= Solution
A real <operational amplifier> has large but finite, frequency-dependent <open-loop gain>; the gain falls and its phase changes at higher frequencies. Finite <bandwidth> and <slew rate> constrain small-signal and large-signal responses respectively. There are also finite <input impedance> and <output impedance>, nonzero <input bias currents> and <input offset voltage>, and internally generated <noise>. Offset and bias can drift with <temperature>.
The output is limited by the supply voltages and output-current capability, and the inputs have a permitted common-mode range. Rejection of common-mode and supply changes is finite. Consequently $v_+-v_-$ need not vanish exactly, and neither the virtual-ground approximation nor linear gain formulas apply after saturation. For the calculation below the stipulated infinite <input impedance> removes the input loading currents, while finite gain and optionally finite output resistance are retained.
Back to article page
