Transient Analysis

The transient simulation is the calculation of a networks response on arbitrary excitations. The results are network quantities (branch currents and node voltages) as a function of time. Substantial for the transient analysis is the consideration of energy storing components, i.e. inductors and capacitors.

The relations between current and voltage of ideal capacitors and inductors are given by

$$V_C(t) = \dfrac{1}{C}\int I_C(t) \cdot dt \;\;\;\; \textrm{ and } \;\;\;\; I_L(t) = \dfrac{1}{L}\int V_L(t) \cdot dt$$ (6.1)

or in terms of differential equations

$$I_C(t) = C\cdot \dfrac{d V_C}{d t} \;\;\;\; \textrm{ and } \;\;\;\; V_L(t) = L\cdot \dfrac{d I_L}{d t}$$ (6.2)

To calculate these quantities in a computer program numerical integration methods are required. With the current-voltage relations of these components at hand it is possible to apply the modified nodal analysis algorithm in order to calculate the networks response. This means the transient analysis attempts to find an approximation to the analytical solution at discrete time points using numeric integration.