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:
qf−q1=Cf(Vo−Vx)−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 V∗o=Viβ. Given Equation (4), The output voltage error, Voutputϵ due to non-ideal gain of op-amp is given by
Voutputϵ=(1β−1β+1β)Vi=1β(11+1βA−1)Vi=(Δ1+Δ)V∗o,
where Δ=1βA. For simplification, we assume that βA≫1; therefore we have:
Voutputϵ≅Δ×V∗o
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