# Active Negative Resistance Model That Is Not Piecewise Linear

Active Negative Resistance Model That Is Not Piecewise Linear

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

RF

R

2

R

1

VIN: Input forcing voltage,

V

IIN: Circuit response current, μA

VBNR: DC bias voltage,

V

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

V

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

V

k

2<k<2.414

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.

I

V

IV

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.

R

1

R

2

RF

1/10,000

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

k

R

1

R

2

RF