We know that, the input resistance of an op amp must be very high where as the output resistance should be quite low. An op amp should also have very high open loop gain. In ideal cases, the input resistance and open loop gain of an op amp should be infinity whereas the output resistance would be zero. So an ideal op amp should have following characteristics.
|Open Loop Gain (A)||∝|
|Bandwith of Operation||∝|
So, an ideal op amp is defined as, a differential amplifier with infinite open loop gain, infinite input resistance and zero output resistance. The ideal op amp has zero input current. This is because of infinite input resistance. As the input resistance of ideal op amp is infinite, an open circuit exists at input, hence current at both input terminals is zero.
There is no current through the input resistance, there will be no voltage drop between the input terminals. Hence no offset voltage appears across the inputs of an ideal operational amplifier.
If v1 and v2 are the voltages of inverting and non-inverting terminals of op amp, and v1 = v2 then in ideal case,
The bandwidth of operation of an ideal op-amp is also infinite. That means the op-amp perform its function for all ranges of frequencies of operation.