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[email protected] Finite Gain Effects in SC Circuits Gabor C Temes School of EECS Oregon State...
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Transcript of [email protected] Finite Gain Effects in SC Circuits Gabor C Temes School of EECS Oregon State...
Finite Gain Effects in SC Circuits
Gabor C Temes
School of EECS
Oregon State University
Rev. 03/09/2013
Non-Idealities of an Op-Amp
• DC offset voltage
• Finite dc gain
• Finite bandwidth
• Nonzero output impedance
• Noise
1/8
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)
3/8
Time Domain Analysis
5/8
q1(n) = C1[vin(n)-v-(n)]=q2(n)
q2(n)=-C2[vo(n) - v-(n) - vo(n-1)+v-(n-1)]
Finite D.C. Gain Effects Analysis
6/8
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.
Finite D.C. Gain Effects Analysis
7/8
• (C1/A)vo(n) error causes a phase error near dc.
• (C1/A)vo error causes phase error near dc.
Φ