EE247 Lecture 5 Summary last lecture Today Effect of integrator non idealities on continuous time filter behavior Integrator frequency characteristics influence on filter response Effect of component non linearities on filter behavior Various integrator topologies utilized in monolithic filters Resistor C based filters Transconductance gm C based filters Switched capacitor filters Continuous time filters Facts about monolithic Rs Cs and its effect on integrated filter characteristics Opamp MOSFET C filters Opamp MOSFET RC filters Gm C filters EECS 247 Lecture 5 Filters 2006 H K Page 1 Summary of Lecture 4 Ladder Type Filters All pole ladder type filters Convert RLC ladder filters to integrator based form Example 5th order Butterworth filter High order ladder type filters incorporating zeros 7th order elliptic filter in the form of ladder RLC with zeros Sensitivity to component mismatch Compare with cascade of biquads Doubly terminated LC ladder filters Lowest sensitivity to component variations Convert to integrator based form utilizing SFG techniques Example Single ended differential high order filter implementation EECS 247 Lecture 5 Filters 2006 H K Page 2 Effect of Integrator Non Idealities on Filter Frequency Characteristics In the section on passive filter design RLC filters Reactive element L C non idealities expressed in the form of Quality Factor Q Filter impairments due to component non idealities explained in terms of component Q In the context of active filter design integrator based filters Integrator non idealities Translated to the form of Quality Factor Q Filter impairments due to integrator non idealities explained in terms of component Q EECS 247 Lecture 5 Filters 2006 H K Page 3 Effect of Integrator Non Idealities on Filter Performance Ideal integrator characteristics Real integrator characteristics Effect of finite DC gain Effect of integrator non dominant poles EECS 247 Lecture 5 Filters 2006 H K Page 4 Effect of Integrator Non Idealities on Filter Performance Ideal Integrator Ideal Intg Intg Ideal l o g H s C R Vin Vo 0 0dB o p a mp DC g a i n S i ng l e p o l e D C no non dominant poles o H s s o 1 RC 90o EECS 247 Lecture 5 Filters 2006 H K Page 5 Ideal Integrator Quality Factor Ideal intg transfer function H s o s Since Q is defined as Then o j 1 1 H j R j X X Q R j o t g Qiidneal EECS 247 Lecture 5 Filters 2006 H K Page 6 Real Integrator Non Idealities Ideal Intg Real Intg l o g H s l o g H s a 0 P1 90o 90o H s o s H s 0 P2P3 0 a a 1 s a o 1 p2s 1 p3s EECS 247 Lecture 5 Filters 2006 H K Page 7 Effect of Integrator Finite DC Gain on Q l o g H s a o 0 P1 2 Arct an P1 o 0 a 89 5 90 P1 o P h a s e l ea d o in radian 90o Example P1 0 1 100 phase error 0 5degree EECS 247 Lecture 5 Filters 2006 H K Page 8 Effect of Integrator Finite DC Gain on Q Ideal intg Intg with finite DC gain Phase lead 0 Magnitude dB Droop in the passband Droop in the passband 1 Normalized Frequency EECS 247 Lecture 5 Filters 2006 H K Page 9 Effect of Integrator Non Dominant Poles l o g H s o 0 2 P2P3 90 90 5 Ar ct an po i 2 i o Phase l ag o p i 2 i in radian 90o Example 0 P2 1 100 phase error 0 5degree EECS 247 Lecture 5 Filters 2006 H K Page 10 Effect of Integrator Non Dominant Poles Magnitude dB Ideal intg Opamp with finite bandwidth Phase lag 0 Peaking in the passband In extreme cases could result in oscillation Peaking in the passband 1 Normalized Frequency EECS 247 Lecture 5 Filters 2006 H K Page 11 Effect of Integrator Non Dominant Poles Finite DC Gain on Q l o g H s a o P1 0 a 0 P2P3 90 2 Arctan P1 o Arctan o i 2 pi 90o Note that the two terms have different signs Can cancel each other s effect EECS 247 Lecture 5 Filters 2006 H K Page 12 Integrator Quality Factor Real intg transfer function H s Based on the definition of Q and assuming that It can be shown that in the vicinity of unity gain frequency a 1 s a o o 1 p2 3 g Qrint eal Phase le EECS 247 Lecture 5 Filters 1 p2s 1 p3s a 1 1 1 1 o a i 2 pi ad 0 Phase l ag 0 2006 H K Page 13 Example Effect of Integrator Finite Q on Bandpass Filter Behavior 0 5 lead ointg 0 5 excess ointg Ideal Ideal Integrator DC gain 100 EECS 247 Lecture 5 Filters Integrator P2 100 o 2006 H K Page 14 Example Effect of Integrator Q on Filter Behavior 0 5 lead 0 5 error excess ointg ointg 0 Ideal Integrator DC gain 100 P2 100 EECS 247 Lecture 5 Filters 2006 H K Page 15 Summary Effect of Integrator Non Idealities on Q int g Qideal int g Qreal 1 1 a o p1 i 2 i Amplifier DC gain reduces the overall Q in the same manner as series parallel resistance associated with passive elements Amplifier poles located above integrator unity gain frequency enhance the Q If non dominant poles close to unity gain freq Oscillation Depending on the location of unity gain frequency the two terms can cancel each other out EECS 247 Lecture 5 Filters 2006 H K Page 16 Effect of Integrator Non Linearities on Overall Integrator Based Filter Performance Maximum signal handling capability of a filter is determined by the non linearities associated with its building blocks Filter specifications wrt linearity are given in terms of Maximum allowable harmonic distortion Maximum tolerable intermodulation distortion EECS 247 Lecture 5 Filters 2006 H K Page 17 Effect of Component Non Linearities on Overall Filter Performance Ideal Components Ideal DC transfer characteristics Vout Vin If Vin A sin t Vout A sin t Vout Vin f1 f f1 EECS 247 Lecture 5 Filters f 2006 H K Page 18 Effect of Component Non Linearities on Overall Filter Linearity Real Components including Non Linearities Real DC transfer characteristics Vout 1 Vin 2 Vin 2 3 Vin3 Vin If Vin A sin t f1 Vout f f1 2f1 3f1 Vout 1 A sin t 2 A sin t 2 f 2 3 A3 sin t 3 2 A2 1 cos 2 t 2 A3 3 3sin t sin 3 t 4 or Vout 1 A sin t EECS 247 Lecture 5 Filters 2006 H K Page 19 Effect of Component Non Linearities on Overall Filter Linearity Harmonic Distortion Vout 1 A sin t 2 A2 2 1 cos 2 t 3 A3 3sin t sin 3 t 4 amplitude 2nd harmonic distortion component HD 2 amplitude fundamental HD3 amplitude 3rd harmonic distortion component amplitude fundamental HD 2 1 2 A 2 1 EECS 247 …
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