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

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Mixed-Signal VLSI Design Course Code: EE719 Department: Electrical Engineering Lecture 14: February 11, 2020 Instructor Name: M. Shojaei Baghini E-Mail ID: mshojaei@ee.iitb.ac.in 1 2 2 Module 15 Introduction to Quantization (Analog to

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Mixed-Signal VLSI Design Course Code: EE719 Department: Electrical Engineering Lecture 14: February 11, 2020

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

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IIT-Bombay Lecture 14 M. Shojaei Baghini

Module 15 Introduction to Quantization (Analog to Digital Conversion) References:

  • Chapter 5, the Data Conversion Handbook, Analog

Devices, 2005.

  • Chapter: Oversampling Converters, First two sections:

Oversampling without and with Noise Shaping, Analog Integrated Circuit Design, T. C. Caruson, D. A. Johns and

  • K. W. Martin, 2012
  • “The delta sigma modulator”, B. Razavi’s article in IEEE

SSC Magazine, Spring 2016

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IIT-Bombay Lecture 14 M. Shojaei Baghini

Ideal Characteristics of DAC/ADC

1 LSB Center point ADC (II) DAC (I)

D: LSB size

  • Analog input range

May be [-VFS/2,VFS/2].

  • Signed output code

may be used. Starting from DAC

Type equation here.

/

012_456 = ∆ 9 :;< =>?

@:×2: bi: bit # i

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IIT-Bombay Lecture 14 M. Shojaei Baghini

Quantization Error in Ideal ADC

!

"# #

$%& $, ( )$ = !

"∆/% ∆/%

$% 1 ∆ )$ = ∆% 12

( )

dB N q x SQNR V x V q

e rms FS rms N FS e

76 . 1 02 . 6 log 10 2 2 12 2 12

2 2 2 2 2 2

+ = ÷ ÷ ø ö ç ç è æ = = ´ = D =

For a sinusoidal signal x(t) and approximate uniform distribution of qe.

Example: N=6 bits Þ SQNR=37.9dB N=10 bits Þ SQNR=62.0dB

… …

t qe(t)

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IIT-Bombay Lecture 14 M. Shojaei Baghini

Modelling of Quantization Noise

LSB size: Δ

Approximation: e(n) is assumed as random white noise, i.e. uniform power density distribution across all frequencies.

Figure: Ken Martin’s book

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IIT-Bombay Lecture 14 M. Shojaei Baghini

Digital Filtering of the Noise

Filtering the noise beyond signal frequency band

  • Total quantization noise power is reduced by the factor

(fs/2)/fB which is called oversampling ratio.

Figure: Boris Murmann

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IIT-Bombay Lecture 14 M. Shojaei Baghini

SQNR = 6.02N + 1.76 + 10log(OSR)

Example: OSR=2

  • SQNR is increased by a factor 2 in linear

scale (3 dB increase in dB scale).

  • Resolution is increased by 0.5 bit.

OSR=4 ⇒ 1 bit extra resolution (6 dB) OSR=16 ⇒ 2 bit extra resolution (12 dB) OSR=64 ⇒ 3 bit extra resolution (18 dB)

  • This is similar to averaging (not precisely

since averaging is not an ideal LPF).

SQNR Improvement by Oversampling

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IIT-Bombay Lecture 14 M. Shojaei Baghini

Is Oversampling Enough?

Assume fB = 500 kHz and ADC resolution = 8 bits. Target resolution: 14 bits ⇒ Required OSR = 2(6/0.5) = 4096 ⇒ fs = 4096 × 2 × 0.5 MHz = 4.096 GHz!

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IIT-Bombay Lecture 14 M. Shojaei Baghini

Module 16 Resolution Enhancement using Oversampling and Noise Shaping

References:

  • Sections: Ovrsampling with and without

Noise Shaping, Analog Integrated Circuit Design T. C. Caruson, D. A. Johns and K. W. Martin, 2012

  • “The delta sigma modulator”, B. Razavi’s article

in IEEE SSC Magazine, Spring 2016

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IIT-Bombay Lecture 14

  • M. Shojaei Baghini

Quantizer Output in Single-Bit ∆" Modulator Two numerical examples in the class (bit stream generation)

  • Pulse width and density

depend on the signal level (modulation)

  • Tone generation issue
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IIT-Bombay Lecture 14 M. Shojaei Baghini

1st Order Discrete-Time Integrator for 1st Order Noise Shaping

Integrator gain à ∞ as z à 1 (i.e. Ω à 0) ⇒ " # − % # ⇒ 0 (i.e. average steady state error ⇒ 0)

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IIT-Bombay Lecture 14 M. Shojaei Baghini

Discrete-Time Model Using A First Order Filter

|A(z)| ≫1 ⇒ |STF| ≈ 1 and |NTF| ≪ 1 in the signal frequency band Y(z) = (1-Z-1) E(z) + z-1X(z) Delayed input A(z)

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IIT-Bombay Lecture 14 M. Shojaei Baghini

Reducing Quantization Noise by High-Pass Filtering of the Noise

  • High-pass filtering of the noise and low-pass filtering of

the quantized signal: Practical concept using feedback

Figure: Boris Murmann

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IIT-Bombay Lecture 14 M. Shojaei Baghini

Discrete-Time Integrator First Order Loop

Figure: Boris Murmann

Integrator gain à ∞ as z à 1 (i.e. Ω à 0)

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IIT-Bombay Lecture 14 M. Shojaei Baghini

Complete Block Diagram of Oversampling ∆" ADC

Simple filter Low-resolution

  • versampled

digital signal High- resolution Nyquist rate digital signal Not required always

Figure: K. Martin’s book

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IIT-Bombay Lecture 14 M. Shojaei Baghini

Details of 1st Order NTF (Noise Transfer Function)

!"# $% = '( $% = )($%) ,($%) 1st order noise shaping

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IIT-Bombay Lecture 14 M. Shojaei Baghini

SQNR for 1st Order NTF

∆: LSB size

⟹ +,-./01 ≊ ∆3 12 × 73 3 1 9:;

<

:=>; ≊ 1 2 2?∆ 2

3

∆3 12 × 73 3 1 9:;

< = 3

2 ×23?× 3 73 ×9:;<

For sinusoidal waveform

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IIT-Bombay Lecture 14 M. Shojaei Baghini

SQNR for 1st Order NTF

  • SQNR ≊

& ' '(∆ ' ' ∆' &'×+' , &

  • ./

, =

1 2 ×224× 1 5' ×6781

  • SQNR (dB) ≊ 1.76 + 6.02? − 5.2 + 30log(678)
  • Hà 2M ⇒ SQNR à SQNR + 9dB

Equivalent to 1.5 bits per octave oversampling

Amount of improvement

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End of Lecture 14