EE247 Lecture 4 Active ladder type filters For simplicity will start with all pole ladder type filters Convert to integrator based form example shown Then will attend to high order ladder type filters incorporating zeros Implement the same 7th order elliptic filter in the form of ladder RLC with zeros Find level of sensitivity to component mismatch Compare with cascade of biquads Convert to integrator based form utilizing SFG techniques Effect of integrator non Idealities on filter frequency characteristics EECS 247 Lecture 4 Active Filters 2010 H K Page 1 Summary Lecture 3 Active Filters Active biquads Integrator based filters Signal flowgraph concept First order integrator based filter Second order integrator based filter biquads High order high Q filters Cascaded biquads first order filters Cascaded biquad sensitivity to component mismatch Ladder type filters EECS 247 Lecture 4 Active Filters 2010 H K Page 2 RLC Ladder Filters Example 5th Order Lowpass Filter Vo Vin L4 L2 Rs C1 C5 C3 RL Made of resistors inductors and capacitors Doubly terminated or singly terminated with or w o RL Doubly terminated LC ladder filters Lowest sensitivity to component mismatch EECS 247 Lecture 4 Active Filters 2010 H K Page 3 LC Ladder Filters Vo Rs Vin L4 L2 C1 C3 C5 RL First step in the design process is to find values for Ls and Cs based on specifications Filter graphs tables found in A Zverev Handbook of filter synthesis Wiley 1967 A B Williams and F J Taylor Electronic filter design 3rd edition McGrawHill 1995 CAD tools Matlab Agilent ADS includes Filter package does the job of the tables Spice EECS 247 Lecture 4 Active Filters 2010 H K Page 4 LC Ladder Filter Design Example Design a LPF with maximally flat passband f 3dB 10MHz fstop 20MHz Rs 27dB fstop fstop f 3dB 2 Rs 27dB 3dB Minimum Filter Order c5th order Butterworth EECS 247 Stopband Attenuation Find minimum filter order Here standard graphs from filter books are used Passband Attenuation Maximally flat passband Butterworth 30dB 1 2 Normalized w From Williams and Taylor p 2 37 Lecture 4 Active Filters 2010 H K Page 5 LC Ladder Filter Design Example Find values for L C from Table Note L C values normalized to w 3dB 1 Denormalization Multiply all LNorm CNorm by Lr R w 3dB Cr 1 RXw 3dB R is the value of the source and termination resistor choose both 1W for now Then L Lr xLNorm C Cr xCNorm EECS 247 Lecture 4 Active Filters From Williams and Taylor p 11 3 2010 H K Page 6 LC Ladder Filter Design Example Find values for L C from Table Normalized values C1Norm C5Norm 0 618 C3Norm 2 0 L2Norm L4Norm 1 618 Denormalization Since w 3dB 2px10MHz Lr R w 3dB 15 9 nH Cr 1 RXw 3dB 15 9 nF R 1 cC1 C5 9 836nF C3 31 83nF cL2 L4 25 75nH EECS 247 From Williams and Taylor p 11 3 Lecture 4 Active Filters Example 2010 H K Page 7 Last Lecture Order Butterworth Filter 5th L4 25 75nH L2 25 75nH Vo Rs 1W Vin C3 31 83nF C1 9 836nF RL 1W C5 9 836nF SPICE simulation Results 0 5 10 fstop 20MHz Rs 27dB Used filter tables to obtain Ls Cs Magnitude dB Specifications f 3dB 10MHz 20 30dB 6 dB passband attenuation due to double termination 30 40 50 0 10 20 30 Frequency MHz EECS 247 Lecture 4 Active Filters 2010 H K Page 8 Low Pass RLC Ladder Filter Conversion to Integrator Based Active Filter V3 V1 V2 Rs I 1 Vin I2 L2 V5 V4 I3 L4 C1 V6 Vo I5 C5 C3 I6 I4 RL I7 To convert RLC ladder prototype to integrator based filer Use Signal Flowgraph technique Name currents and voltages for all components Use KCL KVL to derive equations Make sure reactive elements expressed as 1 s term V C f I I L f V Use state space description to derive the SFG Modify simply the SFG for implementation with integrators e g convert all current nodes to voltage EECS 247 Lecture 4 Active Filters 2010 H K Page 9 Low Pass RLC Ladder Filter Conversion to Integrator Based Active Filter 1 V3 sC V1 V2 Rs I 1 Vin I2 L2 V5 V4 I3 C1 L4 V6 Vo I5 C5 C3 I6 I4 RL I7 Use KCL KVL to derive equations I V1 Vin V2 V2 2 sC1 I V4 4 V5 V4 V6 sC3 EECS 247 V I1 1 Rs I 2 I1 I 3 I4 I3 I5 I5 V5 V3 V2 V4 V6 I3 sL4 Lecture 4 Active Filters I6 sC5 Vo V6 V3 sL2 I 6 I 5 I7 V I7 6 RL 2010 H K Page 10 Low Pass RLC Ladder Filter Signal Flowgraph I V1 Vin V2 V2 2 sC1 I V4 4 V5 V4 V6 sC3 Vin V I1 1 Rs I 2 I1 I 3 I4 I3 I5 I5 1 1 V1 V2 1 Rs 1 I1 1 V5 V3 V2 V4 1 Vo V6 V3 I3 I 6 I 5 I7 sL4 V3 I6 sC5 V6 sL2 V4 1 V I7 6 RL 1 V5 V6 1 1 1 1 1 1 sC1 s L2 sC3 s L4 sC5 1 I2 EECS 247 1 I3 1 I4 SFG 1 RL I6 1 1 I5 Lecture 4 Active Filters Vo I7 2010 H K Page 11 Low Pass RLC Ladder Filter Normalize 1 Vin 1 V1 1 V2 1 Rs Vin I1 1 1 V1 1 EECS 247 sC V3 1 1 1 1 1 s L2 sC3 1 I2 V2 1 V2 1 I3 V3 sC1R 1 V4 sC1 1 R Rs V1 1 1 V3 1 I4 1 V4 Lecture 4 Active Filters s L4 1 V5 1 R sC3R s L2 1 1 1 I6 1 V6 1 sC5 R 1 Vo 1 RL 1 s L4 V5 1 sC5 I5 1 V6 1 1 V4 R 1 V5 V6 1 I7 Vo R RL V7 2010 H K Page 12 Low Pass RLC Ladder Filter Synthesize 1 V2 1 V3 1 R Rs 1 V3 V2 V2 Vin R Rs sC3R 1 V4 1 st 3 1 1 V6 1 R R L V5 V3 EECS 247 st 5 V7 Vo 1 st 4 R RL sC5 R s L4 1 V5 Vo V6 1 st 2 1 1 V4 1 s1t 1 1 V6 R 1 s L2 1 V5 1 R sC1R 1 V4 V1 1 1 V1 Vin Lecture 4 Active Filters 2010 H K Page 13 Low Pass RLC Ladder Filter Integrator Based Implementation 1 1 1 s1t 1 V6 V4 1 1 st 2 st 3 st 4 V3 t 1 C1 R L t 2 2 C2 R R Vo sC V2 Vin R Rs R R 1 st 5 L V5 t 3 C3 R L4 t4 C4 R R t 5 C5 R Main building block Integrator Let us start to build the filter with RC Opamp type integrator EECS 247 Lecture 4 Active Filters 2010 H K Page 14 Opamp …
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