Op-amp "resistance multiplier" - what's it called?

[py-bb]

Morning,

I have doodled a circuit that uses an op-amp that pretends to be a resistor larger than a given resistor (I plan to use a nice large potentiometer of relatively low resistance as a pretend high one, it's only needed to control something else so not-being-an-actual-potentiometer shouldn't be a problem)

As always because I have theoretical knowledge I like to look for what practitioners have done first. What's such a circuit called?

I've tried resistance magnifier, amplifier, multiplier all to no luck - capacitance and inductance ones are easy to find though.

Anyone got a link or at least any tips?

PS: the potentiometer in this case is basically from nothing to 25 ohms (28.2 or something) - I'd like to get this into the range something-to-100Kohm. I plan to use a small resistor in series to stop the minimum resistance being nothing.

Ideally I'd like to say take the range 100ohm to 125ohm and expand that to 10k to 100k but I think that might be too much to ask for. As I said tips welcome.

[bidrohini]

The circuit you have described is called a "resistance multiplier" or "resistance ratio transformer." It uses an operational amplifier (op-amp) to amplify the difference between two input resistances, and the resulting output resistance is a multiple of the input resistance ratio.

One example of a resistance multiplier circuit is the "Wheatstone Bridge Amplifier," which uses an op-amp to amplify the difference between the two legs of a Wheatstone bridge circuit. Another example is the "Voltage-to-Resistance Converter," which uses an op-amp to convert a voltage input to a resistance output.

You can find more information and circuit diagrams for these and other resistance multiplier circuits by searching for "resistance multiplier circuit" or "resistance ratio transformer circuit."

It's worth noting that your desired range expansion is quite large (from 25 ohms to 100 kohms), and it's unlikely that a single op-amp circuit will be able to achieve this. A more realistic goal would be to achieve a smaller range expansion, such as from 25 ohms to 250 ohms or 500 ohms. Also, you may need to use a series of resistance multipliers in cascade to achieve your desired range expansion.

[MrAl]

Morning,

I have doodled a circuit that uses an op-amp that pretends to be a resistor larger than a given resistor (I plan to use a nice large potentiometer of relatively low resistance as a pretend high one, it's only needed to control something else so not-being-an-actual-potentiometer shouldn't be a problem)

As always because I have theoretical knowledge I like to look for what practitioners have done first. What's such a circuit called?

I've tried resistance magnifier, amplifier, multiplier all to no luck - capacitance and inductance ones are easy to find though.

Anyone got a link or at least any tips?

PS: the potentiometer in this case is basically from nothing to 25 ohms (28.2 or something) - I'd like to get this into the range something-to-100Kohm. I plan to use a small resistor in series to stop the minimum resistance being nothing.

Ideally I'd like to say take the range 100ohm to 125ohm and expand that to 10k to 100k but I think that might be too much to ask for. As I said tips welcome.

Also see Capacitance multiplier circuit.
Even more interesting, see "Gyrator Circuit". Turn capacitors into inductors, inductors into capacitors for example.

[mawyatt]

Also see Capacitance multiplier circuit.
Even more interesting, see "Gyrator Circuit". Turn capacitors into inductors, inductors into capacitors for example.

Another interesting topology is called Non-Foster Networks where one can create negative effective inductors and capacitors. This is not the usual resonance between an L and C where the reactance cancels at only one frequency, but a true negative of the L and C reactance. For example, the inductive reactance is Zl = j(w*L) and capacitive reactance is Zc = 1/j(w*C), the Non-Foster negative L is Zl = -j(w*L) and  negative C is Zc = - 1/j(w*C) respectively.

Also see related NIC topologies.


https://www.ieee.li/pdf/viewgraphs/matching_network_design_non_foster_impedances.pdf

https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&ved=2ahUKEwiv14vQ0ur8AhVIQjABHeRTBWgQFnoECCQQAQ&url=https%3A%2F%2Fescholarship.org%2Fcontent%2Fqt2pq549c3%2Fqt2pq549c3_noSplash_320b7d0d4446236cacfd3661740a9143.pdf&usg=AOvVaw06vQue3S3KxmjcFL_U1MWM

https://www.hindawi.com/journals/ijap/2013/531419/



Best,

[MrAl]

Also see Capacitance multiplier circuit.
Even more interesting, see "Gyrator Circuit". Turn capacitors into inductors, inductors into capacitors for example.

Another interesting topology is called Non-Foster Networks where one can create negative effective inductors and capacitors. This is not the usual resonance between an L and C where the reactance cancels at only one frequency, but a true negative of the L and C reactance. For example, the inductive reactance is Zl = j(w*L) and capacitive reactance is Zc = 1/j(w*C), the Non-Foster negative L is Zl = -j(w*L) and  negative C is Zc = - 1/j(w*C) respectively.

Also see related NIC topologies.


https://www.ieee.li/pdf/viewgraphs/matching_network_design_non_foster_impedances.pdf

https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&ved=2ahUKEwiv14vQ0ur8AhVIQjABHeRTBWgQFnoECCQQAQ&url=https%3A%2F%2Fescholarship.org%2Fcontent%2Fqt2pq549c3%2Fqt2pq549c3_noSplash_320b7d0d4446236cacfd3661740a9143.pdf&usg=AOvVaw06vQue3S3KxmjcFL_U1MWM

https://www.hindawi.com/journals/ijap/2013/531419/



Best,

Hi,

Yes and everyone out there trying to declare a new elementary component ha ha, memristors 

I think you meant 1/(j*w*C) and -1/(j*w*C).

It is amazing the things we dont think about that much that are out there and very useful sometimes.

[py-bb]

The circuit you have described is called a "resistance multiplier" or "resistance ratio transformer." It uses an operational amplifier (op-amp) to amplify the difference between two input resistances, and the resulting output resistance is a multiple of the input resistance ratio.

One example of a resistance multiplier circuit is the "Wheatstone Bridge Amplifier," which uses an op-amp to amplify the difference between the two legs of a Wheatstone bridge circuit. Another example is the "Voltage-to-Resistance Converter," which uses an op-amp to convert a voltage input to a resistance output.

You can find more information and circuit diagrams for these and other resistance multiplier circuits by searching for "resistance multiplier circuit" or "resistance ratio transformer circuit."

It's worth noting that your desired range expansion is quite large (from 25 ohms to 100 kohms), and it's unlikely that a single op-amp circuit will be able to achieve this. A more realistic goal would be to achieve a smaller range expansion, such as from 25 ohms to 250 ohms or 500 ohms. Also, you may need to use a series of resistance multipliers in cascade to achieve your desired range expansion.

Thank you for this, I appreciate it greatly.

To the others, all that's available on Wikipedia! This seems to be the odd one out!

[MasterT]

Options: photoresistive optocoupler (vactrol),  JFET based optocoupler H11F1M or JFET+OPA

[py-bb]

The circuit you have described is called a "resistance multiplier" or "resistance ratio transformer." It uses an operational amplifier (op-amp) to amplify the difference between two input resistances, and the resulting output resistance is a multiple of the input resistance ratio.

One example of a resistance multiplier circuit is the "Wheatstone Bridge Amplifier," which uses an op-amp to amplify the difference between the two legs of a Wheatstone bridge circuit. Another example is the "Voltage-to-Resistance Converter," which uses an op-amp to convert a voltage input to a resistance output.

You can find more information and circuit diagrams for these and other resistance multiplier circuits by searching for "resistance multiplier circuit" or "resistance ratio transformer circuit."

It's worth noting that your desired range expansion is quite large (from 25 ohms to 100 kohms), and it's unlikely that a single op-amp circuit will be able to achieve this. A more realistic goal would be to achieve a smaller range expansion, such as from 25 ohms to 250 ohms or 500 ohms. Also, you may need to use a series of resistance multipliers in cascade to achieve your desired range expansion.

Hi again,


I'm having a hard time defining what I actually want to do and I was hoping you could help me with this. I want to say I get the capacitance "amplifiers", I can derive the equations, I'm simply not sure what I'm trying to do.

I have a potentiometer rated for basically nill (0) to 25 ohms (a little over 28) and I'd like to use it to control a circuit which is "programmed" by a larger resistance. I'd like to take that resistor's two terminals and drop "the device" there.


I also couldn't find much on the subjects you mentioned but as I said I'm having a hard time even picturing what I want to make.

Thanks for your time.

[EPAIII]

There is a vast number of 100K potentiometers available, starting at under 1.00 USD. By adding a 10K, fixed resistor in series you get a range from 10K to 110K Ohms.

So why not just use that? What advantage or what problem does an op amp circuit offer or solve? Are you trying to control this device over a long distance with a wired connection? Low impedance on the long wires and then high impedance at the device itself?

Just trying to understand the situation.

An optical isolation device may work better and be easier to design.

https://www.google.com/search?q=optical+isolator+circuit&client=firefox-b-1-d&sxsrf=AJOqlzVdXyBPizBtZ5uw_FMu978kUElbVg%3A1675936639316&ei=f8PkY8D7EqK6qtsPw8We6AM&oq=optical+isolator&gs_lcp=Cgxnd3Mtd2l6LXNlcnAQARgBMgUIABCABDIFCAAQgAQyBQgAEIAEMgUIABCABDIFCAAQgAQyBQgAEIAEMgUIABCABDIFCAAQgAQyBQgAEIAEMgUIABCABDoKCAAQRxDWBBCwAzoECCMQJzoFCAAQkQI6CwgAEIAEELEDEIMBOgsILhCABBDlBBDUAjoOCC4QgAQQxwEQ0QMQ1AI6BAgAEEM6BwgAELEDEEM6EQguEIAEELEDEIMBEMcBENEDOgsILhCABBDHARCvAToICAAQgAQQsQNKBAhBGABKBAhGGABQxR5Yu0lg-W5oA3ABeACAAeQBiAHiDpIBBTcuOC4xmAEAoAEByAEIwAEB&sclient=gws-wiz-serp

[py-bb]

There is a vast number of 100K potentiometers available, starting at under 1.00 USD. By adding a 10K, fixed resistor in series you get a range from 10K to 110K Ohms.

So why not just use that? What advantage or what problem does an op amp circuit offer or solve? Are you trying to control this device over a long distance with a wired connection? Low impedance on the long wires and then high impedance at the device itself?

Just trying to understand the situation.

An optical isolation device may work better and be easier to design.

https://www.google.com/search?q=optical+isolator+circuit&client=firefox-b-1-d&sxsrf=AJOqlzVdXyBPizBtZ5uw_FMu978kUElbVg%3A1675936639316&ei=f8PkY8D7EqK6qtsPw8We6AM&oq=optical+isolator&gs_lcp=Cgxnd3Mtd2l6LXNlcnAQARgBMgUIABCABDIFCAAQgAQyBQgAEIAEMgUIABCABDIFCAAQgAQyBQgAEIAEMgUIABCABDIFCAAQgAQyBQgAEIAEMgUIABCABDoKCAAQRxDWBBCwAzoECCMQJzoFCAAQkQI6CwgAEIAEELEDEIMBOgsILhCABBDlBBDUAjoOCC4QgAQQxwEQ0QMQ1AI6BAgAEEM6BwgAELEDEEM6EQguEIAEELEDEIMBEMcBENEDOgsILhCABBDHARCvAToICAAQgAQQsQNKBAhBGABKBAhGGABQxR5Yu0lg-W5oA3ABeACAAeQBiAHiDpIBBTcuOC4xmAEAoAEByAEIwAEB&sclient=gws-wiz-serp

This is a huge none-answer. I have my reasons but the latest reason is because the concept seems to elude me.

[ejeffrey]

Are you trying to make a two terminal device or one terminal?

Most impedance converters including capacitance multiplier and gyrator circuits are effectively ground referenced.  You get one terminal that has the desired admittance, and the other end is effectively at ground or a fixed reference.  They are generally used to emulate impractically large values of capacitors or inductors.  Not usually resistors, because unlike reactance elements L and C, resistor size doesn't really depend on value.

A true floating or differential impedance converter is possible but much more complicated and rarely worth it.  From what I remember, it basically ends up being two separate impedance converters with a cross feedback network to raise the common mode impedance.  But either it required close matching between the two sides, or was operating at the edge of stability, or both. 

[EPAIII]

I have tried looking up the various names that have been suggested here but none of them seem to provide a resistance to resistance translation. Most seem to provide a resistance to Voltage process.

Many years ago I designed an audio mixer with an RCA chip OTA. IIRC, it did not provide a variable resistance at it's output but rather it allowed a control, DC Voltage to control the audio gain of a signal passing through the chip. I don't think that is what you want. But perhaps there were other uses for that chip. Sorry, I do not recall the part number. And I do not think RCA makes them any longer.

Another circuit that I played with was a Voltage controlled pot. It used two CdS cells and an op-amp with totem pole, transistor driver circuit to apply opposite control Voltages/currents to miniature lamps that were directed at the CdS cells. As one Voltage went up the other went down. The same for the lamps. And the same for the resistance of the two CdS cells. I was able to simulate a 50 or 100 KOhm fader pot with proper selection of the values. The op-amp was driven by a pot, but not one of such a low value as you describe as it would have consumed a lot of current for no reason. I believe it was around 10K. The purpose was to allow inexpensive but noise prone pots to control the audio level with that noise being filtered with a capacitor on the center arm of the control pot while the audio went through the CdS cells without any filtering. I just used ordinary, op amps, nothing special as only DC to very low frequency changes went through them. This idea could easily give you a floating, variable resistance with it's value controlled by a Voltage coming from a pot. In today's world I would use LEDs instead of filament lamps.

Back then assemblies with the lamp and CdS cell in one part were available. I doubt that they are still available today, but you could search. The more modern part would probably be an LED and photo-transistor combination which is called an opto-isolator. But that would not be your floating resistor so a different type of circuit would be needed.

https://www.digikey.com/en/products/filter/photo-detectors-cds-cells/540?s=N4IgTCBcDaIA4AsD2AXJACATgUwM4Etc1MQBdAXyA

[py-bb]

Are you trying to make a two terminal device or one terminal?

Most impedance converters including capacitance multiplier and gyrator circuits are effectively ground referenced.  You get one terminal that has the desired admittance, and the other end is effectively at ground or a fixed reference.  They are generally used to emulate impractically large values of capacitors or inductors.  Not usually resistors, because unlike reactance elements L and C, resistor size doesn't really depend on value.

A true floating or differential impedance converter is possible but much more complicated and rarely worth it.  From what I remember, it basically ends up being two separate impedance converters with a cross feedback network to raise the common mode impedance.  But either it required close matching between the two sides, or was operating at the edge of stability, or both.

Thanks for following up, I think this is where I muddled myself up a bit and I'm not actually sure it can be done with just an op-amp. I have a variable resistor (half a pot) and I'd like to yield a 2 terminal device (ignoring any power connections and whatnot) which I can drop into a circuit which acts a resistor of resistance (some constant) x the variable resistor.

Op-amp and a transistor can do this, but given we can have "capacitance multipliers" and "inductance multipliers" this seemed a bit of an odd one out.