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What is the virtual short of an op-amp?

Virtual short is a circuit node with a steady voltage that is not directly connected to a voltage reference such as ground or a DC voltage source.
The concept of virtual short is commonly used for op-amps. Figure 1 shows a negative feedback amplifier using an op-amp.
Suppose that it is the ideal op-amp, which has:

  1. infinite open-loop gain (AV)
  2. infinite input impedance
  3. zero output impedance

Because the input impedance is infinite, all of the current (i1)
flowing through R1 flows through R2.
i1 = (Vi – V) / R1 = (V - Vo) / R2           (1)
The output voltage of the op-amp is given by the equation:
 Vo = AV(V+ - V)    (2)
From Equation 1 and Equation 2, V+ is calculated as follows:
V+ = {1 + (R1 + R2) / (AV * R1)} * V - R2 * Vi / (AV * R1)
Because AV is infinite, we obtain V = V.
Hence, the voltage at the negative inverting input (V) is equal to
the voltage at the grounded noninverting input (V+).

Roughly speaking, in the event of there being a large difference in voltage between the two inputs, the output voltage becomes abnormally large because an op-amp has a very large open-loop gain (AV).
Even real op-amps have an open-loop gain (AV) around 100 dB (105). This means that, in order to obtain a typical output voltage of several volts, the two inputs must have almost the same voltage (with a difference less than several 10–5 volts).

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