Background: Designing voltage summer without op-amp and Operational Amplifier Adder
I know that op-amp can provide virtual ground for the circuit, and can have benefits in eliminating crosstalk. But the latter part confuses me.
Suppose that voltage sources are modeled as independent voltage source plus resistor. In such a case, resistor can be added to existing resistors to provide total resistance value, and voltage laws to calculate voltage works, so crosstalk does not affect the sum value, as long as resistance value of each source is quite different.
Is the whole concern regarding crosstalk related to different sources having different output impedance? Or am I understanding something completely wrong?
To summarize, I do understand that adding voltage makes the output voltage higher than input voltages, and current flows from high voltage to low voltage. But Kirchoff's voltage laws are still there unless we are talking about distributed circuits, and the calculation using same output impedance for different voltage sources results in an accurate-enough sum. So why active summer over passive summer?
Best Answer
The concern about backfeeding/crosstalk only matters if:
If either of those is false, then you don't care about backfeeding/crosstalk.
If you don't care as defined above, and you want an average voltage, then the passive adder is usually the better solution. If you do care, or if you actually want to add and not average, then you need active.
The reason you need active to actually add signals is because the result could easily be higher than all of the inputs individually. Since you can't get that signal swing from the inputs, it has to come from somewhere else, like a power supply. That's pretty much active by definition. You could feed a passive averager into an amplifier, but that's two separate modules that retain all of their own properties, both good and bad.
You might know this, but it's not clear from your question: The output from an active adder is negative, or inverted. A positive sum is presented as a negative voltage and vice-versa. This is how KCL and KVL still work. If you really want a non-inverting summer, then you need to invert all the inputs (sometimes easier) or invert the output as a separate inverting amplifier/summer with one input.
It often helps my understanding of a particular concept to think of something I already know as a special case of what I'm trying to understand. In this case, a voltage divider can be thought of as a passive averager between the signal and ground. Adjusting the divider ratio and translating that back into a passive summer should show you how to make a weighted average.