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Finite Gain Effects in SC Circuits

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. Model for Finite Gain. Model for Finite-Gain Effect.

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Finite Gain Effects in SC Circuits

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  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 1/8

  3. Model for Finite Gain 2/8

  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) 3/8

  5. Finite Gain Model ∞ 4/8

  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)] 5/8

  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. 6/8

  8. Finite D.C. Gain Effects Analysis Φ (C1/A)vo(n) error causes a phase error near dc. (C1/A)vo error causes phase error near dc. 7/8

  9. Finite Gain Model vcmi vcmo vin vout ∞ 8/8

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