Digital to Analog Converters (DAC)
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Transcript Digital to Analog Converters (DAC)
Digital to Analog Converters
(DAC)
15 March 2006
Doug Hinckley
Lee Huynh
Dooroo Kim
What is a DAC?
A digital to analog converter (DAC)
converts a digital signal to an analog
voltage or current output.
100101…
DAC
Analog Output Signal
What is a DAC?
0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011
Digital Input Signal
Types of DACs
Many types of DACs available.
Usually switches, resistors, and opamps used to implement conversion
Two Types:
Binary Weighted Resistor
R-2R Ladder
Binary Weighted Resistor
Utilizes a summing op-amp circuit
Weighted resistors are used to
distinguish each bit from the most
significant to the least significant
Transistors are used to switch
between Vref and ground (bit high or
low)
Binary Weighted Resistor
Assume Ideal
Op-amp
No current into
op-amp
Virtual ground at
inverting input
Vout= -IRf
Vref
R
2R
I
Rf
4R
+
2nR
Vout
Binary Weighted Resistor
Voltages V1 through Vn are
either Vref if corresponding bit
is high or ground if
corresponding bit is low
V1 is most significant bit
Vref
V1
R
V2
2R
V3
4R
I
Rf
+
Vn is least significant bit
Vn
2n-1R
MSB
Vout
Vn
V1 V2 V3
IRf Rf
n -1
2 R
R 2R 4R
LSB
Vout
Binary Weighted Resistor
If Rf=R/2
Vout
Vn
V1 V2 V3
IRf n
2
2 4 8
For example, a 4-Bit converter yields
Vout
1
1
1
1
Vref b3 b2 b1 b0
4
8
16
2
Where b3 corresponds to Bit-3, b2 to Bit-2, etc.
Binary Weighted Resistor
Advantages
Simple Construction/Analysis
Fast Conversion
Disadvantages
Requires large range of resistors (2000:1
for 12-bit DAC) with necessary high
precision for low resistors
Requires low switch resistances in
transistors
Can be expensive. Therefore, usually
limited to 8-bit resolution.
R-2R Ladder
Each bit corresponds
to a switch:
Vref
If the bit is high,
the corresponding
switch is connected to
the inverting input of
the op-amp.
Bit: 0
0
0
4-Bit Converter
0
Vout
If the bit is low, the
corresponding switch
is connected to ground.
R-2R Ladder
Vref
V1
V2
V3
V3
Ideal Op-amp
2R
2R
2 R 2 R
Req
R
2R 2R
R-2R Ladder
Vref
V1
V2
V2
V3
V3
R
R
1
R
V3
V2 V2
2
RR
I
Likewise,
Vout
1
V1
2
1
V1 Vref
2
Vout IR
V2
R-2R Ladder
Results:
Vref
V1
V2
V3
1
1
1
V3 Vref , V2 Vref , V1 Vref
8
4
2
Vout
Vref
Vref
Vref
Vref
R b3
b2
b1
b0
4R
8R
16R
2R
Where b3 corresponds to bit 3,
b2 to bit 2, etc.
Vout
If bit n is set, bn=1
If bit n is clear, bn=0
R-2R Ladder
For a 4-Bit R-2R Ladder
Vout
1
1
1
1
Vref b3 b2 b1 b0
4
8
16
2
For general n-Bit R-2R Ladder or Binary Weighted Resister DAC
n
Vout Vref bni
i 1
1
i
2
R-2R Ladder
Advantages
Only two resistor values (R and 2R)
Does not require high precision resistors
Disadvantage
Lower conversion speed than binary
weighted DAC
Specifications of DACs
•
•
•
•
•
•
Resolution
Speed
Linearity
Settling Time
Reference Voltages
Errors
Resolution
Smallest analog increment
corresponding to 1 LSB change
An N-bit resolution can resolve 2N
distinct analog levels
Common DAC has a 8-16 bit
resolution
Vref
Resolution VLSB N
2
where N num berof bits
Speed
Rate of conversion of a single digital
input to its analog equivalent
Conversion rate depends on
clock speed of input signal
settling time of converter
When the input changes rapidly, the
DAC conversion speed must be high.
Linearity
Analog Output Signal
The difference between the desired analog
output and the actual output over the full
range of expected values
0000
0001
0010
0011
Digital Input Signal
0100
0101
Linearity
Ideally, a DAC should produce a linear
relationship between the digital input and
analog output
0000
Analog Output Signal
Non-Linearity
Analog Output Signal
Linearity (Ideal)
0001
0010
0011
Digital Input Signal
0100
0101
0000
0001
0010
0011
Digital Input Signal
0100
0101
Settling Time
Time required for the output signal to settle within
+/- ½ LSB of its final value after a given change in
input scale
Limited by slew rate of output amplifier
Ideally, an instantaneous change in analog voltage
would occur when a new binary word enters into
DAC
Reference Voltages
Used to determine how each digital
input will be assigned to each voltage
division
Types:
Non-multiplier DAC: Vref is fixed
Multiplier DAC: Vref provided by external
source
Types of Errors Associated with
DACs
Gain
Offset
Full Scale
Resolution
Non-Linearity
Non-Monotonic
Settling Time and Overshoot
Analog Output
Occurs when
the slope of
the actual
output
deviates from
the ideal
output
.
Gain Error
Digital Input
Ideal Output
Positive Offset Errorr
Negative Offset Error
Analog Output
Occurs when
there is a
constant offset
between the
actual output
and the ideal
output
.
Offset Error
Digital Input
Ideal Output
Positive Offset Errorr
Negative Offset Error
Analog Output
Occurs when
the actual signal
has both gain
and offset
errors
.
Full Scale Error
Digital Input
Ideal Output
Full Scale Error Error
Resolution Error
Poor representation
of ideal output due
to poor resolution
Size of voltage
divisions affect the
resolution
Non-Linearity Error
Occurs when analog output of signal
is non-linear
Two Types
Differential – analog step-sizes changes
with increasing digital input (measure of
largest deviation; between successive
bits
Integral – amount of deviation from a
straight line after offset and gain errors
removed; on concurrent bits
Non-Linearity Error, cont.
Non-Monotonic Error
Occurs when an
increase in digital
input results in a
decrease in the
analog output
Settling Time and Overshoot Error
Analog
Settling Time –
Output
+1/2*VLSB
time required for
Ideal
the output to fall
Output
with in +/- ½ VLSB
-1/2*VLSB
Overshoot – occurs
when analog
output overshoots
Settling
the ideal output
Time
Time
Applications
Digital Motor Control
Computer Printers
Sound Equipment (e.g. CD/MP3
Players, etc.)
Electronic Cruise Control
Digital Thermostat
References
Callis, J. B. “The Digital to Analog Converter.” 2002.
http://courses.washington.edu/jbcallis/lectures/C464_Le
c5_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_F
05.ppt. 14 March 2006
QUESTIONS?