differential amp problem - where and how to start

differential amp problem

hi, anyone could help me with this problem circuit?
i just dont know where and how to start..thanks..
please see attachment..[/img]

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)

Re: differential amp problem

i am actually a freshman of this analog design, so i dont understand fully what you've said..will you please attached the small signal analysis drawing?
or just the answers of the problem questions posted?
it'll be of big help..thanks a lot..

Re: differential amp problem

Hi iainPOT,
If I give you the solution it would not teach you anything. Since you are a freshman then there is all the more reason for you to start doing something. I will give you the leads and places you can learn but I should not give you the solution to this simple problem.
For small signal model you can pick up any Analog Design book and find out how to replace a MOS with its small signal model. Once you do that and I assume you already know KVL and KCL. Then start by trying to solve it. Try something and then ask your doubts and then I will help clarify them. This would be a much more constructive path. All the best.

Re: differential amp problem

hi you acn find such corresponding proplemsand examples in any microelectronic book. you can find such examples in microelectronic books for bolystad and nashalisky , jacop millman , and sedra smith . jacop millman is the best for that.