# How to amplify the resistivity range of a rheostat

I have a black box DC to AC inverter with a 5 kΩ linear taper pot wired to it that acts as an LED light dimmer. I have no idea how the circuitry of the black box is composed - it is encased in a potting compound. The pot is wired up to the wiper and one end (like a rheostat) and the lights get brighter as the resistance increases.

I want to control the dimmer with an original dimmer switch. Unfortunately the original dimmer rheostat only has a 10Ω linear taper range – just a wiper across a wire coil and the resistance decreases as I turn the knob up – opposite of the 5 kΩ Pot.

I'm trying to find a simple circuit that will magnify and invert the 0-10 Ω range to a 0-5000Ω range to control the inverter. I'm not sure if an OpAmp can do the trick. I do know that the voltage running across the 5 kΩ pot is about 8 V perhaps I can use the OpAmp to mimic the expected voltage drop?

An Arduino and a programmable digital potentiometer seems overkill. Also, I haven't liked any of the options I could find to swap the wire coil with something of the right resistivity range.

• "voltage running across the 5 kΩ pot is about 8 V" - does voltage vary linearly from 0 to 8V as you turn the pot? What are the voltages on each pot terminal relative to the power supply? What is the power supply voltage? Commented Jan 30, 2017 at 18:29
• It varies linearly from .6 V to 9.5 V as I turn the pot. I attached a DC volt meter to the two used prongs of the potentiometer. Commented Jan 30, 2017 at 18:41
• @DougCoburn are you sure it's not actually a changing signal, such as the feedback branch from the voltage converter? Commented Jan 30, 2017 at 18:50
• @MarcusMüller I'm not sure but these boxes aren't that expensive and I am willing to fry a few with experimentation. Commented Jan 30, 2017 at 18:57

Since we can't know what the black box actually does with the potentiometer – does it really just control the amount of current flowing through the leads, which is used internally, or is the voltage used, or is, in fact, the potentiometer part of a feedback loop that limits the turn-on time of your inverter's switch mode power supply, there's only one thing that certainly works:

Forming a larger resistance. I'll be frank and say that with a big margin, the easiest solution would be to simply buy a 5 kΩ potentiometer and use it instead what your dimmer switch has.

There's tricks how you could implement this e.g. using transconductance amplifiers, but if it's really the case that the original potentiometer is part of a feedback loop, you might get into trouble for changing the phase of signals.

• We have considered mechanically rotating the 5 kΩ pot with when rotating the original dial. This is a replica project so original look and feel is quite important. If that is truly the simplest solution then we will do it. Also, this is a conversion that we may very well repeat 100 times in the future so I can spend some time to figure it out once and buy the parts in bulk. Commented Jan 30, 2017 at 19:04