How to average two 0-10 V signals?

Question

For an HVAC application I'm searching for a way to average two 0-10 V signals with the ability to give a "weight" to one or another.

Example:

• I have input A at 10 V and input B at 5 V.

• If I make a dumb average I get 7.5 V.

• I want to be able to give more importance to one signal.

• Let's say input A is set at 50% and B 100%. I want an output at 6.667V ([10x0,5+5x1]/[1+0,5]).

I tried simulations online with an op-amp but can't find a way to do it. I made an average circuit using a voltage follower as described here and was hoping that replacing the resistor with a potentiometer would do the job, but unfortunately it didn't.

The highest voltage seems to pass through the potentiometer of the other input if its resistance is lower.

I tried many other things next (diodes, more op-amps, etc.) but I'm a beginner so I didn't manage to find the way to go.

Answer 1

Here is one way, borrowing slightly from Theodore's answer.

The pot is set to 1/3 (0.5 being halfway) since you want 5/15 of the voltage to come from the 10V source.

^{simulate this circuit – Schematic created using CircuitLab}

If \$\alpha\$ is the pot rotation from 0 to 1, the voltage at the output is \$\alpha V_1 + (1- \alpha)V_2\$.

Pot in the center is an unweighted average of the two voltages. Of course you could add resistors to the ends of the pot if you wanted to limit the range. Or replace the pot with two resistors, one of \$\alpha\cdot\$10kΩ and one of \$(1-\alpha)\cdot\$10kΩ

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Alternatively, you could do something like this:

^{simulate this circuit}

Which is exactly what I think you asked for. It requires dual element pots for both adjustments and a negative and positive supply voltage. Tracking of the pots may affect accuracy significantly (especially if the overall gain is high => (a + b) << 1. R1 is coupled to R8 and R4 to R9. The adjustments are linear from 0..1 (0 to 100%) for a and b.

It would also be possible to use (very expensive) multipliers to generate this analog function with single element pots. Or use the dreaded ADC->MCU->DAC approach, which would yield the excellent learning opportunity to spend weeks linking in 100k of potentially buggy code to allow capacitive touch slider controls on a color TFT display.

Answer 2

You are on the right track.

You are basically building a single-purpose analog computer that calculates Ax+By.

The averager and voltage follower you linked should be suitable, but you mentioned one issue:

The highest voltage seems to pass through the potentiometer of the other input if its resistance is lower.

This is because the 0-10V inputs have some output impedance that's not sufficiently low with respect to the input resistors you selected.

You can place voltage followers at the inputs too so that the potentiometers won't load down the sources:

^{simulate this circuit – Schematic created using CircuitLab}

You also probably need to be mindful of your voltage references with respect to the op-amp power rails. Does your supply voltage extend above 10V and below 0V? Most om-amps can't receive input voltages or generate output voltages all the way to their supply voltages.

There are other ways to accomplish this, and some web-searching for analog computers may help.