virtual short

A virtual short is a concept that applies to the inputs of an operational amplifier, or op amp, a common electronic device in analog circuits. Like a real short circuit, a virtual short causes the voltage differential (called V_d) between the two inputs to the op amp to drop to 0. Unlike a real short, however, no current is allowed to flow between the inputs--indeed, an ideal op amp has infinite input impedance.

The reason for the occurance of a virtual short is straight forward and easy to understand. An ideal op amp has the following characteristics:

The voltage gain is infinite:
A_v = ∞

The voltage transfer characteristic equation is:
V_o = A_v·V_d
Where V_o is the output voltage, and V_d is the input voltage differential, as shown in the figure:

      |\
 - ---|-\
Vd    |  \___ Vo
      |  /
 + ---|+/
      |/

Then, if we express V_d in terms of V_o, we get:
V_d = V_o / A_v

And, substituting in A_v:
V_d = V_o / ∞ = 0

Of course, in the real world, the voltage gain is not infinite, but only a rather large number. Nevertheless, V_d will only ever be a small fraction of the output voltage.