# Assumptions for an op-amp and when they do and don't hold?

Correct me if I am wrong but the following is what I think the assumptions we make for an ideal op-amp:

Negative feedback (output connected to the inverting input):

• No current goes into either of the inputs
• The voltage at each of the inputs is the same
• We assume that $A$ in the formula $V_{out}=A(V_+-V_-)$ is equal to $\infty$. (Does this need to be infinity or can it just be very large?)

Positive feedback (output connected to the non-inverting input):

• No current flows into either of the inputs
• The output will always be at saturation (or heading there) (it is bistable) (This does however follow from the other assumptions, namely the one below)
• We assume that $A$ in the formula $V_{out}=A(V_+-V_-)$ is very large. In this case however I don't think we have to assume that it is $\infty$.

In all other cases we assume that no current flows into the op amp.

If we have positive and negative feedback, all we can assume is that no current flows into the op-amp and the voltages depend on the circuit in question. In the specific case of the astable multivariate it happens that the output voltage changes between its two saturation values.

So here are my questions:

1. Firstly, is the above correct and is there any further assumptions that I can add?
2. Are there any exceptions to the above rules (staying of course with ideal op amps)? I was thinking about e.g. a capacitor in the negative feedback situation, like in an op amp integrator circuit, could the rule about the voltage across a capacitor not been allowed to change instantaneously mean that the assumption that the voltages at the inputs are the same does not hold?
1. Is it possible to have a circuit with positive and negative feedback that does not go to one of its saturation points?

If you want me to expand on any point, just ask. Thanks.

• Depends on what you mean by "ideal". An ideal op-amp could mean infinite gain and no saturation. It's definitely possible to have a circuit with both positive and negative feedback that is stable, but it of course depends on the specifics. – John D Dec 10 '14 at 16:06
• You need to add infinite open loop gain. Also, you don't need to have an assumption of saturation for the positive feedback config -- it comes out of the other assumptions. – Scott Seidman Dec 10 '14 at 16:17
• @ScottSeidman I have edited it to inculde your points – user53915 Dec 10 '14 at 16:52
• A negative capacitance amplifier does not saturate if the source capacitance is high, and that has negative and positive feedback -- en.wikipedia.org/wiki/Negative_impedance_converter – Scott Seidman Dec 10 '14 at 17:32
• @ScottSeidman You need more assumptions than Iin = 0 and Vo = A(V+ - V-) for a positive feedback op-amp. Mathematically, all it does is flip the input terminals terminals: Vo = A (V- - V+), which has a mathematically finite solution when V- = V+, like the negative feedback case, which might be interpreted as the "correct" output for ideal positive feedback op-amps, but is completely unstable. – helloworld922 Dec 10 '14 at 18:05