EECS 247 Lecture 5: Integrator-Based Filters © 2007 H.K. Page 1EE247 Lecture 5• Filters– Effect of integrator non-idealities on filter behavior• Integrator quality factor and its influence on filter frequency characteristics• Filter dynamic range limitations due to Integrator linearity • Effect of integrator component variations and mismatch on filter response– 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, gms, & Cs and its effect on integrated filter characteristics• Opamp MOSFET-C filters• Opamp MOSFET-RC filters• Gm-C filtersEECS 247 Lecture 5: Integrator-Based Filters © 2007 H.K. Page 2Summary of Lecture 4• Ladder type RLC filters converted to integrator based active filters– All pole ladder type filters• Convert RLC ladder filters to integrator based form•Example: 5thorder 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 biquadsÆDoubly 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– Effect of integrator non-idealities on continuous-time filter behavior• Effect of integrator finite DC gain & non-dominant poles on filter frequency responseEECS 247 Lecture 5: Integrator-Based Filters © 2007 H.K. Page 3SummaryEffect of Integrator Non-Idealities on Q• 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. Æ Oscillation• Depending on the location of unity-gain-frequency, the two terms can cancel each other out!• Overall quality factor of the integrator has to be much higher compared to the filter’s highest pole Qi11opi2intg.idealintg.1realQQaω∞==≈−∞∑EECS 247 Lecture 5: Integrator-Based Filters © 2007 H.K. Page 4Effect 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• Integrator linearity function of opamp/R/C (or any other component used to build the integrator) linearity• Active filter specifications wrt linearity typically are given in terms of :– Maximum allowable harmonic distortion– Maximum tolerable intermodulation distortion– Intercept points & compression pointEECS 247 Lecture 5: Integrator-Based Filters © 2007 H.K. Page 5Component Linearity versus Overall Filter Performance1- Ideal ComponentsVinVoutf1ff1fVoutVin() ()11Ideal DC transfer characteristics:Perfectly linear output versus input tranfer function with no clippingfor -sin sinVout Vin VinIf Vin A t Vout A tαωαω=∞≤≤∞=→=EECS 247 Lecture 5: Integrator-Based Filters © 2007 H.K. Page 6Component Linearity versus Overall Filter Performance 2- Semi-Ideal ComponentsVinVoutf1ff1fVoutVin() ()11Semi-ideal DC transfer characteristics:Perfectly linear output versus input transfer function with clippingfor --for -for sin sin for Vout Vin VinVout VinVout VinIf Vin A t Vout A tαααωαω=Δ≤≤+Δ=Δ ≤Δ=Δ ≥Δ=→= -Clipped & distorted otherwiseVinΔ≤ ≤+ΔEECS 247 Lecture 5: Integrator-Based Filters © 2007 H.K. Page 7Effect of Component Non-Linearities on Overall Filter LinearityReal Components including Non-LinearitiesVinVoutf1ff1f()331212Real DC transfer characteristics: Both soft non-linearities & hard (clipping) ........for Clipped otherwisesinV Vinout Vin VinIf Vin A tVinα αωα=+ + −Δ≤≤Δ=+?EECS 247 Lecture 5: Integrator-Based Filters © 2007 H.K. Page 8Effect of Component Non-Linearities on Overall Filter LinearityReal Components including Non-Linearities()() () ()()()()() ( )()2222212211 11113333313311 1Real DC transfer characteristics:........ sinThen:si sin sin3sinn ......sin .....sin 341cos22Vout Vin If Vin A tVout A tor VVinAVinAt tAtout A t tAtααααωαωωαωωαωαωαω++−+=+ + =→= + +=+ +−VinVoutf1ff1f2f13f1EECS 247 Lecture 5: Integrator-Based Filters © 2007 H.K. Page 9Effect of Component Non-Linearities on Overall Filter LinearityHarmonic Distortion() ()()() ( )()1223233sin sinsin.......1co....s2212..2233,2314ndrdVout A tamplitude harmonic distortion componentHDamplitude fundamentalamplitude harmonic distortion componentHDamplitude fundamentalAtAtHD Atαωωααωαωα−+→+=×−=+==231341HD Aαα=×EECS 247 Lecture 5: Integrator-Based Filters © 2007 H.K. Page 10Example: Significance of Filter Harmonic Distortion in Voice-Band CODECs• Voice-band CODEC filter (CODEC stands for coder-decoder, telephone circuitry includes CODECs with extensive amount of integrated active filters)• Specifications includes limits associated with maximum allowable harmonic distortion at the output (< typically < 1% Æ -40dB)VinVout1kHZff1kHZ3kHZCODEC Filter including Output/Input transfer characteristic non-linearity'sEECS 247 Lecture 5: Integrator-Based Filters © 2007 H.K. Page 11Effect of Component Non-Linearities on Overall Filter LinearityIntermodulation Distortion() ()21112 21111332DC transfer characteristics including nonlinear terms, input 2 sinusoidal waveforms:........sin sinThen Vout will have the following components:sinVVout VinIf Vin A t A tViniAVinnαωαωααωα=+ ++→+=() ()() () ()()()()()()()()()()() ()() ()222222211222212122221 22122333333311322212231 2 1 2 3121212 12222sin sin3sisin sin 2nsisin sin ....1cos2 1cos22n3sisinn2cos cosVin A t A t A A t tAAttAAVin A t A tAtA tAtAtttAααωαωαωωαωααωαωαωα ωωααωωαωωωω→+ ++→+ + +→− +−⎡⎤+−−++⎣⎦+() ()()()21231
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