Switched capacitor filter

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Switched capacitor filter

  1. 1. Switched Capacitor Filter (SC filters) By student : EE562 Minh Anh Nguyen
  2. 2. Outline <ul><li>Introduction </li></ul><ul><li>Basic building blocks </li></ul><ul><li>(OTAS, Capacitor,Switches and non-overlapping). </li></ul><ul><li>Basic operation and analysis </li></ul><ul><li>(resistor equivalence of switched capacitor filters and integrators). </li></ul><ul><li>Definition of switched-capacitor filters. </li></ul><ul><li>Basics circuit for Switched-capacitor filters </li></ul><ul><li>Disadvantage & advantage of switched-capacitor filters. </li></ul><ul><li>Compared switched-capacitor filter circuit with other circuit </li></ul><ul><li>Summary and reference of switched-capacitor filters </li></ul>
  3. 3. Introduction <ul><li>There are three main types filters, in integrated analog filters. </li></ul><ul><li>1. Switched capacitor filter (SC filter) </li></ul><ul><li>-resistor replaced by switch capacitor </li></ul><ul><li>-sample time but analog values </li></ul><ul><li>2. R-C filter </li></ul><ul><li>-“Standard” active filter RC and Opamp with feed back </li></ul><ul><li>-Resistor often implemented with MOS, so called MOSFET C filter </li></ul><ul><li>3.gm-C filter </li></ul><ul><li>-resistors replaced by trans-conductor used open loop </li></ul><ul><li>-two latter types are continuous time filter </li></ul>
  4. 4. Historical background <ul><li>Due to the difficulty in making fully integrated resistors the active RC filters were not able to fabrication in monolithic form on one silicon chip. </li></ul><ul><li>Switched capacitor filters characterized in the z domain were developed late 70s and earlier 80s. </li></ul><ul><li>The origin of SC principle was first report by Maxwell around 1873. </li></ul><ul><li>The first book fully dedicated to switches capacitor was published in 1948 by P.E.Allen and E.SanchezSinenico “Switches capacitor circuit” Van Nostrand Reinhold,NY,1984. </li></ul>
  5. 5. Basic building blocks <ul><li>The ideal operational amplifier is a voltage-controlled voltage source with: </li></ul><ul><li>Infinite gain and input impedance </li></ul><ul><li>Zero output impedance. </li></ul><ul><li>Vo=A(Vi) </li></ul>
  6. 6. Basic Building Block of OTAS <ul><li>Often realized as single-stage load compensated OTAs since the load is purely capacitive. </li></ul><ul><li>Low dc gain affect the accuracy of the transfer function </li></ul><ul><li>The unity-gain frequency should be at least five time higher than the clock frequency. </li></ul><ul><li>Dc offset can result in high output dc offset depending on the topology chosen. The techniques exist that can significantly reduce this offset and at the same time reduce 1/f noise. </li></ul><ul><li>Not so low output impedance </li></ul><ul><li>Still used as voltage amplifier </li></ul>
  7. 7. Opamps Vs. OTA
  8. 8. Building block of capacitors <ul><li>Double poly capacitors </li></ul><ul><li>A highly linear capacitance is usually constructed between two poly-silicon layers </li></ul><ul><li>Substantial parasitic with large bottom plate capacitor (20% of C1) </li></ul><ul><li>Metal-metal capacitors are used but have even large parasitic capacitances </li></ul>
  9. 9. Building block of switches <ul><li>MOSFET switches are good switches </li></ul><ul><li>Should have as high off resistance Roff as possible. </li></ul><ul><li>At T=300K, MOS switches have Roff on the order of giga ohms. The finite value is caused by finite leakage currents that is typically dominated by reverse biased diodes. </li></ul><ul><li>Should have as low on resistance Ron as possible. </li></ul><ul><li>Ron can be made arbitrarily small by increasing the width of the transistors. But parasitic capacitance and leakage current increase with increasing width. </li></ul><ul><li>MOS switches does not introduce any offset </li></ul><ul><li>BJT switches does introduce offset </li></ul>
  10. 10. MOS Switches <ul><li>Nonlinear capacitance on each side of the switch. </li></ul><ul><li>Charge injection effects </li></ul><ul><li>Capacitive coupling from the logic signal to each side of the switch. </li></ul>
  11. 11. Charge injection <ul><li>An additional charge, coming from the MOS channel when the switch is turn off, stored on the CL </li></ul><ul><li>Charge store in the channel when switch is on. </li></ul><ul><li>Direct coupling capacitance Cgd. (Mainly to overlap capacitance Cgdov). </li></ul><ul><li>When phase1 switches charge injection into Vi and Vo </li></ul>
  12. 12. Charge injection <ul><li>Input node vi is typical low impedance node </li></ul><ul><li>When phase1 switched high(off-on) charge injected into Vi and Vo node collected by input impedance (in this phase the output require follow the input voltage Vi) </li></ul><ul><li>When phase1 switched low(on-off) charge injected into Vi </li></ul>
  13. 13. Charge injection (Const.) <ul><li>For nMOS charge during the on state </li></ul><ul><li>Charge stored in the channel </li></ul><ul><li>Charge during the off state; </li></ul>
  14. 14. Non-overlapping clocks <ul><li>To guarantee that charge is not lost in SC circuits, non overlapping clocks are used. </li></ul><ul><li>Both clocks are never on at the same time. </li></ul><ul><li>Integer values occur at end of phase 1 </li></ul><ul><li>End of phase2 is ½ off integer value </li></ul>
  15. 15. Resistor equivalence to a switched capacitor <ul><li>The capacitor is the </li></ul><ul><li>“ switched capacitor” </li></ul><ul><li>Non-overlapping clocks </li></ul><ul><li>phase1 and phase2 </li></ul><ul><li>controlled M1and M2, </li></ul><ul><li>respectively. </li></ul><ul><li>Vi is the sample at </li></ul><ul><li>falling edge of phase1 </li></ul><ul><li>And sample frequency is f </li></ul>
  16. 16. Resistor equivalence to a switched capacitor (Const.) <ul><li>The charge transferred from V1 to V2 is </li></ul><ul><li>The average current flow from V1 to V2 is </li></ul><ul><li>With the current flow </li></ul><ul><li>through the switch </li></ul><ul><li>capacitor resistor </li></ul><ul><li>proportional to the </li></ul><ul><li>voltage across it, </li></ul><ul><li>the equivalent “switch </li></ul><ul><li>capacitor resistance is </li></ul>
  17. 17. Resistor equivalence to a switched capacitor (Const.)
  18. 18. Resistor equivalence example <ul><li>This equivalence is very large </li></ul><ul><li>Requires only 2 transistors, a clock and relatively small capacitance </li></ul><ul><li>In a CMOS process, large resistor would normally require a huge amount of silicon area </li></ul>
  19. 19. What is Switched capacitor filter? <ul><li>The switched capacitor filter is technique based on the realization that a capacitor switched between two circuit nodes at a sufficiently high rate is equivalent to a resistor connecting these two nodes. </li></ul><ul><li>Used a miller integrator circuit, replaces the input resistor by a ground capacitor together with two MOS transistors acting as switches. </li></ul><ul><li>The switches are driven by a non-overlapping two phase clock. </li></ul><ul><li>SC filters operate on the principle of transferring analog signal samples ( represented as charges on capacitors) from one storage element to another </li></ul>
  20. 20. Switched capacitor filter <ul><li>Let built an SC filter </li></ul><ul><li>We’ll start with a </li></ul><ul><li>simple miller integrate </li></ul><ul><li>circuit </li></ul><ul><li>Replaced the physical </li></ul><ul><li>resistor by an </li></ul><ul><li>equivalent SC resistor . </li></ul>
  21. 21. SC filter Wave form <ul><li>The typical Waveforms </li></ul>
  22. 22. Transfer function <ul><li>The basic idea to calculated the transfer function </li></ul>
  23. 23. RC active filters <ul><li>Calculated the transferred function for RC active filters </li></ul>
  24. 24. SC filters (non-inverting) <ul><li>During phase1(S1 on,S2 off) </li></ul><ul><li>C1 charge up to the current of vi </li></ul><ul><li>During phase2(S1 off, S2 on) </li></ul><ul><li>Discharge into C2 or A charge packet C1Vi is remove from C2 </li></ul>
  25. 25. SC filters <ul><li>Calculated the transferred function for SC filter </li></ul>
  26. 26. SC filters (inverting) <ul><li>Phase1:S1 on, S2 off </li></ul><ul><li>Vi is store in C1, S1 is driven by Vi, S2 is maintained at 0, by the virtual ground. </li></ul><ul><li>Phase2: S1 off, S2 on </li></ul><ul><li>Vi is disconnected, C1 is complete discharge for the next cycle. </li></ul>
  27. 27. SC filters (inverting) <ul><li>Calculated the transfer function </li></ul>
  28. 28. Gm-C filter <ul><li>An ideal transconductor is described by the following expression </li></ul>
  29. 29. First order low pass filter <ul><li>Calculated the transfer function </li></ul>
  30. 30. First order high pas filters <ul><li>Calculated the transfer function </li></ul>
  31. 31. Comparison <ul><li>This is the table compare the transfer function for some of the filter </li></ul>
  32. 32. SC filter Noise <ul><li>The resistance of switch M1 produce a noise voltage on C with variance kT/C </li></ul><ul><li>The corresponding noise charge is </li></ul><ul><li>This charge is sample when M1 is open </li></ul><ul><li>The resistance of switch M2 contribute to an uncorrelated noise charge C at the end of phase 2 </li></ul><ul><li>The mean square of charge transfer from v1 to v2 each sample period is </li></ul>
  33. 33. SC filters noise (const.) <ul><li>The mean square noise current M1 and M2 KT/C noise is </li></ul><ul><li>The noise spectrum are single sided by convention, the distributed between 0 and f/2.The spectra density noise is </li></ul><ul><li>The noise from an SC resistor is equal to the noise of physical resistor </li></ul>
  34. 34. SC resistor noise spectrum
  35. 35. Advantage <ul><li>Reduction of power consumption for filters IC </li></ul><ul><li>High integration density </li></ul><ul><li>Area(switches + capacitor) << area resistor </li></ul><ul><li>Switch capacitor integrator </li></ul><ul><li>R is replaced by C and 2 switched (MOS transistor) </li></ul>
  36. 36. Disadvantage <ul><li>Sample data effect (noise) </li></ul><ul><li>Need clock circuit and anti-aliasing filters </li></ul><ul><li>Not suited for high frequency </li></ul>
  37. 37. Why Switched-capacitors(SC) circuits? <ul><li>Resistors occupy inordently large amount of area in integrated circuits </li></ul><ul><li>AC resistors can be simulated by periodically switching a capacitor between slow varying voltages </li></ul><ul><li>Area(switches + capacitor)<< Area resistor </li></ul>
  38. 38. Application of SC filter <ul><li>Over sampled A/D and D/A converter </li></ul><ul><li>Analog front-end (CDs) </li></ul><ul><li>Stand alone filter (eg. National Semiconductor LMF100) </li></ul><ul><li>Replaced by ADC and DSP in many cases </li></ul>
  39. 39. Summary <ul><li>A miller integrator </li></ul><ul><li>Replaces the input resistor R by a ground capacitor C together with two MOS transistors acting as switches. </li></ul><ul><li>The switches are driven by a non-overlapping two phase clock </li></ul><ul><li>Pole and zero frequencies proportional to sample frequency and capacitor ratios </li></ul><ul><li>Bandwidth required less than the continuous time filter </li></ul><ul><li>“ analog” sample data filters </li></ul>
  40. 40. Reference <ul><li>http://www.ics.ee.nctu.edu.tw/~jtwu/publications/pdf/96isc-lvsc.pdf </li></ul><ul><li>Microelectronic circuit by Sedra/Smith </li></ul><ul><li>Switched Capicitor Filters: Theory, Analysis and Design </li></ul><ul><li>by Anandmohan , Concorde University Ramachandran , Concorde University and Swamy </li></ul><ul><li>Thank You </li></ul>

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