Active Negative Resistance Model That Is Not Piecewise Linear

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This Demonstration models an operational-amplifier (opamp) based negative resistance (NR) implementation. Traditionally, negative resistance has been modeled with piecewise linear (PWL) equations. This model, however, is continuous and differentiable at all points.


In general, the setup has an opamp with three external feedback elements.

Gain element: Any opamp with two inputs and one output; opamp open-loop gain VOH/VOL should be very high

: External feedback resistance between the output pin and the positive input pin, in ohms

: External feedback resistance between the output pin and the negative input pin, in ohms

: External feedback resistance between the negative pin and an appropriately biased bias input (VBNR), in ohms

VIN: Input forcing voltage,

IIN: Circuit response current, μA

VBNR: DC bias voltage,

VOL: Output low voltage of opamp, when configured as unity gain element,

VOH: Output high voltage of opamp, when configured as unity gain element,

: Theoretically derived dimensionless coefficient, with range

cf: Theoretically derived dimensionless coefficient, tending to 1

The differentiability allows the user to investigate important metrics such as the useful NR range, the maximum and minimum currents, the roots of the entire system, and so on, for various values of the resistive feedback elements. The output is a plot of current versus the input forcing voltage , or otherwise the curve.

Though not shown in this Demonstration, the model was verified to have no more than about 12% error for root locations, slopes of the various segments, and so on, using data collected from an LM741 configured as an NR. This accuracy applies when , , and are large enough such that the IIN for the NR configuration is about the opamp's maximum short-circuit current capabilities. In other words, the current flowing through the NR should be an insignificant portion of the opamp's source/sink capabilities.

You can modify the program to change or cf to get a better match for another set of , , and .


Contributed by: Isaac Abraham (March 2011)
Open content licensed under CC BY-NC-SA




[1] V. Drogoreanu and D. Vizireanu, "A Class of MOS Non-Linear Negative Resistance Oscillators," International Symposium on Circuits and Systems (ISCAS) '96, 3, May 1996, pp. 225–228.

[2] D. N. Vizireanu, "A New Class of MOS Transistor Nonlinear Negative Resistance Oscillators," Electrotechnical Conference, 1996, 1, May 1996, pp. 407–410.

[3] D. N. Vizireanu, et al., "A New Class of S-Type Current Controlled Nonlinear Negative Resistances," International Semiconductor Conference, 2, September 2006, pp. 395–398.

[4] L. O. Chua, C. A. Desoer, and E. S. Kuh, "Linear and Nonlinear Circuits," New York: McGraw–Hill, 1987, pp. 192–195.

[5] L. Shafai, "Analysis of a 2-Terminal Negative Resistance," Electronics Letters, September 1971, pp. 572–573.

[6] Maxim Application Note 815, "Negative-Resistance Load Canceller Allows Voltage Reference to Drive Heavy Loads," September 2001.

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