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 Engineering Lecture 2: January 14, 2019

Instructor Name: M. Shojaei Baghini E-Mail ID: mshojaei@ee.iitb.ac.in

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IIT-Bombay Lecture 2 M. Shojaei Baghini

Module 1 Sampling Concept and Bandwidth Limitation

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IIT-Bombay Lecture 2 M. Shojaei Baghini

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

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IIT-Bombay Lecture 2 M. Shojaei Baghini

Bridge Between Analog and Digital Domains

Analog Domain Digital Domain Conditioning A/D Conversion D/A Conversion Smoothing and Equalization

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IIT-Bombay Lecture 2 M. Shojaei Baghini

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”.

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IIT-Bombay Lecture 2 M. Shojaei Baghini

Discrete in Time and Discrete in Signal Value

Source: Boris Murmann, 2013

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IIT-Bombay Lecture 2 M. Shojaei Baghini

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

ω

|X(ω)|

Wb

• Wb

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IIT-Bombay Lecture 2 M. Shojaei Baghini

How much is the bandwidth limitation?

Nyquist Classic Theorem 1924 (It can be violated in some cases without loosing the main information)

Source: Data Conversion Handbook, Analog Devices, Chapter 1 2005

fs

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IIT-Bombay Lecture 2 M. Shojaei Baghini

Ideal Uniform Sampling: Multiplication of Input Signal by Train of Uniform Impulses

´

Xs(t) X(t) s(t) …… …… T Ideal s(t)

!" # = ! # ⊗ 1 ' (

)*+, )*-,

. # − 0#

" = 1

' (

)*+, )*-,

! # − 0#

"

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IIT-Bombay Lecture 2 M. Shojaei Baghini

Ideal Sampling (Impulse Sampling) Repetition in Frequency Domain Bandwidth Constraint

fs - Wb > Wb ⇒ fs > 2Wb (Nyquist Rate: Avoiding Aliasing)

• 2/T -1/T

Wb Repetition of information in frequency domain "# $ = " $ ⊗ 1 ( )

*+,- *+.-

/ $ − 1$

# = 1

( )

*+,- *+.-

" $ − 1$

#

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IIT-Bombay Lecture 2 M. Shojaei Baghini

• 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? ωN

|X(ω)|

2!WbN/ωs

• 2!WbN/ωs

Repetition of Information in Frequency Bands 2!

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IIT-Bombay Lecture 2 M. Shojaei Baghini

Example: Sampling without Aliasing

Source: Boris Murmann, 2013

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IIT-Bombay Lecture 2 M. Shojaei Baghini

Example 1: Sampling with Aliasing

Source: Boris Murmann, 2013

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IIT-Bombay Lecture 2 M. Shojaei Baghini

Example 2: Sampling with Aliasing

Source: Boris Murmann, 2013

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IIT-Bombay Lecture 2 M. Shojaei Baghini

Aliasing Examples

Images (aliases) at |±mfs ±fa|, m =1,2,3,…

Source: Data Conversion Handbook, Analog Devices, Chapter 2, 2005

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IIT-Bombay Lecture 2 M. Shojaei Baghini

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.

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IIT-Bombay Lecture 2 M. Shojaei Baghini

End of Lecture 2

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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

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IIT-Bombay Lecture 3 M. Shojaei Baghini

Module 2 Z-Transform, Discrete Fourier Transform and Non-ideal Sampling

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IIT-Bombay Lecture 3 M. Shojaei Baghini

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

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IIT-Bombay Lecture 3 M. Shojaei Baghini

Definition of Z-Transform Moving from s Domain to z Domain

1 | | , < Þ < W = \ = = W + =

W +

z T e e z j s

T j T Ts

s w s

s

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IIT-Bombay Lecture 3 M. Shojaei Baghini

Box or Rectangular Pulse Function

! " → $ % X(t) → ! −% '()* %+)*"(,)?

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IIT-Bombay Lecture 3 M. Shojaei Baghini

Ideal Sampling Fourier Transform of Sampled Signal

ω = Ω × T

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IIT-Bombay Lecture 3 M. Shojaei Baghini

A Typical Simple T&H Circuit

What happens to the signal spectrum due to the T&H operation as compared to the impulse sampling? Zero order hold

T

With ideal switch 1st order hold?

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IIT-Bombay Lecture 3 M. Shojaei Baghini

Non-ideal Sampling (S & H) but with Ideal Switch!

• Track & Hold with Ttrack << T
• r variation of the input signal during tracking is

negligible. p(t) is a pulse with unit amplitude and width of T. P(f) is a Sinc function. t

p(t)

T 1

) ( ) ( fT Sinc e T P

fT j

´ ´ = W

• p

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IIT-Bombay Lecture 3 M. Shojaei Baghini

Non-ideal Sampling - (S & H) but with Ideal Switch! Zero order hold

T w = WT

å å å ò å ò å

+¥ =

• ¥

=

• ¥

=

• ¥

=

• ¥

¥

• ¥

= ¥ ¥

• ¥

=

• ´

´ = ´ = ÷ ø ö ç è æ = =

• =

÷ ø ö ç è æ

• m

m s jn n jn n t j n t j n

mf f X T fT Sinc T P X P e nT x e P nT x dt e nT t p nT x dt e nT t p nT x ) ( 1 ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( w w w w

w w w w

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IIT-Bombay Lecture 3 M. Shojaei Baghini

Non-ideal Sampling (S & H) but with Ideal Switch! w = WT

Zero order hold

Track & Hold with Ttrack << T

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IIT-Bombay Lecture 3 M. Shojaei Baghini

Example by Illustration

Source: Boris Murmann, 2013

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IIT-Bombay Lecture 3 M. Shojaei Baghini

End of Lecture 3