question on Razavi's 'design of analog cmos IC'

[mathson]

Hi,
I got a question on Razavi's 'design of analog cmos IC'.
in page 112, it said that Resistance looking into the source of M2 is 1/gm but in P147, it said that the equivalant resistance is 1/gm*(1+r4/r2). I don't know why in the Differential pair, he ignore the load resistance.
Thanks a lot.

tony

 

[checkmate]

I don't have razavi's book off my hand now. But your eqn clearly shows that equiv resistance is 1/gm if r2 is infinite.
Clearly, P112 probably has R2 as an ideal current source with infinite output impedance.

 

[LvW]

..................
in page 112, it said that Resistance looking into the source of M2 is 1/gm but in P147, it said that the equivalant resistance is 1/gm*(1+r4/r2). I don't know why in the Differential pair, he ignore the load resistance.
Thanks a lot.

tony

Hi Tony, the equation on page 112 is an approximation.
Quote Razavi: ....neglecting channel-length modulation...

This simplification is identical to the assumption that the drain-source resistance is infinite - and, thus, decouples the load from the source.