Lecture 21
Analog to Digital Conversion
(ADC)
Theory and Examples
1
DIGITAL SIGNAL ACQUISITION
Removes
unwanted
components
picked up by the
Transducer
Amplification
needed to raise
voltage to 0-5 V
range
Physical
Variable
Transducer
Analog quantity:
example
Acoustic
Pressure Wave
(Sound)
Amplifier
Example:
Microphone
converts ACW to
Voltage (mV)
Filter
Analog
To
Digital
Converter
(ADC)
D0
D
. 1 n-bit
Digital
.
Output
.
Dm-1
For example:
removes higher
frequency
background
noise when
capturing
speech
2
INTERFACING WITH mP
PCIAs
3
ANALOG VOLTAGE SIGNAL
CONTINUOUS IN TIME, CONTINUOUS IN VOLTAGE
• Has an infinite number of instances of time.
• Has an infinite number of different voltages
within the range (0 – Vmax).
4
DIGITIZATION PROCESS
1. Sample the analog signal at discrete
points in time, usually at periodic
intervals.
2. For each sample taken, round off the
analog voltage value to a discrete
voltage value.
5
TIME DOMAIN SAMPLING
• Analog signal is sampled at discrete points in time
(Domain Quantization)
• For example: the signal may be sampled at each
second:
6
VOLTAGE QUANTIZATION
• Analog voltage sampled at discrete time t is rounded
off to nearest discrete voltage value.
• For example, the signal may be rounded off to one of 8
discrete levels:
7
DIGITAL REPRESENTATION
• Each level is assigned a digital code, and the signal is
represented as a sequence of digital codes.
• Can store the sequence of digital samples in memory
for future processing.
• For example, for a 3-bit converter:
101, 111, 111, 111, 101, 011, 010, 010, 011, 100, 100, 100, 011, 010, 010
8
VARIOUS N-BIT ADCs
• The analog voltage range may be split into a power-of-2 different
levels, and a digital code is assigned to each level: For examples:
Analog Signal
Vmax
0.0
3-bit Converter
8
7
111
6
110
5
101
4
100
3
011
2
010
1
001
0
000
4-bit Converter
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
1111
1110
1101
1100
1011
1010
1001
1000
0111
0110
0101
0100
0011
0010
0001
0000
…
8-bit Converter
256
240
224
208
192
176
160
144
128
112
96
80
64
48
32
16
0
11111111
11110000
11100000
11010000
11000000
10110000
10100000
10010000
10000000
01110000
01100000
01010000
01000000
00110000
00100000
00010000
00000000
…
9
WHAT IS PRECISION?
• The greater is the number of bits, the greater
is the precision of the ADC
4-bit Converter
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
1111
1110
1101
1100
1011
1010
1001
1000
0111
0110
0101
0100
0011
0010
0001
0000
…
8-bit Converter
256
240
224
208
192
176
160
144
128
112
96
80
64
48
32
16
0
11111111
11110000
11100000
11010000
11000000
10110000
10100000
10010000
10000000
01110000
01100000
01010000
01000000
00110000
00100000
00010000
00000000
…
Analog Signal
Vmax
n-bit
precision
Infinite
precision
0.0
10
ROUND-OFF ERROR
(AKA: QUANTIZATION ERROR)
• Round-off error cannot be recovered
• Amount of round-off error decreases with increasing number of
bits used in the ADC
• How much error is acceptable?
• What is the smallest size (grains of) sugar you can discern?
• One grain, one teaspoon, or other?
• The application determines the number of bits to use in the ADC
• Music: 16-bits
• Telephone quality speech: 8-bit
11
QUANTIZATION
ERROR
Q: Analog input must
change by Q units
before output
changes to next code.
12
3-BIT BIPOLAR EXAMPLE
(LACKS A DIGITAL ZERO REPRESENTATION)
Full Scale (FS) Range:
8.0 V
Precision:
3-Bit,
8 Possibilities
Q
FS
2n
Resolution
(Quantization Step Size, Q):
FS Range/Number of Steps
8.0/8 = 1.0 V
13
3-BIT UNIPOLAR EXAMPLE
(HAS DIGITAL ZERO REPRESENTATION)
Full Scale (FS) Range:
8.0 V
Precision:
3-Bit,
8 Possibilities
Resolution
(Quantization Step Size, Q):
FS Range/Number of Steps
8.0/8 = 1.0 V
Q
FS
2n
14
SAMPLING RATE
• What is the minimum rate a signal should be
sampled to produce an accurate digital
representation of it, so that the original signal can be
reconstructed from the digital sampled version?
• Intuitively, we expect the required sampling rate to
be related to the rate at which the signal changes
(e.g., DC signal, erratic heart rate)
15
EX: SAMPLING A SINUSIOD
Time (s)
0
1
• Maximum frequency component of signal fc = 9 Hz (9 cycles per
second)
• Sampling rate fs = 72 S/s (72 samples per second, or 8 samples per
period)
16
Not Enough Samples
Time (s)
0
1
• The reconstructed version appears to have changed frequency to 3 Hz (Alias)
• In general both phase and frequency will be altered if not sampled at a sufficient
rate
• Aliasing: the change of frequency (and phase) due to insufficient rate of sampling
17
NYQUIST-SHANNON SAMPLING THEOREM
NYQUIST RATE
f s  2 fc
Sampling
Frequency
Highest
Frequency
Component
In Signal
“If a continuous signal containing no frequency components
higher than fc is sampled at a rate greater than 2fc, then the
original signal can be completely recovered from the
sampled version without any error, except for the voltage
quantization error (round-off error).”
18
ADC IMPLMENTATIONS
• There are many different implementations of
ADCs:
– Flash
– Feedback Type of Converters
• Successive Approximation
• Ramp Conversion
– Sigma Delta, Dual Slope, and Others
19
FLASH ADC
Analog Voltage
Range
7/8 FS … 8/8 FS
6/8 FS … 7/8 FS
5/8 FS … 6/8 FS
4/8 FS … 5/8 FS
3/8 FS … 4/8 FS
2/8 FS … 3/8 FS
1/8 FS … 2/8 FS
0/8 FS … 1/8 FS
•
•
•
Example:
FS=8.0 V
7.0 … +∞
6.0 … 7.0
5.0 … 6.0
4.0 … 5.0
3.0 … 4.0
2.0 … 3.0
1.0 … 2.0
-∞ … 1.0
Digital
Code
111
110
101
100
011
010
001
000
Fast since the conversion time is equal
to propagation gate delay
Same (uniform) conversion time for
each possible input amplitude
Expensive, since the number of
components grows exponentially with
the number of bits
•
8-bit flash converter requires 256
resistors, 255 comparators, and a 255 to
8-bit digital encoder
20
DIGITAL TO ANALOG CONVERTER
(DAC)
• A digital to analog converter converts a digital representation of some
quantity to analog form
•
•
•
•
Digital representation is a discrete form of some quantity
Analog form is a continuous quantity representation of some quantity
Converts a vector (string of binary bits) to a scalar (analog quantity (voltage))
Example, 4-bit DAC:
b3
b2
b1
4-bit DAC
Analog Output
b0
21
DAC CONCEPT
•
The analog output is determined by summing the voltage weights where the coefficient
is a ‘1’, For example, for a 4-bit DAC (VR = 1V):
01001 = 8V + 1V = 9V
22
ADC AND DAC PROCESS
ADC
STORED SAMPLES
101, 111, 111, 111, 101,
011, 010, 010, 011, 100,
100, 100, 011, 010, 010
STORED SAMPLES
DAC
101, 111, 111, 111, 101,
011, 010, 010, 011, 100,
100, 100, 011, 010, 010
23