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 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 IIT-Bombay Lecture 14 M. Shojaei Baghini
3 3 Ideal Characteristics of DAC/ADC D : LSB size Starting from DAC =>? @ : ×2 : / 012_456 = ∆ 9 DAC (I) :;< Type equation here. b i : bit # i Center point Analog input range • 1 LSB May be [-V FS /2,V FS /2]. ADC (II) Signed output code • may be used. IIT-Bombay Lecture 14 M. Shojaei Baghini
4 4 Quantization Error in Ideal ADC q e (t) … … t Example: N=6 bits Þ SQNR=37.9dB N=10 bits Þ SQNR=62.0dB 2 D 2 V # 2 = = q FS ( ) $ % & $, ( )$ = ! e 2 12 ´ N 2 12 "# For a sinusoidal signal V = x FS x(t) and approximate rms 2 2 ∆/% ∆ )$ = ∆ % $ % 1 uniform distribution of q e . ! æ ö 2 x 12 ç ÷ = = + SQNR 10 log rms 6 . 02 N 1 . 76 dB "∆/% ç ÷ 2 q è ø e IIT-Bombay Lecture 14 M. Shojaei Baghini
5 5 Modelling of Quantization Noise LSB size: Δ Figure: Ken Martin’s book Approximation: e(n) is assumed as random white noise, i.e. uniform power density distribution across all frequencies. IIT-Bombay Lecture 14 M. Shojaei Baghini
6 6 Digital Filtering of the Noise Figure: Boris Murmann Filtering the noise beyond signal frequency band Total quantization noise power is reduced by the factor • (f s /2)/f B which is called oversampling ratio . IIT-Bombay Lecture 14 M. Shojaei Baghini
7 7 SQNR Improvement by Oversampling 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). IIT-Bombay Lecture 14 M. Shojaei Baghini
8 8 Is Oversampling Enough? Assume f B = 500 kHz and ADC resolution = 8 bits. Target resolution: 14 bits ⇒ Required OSR = 2 (6/0.5) = 4096 ⇒ f s = 4096 × 2 × 0.5 MHz = 4.096 GHz! IIT-Bombay Lecture 14 M. Shojaei Baghini
9 9 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 IIT-Bombay Lecture 14 M. Shojaei Baghini
10 10 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 IIT-Bombay Lecture 14 M. Shojaei Baghini
11 11 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 ) IIT-Bombay Lecture 14 M. Shojaei Baghini
12 12 Discrete-Time Model Using A First Order Filter A(z) |A(z)| ≫ 1 ⇒ |STF| ≈ 1 and |NTF| ≪ 1 in the signal frequency band Delayed input Y(z) = (1-Z -1 ) E(z) + z -1 X(z) IIT-Bombay Lecture 14 M. Shojaei Baghini
13 13 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 IIT-Bombay Lecture 14 M. Shojaei Baghini
14 14 Discrete-Time Integrator First Order Loop Figure: Boris Murmann Integrator gain à ∞ as z à 1 (i.e. Ω à 0) IIT-Bombay Lecture 14 M. Shojaei Baghini
15 15 Complete Block Diagram of Oversampling ∆" ADC Figure: K. Martin’s book High- Low-resolution Simple resolution Not oversampled filter Nyquist rate required digital signal digital signal always IIT-Bombay Lecture 14 M. Shojaei Baghini
16 16 Details of 1 st Order NTF (Noise Transfer Function) 1st order noise shaping !"# $% = ' ( $% = )($%) ,($%) IIT-Bombay Lecture 14 M. Shojaei Baghini
17 17 SQNR for 1 st Order NTF ∆: LSB size < ⟹ + ,-./01 ≊ ∆ 3 12 × 7 3 1 3 9:; 3 2 ? ∆ 1 < = 3 2 ×2 3? × 3 2 2 7 3 ×9:; < :=>; ≊ 12 × 7 3 ∆ 3 1 For sinusoidal waveform 3 9:; IIT-Bombay Lecture 14 M. Shojaei Baghini
18 18 SQNR for 1 st Order NTF ' '(∆ & 1 1 ' ' 2 ×2 24 × 5 ' ×678 1 • SQNR ≊ , = ∆' &' × +' & , -./ • SQNR (dB) ≊ 1.76 + 6.02? − 5.2 + 30log(678) Amount of improvement • H à 2M ⇒ SQNR à SQNR + 9dB Equivalent to 1.5 bits per octave oversampling IIT-Bombay Lecture 14 M. Shojaei Baghini
19 19 End of Lecture 14 IIT-Bombay Lecture 14 M. Shojaei Baghini
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