Universal (magic) Op-Amp Fundamentals

My answer to SE EE question Universal (magic) Op-Amp Fundamentals

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This question touched me with its sincerity and caused (for some time) my indignation at the soulless teaching. It took me far back in my student years when I was trying to figure out what the idea behind basic computing analog devices was...

My answer

Essence. This professor's creature can be called "universal summing-subtracting op-amp circuit" (not "universal op-amp" since the op-amp is just one of the circuit components). It reminds me of the distant past when analog computers tried to compete with digital ones... but soon lost that battle (analog computers consisted of building blocks and this was one main block).

Structure. The curcuit consists of two passive resistor summing circuits and an op-amp:

• The upper 4-input summer consists of the four resistors R1, R2, R3 and Rf. The first three are connected to the external input voltage sources V1, V2 and V3; the "feedback" resistor Rf is connected to an internal "input" voltage source - the op-amp output Vout. The output of the summing circuit is connected to the op-amp inverting input.
• The lower 2-input summer consists of the two resistors R4 and R5. The first is connected to the external input voltage source V4; the second is connected to the internal "ground voltage source" with zero input voltage. The output of this summing circuit (or simply, *voltage divider*) is connected to the op-amp non-inverting input.

Operation. Since the output of the upper summer is connected to the inverting input, the sum of V1, V2 and V3 appears negative at the op-amp output. Since the output of the lower summer is connected to the non-inverting input, the sum of V4 and Vground (0) appears positive at the op-amp output.

The role of the internal "input" Vout is to neutralize the upper three input voltages V1, V2 and V3. As a result, a virtual ground appears at the inverting input (indeed, it is  shifted" by the lower input voltage V4)... and the upper voltage sources are separated from each other.

Calculation. The relation between the voltages can be found by applying the superposition principle.

Properties. Because of the resistors forming voltage dividers, this is a summing circuit with weighted inputs.

You can find more interesting and original considerations about this circuit in the related Wikibooks story; they will help you to figure out the basic ideas behind it.

Finally, I have a request to OP - if possible, to connect me with their professor... I want to exchange some valuable thoughts on how to explain circuits to curious students...

My comments

1. I perfectly understand you since I have been explaining circuit ideas since the middle 80s to such IT students that are interested in software and not so much in circuits. I try to make them think and not just learn so our classes resemble more brainstorming sessions than conventional classes. I share them on web to inspire curious young people. Look at my Wikibooks teacher's story and the related circuit story we created in 2008.
2. I don't mind you asking me more questions... I even want to... but I don't understand your question exactly. If it is a question about the gain value, it depends on each resistor in the circuit. Also, the negative feedback transfer ratio depends not only on Rf but also on R1, R2 and R3; so, it is not correct to call only Rf "feedback resistor". It is a humble resistor like the others and we can call it R6, for example. All voltages of the nodes are with respect to ground and you can consider the 2-terminal Rf as a 4-terminal (2-port) element…
3. I know that you will be able to handle the calculations because it is a routine procedure... or you will find explanations for them... or someone will help you... What you will not find, but what you need most, is the idea of all this. This should start with a teacher (or someone who pretends to be one) and then come up with formulas. So, let me develop my explanations, which I started in my answer (then I can add them in my answer but it is more natural that way). Let's look at the inverting and non-inverting parts of the circuit separately... so it's easier to understand…
4. If we start with the inverting part, it is convenient to assume that V4 = 0 (ie, we turn off the non-inverting part and only an ordinary 3-input inverting adder remains). In principle, the three voltages V1, V2 and V3 can be summed only through the three resistors R1, R2 and R3 thus forming a ‘passive resistor summer)... but there are a few problems. First, the circuit will be an attenuator; second, its output voltage at the common resistor point will not be zero and the input sources will influence each other; third, the load will further reduce its transfer ratio. How do we solve them?
5. We can solve all these problems by the clever ‘compensation trick’. For this purpose, we add another input (resistor) and connect a variable voltage source to it. Then we begin varying its voltage (with opposite polarity) until the voltage of the common resistor node becomes zero (virtual ground). As a result, the input sources will be isolated to each other… the variable voltage will be proportional to the sum of V1-V3… and we can use it instead of the original node voltage; so the load will be isolated by the common node…
6. In most cases of practice, in addition to V4 (R4), there are more inputs and the ground becomes an input also (another source is connected to R5). And this is the same passive adder as above... having the same disadvantages of a passive circuit. But here they are not compensated; there is only an amplification (non-inverting amplifier). By the way, the explanation of the inverting part applies to all op-amp inverting circuits. This is a universal principle that I call "voltage compensation"...
7. I have dedicated a Wikibooks story to it (see also the talk page; it would be interesting to you). I have to stop because my explanations will be interrupted (this is considered as a bad practice here). It would be good to take some attitude to all this… or at least think about them...