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Some confusion on MOS matching property

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waosai

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mos matching

There is a famous equation on current source matching given by M.G.M:

4(Avt)²
---------- +(Aβ)²
(Vgs-Vt)²
W*L= --------------------- (where, Avt and Aβ is determined by process)
σ²/I²
It means that the larger area of MOS transistor, the better the matching of current sources.

But in some papers, there is constant 0.5 at the right of the equal which is:

4(Avt)²
---------- +(Aβ)²
(Vgs-Vt)²
W*L= ---------------------
2*(σ²/I²)

Who can explain why and where this constant come from?
 

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