Statistical Circuit Design: A Monte Carlo Tolerance Analysis of the Integrated, Single-Substrate, RC, Touch-Tone Oscillator

The effective design of a circuit that will be mass-produced and subjected to a wide range of environmental conditions must go beyond the specification of a nominal circuit. It must include consideration of performance deviations due to parameter variations stemming 1263 1264 T H E BELL SYSTEM TECHNICAL JOURNAL, APRIL 1971 from manufacturing tolerances and environmental changes. Bounding these performance deviations is often the most difficult part of the design process.1 Monte Carlo tolerance analysis has proven to be a useful tool in dealing with these broader design questions. The approach, which is depicted in Fig. 1, simulates on a computer the process of picking a random sample of manufactured circuits, following these circuits through factory adjustment, monitoring their operation under field conditions, and compiling statistics on circuit performance. 2,3 Note that the Monte Carlo approach obviates the need for linearizing assumptions that characterize many other techniques for viewing product performance (worst-case, first-order sensitivities, etc.). It should be remembered that the response of even a linear circuit is a nonlinear function of its parameters. 2 This paper contains the results of a computer tolerance analysis of two integrated, single-substrate, Touch-Tone oscillators. Section II describes the two designs and lists the performance specifications that must be met. The study produces distributions of oscillator frequency, amplitude and other measures for the various modes of circuit operation at several values of temperature.