1. ME 4447: Introduction to Mechatronics1
Digital to Analog Converters (DAC)
Jesse Barton
Hyun Gyu Kim
Christopher Neel

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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)

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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).

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DAC Configuration

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DAC Types
Multiplying DAC
- reference source is external to the DAC
package
Nonmultiplying DAC
- reference source is inside the DAC package

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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

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DAC Circuit Types
Two types of DAC Circuits:
1. Binary weighted
2. R-2R ladder

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N-Bit Binary Weighted DAC

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Binary Weighted Principles
( )
MSBb
bitsinputofnumberN
MSBtoingcorrespondresistanceR
junctionleavingcurrentsofsumI
2
1
0
1
10
=
=
=
=
= ∑=
−
N
i
i
i
R
R
b
VI

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Principles Cont’d
V0 = -RfI0
V0 = voltage output from amplifier
Rf = feedback resistance
Resolution= VR/2N
Note: For a gain of 1, R = 2Rf

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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.

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Solution
Rf = (R/2)
R2R4R8R
Vo
VR
1-bit
MSB
2-bit3-bit4-bit
∑ iI

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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

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

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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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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.

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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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R/2R ladder DAC
• Most popular single
package DAC
• Resolves BWL problems
• Only two resistor values

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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

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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

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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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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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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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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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Applications of DAC
• Control Systems
• Digital Audio
• Digital Telephones
• Cruise Control
• Waveform Generation

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Discussion