Simulation and modeling-simulating differential equations with SPICE2

A method for simulating differential equations with SPICE2 is discussed and demonstrated. The range of applications is perhaps limited only by the ability of the user to implement the functional relationships required for each particular problem. Some examples of the implementation of a few specific functional relationships with the aid of the SPICE2 polynomial-controlled sources and other built-in elements are discussed. A transconductance source and a capacitor are utilized for integration, and voltage-controlled sources are used to implement powers, products, division, and sums of voltage variables. Sources to implement square-root and other fractional powers, absolute values, sign functions, etc., can be defined in a similar fashion. Other functions can be implemented by combining sources with other circuit elements and/or by implementing series representations in some cases. In addition, implicit function generation techniques can sometimes be used; with this technique, a differential equation which has a known solution equal to the function desired is simulated.<>