understanding is more easily by:ahmed salad osman

1. UNIVERSITY OF HORMUUD
Analog to digital converter
And
Digital to analog converter
By: Ahmed Salad Osman
1
1

2. Part one
And
Part two
2
2

3. Part one
analog to digital
converter
3
3

4. Outline
Definition
Why we need ADC
Types ADC and each basic operation
Applications of analog to digital converter
4
4

5. Definition
An electronic integrated circuit which
transforms a signal from analog(continues) to
digital(discrete) form
Analog signals are directly measurable
quantities
Digital signals only have two states for digital
computer we refer to binary states, 0 and 1
5
5

6. Continue
The heart of computer-based data acquisition
is usually the analog to digital converter
Basically this device is digital volt meter
Digital Systems require discrète digital data
Analog
?
Digital
6
Digital System
6

7. Continue
Digital computers require signals to be in
digital form whereas most instrumentation
transducers have an output signal in analogue
form.
ADC conversion is therefore required at the
interface between analogue transducers and the
digital computer
7
7

8. Examples of use
• Voltmeter
7.77 V
ΔV
• Cell phone (microphone)
Wave
Voice
8
8

9. Why we need ADC
Microprocessors can only perform complex
processing on digitized signals
When signals are in digital form they are less
susceptible to the deleterious effects of
additive noise
ADC Provides a link between the analog
world of transducers and the digital world of
signal processing and data handling.
9
9

10. Types of analog to digital converter
There are many different types of analog to
digital converters
Each offers something in the way of
Speed
Cost
Power dissipation
complexity
10
10

11. Types of analog to digital converter
Counter type
Successive approximation
There are many types such as flash
type and sigma-delta but we will
cover these two types
11
11

12. Counter type
One of the simplest types of analog to digital
converter is counter type ADC
The input signal of ADC is connected to the
signal input of its internal comparator
The ADC then systematically increases the
voltage of the reference input of the
comparator until the reference becomes larger
than the signal
12
12

13. Continue
And the comparator output goes to 0
Ex: consider an input signal is 4.78 volts. The
initial comparator’s input would be 2.5 volts
The comparator compares the two value then
the result this is less than 4.78 then the next
higher voltage (5.00 volts) is applied
The comparator compares the two value and
says this is greater than 4.78 and switches 0
13
13

14. Continue
The digital output of the ADC is the number of
times the ADC increase the voltage after
starting at the initial 2.5 volts
This scheme is relatively simple , but as the
number of ADC increases the time it takes to
scan through all possible values lower than
input will grow quickly
14
14

15. Components of counter type
This type of converter uses some type of
counter as part of its operation
Counter type contains the following elements:
Digital to analog converter
Some type of counting mechanism
Comparator
clock
15
15

16. Features of counter type
Use a clock to index the counter
Use DAC to generate analog signal to compare
against input
Comparator is used to compare VIN and VDAC
where VIN is the signal to be digitized
The input to the DAC is from the counter
16
16

17. Operation of counter type
START
Comparator
Vin
Control Logic
clock
Counter
DA C
Digital Output
17
17

18. Operation of counter type
START
Comparator
Vin
Control Logic
clock
Counter
DA C
Digital Output
18
18

19. Successive approximation
A Successive Approximation Register (SAR)
is added to the circuit
Instead of counting up in binary sequence, this
register counts by trying all values of bits
starting with the MSB and finishing at the
LSB.
The register monitors the comparators output
to see if the binary count is greater or less than
the analog signal input and adjusts the bits
accordingly
19

20. Continue
The SAR architecture mainly uses the binary
search algorithm
The SAR ADC consists of fewer blocks such
as one comparator, one DAC (Digital to
Analog Converter) and one control logic.
The algorithm is very similar to like searching
a number from telephone book
20
20

21. How Successive Approximation Works
• Example : analog input = 6.428v, reference =
10.000v
MSB
5.000V
2SB
2.500V
3SB
1.250V
LSB
0.625V
VIN > 5.000V
VIN > 7.500V
VIN > 6.250V
VIN > 6.875V
YES
NO
YES
NO
0
1
0
1
21
21

22. Applications
Scanner : when you scan a picture with a
scanner , what scanner is doing is an analog to
digital conversion : it is taking the analog
information provided by the picture(light) and
converting into digital
Recording a voice : when u=you record your
voice or use a VoIP solution on your computer
you r using analog to digital converter to
convert you voice , which is analog into
digital information
22
22

23. Part two
Digital to analog
converter
23
23

24. Outline
Definition
Types of DAC and each operation
DAC performance specifications
Applications of ADC
24
24

25. Definition
To convert digital values to analog voltage
Performs inverse operation of analog to digital
converter
100101…
DAC
25

26. Analog output signal
What is DAC
0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011
Digital input signal
26

27. Continue
REFERENCE
INPUT
DIGITAL
INPUT
ANALOG
OUTPUT
RESOLUTION
= N BITS
Digital Input
Analog Output =
x Reference Input
(2N - 1)
27
27

28. continue
ADC is function that converts digital data(usually
binary) into analog signal(current , voltage, or
electric charge)
digital-to-analog converter, a device (usually a
single chip) that converts digital data into analog
signals.
 Modems require a DAC to convert data to analog
signals that can be carried by telephone wires.
Video adapters also require DACs, called
RAMDACs, to convert digital data to analog
signals that the monitor can process.
28
28

29. Types of DAC
There are two types of ADC
Weighted Resistor or Resistive Divider type
And there is an other type of R -2R ladder
N bit
digital data
0
1
2
Digital to analog
converter
Analog data
n-2
29
29

30. Weighted Resistors
• In this type of DAC components used is
– Operational amplifier
– Switches
– Resistors
R
– Voltage source
MSB
– Ground
Rf = R
Ii
2R
4R
8R
LSB
-VREF
30
30

31. Definition of weighted resistors
Binary Weighted resistors are used to
distinguish each bit from the most significant
to the least significant
Binary weighted resistors Reduces current by a
factor of 2 for each bit
31
31

32. Continue
Binary Weighted resistors is reliable, and
simple to do
The circuit shown is a digital to analog
converter 4-bits weighted binary resistance
network circuit types.
Resistor values ​can be calculated using
the weight of the binary number.
32
32

33. Circuit diagram of weighted resistors
33
33

34. Weighted Binary Resistance
Network
Weighted Binary Resistance Network Circuit
D
C
B
A
18.7K
37.5K
75K
150K
3V
R4
R3
R2
RF
R1
20K
++
34
Vout
Vout O
VVV
UT
34

35. Continue
For example
Referring to the circuit as shown, the highest
value resistor (150KΩ) is a digital input
resistor. The smallest bit (least significant bit),
and the values of other resistor is
35
35

36. Circuit analysis to find Vout
If binary input is 0001
R1 = 150KΩ, RF = 20KΩ, Vref = 3V
Voltage Gain (AV) = RF = 20KΩ = 0.133
R1 150KΩ
Vout = Vref X AV
= 3V X 0.1333
= 0.4V
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36

37. Continue
 If binary input is 0110
R2 = 75KΩ,
R3 = 37.5KΩ, RF = 20KΩ, Vref = 3V
RT = R2//R3 = 25KΩ
Voltage Gain (AV) = RF
RT
Vout
= 20KΩ = 0.8
25KΩ
= Vref X AV
= 3V X 0.8
= 2.4V
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37

38. Calculate
If binary input is 1100
R3 = 37.5KΩ, R4=18.75 RF = 20KΩ, Vref = 3V
RT = R3//R4 = 12.5KΩ
Voltage Gain (AV) = RF
RT
Vout
= 20KΩ = 1.6
12.5KΩ
= Vref X AV
= 3V X 1.6
= 4.8
38
38

39. Simply that we can see the resulting output is shown in the table below
Decimal
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Digital input
D
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
C
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
B
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
A
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
Vout (V)
0
0.4
0.8
1.2
1.6
2.0
2.4
2.8
3.2
3.6
4.0
4.4
4.8
5.2
5.6
39
39

40. Example
Find output voltage and current for a binary
weighted resistor DAC of 4 bits where :
R = 10 k Ohms, Rf = 5 k Ohms and VR = 10
Volts. Applied binary word is 1001.
40
40

41. Solution
Rf = (R/2)
Ii
8R
4R
4-bit
2R
3-bit
Vo
R
2-bit
1-bit
MSB
VR
41
41

42. Solution Cont’d
Io
I0
10 V
1
0
4
2 *10
- 0.001125A
0
1
4
2 *10
0
2
4
2 *10
1
3
4
2 *10
V0 - R f I0
V0
3
(5 *10
)( 0.001125A) 5.625 V
42
42

43. Solution Cont’d
Binary input = 1001 = 9
From example, V0 = 5.625V
V0/VR = 5.625V/10V = 9/16
43
43

44. Binary Weighted Resistor
 Advantages
 Simple Construction/Analysis
 Fast Conversion
 Disadvantages
 Requires large range of resistors (2000:1 for 12bit DAC) with necessary high precision for low
resistors
 Requires low switch resistances in transistors
 Can be expensive. Therefore, usually limited to
8-bit resolution.
44
44

45. Limitations of binary weighted
Has problems if bit length is longer than 8 bits
For example, if R = 10 k Ohms
R8 = 28-1(10 k Ohms) = 1280 k Ohms
If VR = 10 Volts,
I8 = 10V/1280 k Ohms = 7.8 A
Op-amps to handle those currents are expensive
because this is usually below the current noise
threshold.
45
45

46. Limitations Cont’d
If R = 10 Ohms and Vref = 10 V
I = VR/R = 10V/10 Ohms = 1 A
This current is more than a typical op-amp
can handle.
Large resistors more error
46
46

47. DAC performance specification
Resolution
Reference Voltages
Settling Time
Linearity
Speed
Errors
47
47

48. Resolution
Resolution: is the amount of variance in
output voltage for every change of the LSB in
the digital input.
How closely can we approximate the desired
output signal(Higher Res. = finer
detail=smaller Voltage divisions)
A common DAC has a 8 - 12 bit Resolution
VRef
N = Number of bits
Resolution VLSB
N
2
48
48

49. Resolution continue
Better Resolution(3 bit)
Poor Resolution(1 bit)
Vout
Vout
Desired Analog
signal
Desired Analog signal
111
110
8 Volt. Levels
2 Volt. Levels
1
101
110
101
100
100
011
011
010
010
001
0
Approximate
output
0
001
000
000
Digital Input
Approximate
output
49
Digital Input
49

50. Reference voltage
Reference Voltage: A specified voltage used to
determine how each digital input will be
assigned to each voltage division.
Types:
Non-multiplier: internal, fixed, and defined by
manufacturer
Multiplier: external, variable, user specified
50
50

51. Reference voltage types
Multiplier: (Vref = Asin(wt))
Non-Multiplier: (Vref = C)
Voltage
Voltage
11
11
10
10
10
01
01
10
01
01
0
0
00
00
Digital Input
51
00
00
Digital Input
51

52. Settle time
Settling Time: The time required for the input
signal voltage to settle to the expected output
voltage(within +/- VLSB).
Any change in the input state will not be
reflected in the output state immediately. There
is a time lag, between the two events.
52
52

53. Settle time continue
Analog Output Voltage
Expected
Voltage
+VLSB
-VLSB
Settling time
53
Time
53

54. Linearity
Linearity: is the difference between the
desired analog output and the actual output
over the full range of expected values.
Ideally, a DAC should produce a linear
relationship between a digital input and the
analog output, this is not always the case.
54
54

55. Linearity continue
NON-Linearity(Real World)
Desired/Approximate Output
Analog Output Voltage
Analog Output Voltage
Linearity(Ideal Case)
Desired Output
Approximate
output
Digital Input
Digital Input
Miss-alignment
Perfect Agreement
55
55

56. Speed
Speed: Rate of conversion of a single digital
input to its analog equivalent
Conversion Rate
Depends on clock speed of input signal
Depends on settling time of converter
56
56

57. Errors
Non-linearity
Differential
Integral
Gain
Offset
57
57

58. Non linearity: differential
Analog Output Voltage
Differential Non-Linearity: Difference in
voltage step size from the previous DAC
output (Ideally All DLN’s = 1 VLSB)
Ideal Output
2VLSB
Diff. Non-Linearity = 2VLSB
VLSB
Digital Input
58
58

59. Non linearity: integral
Integral Non-Linearity: Deviation of the
actual DAC output from the ideal (Ideally all
INL’s = 0)
Analog Output Voltage
Ideal Output
Int. Non-Linearity = 1VLSB
1VLSB
Digital Input
59
59

60. Gain error
Gain Error: Difference in slope of the ideal
curve and the actual DAC output
High Gain
High Gain Error: Actual
slope greater than ideal
Low Gain Error: Actual
slope less than ideal
Analog Output Voltage
Desired/Ideal Output
Low Gain
Digital Input
60
60

61. Offset
Offset Error: A constant voltage difference
between the ideal DAC output and the actual.
– The voltage axis intercept of the DAC output curve is different than the
ideal.
Output Voltage
Desired/Ideal Output
Positive Offset
Digital Input
Negative Offset
61
61

62. Applications of DAC
Digital Motor Control
Computer Printers
Sound Equipment (e.g. CD/MP3 Players, etc.)
Function Generators/Oscilloscopes
Digital Audio
62
62

63. References
• Callis, J. B. “The Digital to Analog Converter.” 2002.
http://courses.washington.edu/jbcallis/lectures/C464_L
ec5_Sp-02.pdf. 14 March 2006
• “DAC.” 2006. http://en.wikipedia.org/wiki/Digital-toanalog_converter#DAC_types. 14 March 2006.
• Johns, David and Ken Martin. “Data Converter
Fundamentals.” © 1997.
http://www.eecg.toronto.edu/~kphang/ece1371/chap11_
slides.pdf. 14 March 2006
• Goericke, Fabian, Keunhan Park and Geoffrey
Williams. “Digital to Analog Converter.” © 2005.
http://www.me.gatech.edu/mechatronics_course/DAC_
F05.ppt. 14 March 2006
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64. 64
64

65. Questions
65