Overview

With the advance of digital computers, simulation has made giant strides in the past 20 or 30 years in all scientific and technical fields. In the late 1970s, for electrical circuit analysis using computer, one dialed the Control Data Corporation (CDC) with a modem-equipped portable terminal/keyboard, edited the circuit file one component (one line) at a time, debugged the file for syntax errors, ran the file for half an hour or so and ran up a phone bill by the minute, read the dot-matrix printout, and repeated the simulation until the desired, appropriately formatted hard copy was obtained. In the end, the whole effort might take hours, if not all night. By 1990, the same study was regularly done on a personal computer and took only a few minutes to produce a colorful printout. This advancement prompted many new generations of electrical engineers to flock to PC-based circuit simulators and to believe that all circuits can be studied using simulation software like Spice or its derivatives. Following the same line of logic, many designers working on switch-mode power converters also quickly converged or on the idea: electronic breadboarding and testing.

However, as rapidly the simulation wildfire spread, numerous difficulties arose. Among the most troublesome was the convergence issue the simulator faced when solving tens of differential equations that described a complex circuit based on Kirchoff's current and voltage laws. Basically, those differential equations in discrete form were solved at finite time points starting from time zero and zero initial...