Calculate the output voltage of a differential amplifier for

Calculate the output voltage of a differential amplifier for inputs V_in+ = 0.5 mV, V_in = 0.45 mV, Ad = 450, and CMRR = 10^4.

The output voltage Vo = Ad. Vd + Ac. Vc -----------(1)

Where Ad is the differential gain = Vo/Vd (Since Vd is the differential Voltage = V_in+ - V_in-)

Ac is common gain = Vo/Vc (since Vc is the common Voltage = (V_in+ + V_in-)/2 )

CMRR = Ad/Ac --------(2)

The given values are Ad = 450, CMRR = 10⁴ and V_in+ 0.5mV ; V_in- = 0.45mV

from equation (2) CMRR = Ad/Ac

Ac = Ad/CMRR = 450/10⁴ = 0.045

Vd = V_in+ - V_in- = 0.5 - 0.45 = 0.05mV

Vc = (V_in+ + V_in-)/2 = (0.5 + 0.45)/2 =0.475mV

from equation (1) the output voltage is Vo = Ad. Vd + Ac. Vc

= (450 X 0.05 + 0.045 X 0.475 ) mV

= (22.5 + 0.021) mV = 22.521mV