Need help getting my LM324 to work with a three way voltage divider

Question

I have an input voltage signal from a conductivity sensor (output between 0 to 2.3V) which I am need to measure using the ESP32 ADC input. Unfortunately the ADC on the ESP32 is pretty crappy and can only measure signals greater than 0.15V. Therefore I am trying to scale the input signal and add a small offset to it so that I can measure low values as well.

To do this I have made a three resistor voltage divider which I found online. If I remove the op-amp, this works perfectly. However I need the op-amp as without it the load affects the voltage output from my sensor.

The problem I am facing with this design is that at low input voltages, the LM324 does not seem to work. I have played around with various resistor values and my findings are below:

^{simulate this circuit – Schematic created using CircuitLab}

In the case of lower resistors, the circuit was unusable till the input voltage was 0.4V. In the second case with higher resistors, the problem only occurred below 30mV, but still occurs.

From my research, I understood that the LM324 has a limitation of going near the upper rail, but not the lower rail (ground). In my case as well, if I remove R3, then the opamp successfully works perfectly and as expected even at a 10 mV input signal.

Can somebody please help me to understand what is happening. If I want to solve this, can I make some changes to the circuit, or do I need a different op-amp? In that case, what specification in the op-amp datasheet do I need to be looking for? I dont understand very much about opamps yet but am trying to learn!

Thank you!

Answer 1

If you do something like this, you will be able to get much closer:

^{simulate this circuit – Schematic created using CircuitLab}

The above circuit will give you approximately Vin*0.315+0.165V, with some slight error below 50mV in.

Probably good enough for the lousy ADC in that chip.

Below about 600mV out the LM324 has only a (nominal) fixed 50uA current sink to pull the output low, and even that will saturate at some tens of mV.

I would generally not trust even R-R output op-amps very close to the supply rails, the gain and other characteristics change significantly and you could get oscillation, for one example which I have observed. A CMOS-output part might be a better bet than a bipolar R-R output part. You could consider adding two op-amps if the divider is deemed too high impedance for the ADC input, one just as a buffer.

If, at some point, you need real precision near 0V, there's no substitute for bipolar supplies. Or a negative voltage reference. A 7660 + LM4040 would make short work of this for a bit more cost.

Answer 2

Andy already addressed the problem with the expected values, so I'll point out another limitation regarding the op. amp.

 "if I remove R3, then the opamp successfully works perfectly 
 and as expected even at a 10 mV input signal."

When you do that the op. amp. output will only source current to GND through R1 and R2. Check the current direction in this simulation when R3 is connected and V1 varies from 0V to 2.3V:

A possible explanation for the difference you see when using resistors with larger values is the current sinking capability of the op. amp., which is quite low for the lower voltages:

Source: TI datasheet for the LM324

You did well by checking the input and output voltage limitations, but current limitation may also be a problem.

The op. amp. you mentioned in the comment also has similar limitations (and this is what you should always expect):

You can find op. amps. which can really accept 0V at the inputs (or even a few hundreds mV below), but don't expect the same reach at the output. You may also consider other issues, like input voltage offset. Is it worth measuring 20mV with an op. amp. which may have \$\pm\$4mV offset?. I'd like to suggest that you (re)evaluate your precision requirements to know if you can simply ignore these errors at the lowest part of the measurement range or maybe reconsider the circuit topology.

Answer 3

In the left hand side of your table you have this scenario: -

• R1 = 1k
• R2 = 3k
• R3 = 10k

And, when the input voltage is 0 volts, you have an expected output voltage of 245 mV. This has to be wrong because, when Vin = 0 volts, R1 and R2 are in parallel and have a net resistance of 750 Ω (1000 || 3000 = 750).

This forms a potential divider with R3 (10k) and, with 3.3 volts at the top of R3 you should get this: -

$$3.3\text{ volts}\cdot\dfrac{750}{10000 + 750} = 230\text{ mV}$$

So, there is an error at the beginning of your calculations because you are expecting 245 mV.

I suggest you go through some more calculations then, check the resistor values you have fitted.