EE247 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 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 EECS 247 Lecture 8 Filters Continuous Time 2008 H K Page 1 Summary 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 reference signal feedthrough to the filter output Master VCO used in tuning loop Design of reliable stable VCO challenging Issue 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 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 line EECS 247 Lecture 8 Filters Continuous Time 2008 H K Page 2 RLC 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 LNormLP where Lr Rr r and Cr 1 Rr r L4 C4 C2 L2 Rs Vin C1 Rs Vin C3 Lowpass EECS 247 Lecture 8 L3 L1 Highpass Filters Continuous Time 2008 H K Page 3 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 Lecture 8 Vo s RC Vo Vin 1 s R C R Filters Continuous Time 2008 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 Lecture 8 VR 1 Vo 1 IR 2008 H K Page 5 Filters Continuous Time 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 Continuous Time 2008 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 s Vo a Vin 1 a s 1 s a ze ro D C a Vo 1 s a pole pole a oint g 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 ax 0intg This technique used for offset cancellation in systems where the low frequency content is not important and thus disposable EECS 247 Lecture 8 2008 H K Page 7 Filters Continuous Time Bandpass Filters Bandpass filters two cases 1 Low Q or wideband Q 5 Combination of lowpass highpass Bandpass Highpass Lowpass H j H j H j H j 2 High Q or narrow band Q 5 Direct implementation EECS 247 Lecture 8 Filters Continuous Time Q 5 Bandpass Q 5 2008 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 s Q c s c EECS 247 Lecture 8 s c Filters Continuous Time s2 s1 B2 B1 2008 H K Page 9 Lowpass to Bandpass Transformation Lowpass pole zero s plane Bandpass pole zero s plane Pole Zero From Zverev Handbook of filter synthesis Wiley 1967 p 156 EECS 247 Lecture 8 Filters Continuous Time 2008 H K Page 10 Lowpass to Bandpass Transformation Table Lowpass RLC filter structures tables used to derive bandpass filters LP BP BP Values 1 Rr r C QC C C L L 1 QC Rr r Q Q filter L L QL C L From Zverev Handbook of filter synthesis Wiley 1967 p 157 C 1 QC Rr r 1 Rr r C L are normilzed LP values EECS 247 Lecture 8 2008 H K Page 11 Filters Continuous Time 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 L3 Vo C3 RL Each capacitor replaced by parallel L C Each inductor replaced by series L C EECS 247 Lecture 8 Filters Continuous Time 2008 H K Page 12 Lowpass to Bandpass Transformation Example 3rd Order LPF 6th Order BPF C1 QC1 1 R 0 L1 1 R QC1 0 C2 1 1 QL 2 R 0 L2 QL 2 C3 QC3 L3 C2 L2 Rs Vin C1 L1 L3 Vo C3 RL R 0 1 R 0 Where C1 L2 C3 Normalized lowpass values Q Bandpass filter quality factor 0 Filter center frequency 1 R QC3 0 EECS 247 Lecture 8 2008 H K Page 13 Filters Continuous Time Lowpass to Bandpass Transformation Signal Flowgraph L2 C2 Rs Vin C1 L1 L3 Vo C3 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 Continuous Time 2008 H K Page 14 Signal Flowgraph Order BPF versus 3rd Order LPF 6th 1 V1 Vin R Rs R 1 s L1 sC1R V1 s L2 1 R Rs sC1R s L2 EECS 247 Lecture 8 sC3R 1 R s L3 R RL Vo 1 sC3R 1 V2 LPF Vout V3 1 R 1 1 1 V2 1 V1 1 sC2 R V2 1 V3 1 R 1 V1 Vin BPF V2 1 R RL V3 2008 H K Page 15 Filters Continuous Time Signal Flowgraph 6th Order Bandpass Filter Vin R Rs 1 V1 R s L1 V1 1 1 sC1R 1 V2 R s L2 V3 1 1 sC2 R V2 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 Continuous Time 2008 H K Page 16 6th Vin R Rs Signal Flowgraph Order Bandpass Filter 1 V1 0 V2 1 Q C1 0 s Q L 2 1 V1 0 s Q C1 s V3 1 …
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