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Digital to Analog
Converters (DAC)
Adam Fleming
Mark Hunkele
3/11/2005
2
Outline
 Purpose
 Types
 Performance Characteristics
 Applications
3
Purpose
 To convert digital values to analog voltages
 Performs inverse operation of the Analog-to-
Digital Converter (ADC)

DAC
Digital Value Analog Voltage
Reference Voltage
Value
Digital

OUT
V
4
DACs
 Types
 Binary Weighted Resistor
 R-2R Ladder
 Multiplier DAC
 The reference voltage is constant and is set by the manufacturer.
 Non-Multiplier DAC
 The reference voltage can be changed during operation.
 Characteristics
 Comprised of switches, op-amps, and resistors
 Provides resistance inversely proportion to
significance of bit
5
Binary Weighted Resistor
Rf = R
8R
4R
2R
R Vo
-VREF
 i
I
LSB
MSB
6
Binary Representation
Rf = R
8R
4R
2R
R Vo
-VREF
 i
I
Least
Significant Bit
Most
Significant Bit
7
Binary Representation
-VREF
Least
Significant Bit
Most
Significant Bit
CLEARED
SET
( 1 1 1 1 )2 = ( 15 )10
8
Binary Weighted Resistor
Rf = R
8R
4R
2R
R Vo
-VREF
 i
I
LSB
MSB
 “Weighted
Resistors”
based on bit
 Reduces
current by a
factor of 2 for
each bit
9
Binary Weighted Resistor
 Result:
 Bi = Value of Bit i










 R
B
R
B
R
B
R
B
V
I REF
8
4
2
0
1
2
3












8
4
2
0
1
2
3
B
B
B
B
V
R
I
V REF
f
OUT
10
Binary Weighted Resistor
 More Generally:
 Bi = Value of Bit i
 n = Number of Bits
Resolution
Value
Digital
2 1



  

REF
i
n
i
REF
OUT
V
B
V
V
11
R-2R Ladder
VREF
MSB
LSB
12
R-2R Ladder
 Same input switch setup as Binary
Weighted Resistor DAC
 All bits pass through resistance of 2R
VREF
MSB
LSB
13
R-2R Ladder
 The less significant the bit, the more resistors the signal
muss pass through before reaching the op-amp
 The current is divided by a factor of 2 at each node
LSB MSB
14
R-2R Ladder
 The current is divided by a factor of 2 at each node
 Analysis for current from (001)2 shown below
0
I
VREF
R
R R R 2R
2R
2R
2R
Op-Amp input
“Ground”
B0
2
0
I
4
0
I
8
0
I
R
V
R
R
R
V
I REF
REF
3
2
2
2
0 



B1
B2
15
R-2R Ladder
 Result:
 Bi = Value of Bit i









8
4
2
0
1
2 B
B
B
V
R
R
V REF
f
OUT
Rf









8
4
2
3
0
1
2 B
B
B
R
V
I REF
16
R-2R Ladder
 If Rf = 6R, VOUT is same as Binary Weighted:
 Bi = Value of Bit i
 

 1
2 i
n
i
REF
OUT
B
V
V
 
 i
n
i
REF B
R
V
I
2
3
17
0
I
VREF
R
R R R 2R
2R
2R
2R
Op-Amp input
“Ground”
B0
B2
0
I
VREF
R-2R Ladder
 Example:
 Input = (101)2
 VREF = 10 V
 R = 2 Ω
 Rf = 2R
mA
67
.
1
3
2
2
2
0 





R
V
R
R
R
V
I REF
REF
mA
04
.
1
2
8
0
0





I
I
I amp
op
V
17
.
4


  f
amp
op
OUT R
I
V
18
Pros & Cons
Binary Weighted R-2R
Pros Easily understood
Only 2 resistor values
Easier implementation
Easier to manufacture
Faster response time
Cons
Limited to ~ 8 bits
Large # of resistors
Susceptible to noise
Expensive
Greater Error
More confusing analysis
19
Digital to Analog Converters
Performance Specifications
Common Applications
Presented by: Mark Hunkele
20
Digital to Analog Converters
-Performance Specifications
 Resolution
 Reference Voltages
 Settling Time
 Linearity
 Speed
 Errors
21
 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
Digital to Analog Converters
-Performance Specifications
-Resolution
N
LSB
V
V
2
Resolution Ref

 N = Number of bits
22
Digital to Analog Converters
-Performance Specifications
-Resolution
Better Resolution(3 bit)
Poor Resolution(1 bit)
Vout
Desired Analog
signal
Approximate
output
2
Volt.
Levels
Digital Input
0 0
1
Digital Input
Vout
Desired Analog signal
Approximate
output
8
Volt.
Levels
000
001
010
011
100
101
110
111
110
101
100
011
010
001
000
23
 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
Digital to Analog Converters
-Performance Specifications
-Reference Voltage
24
Digital to Analog Converters
-Performance Specifications
-Reference Voltage
Assume 2 bit DAC
Non-Multiplier: (Vref = C)
Digital Input
Multiplier: (Vref = Asin(wt))
0
Voltage
00
01 01
00
10 10
11
0
Voltage
Digital Input
00 00
01 01
10 10
11
25
 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.
Digital to Analog Converters
-Performance Specifications
-Settling Time
26
Digital to Analog Converters
-Performance Specifications
-Settling Time
Analog Output Voltage
Expected
Voltage
+VLSB
-VLSB
Settling time
Time
27
 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.
Digital to Analog Converters
-Performance Specifications
-Linearity
28
Digital to Analog Converters
-Performance Specifications
-Linearity
Linearity(Ideal Case)
Digital Input
Perfect Agreement
Desired/Approximate Output
Analog
Output
Voltage
NON-Linearity(Real World)
Analog
Output
Voltage
Digital Input
Desired Output
Miss-alignment
Approximate
output
29
 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
Digital to Analog Converters
-Performance Specifications
-Speed
30
 Non-linearity
Differential
Integral
 Gain
 Offset
 Non-monotonicity
Digital to Analog Converters
-Performance Specifications
-Errors
31
 Differential Non-Linearity: Difference in voltage step size
from the previous DAC output (Ideally All DLN’s = 1
VLSB)
Digital to Analog Converters
-Performance Specifications
-Errors: Differential Non-Linearity
Digital Input
Ideal Output
Analog
Output
Voltage
VLSB
2VLSB
Diff. Non-Linearity = 2VLSB
32
 Integral Non-Linearity: Deviation of the actual
DAC output from the ideal (Ideally all INL’s = 0)
Digital to Analog Converters
-Performance Specifications
-Errors: Integral Non-Linearity
Digital Input
Ideal Output
1VLSB Int. Non-Linearity = 1VLSB
Analog
Output
Voltage
33
 Gain Error: Difference in slope of the ideal
curve and the actual DAC output
Digital to Analog Converters
-Performance Specifications
-Errors: Gain
High Gain Error: Actual
slope greater than ideal
Low Gain Error: Actual
slope less than ideal
Digital Input
Desired/Ideal Output
Analog
Output
Voltage
Low Gain
High Gain
34
 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.
Digital to Analog Converters
-Performance Specifications
-Errors: Offset
Digital Input
Desired/Ideal Output
Output Voltage
Positive Offset
Negative Offset
35
 Non-Monotonic: A decrease in output
voltage with an increase in the digital input
Digital to Analog Converters
-Performance Specifications
-Errors: Non-Monotonicity
Analog
Output
Voltage
Digital Input
Desired Output
Monotonic
Non-Monotonic
36
 Generic use
 Circuit Components
 Digital Audio
 Function Generators/Oscilloscopes
 Motor Controllers
Digital to Analog Converters
-Common Applications
37
 Used when a continuous analog signal is
required.
 Signal from DAC can be smoothed by a
Low pass filter
Digital to Analog Converters
-Common Applications
-Generic
0 bit
nth bit
n bit DAC
011010010101010100101
101010101011111100101
000010101010111110011
010101010101010101010
111010101011110011000
100101010101010001111
Digital Input
Filter
Piece-wise
Continuous Output
Analog
Continuous Output
38
 Voltage controlled Amplifier
 digital input, External Reference Voltage as control
 Digitally operated attenuator
 External Reference Voltage as input, digital control
 Programmable Filters
 Digitally controlled cutoff frequencies
Digital to Analog Converters
-Common Applications
-Circuit Components
39
 CD Players
 MP3 Players
 Digital Telephone/Answering Machines
Digital to Analog Converters
-Common Applications
-Digital Audio
1. http://electronics.howstuffworks.com/cd.htm
2. http://accessories.us.dell.com/sna/sna.aspx?c=us&cs=19&l=en&s=dhs&~topic=odg_dj
1 2
3
3. http://www.toshiba.com/taistsd/pages/prd_dtc_digphones.html
40
Digital to Analog Converters
-Common Applications
-Function Generators
 Digital Oscilloscopes
 Digital Input
 Analog Ouput
 Signal Generators
 Sine wave generation
 Square wave generation
 Triangle wave generation
 Random noise generation
1
1. http://www.electrorent.com/products/search/General_Purpose_Oscilloscopes.html
2
2. http://www.bkprecision.com/power_supplies_supply_generators.htm
41
 Cruise Control
 Valve Control
 Motor Control
Digital to Analog Converters
-Common Applications
-Motor Controllers
1
1. http://auto.howstuffworks.com/cruise-control.htm
2
2. http://www.emersonprocess.com/fisher/products/fieldvue/dvc/
3
3. http://www.thermionics.com/smc.htm
42
References
 Cogdell, J.R. Foundations of Electrical Engineering. 2nd ed. Upper Saddle River, NJ:
Prentice Hall, 1996.
 “Simplified DAC/ADC Lecture Notes,” http://www-personal.engin.umd.umich.edu/
~fmeral/ELECTRONICS II/ElectronicII.html
 “Digital-Analog Conversion,” http://www.allaboutcircuits.com.
 Barton, Kim, and Neel. “Digital to Analog Converters.” Lecture, March 21, 2001.
http://www.me.gatech.edu/charles.ume/me4447Spring01/ClassNotes/dac.ppt.
 Chacko, Deliou, Holst, “ME6465 DAC Lecture” Lecture, 10/ 23/2003,
http://www.me.gatech.edu/mechatronics_course/
 Lee, Jeelani, Beckwith, “Digital to Analog Converter” Lecture, Spring 2004,
http://www.me.gatech.edu/mechatronics_course/

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5942709.ppt

  • 1. Digital to Analog Converters (DAC) Adam Fleming Mark Hunkele 3/11/2005
  • 2. 2 Outline  Purpose  Types  Performance Characteristics  Applications
  • 3. 3 Purpose  To convert digital values to analog voltages  Performs inverse operation of the Analog-to- Digital Converter (ADC)  DAC Digital Value Analog Voltage Reference Voltage Value Digital  OUT V
  • 4. 4 DACs  Types  Binary Weighted Resistor  R-2R Ladder  Multiplier DAC  The reference voltage is constant and is set by the manufacturer.  Non-Multiplier DAC  The reference voltage can be changed during operation.  Characteristics  Comprised of switches, op-amps, and resistors  Provides resistance inversely proportion to significance of bit
  • 5. 5 Binary Weighted Resistor Rf = R 8R 4R 2R R Vo -VREF  i I LSB MSB
  • 6. 6 Binary Representation Rf = R 8R 4R 2R R Vo -VREF  i I Least Significant Bit Most Significant Bit
  • 8. 8 Binary Weighted Resistor Rf = R 8R 4R 2R R Vo -VREF  i I LSB MSB  “Weighted Resistors” based on bit  Reduces current by a factor of 2 for each bit
  • 9. 9 Binary Weighted Resistor  Result:  Bi = Value of Bit i            R B R B R B R B V I REF 8 4 2 0 1 2 3             8 4 2 0 1 2 3 B B B B V R I V REF f OUT
  • 10. 10 Binary Weighted Resistor  More Generally:  Bi = Value of Bit i  n = Number of Bits Resolution Value Digital 2 1        REF i n i REF OUT V B V V
  • 12. 12 R-2R Ladder  Same input switch setup as Binary Weighted Resistor DAC  All bits pass through resistance of 2R VREF MSB LSB
  • 13. 13 R-2R Ladder  The less significant the bit, the more resistors the signal muss pass through before reaching the op-amp  The current is divided by a factor of 2 at each node LSB MSB
  • 14. 14 R-2R Ladder  The current is divided by a factor of 2 at each node  Analysis for current from (001)2 shown below 0 I VREF R R R R 2R 2R 2R 2R Op-Amp input “Ground” B0 2 0 I 4 0 I 8 0 I R V R R R V I REF REF 3 2 2 2 0     B1 B2
  • 15. 15 R-2R Ladder  Result:  Bi = Value of Bit i          8 4 2 0 1 2 B B B V R R V REF f OUT Rf          8 4 2 3 0 1 2 B B B R V I REF
  • 16. 16 R-2R Ladder  If Rf = 6R, VOUT is same as Binary Weighted:  Bi = Value of Bit i     1 2 i n i REF OUT B V V    i n i REF B R V I 2 3
  • 17. 17 0 I VREF R R R R 2R 2R 2R 2R Op-Amp input “Ground” B0 B2 0 I VREF R-2R Ladder  Example:  Input = (101)2  VREF = 10 V  R = 2 Ω  Rf = 2R mA 67 . 1 3 2 2 2 0       R V R R R V I REF REF mA 04 . 1 2 8 0 0      I I I amp op V 17 . 4     f amp op OUT R I V
  • 18. 18 Pros & Cons Binary Weighted R-2R Pros Easily understood Only 2 resistor values Easier implementation Easier to manufacture Faster response time Cons Limited to ~ 8 bits Large # of resistors Susceptible to noise Expensive Greater Error More confusing analysis
  • 19. 19 Digital to Analog Converters Performance Specifications Common Applications Presented by: Mark Hunkele
  • 20. 20 Digital to Analog Converters -Performance Specifications  Resolution  Reference Voltages  Settling Time  Linearity  Speed  Errors
  • 21. 21  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 Digital to Analog Converters -Performance Specifications -Resolution N LSB V V 2 Resolution Ref   N = Number of bits
  • 22. 22 Digital to Analog Converters -Performance Specifications -Resolution Better Resolution(3 bit) Poor Resolution(1 bit) Vout Desired Analog signal Approximate output 2 Volt. Levels Digital Input 0 0 1 Digital Input Vout Desired Analog signal Approximate output 8 Volt. Levels 000 001 010 011 100 101 110 111 110 101 100 011 010 001 000
  • 23. 23  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 Digital to Analog Converters -Performance Specifications -Reference Voltage
  • 24. 24 Digital to Analog Converters -Performance Specifications -Reference Voltage Assume 2 bit DAC Non-Multiplier: (Vref = C) Digital Input Multiplier: (Vref = Asin(wt)) 0 Voltage 00 01 01 00 10 10 11 0 Voltage Digital Input 00 00 01 01 10 10 11
  • 25. 25  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. Digital to Analog Converters -Performance Specifications -Settling Time
  • 26. 26 Digital to Analog Converters -Performance Specifications -Settling Time Analog Output Voltage Expected Voltage +VLSB -VLSB Settling time Time
  • 27. 27  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. Digital to Analog Converters -Performance Specifications -Linearity
  • 28. 28 Digital to Analog Converters -Performance Specifications -Linearity Linearity(Ideal Case) Digital Input Perfect Agreement Desired/Approximate Output Analog Output Voltage NON-Linearity(Real World) Analog Output Voltage Digital Input Desired Output Miss-alignment Approximate output
  • 29. 29  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 Digital to Analog Converters -Performance Specifications -Speed
  • 30. 30  Non-linearity Differential Integral  Gain  Offset  Non-monotonicity Digital to Analog Converters -Performance Specifications -Errors
  • 31. 31  Differential Non-Linearity: Difference in voltage step size from the previous DAC output (Ideally All DLN’s = 1 VLSB) Digital to Analog Converters -Performance Specifications -Errors: Differential Non-Linearity Digital Input Ideal Output Analog Output Voltage VLSB 2VLSB Diff. Non-Linearity = 2VLSB
  • 32. 32  Integral Non-Linearity: Deviation of the actual DAC output from the ideal (Ideally all INL’s = 0) Digital to Analog Converters -Performance Specifications -Errors: Integral Non-Linearity Digital Input Ideal Output 1VLSB Int. Non-Linearity = 1VLSB Analog Output Voltage
  • 33. 33  Gain Error: Difference in slope of the ideal curve and the actual DAC output Digital to Analog Converters -Performance Specifications -Errors: Gain High Gain Error: Actual slope greater than ideal Low Gain Error: Actual slope less than ideal Digital Input Desired/Ideal Output Analog Output Voltage Low Gain High Gain
  • 34. 34  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. Digital to Analog Converters -Performance Specifications -Errors: Offset Digital Input Desired/Ideal Output Output Voltage Positive Offset Negative Offset
  • 35. 35  Non-Monotonic: A decrease in output voltage with an increase in the digital input Digital to Analog Converters -Performance Specifications -Errors: Non-Monotonicity Analog Output Voltage Digital Input Desired Output Monotonic Non-Monotonic
  • 36. 36  Generic use  Circuit Components  Digital Audio  Function Generators/Oscilloscopes  Motor Controllers Digital to Analog Converters -Common Applications
  • 37. 37  Used when a continuous analog signal is required.  Signal from DAC can be smoothed by a Low pass filter Digital to Analog Converters -Common Applications -Generic 0 bit nth bit n bit DAC 011010010101010100101 101010101011111100101 000010101010111110011 010101010101010101010 111010101011110011000 100101010101010001111 Digital Input Filter Piece-wise Continuous Output Analog Continuous Output
  • 38. 38  Voltage controlled Amplifier  digital input, External Reference Voltage as control  Digitally operated attenuator  External Reference Voltage as input, digital control  Programmable Filters  Digitally controlled cutoff frequencies Digital to Analog Converters -Common Applications -Circuit Components
  • 39. 39  CD Players  MP3 Players  Digital Telephone/Answering Machines Digital to Analog Converters -Common Applications -Digital Audio 1. http://electronics.howstuffworks.com/cd.htm 2. http://accessories.us.dell.com/sna/sna.aspx?c=us&cs=19&l=en&s=dhs&~topic=odg_dj 1 2 3 3. http://www.toshiba.com/taistsd/pages/prd_dtc_digphones.html
  • 40. 40 Digital to Analog Converters -Common Applications -Function Generators  Digital Oscilloscopes  Digital Input  Analog Ouput  Signal Generators  Sine wave generation  Square wave generation  Triangle wave generation  Random noise generation 1 1. http://www.electrorent.com/products/search/General_Purpose_Oscilloscopes.html 2 2. http://www.bkprecision.com/power_supplies_supply_generators.htm
  • 41. 41  Cruise Control  Valve Control  Motor Control Digital to Analog Converters -Common Applications -Motor Controllers 1 1. http://auto.howstuffworks.com/cruise-control.htm 2 2. http://www.emersonprocess.com/fisher/products/fieldvue/dvc/ 3 3. http://www.thermionics.com/smc.htm
  • 42. 42 References  Cogdell, J.R. Foundations of Electrical Engineering. 2nd ed. Upper Saddle River, NJ: Prentice Hall, 1996.  “Simplified DAC/ADC Lecture Notes,” http://www-personal.engin.umd.umich.edu/ ~fmeral/ELECTRONICS II/ElectronicII.html  “Digital-Analog Conversion,” http://www.allaboutcircuits.com.  Barton, Kim, and Neel. “Digital to Analog Converters.” Lecture, March 21, 2001. http://www.me.gatech.edu/charles.ume/me4447Spring01/ClassNotes/dac.ppt.  Chacko, Deliou, Holst, “ME6465 DAC Lecture” Lecture, 10/ 23/2003, http://www.me.gatech.edu/mechatronics_course/  Lee, Jeelani, Beckwith, “Digital to Analog Converter” Lecture, Spring 2004, http://www.me.gatech.edu/mechatronics_course/