Mixed-Signal VLSI Design Course Code: EE719 Department: Electrical - - PowerPoint PPT Presentation

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Mixed-Signal VLSI Design Course Code: EE719 Department: Electrical - - PowerPoint PPT Presentation

Jan 10, 2024 140 likes •298 views

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

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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

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IIT-Bombay Lecture 16 M. Shojaei Baghini

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.

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IIT-Bombay Lecture 16 M. Shojaei Baghini

Resistor Emulation using Switched Capacitors

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IIT-Bombay Lecture 16 M. Shojaei Baghini

Resistor Emulation using Switched Capacitors

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IIT-Bombay Lecture 16 M. Shojaei Baghini

Analysis of FE Approximation

Forward Euler Approximation

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IIT-Bombay Lecture 16 M. Shojaei Baghini

Analysis of FE Approximation

Forward Euler Approximation

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IIT-Bombay Lecture 16 M. Shojaei Baghini

Forward Euler Approximation

Switched Capacitor Integrator - Analysis

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IIT-Bombay Lecture 16 M. Shojaei Baghini

Forward Euler Approximation

Switched Capacitor Integrator – Analysis

( )

( ) ( )

1 2 1 2 2 1 2 2 1

1 ... 2 ... 2 C T R T j T C C T j T C C T T j C C e H

eq T j

= << W W

  • »
  • W
  • W
  • =
  • W
  • W
  • =

W

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IIT-Bombay Lecture 16 M. Shojaei Baghini

Forward Euler Approximation

Switched Capacitor Integrator – Analysis

( )

( ) ( )

1 2 1 2 2 1 2 2 1

1 ... 2 ... 2 C T R T j T C C T j T C C T T j C C e H

eq T j

= << W W

  • »
  • W
  • W
  • =
  • W
  • W
  • =

W

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IIT-Bombay Lecture 16 M. Shojaei Baghini

Various Sampling Approximations

Forward Euler Approximation Backward Euler Approximation Bilinear Approximation

⇨

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IIT-Bombay Lecture 16 M. Shojaei Baghini

Effect of FE Approximation on the Discrete Time Frequency Approximation

W=0 Þ z=1 Þ wd=0

  • 1 0 1

sd wd

1

  • 1

Image of jW axis in Z plane

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IIT-Bombay Lecture 16 M. Shojaei Baghini

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

wd=0) and hence no infinite loss in stopband.

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IIT-Bombay Lecture 16 M. Shojaei Baghini

sd wd

l High-Q poles of

continuous-time filter appear with lower Q.

l BE Approximation

results in rounding effects in the passband edge.

  • 1 0 ½ 1

Z plane

1

  • 1

Stability is preserved.

Image of jW axis in Z plane

Effect of BE Approximation on the Discrete Time Frequency Approximation

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IIT-Bombay Lecture 16 M. Shojaei Baghini

Effect of Bilinear Approximation on the Discrete Time Frequency Approximation

sd wd

Z plane

1

  • 1
  • 1 0 1
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IIT-Bombay Lecture 16 M. Shojaei Baghini

End of Lecture 16