APPLICATION NOTE
9
Figure 12: RC circuit
The symbol containing "1.0" is an integrator with gain 1. Its output is obtained by integrating the voltage at its
input. This voltage is constrained to be -1/RC times the output voltage, V, by closing the feedback loop.
This way of setting up differential equations for solution is the way that analog computers were used. In this
example, an integrator block would be used; the constant 1/RC would be supplied by a gain block and using the
inverting input to the integrator would provide the -1.
The initial condition for this problem is that the initial voltage is V0. On an analog computer this voltage would be
derived from a reference and patched to the initial condition input of the integrator. Using the ABM integrator
symbol, INTEG, the initial voltage is specified by setting the value of the "IC=" attribute on the symbol.
Running a Transient Analysis on the ABM representation of the problem shows the expected exponential decay
of voltage with time.
Solving Coupled Differential Equations
Systems of interest usually contain more than one variable. There may be several interacting voltages in a circuit.
In a chemical reaction, the rate of production of a component may depend on the concentrations of several other
components.
For example, if we have three components x1, x2, and x3, the equations controlling their rates of decay and
production might be:
