# Simulating Nine Common Nonlinearities

June 18, 2001
Analog simulation of discontinuous nonlinearities associated with electronic and electromechanical components is becoming a necessity. It is difficult to take advantage of an analog computer in control systems design unless the nonlinearities in the...

Analog simulation of discontinuous nonlinearities associated with electronic and electromechanical components is becoming a necessity. It is difficult to take advantage of an analog computer in control systems design unless the nonlinearities in the system can be accurately simulated. But, while many schemes for introducing nonlinearities into analog computer set-ups exist, their lack of precision is often a limiting factor in the usefulness of the simulation. Techniques developed in recent years using the "idealized diode" have proved especially effective in mechanizing reliable and accurate nonlinearities.

The circuits usually presented in analog computer texts are based on the ability of the standard diode to function as a perfect switch, i.e., a two-terminal network element with zero forward and infinite backward impedances. This assumption leads to an inexact representation of the required nonlinearity and may result in a misleading over-all system simulation. To minimize the usual diode inaccuracies, the silicon diode's transfer function may be greatly improved by using a high-gain amplifier.

In the flip-flop circuit shown, the initial output shunt limiter is employed only to prevent amplifier A-4 from overloading while the diode bridge provides an accurate output amplitude limit.

Assume A-4 to be excited by a small-amplitude, negative-polarity input. When multiplied by the open-loop amplifier gain (typically −50 × 106), a large positive voltage appears at the output terminal. Amplifier saturation is prevented by the arm of P5 sensing (at some predetermined level) a positive potential. At this point D2 conducts and maintains E1 at an approximately constant value.

The bridge limiter, functioning as a pair of idealized diodes, clips the input and produces a constant output Y. Potentiometers P1, P2, P4, and P5 are adjusted by trial and error. The comparator, whose input-output relationship is presented with dotted lines indicating Ein-Eout transfer function, is obtained with a flip-flop biased to operate about point A. (Electronic Design, June 21, 1961, p. 38)

By the early '60s, analog computers were reliable tools in simulation studies, and transistor circuits were well-understood. This is an extract from an article by Addison W. Langill Jr. of General Motors' AC Spark Plug Group, El Segundo, Calif. In addition to the flip-flop described above, the article covered simulations of nonlinearities involved in limiters, dead space, absolute value, a polarized double-throw relay, a solenoid valve, a quantizer, backlash, and a free-running multivibrator.

See associated figure