# How can I realize this nonlinear resistor?

I want to know if it's possible to realize a circuit described by the equation

$$I = \sin(w V)$$

where $$\I\$$ is the current, $$\V\$$ the potential and $$\w\$$ a variable which characterizes the single circuit.

• It is possible, but it's a little involved. What you're looking for is a sine converter, generally made out of a multiplying DAC or analog multiplier, then a simple amplifier to convert that output voltage to a current. I suggest you read up on them, as there are limits to how well they can represent the sine transform. – Reroute Aug 26 at 8:11
• V is what potential? Do some sketch, use circuit editor to draw a basic schematics. w has units rad/V ? Since sin(x) gives no units, you missed something else. – Marko Buršič Aug 26 at 8:46
• I'm not sure if I'm right but isn't that just a voltage controlled oscillator with zero f0? – Prateek Dhanuka Aug 26 at 13:03
• What should your circuit do with sin(a) and sin(a + 360 °)? Is it possible to restrict a to the interval -90 to +90 °? – Uwe Aug 26 at 15:30

## 3 Answers

A bit like a SQUID, which has a (ideally) sinusoidal response.

If your function is monotonic you could use some simple nonlinear circuit arrangement.

If your allowable values of wV cause the current function to be multivalued you could use a voltage-driven LUT (like an arbitrary function generator) and current source, but of course the resulting current would be dependent on the voltage history and initial conditions.

If what you truly want is a resistor, consider using a motor with a lever arm. The motor position (which can be servo-controlled to be a number of clockwise turns equal to V *W/(2*pi) ) will then put the end of the lever arm at an excursion which can be linkage-connected so that it drives a variable resistor. The negative resistance cases will be a bit of a problem, but a current driven positive or negative is a relatively easy thing to arrange (the resistor can span +1 to -1 volts, and a voltage-controlled current source driven from it).

A related probem, building a sinusoidal voltage-controlled oscillator, requires only proportioning a frequency to the input voltage, not holding any absolute phase relationship.

A common way to implement this is to use a piecewise-linear approximation to a sine curve, built using multiple resistors and diodes. One such implementation is described here, regarding the HP3311A function generator.