Constant-gm bias circuit

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Do you guys know how to come up with the equation for RDS4C ?

 

I got a different answer, maybe I made a mistake in the derivation but you can check to see if it's right though.


edit:
Oh I see my mistake now, when I absorbed (W/L)4c into the square root I forgot to square it. and (W/L)4c=P/M * (W/L)2E which would make
Rds=[2uCox(P/M)^2(W/L)2E*ID]^-1/2 which would equate to gm2E^-1/2 * M/P
 
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Thanks. Could you rewrite the correct solution ?

I am having problem following your derivation (with mistake).
 

If I made any mistakes, please point them out. Thanks.

 
Besides P, the M should have been squared inside the square root. I think you forgot it.

I do not understand why gm4e is always independent of process, temperature and load variations ?
 

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