Electric Circuit Simulation
S.H.M.J. Houben
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The goal of circuit simulation is to predict the behaviour of an electrical
circuit given a description of the circuit. Mathematically, an electrical circuit
can be considered to be a graph, where every branch is labelled with an algebraical
or differential equation relating the voltage  over the branch with the current i through
the branch. See figure 1
for an example. The actual form of these branch equations depend on the type
of the branch, i.e. whether it is a resistor, a capacitor, a voltage source,
or something else altogether.
Figure 1: A simple free-running oscillator
circuit
An electrical circuit can be completely described by giving a
list of all branches, the nodes to which every branch connects,
and the type of the branch. Such a description of the circuit is
called a network list or netlist for short. The netlist
is the form in which the circuit is typically peresented to a
computer program.
From this description of the circuit, a differential-algebraic
equation can be derived. The resulting equation has the form:
The complete simulation pipeline is illustrated in figure 2.
Figure 2: The simulation pipeline
- Some circuits are not driven by a periodic input signal, yet
produce an oscillating output signal nevertheless. Such
free-running oscillators have an additional unknown,
namely their oscillation period T. An example of such a
circuit is shown in figure 1.
- Some circuits have two or more different operating frequencies. In this
case, a multi-tone analysis might be necessary. Results of such an
analysis (for two input frequencies
 and  ) is shown in figure 3.
Figure 3: Results of a two-tone analysis
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