Download 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  
V

V2
 2
2
 RR
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
16 R 
 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  bn i
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  number of 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?