EECS 247 Lecture 8: Filters: Continuous-Time© 2008 H.K. Page 1EE247 Lecture 8• Summary of various continuous-time filter frequency tuning techniques• 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 topologiesEECS 247 Lecture 8: Filters: Continuous-Time© 2008 H.K. Page 2Summary: Continuous-Time Filter Frequency Tuning•Trimming Expensive & does not account for temperature and supply etc… variations• Automatic frequency tuning– Continuous tuning Master VCF used in tuning loop, same tuning signal used to tune the slave (main) filter– Tuning quite accurate– Issue Æ reference signal feedthrough to the filter output Master VCO used in tuning loop– Design of reliable & stable VCO challenging– Issue Æ 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 Æ less feedthrough issues DC locking of a replica of the integrator to an external resistor– DC offset issues & does not account for integrating capacitor variations– Periodic digitally assisted tuning– Requires digital capability + minimal additional hardware– Advantage of no reference signal feedthrough since tuning performed off-lineEECS 247 Lecture 8: Filters: Continuous-Time© 2008 H.K. Page 3RLC Highpass Filters• Any RLC lowpass 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/ωr and Cr=1/(Rrωr)RsC1C3L2inVRsL1L3C2inVC4L4LowpassHighpassEECS 247 Lecture 8: Filters: Continuous-Time© 2008 H.K. Page 4Integrator Based High-Pass Filters1st Order• Conversion of simple high-pass RC filter to integrator-based type by using signal flowgraph techniqueinsCVRosCV1R=+oVRCinVEECS 247 Lecture 8: Filters: Continuous-Time© 2008 H.K. Page 51stOrder Integrator Based High-Pass FilterSignal FlowgraphoVRCinV+ VC -+VR-ICIRVVVRinC1VICCsCVVoR1IVRRRIICR=−=×==×=11R1sCRICICVinV1−1SFGoV1VREECS 247 Lecture 8: Filters: Continuous-Time© 2008 H.K. Page 61stOrder Integrator Based High-Pass FilterSGF1sCR−oVinV11oVRCinVoVinV∫-SGFNote: Addition of an integrator in the feedback path Æ High pass frequency shaping+++ VC-+ VR-EECS 247 Lecture 8: Filters: Continuous-Time© 2008 H.K. Page 7Addition of Integrator in Feedback PathoVinV∫-a1/sτLet us assume flat gain in forward path (a)Effect of addition of an integrator in the feedback path:++ininintgpole oVaoV1afsVaossV1a/ 1 /aazero@ DC & pole @ aτττωωτ=+==++→=−=−×Note: For large forward path gain, a, can implement high pass function with high corner frequency Addition of an integrator in the feedback path Æ zero @ DC + pole @ axω0intgThis technique used for offset cancellation in systems where the low frequency content is not important and thus disposableEECS 247 Lecture 8: Filters: Continuous-Time© 2008 H.K. Page 8()Hjω()HjωLowpassHighpassω()HjωωωQ<5Q>5• Bandpass filters Æ two cases:1- Low Q or wideband (Q < 5) Æ Combination of lowpass & highpass2- High Q or narrow-band (Q > 5)Æ Direct implementationω()Hjω+Bandpass FiltersBandpassBandpassEECS 247 Lecture 8: Filters: Continuous-Time© 2008 H.K. Page 9Narrow-Band Bandpass FiltersDirect Implementation• Narrow-band BP filters Æ Design based on lowpass prototype• Same tables used for LPFs are also used for BPFsLowpass Freq. Mask Bandpass Freq. Maskccss2 s1cB2B1ssQsωωΩΩ−ΩΩΩ−Ω⎡⎤×+⎢⎥⎣⎦⇒⇒EECS 247 Lecture 8: Filters: Continuous-Time© 2008 H.K. Page 10Lowpass 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 8: Filters: Continuous-Time© 2008 H.K. Page 11Lowpass to Bandpass Transformation TableFrom: Zverev, Handbook of filter synthesis, Wiley, 1967- p.157.''''1111rrrrrrrrCQCRRLQCRLQLCRQCωωωω=×=×=×=×CLC’LP BP BP ValuesLCL’Lowpass RLC filter structures & tables used to derive bandpass filters''C &L are normilzed LP valuesfilterQQ=EECS 247 Lecture 8: Filters: Continuous-Time© 2008 H.K. Page 12Lowpass to Bandpass TransformationExample: 3rdOrder LPF Æ 6thOrder BPF• Each capacitor replaced by parallel L& C• Each inductor replaced by series L&CoVL2C2RsC1C3inVRLL1L3RsC1’C3’L2’inVRLoVLowpass BandpassEECS 247 Lecture 8: Filters: Continuous-Time© 2008 H.K. Page 13Lowpass to Bandpass TransformationExample: 3rdOrder LPF Æ 6thOrder BPF'1101'012'02'220'3303'03111111CQCRRLQCCRQLRLQLCQCRRLQCωωωωωω=×=×=×=×=×=×oVL2C2RsC1C3inVRLL1L3Where:C1’, L2’, C3’Æ Normalized lowpass valuesQ Æ Bandpass filter quality factor ω0Æ Filter center frequencyEECS 247 Lecture 8: Filters: Continuous-Time© 2008 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: Continuous-Time© 2008 H.K. Page 15Signal Flowgraph6thOrder BPF versus 3rdOrder LPF1−*RRs−*11sCR1*RRs−*11sCR1−*1RsL−1−1*RRL−*31sCR*3RsL−*21sCR−*2RsL1V1’V2V3’V1V2’VoutVinV3inV11VoV1−11−1V1’V3’V2’*2RsL*RRL−V2*31sCRLPFBPFEECS 247 Lecture 8: Filters: Continuous-Time© 2008 H.K. Page 16Signal Flowgraph6thOrder Bandpass
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