Re: Regarding Offset Volatge
There are two view points for the gm of matched transistors and how it affects offset and current matching.
gm increases as you reduce Vgs-Vt i.e the overdrive voltage.
If you have an offset in a diff amplifier, you'd want to apply a compensating differential voltage at the input in order do remove the offset. This is in fact the input referred offset of the amplifier. The smaller it is, the better. That means that we want to have an amplifier that is quite sensitive, so a small input voltage is enough to compensate for a given offset at the output. In general vout=gm*ro*vin.
ro is not very much under our control, but gm is. Increasing gm makes the amplifier more sensitive and hence a smaller input referred offset results. And this means we need the diff. pair transistors to have small overdrive voltage.
In matching currents in a current mirror we want exactly the oposite thing - if two transistors who are supposed to be perfectly matched are in fact not, then this will result in mismatch in the output current of the mirror. That is, if there is a threshold voltage difference between the two transistors, the current error will be of the order of gm*(deltaVth) and of course we need to reduce gm to have small error i.e. we want a mirror that is not very sensitive as oposed to what we wanted for differential amplifiers. As a result, the overdrive voltage of the mirror transistors needs to be big.