EE247 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 filters EECS 247 Lecture 5 Integrator Based Filters 2007 H K Page 1 Summary 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 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 Effect of integrator non idealities on continuous time filter behavior Effect of integrator finite DC gain non dominant poles on filter frequency response EECS 247 Lecture 5 Integrator Based Filters 2007 H K Page 2 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 Overall quality factor of the integrator has to be much higher compared to the filter s highest pole Q EECS 247 Lecture 5 Integrator Based Filters 2007 H K Page 3 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 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 point EECS 247 Lecture 5 Integrator Based Filters 2007 H K Page 4 Component Linearity versus Overall Filter Performance 1 Ideal Components Ideal DC transfer characteristics Perfectly linear output versus input tranfer function with no clipping Vout Vin for Vin If Vin A sin 1t Vout A sin 1t Vout Vout Vin Vin f1 f f1 EECS 247 Lecture 5 Integrator Based Filters f 2007 H K Page 5 Component Linearity versus Overall Filter Performance 2 Semi Ideal Components Semi ideal DC transfer characteristics Perfectly linear output versus input transfer function with clipping Vout Vin for Vin Vout for Vin Vout for Vin If Vin A sin 1t Vout A sin 1t for Vin Clipped distorted otherwise Vout Vout Vin Vin f1 EECS 247 f f1 Lecture 5 Integrator Based Filters f 2007 H K Page 6 Effect of Component Non Linearities on Overall Filter Linearity Real Components including Non Linearities Real DC transfer characteristics Both soft non linearities hard clipping Vout 1Vin 2 Vin 2 3 Vin 3 for Vin Clipped otherwise If Vin A sin 1t Vout Vin f1 f EECS 247 f1 Lecture 5 Integrator Based Filters f 2007 H K Page 7 Effect of Component Non Linearities on Overall Filter Linearity Real Components including Non Linearities Real DC transfer characteristics Vout 1Vin 2 Vin 2 3 Vin 3 If Vin A sin 1t Then Vout 1 A sin 1t 2 A2 sin 1t 3 A3 sin 1t 3 2 or Vout 1 A sin 1t 2 A2 2 1 cos 2 t 1 3 A3 4 EECS 247 1 1 Vout Vin f1 3sin t sin 3 t f f1 2f1 3f1 Lecture 5 Integrator Based Filters f 2007 H K Page 8 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 HD3 1 3 2 A 4 1 Lecture 5 Integrator Based Filters 2007 H K Page 9 Example 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 40dB CODEC Filter including Output Input transfer characteristic non linearity s Vin 1kHZ EECS 247 f Lecture 5 Integrator Based Filters Vout 1kHZ 3kHZ f 2007 H K Page 10 Effect of Component Non Linearities on Overall Filter Linearity Intermodulation Distortion DC transfer characteristics including nonlinear terms input 2 sinusoidal waveforms Vout 1Vin 2 Vin 2 3 Vin 3 If Vin A1 sin 1t A2 sin 2 t Then Vout will have the following components 1Vin 1 A1 sin 1t 1 A2 sin 2 t 2 Vin 2 2 A12 sin 1t 2 A2 2 sin 2 t 2 2 A1 A2 sin 1t sin 2 t 2 2 A12 2 2 2 1 cos 2 t 2A 1 cos 2 t 2 1 2 2 2 A1 A2 cos 1 2 t cos 1 2 t 3 Vin 3 A13 sin 1t 3 A2 3 sin 2 t 3 3 3 3 3 A1 A2 sin 1t sin 2 t 3 3 A2 A1 sin 2 t sin 1t 2 2 2 2 2 3 3 A1 A2 sin 2 1 2 t sin 2 1 2 t 4 EECS 247 Lecture 5 Integrator Based Filters 2007 H K Page 11 Effect of Component Non Linearities on Overall Filter Linearity Intermodulation Distortion Real DC transfer characteristics input 2 sin waves Vout 1 Vin 2 Vin 2 3 Vin3 If Vin A1 sin 1t A2 sin 2t Vin f1 f2 Vout f f1 f2 2f1 f2 f 2f2 f1 For f1 f2 close in frequency Components associated with 2f1 f2 2f2 f1 are the closest to the fundamental signals on the frequency axis and thus most harmful EECS 247 Lecture 5 Integrator Based Filters 2007 H K Page 12 Effect of Component Non Linearities on Overall Filter Linearity Intermodulation Distortion Intermodulation non idealities measured in terms of IM2 and IM3 Typically for input two sinusoids with equal amplitude A1 A2 A IM 2 amplitude 2nd IM component amplitude fundamental IM 3 amplitude 3rd IM component amplitude fundamental IM 2 2 A 1 EECS 247 IM 3 3 3 2 25 5 4 A A 4 1 8 1 Lecture 5 Integrator Based Filters 2007 H K Page 13 Wireless Communications Measure of Linearity Output Power dBm 1dB
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