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Finite Gain Effects in SC Circuits

Gabor C Temes

School of EECS

Oregon State University

Rev. 03/09/2013

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Non-Idealities of an Op-Amp

• DC offset voltage

• Finite dc gain

• Finite bandwidth

• Nonzero output impedance

• Noise

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Model for Finite Gain

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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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Finite Gain Model

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∞

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Time Domain Analysis

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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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Finite D.C. Gain Effects Analysis

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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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Finite D.C. Gain Effects Analysis

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• (C1/A)vo(n) error causes a phase error near dc.

• (C1/A)vo error causes phase error near dc.

Φ

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Finite Gain Model

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∞

voutvin

vcmi vcmo