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Why is the Open Loop Gain of the Ideal Operational Amplifier Infinitely Large?

(1) the actual open loop gain of the operational amplifier is more than 100 thousand, very large, therefore, the open loop gain of the actual operational amplifier is thought to be infinitely large, and thus the virtual earth is derived.

(2) the derived virtual earth only aims at the reverse phase amplifier.

I see in the book that the open loop gain of the operational amplifier is infinite, which makes the closed-loop gain not restricted by the open loop gain but only depend on the external components when we design the circuit. That is to get the stability of the closed-loop gain at the expense of the large open loop gain.

(3) the derived virtual ground directs at operational amplifiers in negative feedback connection not only at reverse phase amplifiers. There is no virtual ground for positive feedback.

(4) it is easy to understand that, suppose that the gain is very small, the difference value between the output voltage and the voltage at both ends of the amplifier is relatively large. If a negative feedback state is connected, the voltage at both ends of the operational amplifier will be inconsistent, which causes the magnification error.

(5) there are two conditions for the implementation of "virtual short" of the operational amplifier:
1)A, the open loop gain of the operational amplifier, is large enough;

2) have negative feedback circuits.

Let's start with the first point. we know that the output voltage of the op amp is Vo, equal to that Vid, the difference value between the positive phase input end voltage and the reverse phase input end voltage, multiplies A, the open loop gain of the amplifier. Vo = Vid * A = (VI+ - VI-) * A (1)the output voltage of the operational amplifier is a finite value because in practice it will not exceed the power supply voltage. In this case, if A is large, (VI+ - VI -) must be small; if (VI+ - VI -) is small to some degree, then we can actually view this as 0, and then we can get VI+ = VI-, that is, the voltage of the in-phase input terminal is equal to the voltage of the reverse phase input, as if it was connected together, which we call "virtual short circuit".
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