A complementary (push-pull) amplifier is an inverter. The working area in a digital circuit is the steady-state area, and there is always one tube in the cut-off state. The working area in an analog circuit is the transition area between two steady states, and both MOS tubes are in saturation.
Assume that the DC currents passing through the two MOS tubes are equal, Id1=Id2
We get 0.5*β1*(Vin – Vss – Vt1)exp2 * [1+λn*(Vout – Vss)]
=0.5*β2*(Vdd – Vin – Vt2)exp2 * [1+λp*(Vdd – Vout)]
Assume I = Id1 = Id2
So, Av = Vout/Vin = - [(2*β1)exp(0.5) + (2*β2)exp(0.5)]/[(λn+λp)*Iexp0.5]
It can be seen that the AC gain of the complementary amplifier is inversely proportional to the square root of the DC current.
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