If the gain bandwidth product of an operational amplifier is a constant and |Vout/Vin| is also a constant does that mean that the operational amplifier will not function for all but 1 frequency? Please explain.
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Open loop Vout / Vin isn't constant - it rolls off with frequency and obeys the gain-bandwidth product approximation: -
What you may be being confused with is the DC open loop gain and, from the diagram above that would be quoted in a data sheet as 1 million.