To design any electrical circuit, either analog or digital, electrical engineers need to be able to predict the voltages and currents at all places within the circuit. Linear circuits, that is, circuits with the same input and output frequency, can be analyzed by hand using complex number theory. Other circuits can only be analyzed with specialized software programs or estimation techniques such as the piecewiselinear model.
Circuit simulation software, such as HSPICE, and languages such as VHDLAMS and verilogAMS allow engineers to design circuits without the time, cost and risk of error involved in building circuit prototypes.
Other more complex laws may be needed if the network contains nonlinear or reactive components. Nonlinear selfregenerative heterodyning systems can be approximated. Applying these laws results in a set of simultaneous equations that can be solved either algebraically or numerically.
Network simulation software
More complex circuits can be analyzed numerically with software such as SPICE or 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 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 points of each element in the circuit are known. For a small signal analysis, every nonlinear element can be linearized around its operation point to obtain the smallsignal 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.
Piecewiselinear approximation
Software such as the PLECS interface to Simulink uses piecewiselinear approximation of the equations governing the elements of a circuit. The circuit is treated as a completely linear network of ideal diodes. 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.
See also

Impedance transforms


Generator theorems

Network theorems



Network analysis methods


Twoport parameters




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