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Lecture%203:%20Quantization

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Lecture 3: Quantization The last major stage of an A/D converter is the conversion of the sampled signal to a digital signal: quantized signal – PowerPoint PPT presentation

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Title: Lecture%203:%20Quantization


1
Lecture 3 Quantization
  • The last major stage of an A/D converter is the
    conversion of the sampled signal to a digital
    signal

quantized signal
sampled analog signal
A/D converter
vin
vout
B bits/sample
vout
example mapping from input to output
vin
2
Quantization
  • Key parameters for an A/D converter
  • full-scale voltage range R
  • number of bits B
  • number of quantization levels 2B
  • quantization width Q R / 2B

quantized signal
3 bit unsigned binary code
8Q
input signal
111
7Q
110
6Q
101
5Q
R
100
4Q
011
3Q
010
2Q
001
Q
000
0
t
3
Quantization Error
  • The rounding operation replaces each sample by
    the nearest quantized value.
  • quantization error e then lies in the interval
  • maximum error (magnitude) Q/2

average error 0
error
Q/2
average square error Q2/12
vout
Vin Q/2
Vout- Q/2

-Q/2
4
Quantization Error
  • Signal to Noise Ratio (SNR) or Dynamic Range
  • maximum signal range R
  • maximum noise range Q
  • 6 dB per bit
  • Example The human ear has a dynamic range of
    about 100 dB. This requires approximately 16
    bits which is the number of bits associated with
    CD quality recording.

5
Quantization Error
  • Large dynamic ranges can be obtained with fewer
    bits, provided
  • the sampling rate is increased and
  • noise-shaping is performed.

Advanced topic noise shaping quantizers
6
D/A Conversion
  • unipolar natural binary
  • bipolar offset binary
  • twos complement

b1
b2
input bits
analog output
DAC
b3
x
bB
R
7
D/A Conversion
  • Horners algorithm

sum 0 b1 1-b1 for iB, B-1, B-2, , 1
sum 0.5(sum bi) end x R(sum - 0.5)
8
A/D Conversion
  • Successive approximation (rounding)

ADC
comparator
analog input
x
successive approximation register
u(x-xQ)


xQ
-
b1
b2
b3
bB
Q/2
digital output
b1
b2
b3
bB
DAC
R
9
A/D Conversion
  • Example
  • 4 bits
  • bipolar twos complement
  • R 5 V (Q 0.3125 V)
  • input voltage -1.8V
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