Types of circuits that have a nonlinear response to R

[BiGyElLoWhAt]

TL;DR Summary

I'm looking to be able to approximate a few orders of a taylor series expansion using a potentiometer, particularly a sin wave.

Hi, I am ultimately looking to be able to have an analog circuit with an amplifier that uses a pot for the resistor over the op amp (maybe there's a better way, let me know if there is). I want to be able to control the shape of the gain roll-on/roll-off, and have it be functions of R, particularly sin(R_pot).

Is there a "simple" way to do this? I.e. can I construct a circuit that gets me $V_{out}/V_{in} = f(\vec{x}) sin(R)$ or something to that extent? x vector here is just some set of variables, probably w, L, c, etc. My other thought is if I have something with 3 degrees of freedom, so maybe 3 capacitors or something, I should be able to tune the values to the coefficients of the taylor series for sin, assuming I can construct a circuit that has R, R^3, and preferably R^5. I checked a graph and the first 2 terms are decent, but the 5th order term really makes it nice. I am looking for when the pot is halfway on, the gain is sqrt(2)/2, when it's 2/3 on root 3/2, 1/3 on it's 1/2, up to full on gain is 1... or at least really close to those values.

Ideally I would like either near-constant frequency response or no frequency response, although I think there are ways to adjust the phase afterwards.

 

[berkeman]

There are a couple of ways you can do this using a microcontroller (uC) and an ADC and DAC. Or are you wanting to try to do this only with analog components? What accuracy and temperature stability do you need?

 

[DaveE]

There are several solutions. Each depends on the methods you like and the accuracy you need. So, you may need to be more specific. In the digital world, it would be an ADC, some calculations in SW, and DAC. In the analog world, you could use a network of forward biased diodes (piece-wise linear response), but I would probably just use a multiplier IC (Gilbert Cell, if you want the steam punk DIY version).

 

[tech99]

Can you just apply a sin wave to a variable clipper?

 

[BiGyElLoWhAt]

I would prefer to do it analog. It's just coding with psoc or arduino, which is easy enough. It's partially an exercise/trying to understand circuits better, partially I want to build something.

 

[BiGyElLoWhAt]

Actually, something like this clipper and multiplier might work. Multiply Vout by my source signal. I might need a latch as well. I never consider diodes when I'm trying to design stuff, I'm not sure why.

 

[berkeman]

I never consider diodes when I'm trying to design stuff, I'm not sure why.

Probably your good instincts to worry about tempco and matching issues destroying your signal accuracy...

 

[berkeman]

Probably your good instincts to worry about tempco and matching issues destroying your signal accuracy...

BTW, just to expand on that since you are using this project as a learning experience...

When analog design engineers want to use something like diodes or transistors in precision analog circuits, they lay them out on the same die and with special layout techniques to ensure good matching and thermal tracking. When you buy a matched transistor pair (all in the same package), the matched transistors are on the same die, and usually would consist of multiple interconnected transistors to form each overall transistor of the matched pair. The multiple transistors from each of the matched pair are interleaved in ways to try to ensure that they will thermally track each other, and other non-linear effects are matched as well by the layout.

When you try to use discrete diodes and transistors in a design, it is not possible to do this sort of interleaved matching layout on the same die, so your design performance will suffer. For hobby-level circuits, that may be okay. But it's important to understand the limitations of non-matched components so you can set your expectations for the performance/accuracy of your circuit.

 

[BiGyElLoWhAt]

OK, thanks, I will keep that in mind. This might turn into something where I will have to be very concerned with accuracy. Only time will tell. I appreciate the help everyone. One more question, is there a good online simulator that's free (actually) that I can use? All of the ones I've used so far have tried to make me buy or sign up after just 2-3 simulations.

 

[berkeman]

This might turn into something where I will have to be very concerned with accuracy.

Then IMO you will either have to design and lay it out on a single die, or you should go the route suggested by a couple of us above of using a uC and ADC/DAC.

is there a good online simulator that's free (actually) that I can use?

What kind of simulator? If you want a circuit simulator LTSPICE is free to download.

 

[BiGyElLoWhAt]

I did mean circuit simulator. Thank you.

 

[berkeman]

I did mean circuit simulator. Thank you.

Keep in mind that when you use a SPICE simulator and place multiple diodes or transistors, they all will have default/matched parameters, and their temperature will not change with power dissipation. To get an idea of how your real-world circuit will perform, you will need to use the Monte Carlo simulation option in any SPICE package. That will vary all of your component values within their tolerances in different simulation runs to give you an idea of the overall circuit performance. Monte Carlo simulations are an important part of any production quality analog circuit design.

 

[BiGyElLoWhAt]

OK, I'm messing with the program now. I'll keep that in mind for when I get further into the circuit.

 

[Baluncore]

The first approximation to a sinusoid is a parabola.
If I remember rightly, from 1974, you can get a square law response from a linear pot.
Consider a linear potentiometer, with the cw and acw ends connected. The resistance between the connection and the wiper follows a parabola as you rotate the pot.
If you only want one side of the parabola, connect cw and acw with a fixed value resistor, having the same resistance as the pot. You will then have a resistance between the wiper and cw or acw following a square law response. Select cw or acw, according to the direction you want the change.