EECS 247 Lecture 7: Filters © 2004 H.K. Page 1EE247 Lecture 7• Summary last lecture• Continuous-time filters – Bandpass filters• Example Gm-C BP filter using simple diff. pair– Linearity– Noise– Various Gm-C Filter implementations– Comparison of continuous-time filter topologiesEECS 247 Lecture 7: Filters © 2004 H.K. Page 2Summary last lecture• Automatic on-chip filter tuning– Continuous tuning• Master-slave tuning– Periodic off-line tuning• Systems where filter is followed by ADC & DSP, existing hardware can be used to periodically update filter freq. responseEECS 247 Lecture 7: Filters © 2004 H.K. Page 3Master-Slave Frequency TuningReference Voltage-Controlled-Oscillator (VCO)•Instead of VCF a voltage-controlled-oscillator (VCO) is used •VCO made or replica integrators•Tuning circuit operates exactly as a conventional phase-locked loop(PLL)•Tuning signal used to tune main filterRef: K.S. Tan and P.R. Gray, “Fully integrated analog filters using bipolar FET technology,” IEEE, J. Solid-State Circuits, vol. SC-13, no.6, pp. 814-821, December 1978.. EECS 247 Lecture 7: Filters © 2004 H.K. Page 4Master-Slave Frequency TuningReference Filter (VCF)tuneVinV1+ -- +- ++ -+ -*RRs−*RRL21sτ31sτ41sτ51sτ11sτLPVrefV11Q--01sτPhase ComparatorAmp.+ FilterMain Filter (Slave)Replica Filter(Master)oVRef: H. Khorramabadi and P.R. Gray, “High Frequency CMOS continuous-time filters,” IEEE Journal of Solid-State Circuits, Vol.-SC-19, No. 6, pp.939-948, Dec. 1984. 01sτEECS 247 Lecture 7: Filters © 2004 H.K. Page 5Reference C/Gm Locked to Ref. FrequencyP2 high à S2 closedS2S3GmC1C2VrefACharge C1 with I=Gm*VrefI=Gm*VrefP2VC1C1refVGmVT2C1≈××T1T2EECS 247 Lecture 7: Filters © 2004 H.K. Page 6Reference C/Gm Locked to Ref. Frequency P3 high à S3 closedCharge on C1 shared with C2Feedback forces Gm to assume a value:S2S3GmC1C2VrefAC1C2C1refrefrefVVVrefsinceVGmVT2C1then:VGmVT2C1C1or:T2N/fclkGm:===××=××==T1T2EECS 247 Lecture 7: Filters © 2004 H.K. Page 7Gm-cell à two sets of input pairs Aux. input pair +C3a,bà Offset cancellation Same clock timingReference C/Gm Locked to Ref. FrequencyIncorporating Offset Cancellation +--+P2P2B-+P3P1+-+-P1P2P3P2BP3P2P3P2Vcm+Vref/2-Vref/2Vtune C1C2C3aC3bEECS 247 Lecture 7: Filters © 2004 H.K. Page 8DC Tuning of Resistive Timing ElementVtune Rext used to lock Gm or on-chip RFeedback forces Gm=1/RextAccount for Cap. variations in the gm-C implementation by trimmingRext.-+-+IIGmRef: C. Laber and Gray, “A 20MHz 6th Order BiCOM Parasitic Insensitive Continuous-time Filter and Second Order Equalizer Optimized for Disk Drive Read Channels,” IEEE Journal of Solid State Circuits, Vol. 28, pp. 462-470, April 1993EECS 247 Lecture 7: Filters © 2004 H.K. Page 9Off-line Frequency Tuning Example:Wireless Receiver Baseband Filters• Systems where filter is followed by ADC & DSP– Take advantage of existing digital signal processor to periodically update the filter critical frequency– Filter tuned only at the outset of each data transmission session (off-line tuning)RF AmpOsc.A/D Digital Signal Processor (DSP)A/D π2IF Stage ( 0 to 2 ) EECS 247 Lecture 7: Filters © 2004 H.K. Page 10Offline Filter Tuning ConceptEECS 247 Lecture 7: Filters © 2004 H.K. Page 11Summary Filter Frequency Tuning• Trimming• Expensive• Does not account for variations associated with temperature and supply etc…• Automatic frequency tuning– Continuous tuning• Master VCF used in tuning loop– Tuning quite accurate– Issue à reference signal feedthrough to the filter output• Master VCO used in tuning loop– Design of reliable & stable VCO challenging– Issue à reference signal feedthrough• Single integrator in negative feedback loop forces time-constant to be a function of accurate clock frequency– More flexibility in choice of reference frequency à less feedthrough issues• Locking a replica of the Gm-cell to an external resistor– DC offset issues– Does not account for integrating capacitor variations• Periodic tuning– Requires digital capability + minimal additional hardware– Advantage of no reference signal feedthrough since tuning performed off-lineEECS 247 Lecture 21: Filters © 2004 H.K. Page 12Bandpass Filters( )Hjω( )HjωLowpassHighpassω( )HjωωωQ<5Q>5• Bandpass Filters:– Q < 5 à Combination of lowpass & highpass– Q > 5 à Direct implementationω( )Hjω+EECS 247 Lecture 7: Filters © 2004 H.K. Page 13Direct ImplementationNarrow Band Bandpass Filters• Design based on lowpass prototype for narrow band filters• Same lowpass tables usedLowpass Freq. Mask Bandpass Freq. Maskccss2s1cB2B1ssQsωωΩΩ−Ω==ΩΩ−Ω×+⇒EECS 247 Lecture 7: Filters © 2004 H.K. Page 14Lowpass to Bandpass TransformationLowpass pole/zero (s-plane) Bandpass pole/zero (s-plane)From: Zverev, Handbook of filter synthesis, Wiley, 1967- p.156.PoleZeroEECS 247 Lecture 7: Filters © 2004 H.K. Page 15Lowpass to Bandpass Transformation TableFrom: Zverev, Handbook of filter synthesis, Wiley, 1967- p.157.( )1filterB2B1aQa−Ω−Ω==EECS 247 Lecture 7: Filters © 2004 H.K. Page 16Lowpass to Bandpass Transformation• Each capacitor replaced by parallel L& C• Each inductor replaced by series L&CoVL2C2RsC1C3inVRLL1L3RsC1C3L2inVRLoVLowpass BandpassEECS 247 Lecture 7: Filters © 2004 H.K. Page 17Lowpass to Bandpass Transformation'1101'012'02'220'3303'03111111CQCRRLQCCRQLRLQLCQCRRLQCωωωωωω=×=×=×=×=×=×oVL2C2RsC1C3inVRLL1L3Where:C1’, L2’, C3’, à normalized lowpass valuesQ à bandpass filter quality factor & ω0à filter center frequencyEECS 247 Lecture 7: Filters © 2004 H.K. Page 18Signal Flowgraph6thOrder Bandpass Filter1*RRs−*11sCRinV1−*1RsL−1−1*RRL−*31sCR*3RsL−*21sCR−*2RsL1−Note each C & L in the original lowpass prototype à replaced by a resonatorSubstituting the bandpass L1, C1,….. by their normalized lowpass equivalent previous pageThe resulting SFG is:oVL2C2RsC1C3inVRLL1L3outV1EECS 247 Lecture 7: Filters © 2004 H.K. Page 19Signal Flowgraph6thOrder Bandpass Filter1*RRs−01'QCsωinV1−'10QCsω−1−1*RRL−'30QCsω'30QCsω−20'QLsω−02'QLsω1−•Note the integrators have different time constants• Ratio of time constants for each resonator ~1/Q2à typically, requires high component ratiosà poor matching•Desirable to convert SFG so that all integrators
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