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Thursday, September 7, 2017

switch capacitor multiplier: op-amp with non-ideal DC gain



continue the discussion in previous post: here we assume a non-ideal op-amp, i.e. op-amp gain is equal A. For simplification, lets assume the circuit is in phase 2 and Vd=0 (similar to case b). Again, in equilibrium, sampling charge on C1 and Cf is conserved by the feedback loop (as much as DC gain of the op-amp allows). We have:

qfq1=Cf(VoVx)C1Vx=(C1+Cf)Vi.

If Vo=A×Vx then

VoCf+VoA(C1+Cf)=(C1+Cf)ViVo=C1+CfCf+C1+CfAVi=1β+1AVi,
where β=CfC1+Cf. If A then Vo=Viβ. Given Equation (4), The output voltage error, Voutputϵ due to non-ideal gain of op-amp is given by

Voutputϵ=(1β1β+1β)Vi=1β(11+1βA1)Vi=(Δ1+Δ)Vo,
where Δ=1βA. For simplification, we assume that βA1; therefore we have:

VoutputϵΔ×Vo


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