I was hoping someone could help me resolve a little difficulty I have.

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Question number one: Say you have an op amp with a negative feedback. I've been taught that the principle of 'virtual ground' must hold. But what happens for a circuit for like this?

As you can see, I intentionally made the other resistor zero in this configuration (invertible amplifier), so I could force voltage directly into the op amps input. It also makes the gain of this circuit infinite. I understand this is not something that can happen in reality, but from a theoretical point of view, how would you analyze this problem? Is the concept of the virtual ground still valid? If it is, I don't see how.

I still consider this to be the case of a negative feedback, as the portion of the output is brought back into the negative input.

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Question number two: I have a problem with the way people analyze positive feedback. For example, consider this slide from the presentation. I see absolutely no reason why would anything change if I would just switch the plus and the minus sign on the op amp, and thus go from negative to positive feedback. Following that logic, I would get my virtual ground even with a positive feedback.

Conceptually, I understand how both negative and positive feedback work. However, I would like to prove myself mathematically that negative feedback forces the inputs to be equal, and positive feedback forces the op amp to go into saturation. I don't know how to do that. If I use the general model, something like:

I could write that:

A = A/(Aβ + 1) for negative feedback;

A = A/(Aβ - 1) for positive feedback.

I don't what to make of that, though. I see no insight in these equations, just new values for gains, respectively.

So, any help about these two questions would be immensely appreciated. Thanks!