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Mixed-Signal VLSI Design Course Code: EE719 Department: Electrical Engineering Lecture 16: February 08, 2018 Instructor Name: M. Shojaei Baghini E-Mail ID: mshojaei@ee.iitb.ac.in 1 2 2 Module 22 Sampling Approximations s to Z Domain

  1. Mixed-Signal VLSI Design Course Code: EE719 Department: Electrical Engineering Lecture 16: February 08, 2018 Instructor Name: M. Shojaei Baghini E-Mail ID: mshojaei@ee.iitb.ac.in 1

  2. 2 2 Module 22 Sampling Approximations – s to Z Domain Reference Chapter: Switched Capacitor Circuits Analog integrated circuit design by T. Chan Carusone David A. Johns and Ken Martin, John Wiley & Sons, 2012. IIT-Bombay Lecture 16 M. Shojaei Baghini

  3. 3 3 Resistor Emulation using Switched Capacitors IIT-Bombay Lecture 16 M. Shojaei Baghini

  4. 4 4 Resistor Emulation using Switched Capacitors IIT-Bombay Lecture 16 M. Shojaei Baghini

  5. 5 5 Analysis of FE Approximation Forward Euler Approximation IIT-Bombay Lecture 16 M. Shojaei Baghini

  6. 6 6 Analysis of FE Approximation Forward Euler Approximation IIT-Bombay Lecture 16 M. Shojaei Baghini

  7. 7 7 Forward Euler Approximation Switched Capacitor Integrator - Analysis IIT-Bombay Lecture 16 M. Shojaei Baghini

  8. 8 8 Forward Euler Approximation Switched Capacitor Integrator – Analysis C C C - - - T T 1 1 1 ( ) C C C W = = » j T H e 2 2 2 ( ) 2 W 2 W W T j T W - - W - - j ... j T ... 2 2 ( ) W << T 1 T = R eq C 1 IIT-Bombay Lecture 16 M. Shojaei Baghini

  9. 9 9 Forward Euler Approximation Switched Capacitor Integrator – Analysis C C C - - - T T 1 1 1 ( ) C C C W = = » j T H e 2 2 2 ( ) 2 W 2 W W T j T W - - W - - j ... j T ... 2 2 ( ) W << T 1 T = R eq C 1 IIT-Bombay Lecture 16 M. Shojaei Baghini

  10. 10 10 Various Sampling Approximations Forward Euler Approximation Backward Euler Approximation Bilinear Approximation ⇨ IIT-Bombay Lecture 16 M. Shojaei Baghini

  11. 11 11 Effect of FE Approximation on the Discrete Time Frequency Approximation Image of j W w d axis in Z plane 1 -1 0 1 s d W =0 Þ z=1 Þ w d =0 -1 IIT-Bombay Lecture 16 M. Shojaei Baghini

  12. 12 12 Effect of FE Approximation on the Discrete Time Frequency Approximation l In FE approximation poles may be mapped to poles outside unit circle and hence discrete-time circuit becomes unstable. l FE approximation brings poles close to unit circle circumference. Peaking will occur at passband edge. l No zero on unit circle (except possibly at w d =0) and hence no infinite loss in stopband. IIT-Bombay Lecture 16 M. Shojaei Baghini

  13. 13 13 Effect of BE Approximation on the Discrete Time Frequency Approximation w d Z plane l High-Q poles of 1 continuous-time filter appear with lower Q. l BE Approximation s d -1 0 ½ 1 results in rounding effects in the passband Stability is edge. -1 preserved. Image of j W axis in Z plane IIT-Bombay Lecture 16 M. Shojaei Baghini

  14. 14 14 Effect of Bilinear Approximation on the Discrete Time Frequency Approximation w d 1 Z plane -1 0 1 s d -1 IIT-Bombay Lecture 16 M. Shojaei Baghini

  15. 15 15 End of Lecture 16 IIT-Bombay Lecture 16 M. Shojaei Baghini

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