# Is there a limit to the number of inputs that can be summed with an op-amp summing circuit?

I'm interested in the limits you encounter if you try to add many inputs into an op amp summing circuit. I've read that the inverting configuration is more natural for adding many inputs since the gain for an input is just determined by the feedback resistor and the resistor on that particular branch. Is there a maximum number of inputs you can get away with?

This answer maximun number of inputs on a opamp adder circuit (dealing with a non-inverting amplifier) says that noise is a limiting factor as you add each input. I guess I would assume that the noise would add in quadrature so that the noise would go as sqrt(N) for N inputs. Is this right - and are there any other factors that would limit you from adding inputs indefinitely? Thanks!

• Your gain and output range if you want to re-amplify things for 1:1 correspondence. If you add a thousand 1V signals you would expect a 1000V output. That means you need an op-amp that provide sufficient amplification, but more tricky is to output 1000V. – DKNguyen Jun 8 '20 at 22:59
• Incorrect. It is my answer that you have linked in the question and that answer is dealing with an inverting summing amplifier. Did the phrase "Regard R2 is one limb of your mixer" not mean anything to you? Did you look at the circuit and see that R2 is on the inverting input of the op-amp? – Andy aka Jun 9 '20 at 9:53
• The advantage of the inverting is not that it is "more natural". It is that each source does not interfere (crosstalk) with every other source because the potential at the summing point is 0. – user_1818839 Jun 9 '20 at 15:13

## 3 Answers

A summing amplifier: -

A summing amplifier showing the internal noise source of the op-amp: -

Now let's show that circuit with all the summed inputs connected to ground: -

The noise gain of this circuit is: -

$$1 + \dfrac{R2}{R1/3}$$

So, as you add more inputs (more R1 resistors connected to ground) the R1/3 term becomes R1/4 (four inputs) then R1/5 for 5 inputs. This means that the output noise caused by the grounding of inputs gets bigger as you add more inputs.

But you might say that the inputs are connected to voltage sources and not grounded. And I would say it matters not one bit because whether inputs are connected to ground or a real voltage source then noise becomes progressively amplified as you add more inputs. Sure, an unconnected input won't add more noise gain.

But also, as you incorporate more summing inputs the non-inverting input node acquires more parasitic capacitance to ground and it eventually dominates the input resistors at high frequencies (hence why I've removed the input resistors): -

And the noise gain clearly becomes very massive at higher frequencies because Xc becomes very large.

are there any other factors that would limit you from adding inputs indefinitely?

• The inability of the op-amp to provide the current to all the inputs and thus not maintain the virtual earth condition required for proper numerical summing.

The current from the output back through the feedback resistor will be limited by the current capability of the op amp. The total current, through all summing resistors, can't exceed this maximum feedback current. As the number of inputs increases the current passed through each of the summing resistors must also decrease (the summing resistors will be very large compared to the feedback resistor).

Eventually, as the number of inputs gets large, the current through the summing resistors will be comparable to the input bias current of the op amp. The summing function will no longer be determined primarily by the ratios of the resistors...the input bias current will start to cause a significant bias voltage. Furthermore, any noise or variation in the bias current will cause a corresponding noise voltage on all summing resistors.

All those solder joints and PCB traces will add parasitic capacitance onto the Virtual Ground node, causing more and more phase shift, degrading the transient settling, and eventually you'll have an oscillator.