Analog-to-Digital Conversion
Microcomputer Architecture and Interfacing
Colorado School of Mines
Professor William Hoff
Analog-to-Digital (A/D) Conversion
• Sensors measure nonelectric quantities such as temperature, etc
• These must be converted into an electric quantity (i.e., voltage) using a
transducer
• Analog voltages must be converted into digital values so that they can be
processed by the computer
• A signal conditioning circuit is needed to shift and scale the transducer
output to a range suitable for A/D conversion
Temperature
Pressure
Light
Weight
Airflow
Humidity
.
.
.
Transducer
Voltage
Such as a
sensor,
load cell,
photocall, or
thermocouple
.
.
Microcomputer Architecture and Interfacing
Signalconditioning
circuit
Voltage
A/D
converter
Digital
value
Computer
(optional)
In this unit we focus on
the A/D converter
Figure 12.1 The A/D conversion process
Colorado School of Mines
Professor William Hoff
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Digital codes
• Ideally we would want a continuous relationship between input voltage
and output digital code value
• However, we have only a discrete number of code values – for n bits, we
have 2^n codes
Output code
Digital Code
2n-1
Note the horizontal
shift to center the
error about ±1/2 bit
The area above and below
the dotted line is called
quantization error
Voltage
Figure 12.2 An ideal A/D converter output characteristic
VDD/2n
VDD
Voltage
Figure 12.3 Output characteristic of an ideal n-bit A/D converter
Microcomputer Architecture and Interfacing
Colorado School of Mines
Professor William Hoff
3
Digital-to-analog (D/A) conversion
• To understand how A/D conversion works, we first
look at digital to analog conversion
• D/A is the opposite of A/D – it takes an input digital
number and outputs an analog voltage proportional
to that number
• We’ll look at two methods:
– A resistor ladder (used in discrete D/A chips)
– A charge-redistribution circuit (this is what is used in the
microcontroller)
Microcomputer Architecture and Interfacing
Colorado School of Mines
Professor William Hoff
4
Resistor ladder
• b3,b2,b1,b0 is a 4-bit
binary number
• Current in each branch:
3
3
2
2
• Total
current:
Microcomputer Architecture and Interfacing
Colorado School of Mines
Professor William Hoff
5
Convert current to voltage
• Ideal op-amp
Ideally,
• Ri = ∞
• R0 = 0
• A=∞
• Negative gain amplifier
(Vi – V-)/R1 = (V- - V0)/R2
Vi/R1 = -V0/R2
V0 = -Vi/(R2/R1)
Microcomputer Architecture and Interfacing
Colorado School of Mines
Professor William Hoff
6
Resistor ladder
For n=3 bits:
I = (Vref/4R)(4b2 + 2b1 + b0)
= (Vref/4R) B
R
Microcomputer Architecture and Interfacing
Colorado School of Mines
Professor William Hoff
7
Resistor ladder
• To avoid large current swings:
The current in
each branch is
constant
Microcomputer Architecture and Interfacing
Colorado School of Mines
Professor William Hoff
8
Problem with binary-weighted resistor ladder
• It is difficult to make resistor values precise over a wide range
• Example: a 12 bit D/A would have resistor values R, 2R, 4R, …,
212 R
• Instead we can design a resistor ladder with only two values,
R and 2R
Microcomputer Architecture and Interfacing
Colorado School of Mines
Professor William Hoff
9
R-2R ladder
• What is equivalent resistance?
R and R in
series is 2R
2R and 2R in
parallel is R
2R and 2R in
parallel is R
• At each step, the equivalent resistance is R
• So equivalent resistance of entire network is R
Microcomputer Architecture and Interfacing
Colorado School of Mines
Professor William Hoff
10
R-2R ladder
Iin = b2(I/2)+b1(I/4)+b0(I/8)
= (Vref/8R)(4b2 + 2b1 + b0)
Vout = -(Vref/8) B
Microcomputer Architecture and Interfacing
Colorado School of Mines
Professor William Hoff
11
A/D Conversion
• Strategy: generate a series of analog voltages corresponding
to known digital values (using a D/A converter)
• Compare unknown voltage to the generated voltages
• When a match occurs, we know the corresponding digital
value
• Voltage comparison
– We can use a comparator, which is just an op-amp with a large gain
– The output saturates one way if Vunknown > Vknown, and saturates the
other way if Vunknown < Vknown
Microcomputer Architecture and Interfacing
Colorado School of Mines
Professor William Hoff
12
Successive approximation A/D converter
• At each iteration, we generate a voltage and test if the unknown voltage is
greater than or less than the known voltage
• If less, we try a lower voltage; if greater, we try a higher voltage
analog
comparator
+
Vin (analog input)
-
Clock
Successive
Control
Logic approximation
register (SAR)
Digital-to-analog
converter
Output
Latch
VRH
VRL
Digital
code
Figure 12.4 Block diagram of a successive approximation A/D converter
Microcomputer Architecture and Interfacing
Colorado School of Mines
Professor William Hoff
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Successive approximation A/D converter
• The converter does a binary search
– Let VU = unknown voltage
– Let VG(D) = generated voltage for digital value D
yes
yes
VU < VG(64) ?
Example: 8 bit
A/D converter
no
VU < VG(128)
?
no
yes
VU < VG(192)
?
no
:
:
yes
VU < VG(96) ?
:
yes
no
VU < VG(112)
?
100 <VU < 101
Microcomputer Architecture and Interfacing
no
:
:
the answer is
actually a range
:
Colorado School of Mines
the search takes n
steps, for n bits
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14
A/D Converter Specifications
• Conversion time
– The time required to do one A/D conversion
– Determines upper limit on frequency that can be sampled without
aliasing: fmax = 1/(2*conversion time)
• Resolution
– Can express in volts, or #bits
• Accuracy
– Vresolution/Vsignal (%)
• Linearity
– Deviation from straight line (best possible is ±1/2 LSB)
Microcomputer Architecture and Interfacing
Colorado School of Mines
Professor William Hoff
15
A/D Converter Specifications (continued)
• Aperture time
– It takes a finite amount of time to sample the input signal – this is
called the aperture time
– If signal is changing during sampling time, can cause an error
– Maximum aperture time to reduce this error to ±1/2 LSB is
t AP 
1
2 f max 2 N
Microcomputer Architecture and Interfacing
Colorado School of Mines
Professor William Hoff
16
Example
• A 10-bit A/D converter uses successive approximation, with a 800 KHz
clock. Each step in the conversion cycle takes 4 clock cycles
– What is the conversion time?
– If Vref is 10 volts, what is the resolution?
– What is the maximum frequency you can digitize, without aliasing?
– Find the aperture time for the sampling error to be less that ±1/2 LSB
Microcomputer Architecture and Interfacing
Colorado School of Mines
Professor William Hoff
17
Example
• A 10-bit A/D converter uses successive approximation, with a 800 KHz
clock. Each step in the conversion cycle takes 4 clock cycles
– What is the conversion time?
There are 10 steps, each taking 4 clock cycles, so 40 clock cycles
Total time is 40 x (1/800 KHz) = 50 microseconds
– If Vref is 10 volts, what is the resolution?
10 bits; or in terms of voltage: 10V/(2^10) = 10V/1024 = 0.01 V
– What is the maximum frequency you can digitize, without aliasing?
fmax = 1/(2 x tconv) = 1/(2x50 us) = 10^4 Hz
– Find the aperture time for the sampling error to be less that ±1/2 LSB
tAP= 1/(2 pi fmax 2^N) = 1/(2 pi x 10^4 Hz) x 2^10) = 0.016 us
the aperture time is much smaller than the conversion time
Microcomputer Architecture and Interfacing
Colorado School of Mines
Professor William Hoff
18
Summary / Questions
• Why is a “digital-to-analog” element needed in a
“analog-to-digital” converter?
• Typical specifications for A/D systems are
–
–
–
–
–
Conversion time
Resolution
Accuracy
Linearity
Aperture time
Microcomputer Architecture and Interfacing
Colorado School of Mines
Professor William Hoff
19