Fundamentals of Sigma-Delta ADCs

45 Pages·2008·0.83 MB·Dutch

Fundamentals of Sigma-Delta ADCs
Jinseok Koh, Ph.D.
Texas Instruments Inc.
Dallas, TX
IEEE SSCS Dallas Chapter, June 2007
Jinseok Koh ([email protected])
Why Analog to Digital Conversion?
(cid:252) Naturally occurring signals are analog signal
(cid:252) Human beings perceive and retain information in analog form
(cid:252) BUT, Analog signal is more sensitive to noise than digital signal
Jinseok Koh ([email protected])
How Analog to Digital Conversion?
110
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010 010
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t t t t t t t t t
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1. Sample analog signal
2. Quantize sampled analog signal(cid:224) Quantization noise
3. Faster sampling time, better accuracy
4. Higher quantization levels, better accuracy
Jinseok Koh ([email protected])
Continuous Time Signal
e
d
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t
i
l
p
m
A
Time
f , band of
B
interest Signal
r
e
w
o
P
0 f f
C B
Frequency
Signal frequency, f = band of interest, f (Maximum frequency of the signal)
C B
Jinseok Koh ([email protected])
Jinseok Koh ([email protected])
Typical Architecture for Analog to Digital Conversion
ADC
Continuous Sampled Digital
Analog
Time Signal Analog Signal Signal
Signal
Anti
Aliasing Quantization DSP
S/H
Filter
Jinseok Koh ([email protected])
Nyquist Rate vs. Oversampled
Jinseok Koh ([email protected])
Modeling of Quantizer
• Quantizer is non-linear building block
– Need modeling for simplifying the analysis
• White additive noise assumptions
– It is not fulfilled in many applications, However
– It makes analysis easy and makes possible the use of z-tansformation
Jinseok Koh ([email protected])
Quantization Noise
• Quantity of in-band noise depends on the over-sampling ratio
– SNR = 10log(s 2) -10log(s 2) +3.01r(dB), where
x n
– s 2 and s 2 are input signal power and in-band noise power respectively, and
x n
– r is defined by over-sampling ratio, f /2f =2r
s b
PervezM. Aziz, “An overview of sigma-delta converters,”IEEE Signal processing Magazine, pp 61-84, Jan. 1996
Jinseok Koh ([email protected])
Over-sampling and Noise Shaping
Every doubling of sampling frequency
1RLVH leads approximately 3 dB enhancement in SNR
%DQG(cid:3)RI(cid:3),QWHUHVW
I I I
V V V
Noise shaping pushes quantization noise
to higher frequency resulting in suppressing
Q. noise in the band of interest
Jinseok Koh ([email protected])