How to convert a linear potentiometer into an inverse log variable resistor?

Question

Frequently potentiometers are used as variable resistors.

It is easy to convert a linear pot into a (pseudo)logarithmic variable resistor:

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How a linear potentiometer can be converted into an inverse (pseudo)log variable resistor (rheostat) to get this kind of dependence of the total resistance from the wiper position:

enter image description here

Can this be simulated by any circuitry?

• Transistor: The pot in your schematic will short out the 12 V supply when the wiper is at the top tag. It won't last long!
• Thomas Anderson: This is just a test circuit to calculate the total resistance for the plot. It is not a working circuit. In the working circuit there will be a small and (relatively) constant current.
• Transistor: I suggest you remodel with a current source rather than a voltage source. Your chart is based on infinite current when wiper is at top tag. Can you edit to give some context about where you need this pot? Can one end be grounded or is it in a feedback loop? (That will make a difference.) Post a schematic if you can.
• Thomas Anderson: @Transistor Thank you for the help. For the first circuit it does not matter how to model it, with a voltage source or a current source, the total resistance will be the same. Just look at the plot of the total resistance and don't think about the circuit. For my working circuit I do not want a workaround solution, because I know it, but it is not acceptable for me. I am looking for a general solution, if it exists. Preferably, the simplest one. One end can be grounded.
• Raonoke: Add a resistor from the wiper to ground (or 12V). Try different resistor values until you come close to log behaviour.

Answer 1

To get the inverse log response, you can try to invert the output of the logarithmic amplifier. This can be done using one op-amp to make a (pseudo)logarithmic signal and then another op-amp configured as an inverter of the first cascade. The output voltage will follows the inverse log relationship with the potentiometer's position. The inverse log voltage can be converted back to a resistance using a voltage-to-resistance converter circuit. This typically involves using a transistor whose resistance varies with the input voltage. But designing such circuits can be complex and may require a good understanding of analog electronics.

• Thomas Anderson: Thank you for the reply. You scared me. I still hope there might be a simpler solution. I mean, what is a resistor? It's a device that converts current into voltage. So basically we want to control that conversion with a linear potentiometer. I feel that there might be a way to do it simpler. Of course, I may be wrong.

Answer 2

Use somethig logarithmic like a PN junction:

schematic

^{simulate this circuit – Schematic created using CircuitLab}

real log amplifiers do a better job than the above, but that should be enough for a demonstration.

• Thomas Anderson: I don't see how this circuit can be used as a replacement for a variable resistor. Say, if we connect a variable resistor between a current source and a ground, and vary the resistance, the voltage drop across the resistor will vary accordingly. How can we connect this circuit to obtain a voltage drop from 0V (wiper at 0%) to, for example, 10V (wiper at 100%)? Also, this circuit is going to be very temperature-unstable. How can we add a temperature compensation to it?
• Jasen Слава Україні: yes it needs temperature compensation, to get a variable voltage drop you'll need to connect a current source instead of a voltage source. Your example used a voltage source.