Analog-to-Digital Conversion
Terminology
analog: continuously valued signal, such as temperature or speed,
with infinite possible values in between
digital: discretely valued signal, such as integers, encoded in binary
ADC-DAC
analog-to-digital converter: ADC, A/D, A2D; converts an analog
signal to a digital signal
ผศ.ดร. สุรินทร์ กิตติธรกุล และ อ.สรยุทธ กลมกล่อม ภาควิชาวิศวกรรมคอมพิวเตอร์ คณะวิศวกรรมศาสตร์ สถาบันเทคโนโลยีพระจอมเกล้าเจ้าคุณทหารลาดกระบัง digital-to-analog converter: DAC, D/A, D2A
An embedded system s surroundings typically involve many analog
signals.
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2
Proportional Signals
Analog-to-digital converters
Simple Equation
1111
7.0V
6.5V
6.0V
5.5V
1110
5.0V
4.5V
4.0V
3.5V
1010
3.0V
2.5V
2.0V
1.5V
1.0V
0.5V
0V
0110
4
4
3
3
1100
1011
1001
1000
0111
0101
0100
0011
0010
analog output (V)
1101
analog input (V)
Vmax = 7.5V
2
1
t1
0100
t2
time
t3
0110
t4
0110
0101
Digital output
2
1
t1
0100
t2
t3
1000
0110
Digital input
t4
time
0101
Vmax
Assume minimum voltage of 0 V.
Vmax = maximum voltage of the
analog signal
a = analog value
n = number of bits for digital encoding
1..1 = 2n-1
…
2n = number of digital codes
M = number of steps, either 2n or 2n – 1
d = digital encoding
0001
0000
proportionality
a / Vmax = d / M
analog to digital
digital to analog
0V
Embedded Systems Design: A Unified Hardware/Software
Introduction, (c) 2000 Vahid/Givargis
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0..0 = 0
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Resolution
Let n = 2
Vmax
DAC vs. ADC
DAC:
n digital inputs for digital encoding d
analog input for Vmax
analog output a
3=11
M = 2n – 1
r
3 steps on the digital scale
d0 = 0 = 0b00
dVmax = 3 = 0b11
Vmax
x0
x1
…
DAC
a
Xn-1
3=11
ADC:
2=10
M = 2n
Given a Vmax analog input and an analog input a, how does the
converter know what binary value to assign to d in order to satisfy the
ratio?
2=10
4 steps on the digital scale
d0 = 0 = 0b00
dVmax - r = 3 = 0b11 (no dVmax )
1=01
–
–
1=01
r, resolution: smallest analog change
resulting from changing one bit
0V
0=00
0=00
–
may use DAC to generate analog values for comparison with a
ADC guesses an encoding d, then checks its guess by inputting d into the
DAC and comparing the generated analog output a with original analog
input a
How does the ADC guess the correct encoding?
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Applications
Digital Signal Processing
•  Audio
–  Speech recognition
–  special effects (reverb, noise cancellation, etc)
•  Video
Vref
Analog signal (time
varying, continuous)
0
–  Filtering
–  Special effects
–  Compression
Incoming
samples
Analog-toDigital
Converter
(ADC)
0x030,
0x4A, 0x12,
0xAF, etc.
Digital-toAnalog
Converter
(DAC)
0x0B3,
0x23, 0xCF,
µProcessor
0x78, etc.
performs
computation
Time
Vref
•  Data logging
new
waveform
0
Time
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Outgoing samples
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Vocabulary
Bit Weight
•  ADC (Analog-to-Digital Converter) – converts an analog signal
(voltage/current) to a digital value
•  DAC (Digital-to-Analog Converter) – converts a digital value to
an analog value (voltage/current)
•  Sample period – for ADC, time between each conversion
Notice the concept of bit weight in
the last example:
bit 7 = 7.5 V = 15/2
bit 6 = 3.75 V = 15/4
Each bit is weighted with an analog
value, such that a 1 in that bit
position adds its analog value to the
total analog value represented by
the digital encoding.
–  Typically, samples are taken at a fixed rate
•  Vref (Reference Voltage) – analog signal varies between 0 and
Vref, or between +/- Vref
•  Resolution – number of bits used for conversion (8 bits, 10 bits,
12 bits, 16 bits, etc).
•  Conversion Time – the time it takes for a analog-to-digital
conversion
Example: -5 V to +5 V analog
range, n=8
Digital Bit
Bit Weight (V)
7
10/2 = 5
6
10/4 = 2.5
5
10/8 = 1.25
4
10/16 = 0.625
3
10/32 = 0.313
2
10/64 = 0.157
1
10/128 = 0.078
0
10/256 = 0.039
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Sample ADC Computations
Bit Weight
Example (continued): -5 V to +5
V analog range, n=8
Digital numbers for a few analog
values
–
–
Values shown increment by 6 bits
(weight for bit position 5 is 1.25
V)
Maximum digital number only
approximates the maximum
analog value in the range
•
Try (-5) + sum of all bit
weights
10
Analog (V)
Digital (hex)
-5
00
-3.75
20
-2.5
40
-1.25
60
0
80
1.25
A0
2.5
C0
3.75
E0
5-0.039 = 4.961
FF
If Vref = 5V, and the 10-bit A/D output code is 0x12A, what is
the ADC input voltage?
output_code/2N * Vref = (0x12A)/210 * 5 V
= 298/1024 * 5 V = 1.46 V (Vin)
If Vref = 5V, and the upper 8 bits of the A/D output code is
0xA9, what is the ADC input voltage?
output_code/2N * Vref = (0xA9)/28 * 5 V
= 169/256 * 5 V = 3.3 V (Vin)
If Vref = 4V, and the A/D input voltage is 2.35 V, what is the
ADC output code, upper 8-bits?
11
Vin/ Vref * 2N = 2.35 V/ 4 V * 28
= .5875 * 256 = 150.4 = 150 = 0x96
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A 1-bit ADC
Vref
analog signal
Vin
R
Vref/2
A 2-bit ADC
R
Vin
+
-
Vdd
R
+
Vout=Vdd is Vin > Vref/2
-
Vout=0 if Vin < Vref/2
A
3/4Vref
Vin
+
B
-
1/2Vref
R
Vin +
C
-
R
1/4Vref
digital signal
R
A B C
D1 D0
------------0 0 0
0 0
0 0 1
0 1
0 1 1
1 0
1 1 1
1 1
D[1:0]
(other codes
don t cares)
Encoding logic
comparator
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Successive Approximation ADC
ADC Architectures
First, set DAC to produce Vref/
2.
•  The previous architectures are called Flash ADCs
Output of Comparator is
Q[N-1] (MSB)
–  Fastest possible conversion time
–  Requires the most transistors of any architecture
–  N-bit converter requires 2N-1 comparators.
–  Commercially available flash converters up to 12 bits.
–  Conversion done in one clock cycle
If MSB =1 , then Vin between
Vref and Vref/2, so set DAC to
produce ¾ Vref.
If MSB=0, then Vin between
Vref/2 and 0, so set DAC to ½
Vref.
•  Successive approximation ADCs
–  Use only one comparator
–  Take one clock cycle per bit
–  High precision (16-bit converters are available)
Output of comparator is now
Q[N-2].
Do this for each bit.
Output is Q[N].
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From http://www.allaboutcircuits.com
Takes N cycles.
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ADC, DAC Equations
ADC: Digital Encoding
ADC: Vin = input voltage, Vref = reference voltage
Vref
N = number of bits of precision
Vin/ Vref * 2N = output_code
output_code/ 2N * Vref = Vin
Guessing the encoding is similar to finding an item in a list.
output
code
ADC
Vin
1.
N
•  2n comparisons: Slow!
1 LSB = Vref/2N
2.
DAC: Vout = output voltage, Vref = reference voltage,
N = number of bits of precision
Vref
2N
Vout/ Vref *
= input_code
input_code/ 2N * Vref = Vout
Sequential search – counting up: start with an encoding of 0,
then 1, then 2, etc. until find a match.
Vout
input
code
DAC
Binary search – successive approximation: start with an
encoding for half of maximum; then compare analog result with
original analog input; if result is greater (less) than the original,
set the new encoding to halfway between this one and the
minimum (maximum); continue dividing encoding range in half
until the compared voltages are equal
•  n comparisons: Faster, but more complex converter
N
1 LSB = Vref/2N
!
Takes time to guess the encoding: start conversion input,
conversion complete output
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ADC using successive approximation
ADC using successive approximation
•  Given an analog input signal whose voltage should
range from 0 to 15 volts, and an 8-bit digital encoding,
calculate the correct encoding for 5 volts. Then trace
the successive-approximation approach to find the
correct encoding.
•  Assume M = 2n – 1
a / Vmax = d / M
5 / 15 = d / (256 - 1)
d = 85 or binary 01010101
Step 1-4: determine bits 0-3
½(Vmax – Vmin) = 7.5 volts
Vmax = 7.5 volts.
0
0
0
0
0
0
0
0
½(7.5 + 0) = 3.75 volts
Vmin = 3.75 volts.
0
1
0
0
0
0
0
0
½(7.5 + 3.75) = 5.63 volts
Vmax = 5.63 volts
0
1
0
0
0
0
0
0
½(5.63 + 3.75) = 4.69 volts
Vmin = 4.69 volts.
0
1
0
1
0
0
0
0
Embedded Systems Design: A Unified Hardware/Software
Introduction, (c) 2000 Vahid/Givargis
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Constructing ADC
ADC using successive approximation
State
machine
Analog
input
Step 5-8: Determine bits 4-7
½(5.63 + 4.69) = 5.16 volts
Vmax = 5.16 volts.
0
1
0
1
0
0
0
0
½(5.16 + 4.69) = 4.93 volts
Vmin = 4.93 volts.
0
1
0
1
0
1
0
0
½(5.16 + 4.93) = 5.05 volts
Vmax = 5.05 volts.
0
1
0
1
0
1
0
0
½(5.05 + 4.93) =
4.99 volts
0
1
0
1
0
1
0
1
Timing
control
Vmax
Vmin
DAC
Comparator
SAR
BUF
SAR
SAR: Successive
approximation register
Embedded Systems Design: A Unified Hardware/Software
Introduction, (c) 2000 Vahid/Givargis
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Digital-to-Analog Conversion
DAC Output Plot
For a particular binary code, output a voltage between 0
and Vref
Vref
D[7:0]
DAC
Digital
output
Vout
Output signal increases
in 1 LSB increments.
Vout
4/256 Vref
Assume a DAC that uses an unsigned binary input code, with 0 <
Vout < Vref. Then
3/256 Vref
2/256 Vref
D= 0000 0000 Vout = 0V
D= 0000 0001 Vout = Vref(1/256 ) (one LSB)
D = 0000 0010 Vout = Vref(2/256)
...
D = 1111 1111 Vout = Vref(255/256) (full scale)
1/256 Vref
0
1
2
3
Input code
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Sample DAC Computations
Typical DAC Output
If Vref = 5V, and the 8-bit input code is is 0x8A, what is the
DAC output voltage?
input_code/2N * Vref = (0x8A)/28 * 5 V
= 138/256 * 5 V = 2.70 V (Vout)
If Vref = 4V, and the DAC output voltage is 1.25 V, what is the
8-bit input code?
Vout/ Vref * 2N = 1.25 V/4 V * 28
= 0.3125 * 256 = 80 = 0x50 (input_code)
From http://www.allaboutcircuits.com
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DAC Architecture (cont)
DAC Architecture
Note ratios of
resistors
This is a binary code
Operational
Amplifier can be
used to sum
voltages.
From http://www.allaboutcircuits.com
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From http://www.allaboutcircuits.com
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Another View
DAC Architecture (cont)
A 3-bit DAC, called an R/2NR DAC. Resistors are scaled
by powers of 2 (this is hard to do in practice).
Resistance values are still R, 2R, 4R
From http://www.allaboutcircuits.com
From http://www.allaboutcircuits.com
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R/2R DAC
DAC Application
Phosper
Vertical Deflection
Cathode
R
DAC
G 8
B 8
8
Via circuit analysis, can prove this is an
equivalent circuit.
Now only need resistances of R, 2R – this is
easy to do. This is the most common DAC
From http://www.allaboutcircuits.com
architecture.
DAC
DAC
Red
Electron Beams
(Red, Green Blue)
Green
Blue
Grid
High speed video
DACs produce RGB
signals for color CRT
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Horizontal Deflection
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What do you have to know?
•
•
•
•
ADC (Analog to Digital Converter) Input
Vocabulary
DAC R/2N architecture
ADC Flash, Successive approximation architectures
STM32 A/D
–  How to configure
–  Acquisition, Conversion time
–  How to start do conversion, read result
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