| An argument is made that computer-aided methods of circuit analysis, both numerical and symbolic, can be introduced at the very beginning of formal instruction. The essence of this argument rests on the observation that all circuit analysis problems can be readily recognized as one of a small number of formal mathematical exercises. The computer hardware plus software thus becomes the solution engine for these exercises. The learning process then shifts naturally to acquiring competence in using computer tools, learning how to configure and delimit the exercise and interpret the output. Two leading software packages, PSpice by OrCad and Analog Insydes distributed by Wolfram Research and based on Mathematica, are introduced and discussed in detail. The interactive nature of their operation is demonstrated by simple pedagogic examples, taken first from the strictly linear class then from elementary electronics.; Symbolic methods or computer algebra has been around for many years; only recently, however, have powerful simplification algorithms been developed and implemented. This improvement has increased the value of symbolic methods enormously both for pedagogic and for serious design purposes. One example: By use of symbolic methods, it is now possible to identify specific small-signal parameters of specific transistors as important contributors to dominant system poles and zeros. This capability can be exploited as one way to approach the general problem of transistor sizing in modern analog CMOS design. Symbolic results imply tradeoffs, but tradeoffs can be quantified only through device models. An overview of MOSFET models is done with emphasis on models for contemporary deep sub-micrometer technologies. An example is done whereby a classical two-stage CMOS op amp originally done in 1.0 μm technology is migrated to a 0.18 μm technology. This is done to illustrate that the symbolic analysis transcends both the technology and the large-signal models employed.; Future progress in symbolic methods is expected, but the specifics are uncertain: an extension to nonlinear systems? Possible. A tighter integration of symbolic methods into larger multi-tool design environments? Very likely. To date, symbolic methods have relied almost exclusively on formal mathematical routines. Can artificial intelligence be invoked to advantage? Intriguing but unclear. Bringing symbolic analysis into introductory circuits and electronics courses offers enormous potential for accelerating the learning process and thereby increasing greatly the sophistication gained per hour invested. To realize this potential will require overcoming some resource problems yes, but the larger problem will be breaking the grip of habit and tradition. |
