APPLICATION NOTE
8
Solving Simple Differential Equations
PSpice is well known for its ability to solve the equations which arise in circuit analysis. What is less well known is
that PSpice can also be used to solve problems in other domains which can be expressed as differential
equations. This article presents some examples of using PSpice as an "analog computer" to solve sets of
differential equations describing the kinetics of a chemical reaction.
Consider a familiar example: the voltage across a parallel capacitor/resistor combination as a function of time.
The circuit equation for this example is:
rearranging a little,
where:
Because V is a function of the single variable, t, this is an Ordinary Differential Equation (ODE). Its solution is the
equation of exponential decay, which is:
where V0 is the initial voltage on the capacitor.
To see how PSpice can be used to solve the equation above, consider an ideal integrator. Suppose its output is
the voltage we want: V. Now the input to the ideal integrator is evidently dV/dt.
A circuit which represents the equation is shown in the following schematic. The schematic was drawn using
OrCAD® Capture. The parts shown come from the Analog Behavioral Modeling (ABM) symbol library, "abm.olb,"
supplied with the program. The symbols INTEG (integrator) and MULT (multiplier) are used.
