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

Mixed-Signal VLSI Design Course Code: EE719 Department: Electrical Engineering Lecture 2: January 14, 2019 Instructor Name: M. Shojaei Baghini E-Mail ID: mshojaei@ee.iitb.ac.in 1

2 2 Module 1 Sampling Concept and Bandwidth Limitation IIT-Bombay Lecture 2 M. Shojaei Baghini

3 3 Reference • Sections 1 to 4, Chapter: Discrete-Time Signals Analog Integrated Circuit Design , 2nd edition, 2012 onwards T. C. Carusone, D. A. Johns and K. W. Martin • Data Conversion Handbook, Analog Devices, Chapter 2, 2005 IIT-Bombay Lecture 2 M. Shojaei Baghini

4 4 Bridge Between Analog and Digital Domains A/D Conditioning Conversion Analog Digital Domain Domain Smoothing D/A and Conversion Equalization IIT-Bombay Lecture 2 M. Shojaei Baghini

5 5 Basic Terms Signal Domain Analog Domain • Quantized Domain • Digital Domain • Time Domain Continuous-time Domain • Discrete-time Domain • Analog: Continuous time and continuous signal value Discrete time: Discrete time and continuous signal value Digital: Discrete time and quantized signal value but represented with bits Notice: In some literatures “amplitude” is used but it’s better to use “value”. IIT-Bombay Lecture 2 M. Shojaei Baghini

6 6 Discrete in Time and Discrete in Signal Value Source: Boris Murmann, 2013 IIT-Bombay Lecture 2 M. Shojaei Baghini

7 7 Implications of Discrete in Time and Discrete in Signal Value Discrete-time observation implies to take samples of the • signal ideally at discrete sampling times and practically discrete time intervals. ⟹ Limitation on the signal bandwidth |X (ω)| ω 0 -W b W b IIT-Bombay Lecture 2 M. Shojaei Baghini

8 8 How much is the bandwidth limitation? Nyquist Classic Theorem 1924 (It can be violated in some cases without loosing the main information) f s Source: Data Conversion Handbook, Analog Devices, Chapter 1 2005 IIT-Bombay Lecture 2 M. Shojaei Baghini

9 9 Ideal Uniform Sampling: Multiplication of Input Signal by Train of Uniform Impulses X(t) X s (t) ´ Ideal s(t) s(t) …… …… T )*-, )*-, ! " # = ! # ⊗ 1 " = 1 ' ( . # − 0# ' ( ! # − 0# " )*+, )*+, IIT-Bombay Lecture 2 M. Shojaei Baghini

10 10 Ideal Sampling (Impulse Sampling) Repetition in Frequency Domain Bandwidth Constraint Repetition of W b information in frequency domain -2/T -1/T *+.- *+.- " # $ = " $ ⊗ 1 # = 1 ( ) / $ − 1$ ( ) " $ − 1$ # *+,- *+,- f s - W b > W b ⇒ f s > 2W b (Nyquist Rate: Avoiding Aliasing) IIT-Bombay Lecture 2 M. Shojaei Baghini

11 11 Repetition of Information in Frequency Bands |X (ω)| ω N 0 2 ! 2 ! W bN /ω s - 2 ! W bN /ω s • What are the conditions at which sampling rate of below Nyquist rate may be used? What is the real meaning of BW in this context? • Does Nyquist rate sampling result in perfect signal retrieve? IIT-Bombay Lecture 2 M. Shojaei Baghini

12 12 Example: Sampling without Aliasing Source: Boris Murmann, 2013 IIT-Bombay Lecture 2 M. Shojaei Baghini

13 13 Example 1: Sampling with Aliasing Source: Boris Murmann, 2013 IIT-Bombay Lecture 2 M. Shojaei Baghini

14 14 Example 2: Sampling with Aliasing Source: Boris Murmann, 2013 IIT-Bombay Lecture 2 M. Shojaei Baghini

15 15 Aliasing Examples Images (aliases) at |±mf s ±f a |, m =1,2,3,… Source: Data Conversion Handbook, Analog Devices, Chapter 2, 2005 IIT-Bombay Lecture 2 M. Shojaei Baghini

16 16 Aliasing Examples Source: Boris Murmann, 2013 • Folded back to the low frequency (same as down conversion) • Anti-aliasing filter is required to limit the bandwidth. IIT-Bombay Lecture 2 M. Shojaei Baghini

17 17 End of Lecture 2 IIT-Bombay Lecture 2 M. Shojaei Baghini

Mixed-Signal VLSI Design Course Code: EE719 Department: Electrical Engineering Lecture 3: January 16, 2020 Instructor Name: M. Shojaei Baghini E-Mail ID: mshojaei@ee.iitb.ac.in 1

2 2 Module 2 Z-Transform, Discrete Fourier Transform and Non-ideal Sampling IIT-Bombay Lecture 3 M. Shojaei Baghini

3 3 References • Sections 1 to 4, Chapter: Discrete-Time Signals Analog Integrated Circuit Design, 2nd edition, 2012 onwards T. C. Carusone, D. A. Johns and K. W. Martin IIT-Bombay Lecture 3 M. Shojaei Baghini

4 4 Definition of Z-Transform Moving from s Domain to z Domain s + W = s + W = = Ts T j T s j , z e e \ w = W T s < Þ < 0 | z | 1 IIT-Bombay Lecture 3 M. Shojaei Baghini

5 5 Box or Rectangular Pulse Function ! " → $ % X(t) → ! −% '()* %+)*"(,)? IIT-Bombay Lecture 3 M. Shojaei Baghini

6 6 Ideal Sampling Fourier Transform of Sampled Signal ω = Ω × T IIT-Bombay Lecture 3 M. Shojaei Baghini

7 7 A Typical Simple T&H Circuit T With ideal switch Zero order hold 1st order hold? What happens to the signal spectrum due to the T&H operation as compared to the impulse sampling? IIT-Bombay Lecture 3 M. Shojaei Baghini

8 8 Non-ideal Sampling (S & H) but with Ideal Switch! • Track & Hold with T track << T or variation of the input signal during tracking is negligible. p(t) is a pulse with unit p (t) 1 amplitude and width of T . P(f) is a Sinc function . - p W = ´ ´ j fT P ( ) T e Sinc ( fT ) t 0 T IIT-Bombay Lecture 3 M. Shojaei Baghini

9 9 Non-ideal Sampling - (S & H) but with Ideal Switch! T Zero order hold w = WT ¥ æ ö ¥ ¥ ¥ å å ò ò - w - w ç - ÷ = - j t j t x ( nT ) p ( t nT ) e dt x ( nT ) p ( t nT ) e dt - ¥ è ø = = n 0 n 0 - ¥ æ ö ¥ ¥ å å = w - w = - w w = w ´ w jn ç jn ÷ x ( nT ) P ( ) e x ( nT ) e P ( ) X ( ) P ( ) è ø = = n 0 n 0 = + ¥ 1 m å = ´ ´ - T Sinc ( fT ) X ( f mf ) s T = -¥ m IIT-Bombay Lecture 3 M. Shojaei Baghini

10 10 Non-ideal Sampling (S & H) but with Ideal Switch! Track & Hold with T track << T Zero order hold w = WT IIT-Bombay Lecture 3 M. Shojaei Baghini

11 11 Example by Illustration Source: Boris Murmann, 2013 IIT-Bombay Lecture 3 M. Shojaei Baghini

12 12 End of Lecture 3 IIT-Bombay Lecture 3 M. Shojaei Baghini