HO7_315aSP09_RC_nonidealities

HO7_315aSP09_RC_nonidealities - RC Integrator Nonidealities...

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RC Integrator Nonidealities Corrections: Boris Murmann Stanford University Slide 9: 1/sqrt(wp1*wp2) Æ sqrt Slide 11: α a Æ α i , β a Æ β i Slide 15: Replaced content entirely Slide 16: new Slide 39 (38): ω Æ ω [email protected] Copyright © 2009 by Boris Murmann Slide 39 (38): 0 x 5/17/09: Slides 39-41: fixed algebraic errors in derivation (same end result) Slide 44: Modified plot to show only amp noise contribution B. Murmann 1 EE315A HO #7 Outline Impact of finite amplifier bandwidth and gain – Integrator – Filter Thermal noise Passive filters • RC • RLC • Ladder Active filters Active RC • Biquad B. Murmann 2 EE315A HO #7

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Amplifier Model with First Order Nonidealities 0 u 1 a -a 0 noise p noiseless 0 1 p u p a R C = ω ω ω a a a 0 0 ( ) 1 p u p a a a s for s s s = − ≅ − ≅ − >> + ω ω ω ω ω B. Murmann 3 EE315A HO #7 p RC Integrator with Nonideal Amplifier Using return ratio analysis, we can write 0 1 A sRC s = − = − ω ( ) ( ) ( ) ( ) 1 ( ) out in V s T s A s A V s T s = = + 0 0 ( ) ( ) 1 1 1 s a R T s a s s s R = − = + + + ω 0 u p a ω ω 0 p sC ω ω As long as T(s) is large, the transfer function A(s) is close to the desired ideal transfer function (A ) B. Murmann 4 EE315A HO #7 desired ideal transfer function (A )