1. Finite Gain Effects in SC Circuits
Gabor C Temes
School of EECS
Oregon State University
Rev. 03/09/2013

2. Non-Idealities of an Op-Amp
DC offset voltage
Finite dc gain
Finite bandwidth
Nonzero output impedance
Noise
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3. Model for Finite Gain
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4. Model for Finite-Gain Effect
∆Qi=Yi(Vi+-Vi-)
∆Q is the charge flow in one clock period.
For Ao infinity, ∆Q1=Y1*Vin=-∆Q2=-Y2*Vo
So, H(z) = -Y1/Y2 when Ao infinity
For finite Ao:
∆Q1=Y1(Vin+Vo/Ao) =-∆Q2=-Y2(Vo+Vo/Ao)
H(z) = -Y1/(Y2+Y1/Ao+Y2/Ao)
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5. Finite Gain Model ∞
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6. Time Domain Analysis q1(n) = C1[vin(n)-v-(n)]=q2(n)
q2(n)=-C2[vo(n) - v-(n) - vo(n-1)+v-(n-1)]
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7. Finite D.C. Gain Effects Analysis
C1vin(n) = -C2vo(n)+v-(n)[C1+C2]+C2vo[n-1] – C2v-(n-1)
C1vin(n) = -C2[vo(n)-vo(n-1)] - [C1+C2)/A]vo(n)+(C2/A)vo(n-1)
C1vin(n) =-C2(1+1/A)[vo(n)-vo(n-1)]+(C1/A)vo(n)
(C1/A)vo(n) error is critical. It causes a phase error near dc
C2(1+1/A)[vo(n)-vo(n-1)] error is negligible.
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8. Finite D.C. Gain Effects AnalysisΦ
(C1/A)vo(n) error causes a phase error near dc.
(C1/A)vo error causes phase error near dc.
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9. Finite Gain Model
vcmi
vcmo
vin
vout ∞
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