.
Every node in a circuit has an electric potential, and every device carries an electric current. (Transistor base and collector currents are considered separate variables in the simulation, while the emitter current is constrained to be equal to the negative sum of them.)
The differential equations are ordinary and of the first order, because they involve these potentials and currents and their first derivatives with respect to time only.
Stiffness and convergence problems
Convergence problems [5] have plagued many SPICE (Simulation Program with Integrated Circuit Emphasis) implementations.
... [6]
- ↑ LTspice: Fast • Free • Unlimited https://www.analog.com/en/resources/design-tools-and-calculators/ltspice-simulator.html
- ↑ ngspice - open source spice simulator https://ngspice.sourceforge.io/
- ↑ Circuit simulation and schematics. https://www.circuitlab.com/
- ↑ Circuit Design and Simulation Software https://www.keysight.com/us/en/products/software/pathwave-design-software/eda-software-for-circuit-design.html
- ↑ LT wiki: Convergence Problems. https://ltwiki.org/index.php?title=Convergence_problems%3F
- ↑ Chris Rackauckas. Solving Stiff Ordinary Differential Equations. October 14th, 2020 https://book.sciml.ai/notes/09-Solving_Stiff_Ordinary_Differential_Equations/
