A Coherent VLSI Design Environment
Semi-Annual Technical rept. 1 Oct 1986-31 Mar 1987
MASSACHUSETTS INST OF TECH CAMBRIDGE MICROSYSTEMS RESEARCH CENTER
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It has been an open question in electrical network theory whether it is possible to synthesize a network with a prescribed natural frequency in the complex s-plane out of a restricted class of components. It was possible to say since the 1950s that no natural frequencies can be obtained in certain parts of the s-plane, but not the converse, namely that at other points a circuit can be devised. This question is of modern importance since the components in question may be MOS transistors and RC lines, whose accurate high-frequency models are complicated. It is important to know how fast a rise time can be achieved, or at what frequencies unwanted oscillations might occur. A set of necessary and sufficient bounds are now possible, in the sense that every point in the s-plane can be easily discovered to be either a frequency at which oscillation cannot occur with any possible combination of components and ideal transformers, or else a point at which a circuit consisting of a few such components and ideal transformers can be made to oscillate. The inclusion of ideal transformers is necessary since otherwise generally only a finite or countable number of natural frequencies can be found.
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