# Summing Op-Amps vs Difference Op-Amps

How do you tell the difference between a summing amplifier (non-inverting) op-amp and a difference amplifier just by looking at its configuration?

Please note that in both of these cases, both the (+) and (-) terminals have inputs, thus leading to my confusion on how do you really know if it's summing or difference op-amp

... just by looking at its configuration?

So you are looking for a practical way.

The first thing I look for is the voltage divider coming towards the inverting input. See the R3-RF pair below:

simulate this circuit – Schematic created using CircuitLab

If I see this divider then I know something "positive" is going to happen i.e. this MUST be a non-inverting thing (non-inverthing hehe). So, anything coming towards the non-inverting input will NOT appear with a minus sign at the output. For example, if there's a passive summer/mixer it's going to be amplified without any sign change i.e. non-inverting summer/mixer.

If you see R3's bottom end is going to a non-zero voltage, say $$\V_X\$$, instead of the ground then it's going to appear as $$\-V_X\$$ in the output voltage equation. This could be an inverting summer, a differential amplifier (subtractor), etc. In any case, there's going to be a subtraction or sign inversion.

If you are looking for a more technical explanation, here it is:

Both of them can be thought of as "sub-genres" of the following circuit:

simulate this circuit

The equation for the output is

$$V_{OUT}=\frac{1}{R_3}\Bigg((R_3+R_F)\Big(\frac{R_1}{R_1+R_2}V_1 +\frac{R_2}{R_1+R_2}V_2 \Big)-R_F \ V_3\Bigg)$$

NOTE: If you add another resistor from another source (say, $$\V_4\$$) to the inverting input you can derive the inverting summer as well.

If you make $$\V_1=0\$$ the circuit turns into subtractor because $$\V_{OUT}\$$ becomes $$\(a \ V_2 - b \ V_3)\$$.

If you make $$\V_3=0\$$ the circuit turns into non-inverting summer because $$\V_{OUT}\$$ becomes $$\(c \ V_1+d \ V_2)\$$.

So,

• if you see the non-inverting input go to the ground through a resistor, that's a subtractor (diff-amp).

simulate this circuit

Here, the output voltage is in $$\(a \ V_2 - b \ V_3)\$$ form.

• If you see the inverting input go to the ground through a resistor, that's a summer (non-inv).

simulate this circuit

• ...and if you see a resistor connecting the output to the non-inverting input, either this is a comparator with hysteresis, a mistake, or someone is doing some really deep magic. Dec 8, 2023 at 20:09
• @Hearth ... or an oscillator (if this was not one of the things that you meant with "deep magic"). Dec 8, 2023 at 20:12
• I forgot to mention oscillators. By "deep magic" I meant more "applying small amounts of positive feedback to maintain gain at very high frequencies", which is possible to do but dramatically reduces your phase margin. Dec 8, 2023 at 20:23

Good question... the kind you don't see in textbooks... Here is an initial explanation.

## Comparison

The two configurations differ in how the two input voltages are applied to the circuit input:

• In the summing configuration, the two input voltages are applied in parallel through resistors to the single-ended (grounded) input of a non-inverting or inverting amplifier (the two resistors form a passive resistor summer). Two input voltages with the same polarity regarding the ground act in the same direction; that is why this configuration is summing. In the first case, it is a non-inverting summer; in the second case, it is an inverting summer.

• In the subtracting configuration, the two input voltages are applied in series to the differential (floating) input of a differential amplifier. Two input voltages with the same polarity regarding the ground act in opposite directions when traveling the input loop; that is why this configuration is subtracting.

Generally speaking, both configurations are summing. By changing the sign of one of the two quantities, they can become subtracting.

## How to tell them apart

• If the two input voltages are applied through resistors to the input of a single-ended amplifier, this is a summing amplifier.

• If the two input voltages are applied separately to the two single-ended inputs of a differential amplifier, this is a subtracting amplifier.

# CircuitLab experiments

The best way to understand the ideas behind these summing circuits is through step-by-step experiments; by them we can trace circuit evolution.

## Passive summers

The actual operation (addition/subtraction) in these op-amp circuits is performed by passive sub-circuits, and the amplifiers only amplify the result.

Series summer: The simplest way to sum two voltages is, according to KVL, to connect the input voltage sources in series. In this extremely simple configuration, the "summer" is actually the loop, a piece of wire... "nothing".

But there is a problem - the output voltage is "floating" and requires an amplifier with a differential input. Indeed, for now we still do not have this problem since we have initially connected a "floating" voltmeter (multimeter) in the place of the amplifier.

simulate this circuit – Schematic created using CircuitLab

Parallel summer: If we want to use a single-ended amplifier (with one referenced to ground input), we can sum the voltages through a 2-resistor circuit. It is a more sophisticated (2-input) version of the humble voltage divider. We can understand it by the help of the superposition principle. As you can see, this is a summer with weighted (x0.5) inputs because of the attenuation.

simulate this circuit

## Amplifier summers

We can compensate for the attenuation by connecting an amplifier with a fixed gain of 2 after the passive resistor summer. Since there are no special fixed-gain amplifiers in CircuitLab, we can use op-amps as such by setting the desired gain of 2 in their "parameters" window. Indeed, a gain-of-two op-amp looks rather strange, but it works.

Non-inverting: It can be non-inverting...

simulate this circuit

Inverting: ... or inverting amplifier.

simulate this circuit

Differential: If we want to use a series summer, we have to convert its "floating" output to a single-ended one. For this purpose, we connect a differential amplifier with a gain of 1 (follower).

simulate this circuit

## Op-amp summers

The amplifiers with a fixed gain above are implemented by op-amps with negative feedback.

Non-inverting: In the basic op-amp non-inverting amplifier, the summer output is connected to the non-inverting input, and the feedback network is connected to the inverting input.

simulate this circuit

Inverting: In the basic op-amp inverting amplifier, both summer output and feedback network are connected to the inverting input.

simulate this circuit

Differential: The classic 4-resistor op-amp differential amplifier combines the two (non-inverting and inverting) versions above with additional voltage divider (R1-R4) that equalizes the two input gains.

simulate this circuit