EE247 Lecture 8 Continuous time filter design considerations Monolithic highpass filters Active bandpass filter design Lowpass to bandpass transformation Example 6th order 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 1 Summary 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 response EECS 247 Lecture 8 Filters 2010 H K Page 2 RLC 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 LNormLP where Lr Rr wr and Cr 1 Rrwr L4 C4 C2 L2 Rs Vin C1 Rs Vin C3 Lowpass EECS 247 L3 L1 Highpass 2010 H K Page 3 Lecture 8 Filters Integrator Based High Pass Filters 1st Order Conversion of simple high pass RC filter to integrator based type by using signal flowgraph technique C Vin EECS 247 Vo s RC Vo Vin 1 s R C R Lecture 8 Filters 2010 H K Page 4 1st Order Integrator Based High Pass Filter Signal Flowgraph C I V o C IR VR Vin VC 1 VC IC sC Vo VR 1 I R VR R IC I R VC VR R Vin SFG Vin 1 VC 1 1 1 R sC IC EECS 247 VR 1 Vo 1 IR 2010 H K Page 5 Lecture 8 Filters 1st Order Integrator Based High Pass Filter SGF SGF C VC Vin Vo 1 Vin R VR 1 Vo 1 sC R Vin Vo Note Addition of an integrator in the feedback path High pass frequency shaping EECS 247 Lecture 8 Filters 2010 H K Page 6 Addition of Integrator in Feedback Path Let us assume flat gain in forward path a Effect of addition of an integrator in the feedback path Vin Vo a Vin 1 af st Vo a Vin 1 a s t 1 s t a ze ro DC a Vo 1 st a pole w pole a woint g t 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 axw0intg This technique used for offset cancellation in systems where the low frequency content is not important and thus disposable EECS 247 2010 H K Page 7 Lecture 8 Filters Bandpass Filters Bandpass filters two cases 1 Low Q or wideband Q 5 Combination of lowpass highpass Bandpass Highpass Lowpass H jw H jw H jw Q 5 w w w H jw 2 High Q or narrow band Q 5 Direct implementation EECS 247 Lecture 8 Filters Bandpass Q 5 w 2010 H K Page 8 Narrow Band Bandpass Filters Direct Implementation Narrow band BP filters Design based on lowpass prototype Same tables used for LPFs are also used for BPFs Lowpass Freq Mask Bandpass Freq Mask s wc s Q s wc EECS 247 s s2 s1 c B2 B1 2010 H K Page 9 Lecture 8 Filters Lowpass to Bandpass Transformation S plane Comparison Lowpass pole zero s plane Bandpass pole zero s plane x x x x x Pole Zero x From Zverev Handbook of filter synthesis Wiley 1967 p 156 EECS 247 Lecture 8 Filters 2010 H K Page 10 Lowpass to Bandpass Transformation Table Lowpass RLC filter structures tables used to derive bandpass filters LP C BP BP Values C C QC L L 1 Rrwr 1 R r QC wr Q Q filter L L QL C L From Zverev Handbook of filter synthesis Wiley 1967 p 157 C Rr wr 1 1 QL Rrwr C L are normilzed LP values EECS 247 2010 H K Page 11 Lecture 8 Filters Lowpass to Bandpass Transformation Example 3rd Order LPF 6th Order BPF Lowpass Bandpass L2 Vo L2 Rs Vin C1 C2 Rs C3 RL Vin C1 L1 Vo C3 L3 RL Each capacitor replaced by parallel L C Each inductor replaced by series L C EECS 247 Lecture 8 Filters 2010 H K Page 12 Lowpass to Bandpass Transformation Example 3rd Order LPF 6th Order BPF C1 QC1 L1 1 Rw0 Rs Vin 1 1 C2 QL2 Rw0 L2 QL 2 C3 QC3 L3 C2 L2 1 R QC1 w0 C1 Vo C3 L1 RL L3 R w0 1 Rw0 Where C1 L2 C3 Normalized lowpass values Q Bandpass filter quality factor w0 Filter center frequency 1 R QC3 w0 EECS 247 2010 H K Page 13 Lecture 8 Filters Lowpass to Bandpass Transformation Signal Flowgraph L2 C2 Rs Vin C1 L1 Vo C3 L3 RL 1 Voltages currents named for all components 2 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 SFG 5 Convert all current nodes to voltage EECS 247 Lecture 8 Filters 2010 H K Page 14 Signal Flowgraph 6th Order BPF versus 3rd Order LPF 1 V1 Vin R Rs R 1 s L1 sC1R V1 1 sC1R s L2 1 1 R 1 s L1 sC1R V1 Vout sC3R s L3 R RL V3 Vo 1 sC3R V2 LPF 1 R RL V3 2010 H K Page 15 Signal Flowgraph Order Bandpass Filter 1 V1 1 R Lecture 8 Filters 6th R Rs 1 V2 R EECS 247 Vin 1 1 V2 1 V1 V3 1 sC2R s L2 1 R Rs 1 R 1 V1 Vin BPF V2 1 R 1 1 V2 1 sC2R s L2 V2 V3 1 R s L3 1 1 sC3R Vout R RL V3 Note each C L in the original lowpass prototype replaced by a resonator Substituting the bandpass L1 C1 by their normalized lowpass equivalent from page 13 The resulting SFG is EECS 247 Lecture 8 Filters 2010 H K Page 16 Signal Flowgraph 6th Order Bandpass Filter Vin R Rs 1 V1 w0 Q C1w0 w0 s Q C1 s s Q L 2 1 V1 1 V2 1 V3 Q C3w0 w0 s Q C3 Q L 2w0 V2 1 s Vout R RL s V3 1 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 scaling EECS 247 Signal Flowgraph Order Bandpass Filter 6th 1 Vin R 1 Rs QC1 2010 H K Page 17 Lecture 8 Filters 1 V1 w 0 s QL 2 V2 QL2 w0 s w0 V1 QC1 …
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