1.
ME 4447: Introduction to Mechatronics1
Digital to Analog Converters (DAC)
Jesse Barton
Hyun Gyu Kim
Christopher Neel
2.
ME 4447: Introduction to Mechatronics2
What is a DAC?
A digital-to-analog converter (DAC) is a circuit
that produces an analog current or voltage that
is proportional to an analog reference (voltage or
current) and an N-bit binary word.
Vout = k x Vref x (Binary Word)
3.
ME 4447: Introduction to Mechatronics3
In English
• DACs generate piecewise continuous signals
from digital code.
OR
• DAC converters are devices that receive a
binary word from the microprocessor and
convert it to a scaled analog voltage (or current).
4.
ME 4447: Introduction to Mechatronics4
DAC Configuration
5.
ME 4447: Introduction to Mechatronics5
DAC Types
Multiplying DAC
- reference source is external to the DAC
package
Nonmultiplying DAC
- reference source is inside the DAC package
6.
ME 4447: Introduction to Mechatronics6
Multiplying DAC advantages
• External ref. can be time-varying analog voltage that
multiplies binary function
fixed programmable byte scales continuous
output instead of using time-varying bytes w/ fixed VR
to produce discrete output
• External reference can be fixed
less likely to produce error from reference voltage
drift with temperature than internal reference
7.
ME 4447: Introduction to Mechatronics7
DAC Circuit Types
Two types of DAC Circuits:
1. Binary weighted
2. R-2R ladder
8.
ME 4447: Introduction to Mechatronics8
N-Bit Binary Weighted DAC
9.
ME 4447: Introduction to Mechatronics9
Binary Weighted Principles
( )
MSBb
bitsinputofnumberN
MSBtoingcorrespondresistanceR
junctionleavingcurrentsofsumI
2
1
0
1
10
=
=
=
=
= ∑=
−
N
i
i
i
R
R
b
VI
10.
ME 4447: Introduction to Mechatronics10
Principles Cont’d
V0 = -RfI0
V0 = voltage output from amplifier
Rf = feedback resistance
Resolution= VR/2N
Note: For a gain of 1, R = 2Rf
11.
ME 4447: Introduction to Mechatronics11
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.
12.
ME 4447: Introduction to Mechatronics12
Solution
Rf = (R/2)
R2R4R8R
Vo
VR
1-bit
MSB
2-bit3-bit4-bit
∑ iI
13.
ME 4447: Introduction to Mechatronics13
Solution Cont’d
V625.5)A001125.0)(5(
IR-V
A0.001125-
10*2
1
10*2
0
10*2
0
10*2
1V10
3
0
0f0
0
43424140
=−Ω−=
=
=
+++
Ω
−=
V
I
Io
14.
ME 4447: Introduction to Mechatronics14
Solution Cont’d
Binary input = 1001 = 9
From example, V0 = 5.625V
V0/VR= 5.625V/10V = 9/16
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ME 4447: Introduction to Mechatronics15
Limitations of the Binary Weighted
DAC
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 µA
Op-amps to handle those currents are expensive
because this is usually below the current noise
threshold.
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ME 4447: Introduction to Mechatronics16
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.
17.
ME 4447: Introduction to Mechatronics17
Limitations Cont’d
Intuitively, the resistance values must be
accurate to less than one part in 2N
for the RN
input to be meaningful. This is difficult to do,
especially in IC’s.
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ME 4447: Introduction to Mechatronics18
R/2R ladder DAC
• Most popular single
package DAC
• Resolves BWL problems
• Only two resistor values
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ME 4447: Introduction to Mechatronics19
Equations governing R/2R
bitsofnumberisNwhere;
2
Resolution N
RV
=
MSBisbwhere;
2
1
1
∑=
−=
N
i
i
i
Ro
b
VV
( ) bitsofnumberisNwhere;
2
1
1
−−= NRfso VV
( ) MSBisbwhere;
22
1
1
1∑∑ =
−
=
N
i
i
iR
i
b
R
V
I
20.
ME 4447: Introduction to Mechatronics20
Principles of Operation
• Binary Switch true
ground w/ LOW input
• Binary Switch op-
amp virtual ground w/ HI
input
• Splits current at each bit
• After multiplication of
binary word Io
• Inverting Op-amp used
to generate analog
output voltage
• Performed many times
per second semi-
continuous DAC
21.
ME 4447: Introduction to Mechatronics21
Specifications of DAC’s
• Resolution
– Increases (improves) as number of bits increases
– Most microcontrollers use 8 bit DAC
– Some 12 bit DAC used in high end applications
• Linearity
– Max deviation over full range of output @ room temp.
• Settling Time
– Time for DAC to come w/in 0.5 LSB {Vo± 0.5*(VR /2N
)} of new voltage after
binary change
– Typ. current output DAC’s conversion times (10 ns to 1 μs)
• Reference Voltage
– Internal / external
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ME 4447: Introduction to Mechatronics22
DAC Errors
• Resolution:
more bits = more precise
• Overshoot & Settling Time:
String of amplifiers w/ feedback loops = very rapid response or
very slow response depending on system properties
• Absolute Accuracy Error:
Difference between theoretical and actual output
• Conversion Speed:
Rapidly fluctuating inputs require high conversion speed to be
interpreted accurately
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ME 4447: Introduction to Mechatronics23
DAC Errors Cont’d
• Non-Monotonicity:
Certain conditions where increased input results in decrease Vo
• Differential Non-Linearity:
Deviation of actual converter step size from the ideal predicted wave
step
• Gain Error:
Gain too low = same analog output; gain too high = too large an
output
• Offset Error:
Constant error of DAC
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ME 4447: Introduction to Mechatronics24
DAC Errors Cont’d
• Resistance Error:
Pertains mainly to BWR DAC since large variety of resistors used
error varies greatly disturbing DAC performance
• Saturation:
Use of op-amps requires that input voltage and scaling voltages be
bounded to the specifications of the op-amp.
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ME 4447: Introduction to Mechatronics31
Applications of DAC
• Control Systems
• Digital Audio
• Digital Telephones
• Cruise Control
• Waveform Generation
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ME 4447: Introduction to Mechatronics32
Discussion
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