Editing Electrical network (section)

==Network simulation software==
More complex circuits can be analyzed numerically with software such as [[SPICE]] or [[GNU Circuit Analysis Package|GNUCAP]], or symbolically using software such as [[SapWin]].

===Linearization around operating point===
When faced with a new circuit, the software first tries to find a [[Steady state|steady state solution]], that is, one where all nodes conform to Kirchhoff's current law ''and'' the voltages across and through each element of the circuit conform to the voltage/current equations governing that element.

Once the steady state solution is found, the ''[[operating point]]s'' of each element in the circuit are known.  For a small signal analysis, every non-linear element can be linearized around its operation point to obtain the small-signal estimate of the voltages and currents.  This is an application of Ohm's Law.  The resulting linear circuit matrix can be solved with [[Gaussian elimination]].

===Piecewise-linear approximation===
Software such as the [[PLECS]] interface to [[Simulink]] uses [[Piecewise linear function|piecewise-linear]] approximation of the equations governing the elements of a circuit.  The circuit is treated as a completely linear network of [[Diode modelling#Mathematically idealized diode|ideal diode]]s.  Every time a diode switches from on to off or vice versa, the configuration of the linear network changes.  Adding more detail to the approximation of equations increases the accuracy of the simulation, but also increases its running time.