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how to get OP load of a integrator(used in Delta Sigma AD).

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In this figure, Integrator is in integrate phase. Cs is sampling cap.
Cin is parasitic cap in the input of op, Cf is feedback cap,and Cload
is load cap at the output of integrator.

Ceq in open loop state is given : Ceq_open=Cload+(Cs+Cin)*Cf/(Cs+Cin+Cf)

and Ceq in closd loop state is given: Ceq_close=Ceq_open/feedback_factor
=Cs+Cin+(Cs+Cin+Cf)*Cload/Cf.

Ceq is meaningful for determining OP GBW.
I made some efforts, but didn't derive the formulas above.
Can someone give critical steps or give some useful hint?
Thanks in advance.
 

Ceq_openloop is the series combination of Cf and (Cs // Cin). I'd put Cload aside for the moment

The feedback factor is simply the potential divider Cf and (Cs//Cin). Lets call Cf -> Zf and Cin // Cs -> Zin

Beta = Zin / (Zf + Zin)

after finding the Beta factor in terms of Cs, Cf, and Cin, the Ceq_closed loop is Ceq_openloop/Beta.

The Cload is added in parallel to the final result, since it is not part of the feedback loop.
 

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