Re: differential amp problem
Hi iainPOT,
Assuming that the 2 inputs are applied at the MOS differential pair(M1 and M2), you can draw the small signal model of the diff pair with the tail current and calculate the differential mode gain(Adm) i.e. vout/(vin1-vin2) where vin1 is applied to where vin is shown in the diagram and vin2 is applied to the terminal which is grounded. Similarly you can find out the common mode gain (Acm) i.e. vout/vin where vin is applied to both terminals (Gates of M1 and M2) shorted together.
Now you can represent the signal shown in the diagram i.e. vin on M1 and 0 on M2 as a sum of a common mode and differential mode signal. Once you split that simply multiply the respective quantities with their respective gain expressions calculated above to get vout/vin.
vout/vin can be calculated as Gm Ro where you can calculate the circuit Gm by applying an input voltage at vin and grounding (small signal) the output and finding out how much current the circuit pulls into it from smal signal ground. So then Gm = Io/vin where Io is the current pulled by the circuit for vin small signal voltage.
For Ro ground all inputs i.e. vin will also get grounded and apply a small signal test source (Vx) at the output and calculate the current going into the circuit (Ix). Ro=Vx/Ix.
Knowing both Gm and Ro you can calculate the gan vout/vin.
vout max and vout min can be calculated assuming the extreme conditions on M1 one being M1 takes all current going into M4 (vin=VDD) and one being M1 takes no current at all (vin=-VDD)