EECS 247 Lecture 8: Filters© 2010 H.K. Page 1EE247 Lecture 8• Continuous-time filter design considerations– Monolithic highpass filters– Active bandpass filter design• Lowpass to bandpass transformation• Example: 6thorder bandpass filter• Gm-C bandpass filter using simple diff. pair–Various Gm-C filter implementations• Performance comparison of various continuous-time filter topologies• Introduction to switched-capacitor filters EECS 247 Lecture 8: Filters© 2010 H.K. Page 2Summary Lecture 7• Automatic on-chip filter tuning (continued from last lecture)– Continuous tuning (continued)• Replica single integrator in a feedback loop locked to a reference frequency• DC tuning of resistive timing element– Periodic digitally assisted filter tuning• Systems where filter is followed by ADC & DSP, existing hardware can be used to periodically update filter freq. responseEECS 247 Lecture 8: Filters© 2010 H.K. Page 3RLC Highpass Filters• Any RLC lowpass and values derived from tables can be converted to highpass by:– Replacing all Cs by Ls and LNormHP= 1/ CNormLP– Replacing all Ls by Cs and CNormHP= 1/ LNormLP– LHP=Lr / CNormLP, CHP=Cr / LNormLPwhere Lr=Rr/wr and Cr=1/(Rrwr)RsC1C3L2inVRsL1L3C2inVC4L4LowpassHighpassEECS 247 Lecture 8: Filters© 2010 H.K. Page 4Integrator Based High-Pass Filters1st Order• Conversion of simple high-pass RC filter to integrator-based type by using signal flowgraph techniqueinsCVRosCV 1 RoVRCinVEECS 247 Lecture 8: Filters© 2010 H.K. Page 51stOrder Integrator Based High-Pass FilterSignal FlowgraphoVRCinV+ VC -+VR-ICIRV V VR in C1VICCsCVVoR1IVRRRIICR11R1sCRICICVinV11SFGoV1VREECS 247 Lecture 8: Filters© 2010 H.K. Page 61stOrder Integrator Based High-Pass FilterSGF1sCRoVinV11oVRCinVoVinV-SGFNote: Addition of an integrator in the feedback path High pass frequency shaping+++ VC-+ VR-EECS 247 Lecture 8: Filters© 2010 H.K. Page 7Addition of Integrator in Feedback PathoVinV-a1/stLet us assume flat gain in forward path (a)Effect of addition of an integrator in the feedback path:++ininint gpole oVaoV 1 afsVaossV 1 a / 1 / aazero@ DC & pole @ atttwwt Note: For large forward path gain, a, can implement high pass function with high corner frequency Addition of an integrator in the feedback path zero @ DC + pole @ axw0intgThis technique used for offset cancellation in systems where the low frequency content is not important and thus disposableEECS 247 Lecture 8: Filters© 2010 H.K. Page 8 Hjw HjwLowpassHighpassw HjwwwQ<5Q>5• Bandpass filters two cases:1- Low Q or wideband (Q < 5) Combination of lowpass & highpass2- High Q or narrow-band (Q > 5) Direct implementationw Hjw+Bandpass FiltersBandpassBandpassEECS 247 Lecture 8: Filters© 2010 H.K. Page 9Narrow-Band Bandpass FiltersDirect Implementation• Narrow-band BP filters Design based on lowpass prototype• Same tables used for LPFs are also used for BPFsLowpass Freq. Mask Bandpass Freq. Maskccs s2 s1c B2 B1ssQsww EECS 247 Lecture 8: Filters© 2010 H.K. Page 10Lowpass to Bandpass TransformationS-plane ComparisonLowpass pole/zero (s-plane) Bandpass pole/zero (s-plane)From: Zverev, Handbook of filter synthesis, Wiley, 1967- p.156.PoleZeroxxxxxxEECS 247 Lecture 8: Filters© 2010 H.K. Page 11Lowpass to Bandpass Transformation TableFrom: Zverev, Handbook of filter synthesis, Wiley, 1967- p.157.''''1111rrrrrrrrC QCRRLQCRL QLCRQLwwwwCLC’LP BP BP ValuesLCL’Lowpass RLC filter structures & tables used to derive bandpass filters''C &L are normilzed LP valuesfilterQQEECS 247 Lecture 8: Filters© 2010 H.K. Page 12Lowpass to Bandpass TransformationExample: 3rdOrder LPF 6thOrder BPF• Each capacitor replaced by parallel L& C• Each inductor replaced by series L&CoVL2C2RsC1C3inVRLL1L3RsC1’C3’L2’inVRLoVLowpass BandpassEECS 247 Lecture 8: Filters© 2010 H.K. Page 13Lowpass to Bandpass TransformationExample: 3rdOrder LPF 6thOrder BPF'1101'012'02'220'3303'03111111C QCRRLQCCRQLRL QLC QCRRLQCwwwwwwoVL2C2RsC1C3inVRLL1L3Where:C1’, L2’ , C3’ Normalized lowpass valuesQ Bandpass filter quality factor w0 Filter center frequencyEECS 247 Lecture 8: Filters© 2010 H.K. Page 14Lowpass to Bandpass TransformationSignal FlowgraphoVL2C2RsC1C3inVRLL1L31- Voltages & currents named for all components2- Use KCL & KVL to derive state space description 3- To have BMFs in the integrator form Cap. voltage expressed as function of its current VC=f(IC)Ind. current as a function of its voltage IL=f(VL)4- Use state space description to draw SFG5- Convert all current nodes to voltageEECS 247 Lecture 8: Filters© 2010 H.K. Page 15Signal Flowgraph6thOrder BPF versus 3rdOrder LPF1*RRs*11sCR1*RRs*11sCR1*1RsL11*RRL*31sCR*3RsL*21sCR*2RsL1V1’V2V3’V1V2’VoutVinV3inV11VoV1111V1’V3’V2’*2RsL*RRLV2*31sCRLPFBPFEECS 247 Lecture 8: Filters© 2010 H.K. Page 16Signal Flowgraph6thOrder Bandpass Filter1*RRs*11sCR1*1RsL11*RRL*31sCR*3RsL*21sCR*2RsL1Note: each C & L in the original lowpass prototype replaced by a resonatorSubstituting the bandpass L1, C1,….. by their normalized lowpass equivalent from page 13The resulting SFG is:1V1’V2V3’V1V2’VoutVinV3EECS 247 Lecture 8: Filters© 2010 H.K. Page 17Signal Flowgraph6thOrder Bandpass Filter1*RRs01'QCsw1'10QCsw11*RRL'30QCsw'30QCsw20'QLsw02'QLsw1• Note the integrators different time constants• Ratio of time constants for two integrator in each resonator loop~ Q2 Typically, requires high component ratios Poor matching• Desirable to modify SFG so that all integrators have equal time constants for optimum matching.• To obtain equal integrator time constant use node
View Full Document
Unlocking...