HdrChopper wrote on Nov 18^th, 2009, 6:55pm:


Oh I miss the days when i seemed to be the only one who seemed to know this stuff Great explanation, but one minor issue, which I expect was just a typo. Mismatch isn't proportional to W in a current mirror. When considering the mismatch in a current mirror, it is independent of width: as width goes up, gm goes up, but also ΔVth goes down so they cancel each other (at least in ideal strong inversion). But I agree, increase L (or current) and then adjust W to get the same Vgs-Vth.

In an opamp current mirror mismatch also gets input referred via the gm of the diff pair. In other words, you should always have the gm of the diff pair much larger than the gm of your current mirror. You can see it in the equation
Vos^2 = ΔVth_diff²+(gm_mir/gm_diffΔVth_mir)²

Another way to think about it is to maximize the overdrive (i.e. Vgs-Vth) of a current mirror and minimize overdrive for a diff pair. In the end you need to fit everything between the rails so that is what you need to do physically. Chew up as much headroom as possible with your mirror, not your diff pair.

RE the original question, the reason the mismatch got better with more overdrive is because the ΔVt becomes negligible compared to the overdrive voltage (Vgs-Vth). Once this happens the mismatch is determined by β mismatch. You can see it in the equation:
I+ΔI = (β+Δβ)(Vgs-Vth+ΔVt)²
You can solve this for ΔI/I.
But as Tosie noted, this is the case of a current mirror.

Sigh, I'm always late to these things.
Rob