Download Slide 1

Digital to Analog Converters
Andrew Gardner
Muhammad Salman
David Fernandes
Jevawn Roberts
Introduction to Mechatronics
Student Lecture – 10/23/06
Outline
What is a DAC?
Different Types of DACs
Binary Weighted Resistor
R-2R Ladder
Specifications
Commonly used DACs
Application
Introduction to Mechatronics
Student Lecture – 10/23/06
Introduction
A DAC is a Digital to Analog converter.
It converts a binary digital number into
an analog representation, most
commonly voltage though current is
also used sometimes.
1
0
0
1
0
1
0
1
0
0
1
1
0
1
1
1
1
0
0
1
1
0
1
0
1
0
1
1
DAC
Introduction to Mechatronics
Student Lecture – 10/23/06
Introduction
Analog Output Signal
Each binary number sampled by the DAC
corresponds to a different output level.
0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011
Digital Input Signal
Introduction to Mechatronics
Student Lecture – 10/23/06
Typical Output
DACs capture and hold a number, convert it
to a physical signal, and hold that value for a
given sample interval. This is known as a
zero-order hold and results in a piecewise
constant output.
DAC
Ideally Sampled Signal
Output typical of a real, practical
Introduction to MechatronicsDAC due to sample & hold
Student Lecture – 10/23/06
Binary Weighted Resistor DAC
• 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)
Introduction to Mechatronics
Student Lecture – 10/23/06
Summing OP-Amps
• Inverting summer circuit used in Binary
Weighted Resistor DAC.
• V(out) is 180° out of phase from V(in)
Introduction to Mechatronics
Student Lecture – 10/23/06
Binary Weighted Input DAC
• Ideal Op-amp
• No current into
op-amp
• Virtual ground at
inverting input
MSB
• Vout= -IRf
Vout
Vref
V1
R
V2
2R
V3
4R
I
Rf
+
Vn
2n-1R
LSB
V
Vn 
 V1 V2
3
  IRf   Rf  

  n -1 
2 R
 R 2R 4R
Introduction to Mechatronics
Student Lecture – 10/23/06
Vout
Calculation
bn 1 bn  2
b0
VOUT  Vref  R(

 ...  n
2R 4R
2 R
VOUT 
 Vref
2
n
(2n 1  bn 1  2n 2  bn2  ...  2  b1  b0
Introduction to Mechatronics
Student Lecture – 10/23/06
Cont’d
Example:
n4
Vout 
 Vref
2n
 Vref
Vout 
Vout 
V fs
 Vref
(2n1 bn1  2n2 bn 2  ...  2b1  b0 )
16
(8b3  4b2  2b1  b0 )
(8(0)  4(0)  2(1)  1(1)) 
16
 Vref  RES
3
Vref
16
RES  1 / 2 n
n = totalbits
V fs  Vref
 24  1 
Introduction to Mechatronics

 24 
  0.9375 Vref

 Student Lecture – 10/23/06
Advantages and Disadvantages
Advantage
– Easy principle/construction
– Fast conversion
Disadvantages
– Requirement of several different precise input
resistor values: Requires large range of resistors
(2048:1 for 12-bit DAC) with necessary high
precision for low resistors one unique value per
binary input bit. (High bit DACs)
– Larger resistors ~ more error.
– Precise large resistors – expensive.
Introduction to Mechatronics
Student Lecture – 10/23/06
R-2R Resistor Ladder DAC
Vref
MSB
Bit:
LSB
0
0
0
0
4-Bit Converter
Introduction to Mechatronics
Student Lecture – 10/23/06
Vout
R-2R DAC Example
Vref
V2
V1
V0
• Convert 0001 to analog
Introduction to Mechatronics
Student Lecture – 10/23/06
R-2R DAC Example (cont.)
V0
V1
V1
=
V0
V1  V0 V0

R
R
Req 
2 R 
1
1
 2 R 
1
V1  2 V0
Nodal Analysis
R
Likewise,
Voltage Divider
V1 
R
1
V2  V2
RR
2
Introduction to Mechatronics
Student Lecture – 10/23/06
V2 
R
1
V3  V3
RR
2
Conversion Equation
Vout
1
1
1
 1
 Vref  b3  b2  b1  b0 
4
8
16 
 2
For a 4-Bit R-2R Ladder
For general n-Bit
R-2R Ladder
Binary Weighted
Resister DAC
n
1
Vout  Vref  bni i
2
i 1
Introduction to Mechatronics
Student Lecture – 10/23/06
R-2R DAC Summary
• Advantages
– Only two resistor values
– Does not need as precision resistors as Binary weighted
DACs
– Cheap and Easy to manufacture
• Disadvantages
– Slower conversion rate
Introduction to Mechatronics
Student Lecture – 10/23/06
DAC Specification
•
•
•
•
•
Resolution
Reference Voltage
Speed
Settling Time
Linearity
Introduction to Mechatronics
Student Lecture – 10/23/06
Resolution
• The change in output voltage for a change of the LSB.
• Related to the size of the binary representation of the
voltage. (8-bit)
• Higher resolution results in smaller steps between
voltage values
Resolution 
Vref
Introduction to Mechatronics
Student Lecture – 10/23/06
2
n
Reference Voltage
• Multiplier DAC
– Reference voltage is a constant set by the
manufacturer
• Non-Multiplier DAC
– Reference voltage is variable
• Full scale Voltage
– Slightly less than the reference voltage (Vref-VLSB)
Introduction to Mechatronics
Student Lecture – 10/23/06
Speed
• Also called the conversion rate or sampling rate
– rate at which the register value is updated
• For sampling rates of over 1 MHz a DAC is designated
as high speed.
• Speed is limited by the clock speed of the microcontroller
and the settling time of the DAC
Introduction to Mechatronics
Student Lecture – 10/23/06
Settling Time
• Time in which the DAC output settles at the desired
value ± ½ VLSB.
• Faster DACs decrease the settling time
Introduction to Mechatronics
Student Lecture – 10/23/06
Linearity
• Represents the relationship between digital values and
analog outputs.
• Should be related by a single proportionality constant.
(constant slope)
Introduction to Mechatronics
Student Lecture – 10/23/06
DAC Error
• Non-Linearity
– Differential
– Integral
• Gain Error
• Offset Error
• Monotonicity
• Resolution
Introduction to Mechatronics
Student Lecture – 10/23/06
Non-linearity
Analog Output Voltage
• Deviation from a linear relationship between digital input
and analog output.
Desired Output
Digital Input
Introduction to Mechatronics
Student Lecture – 10/23/06
Non-Linearity
Analog Output Voltage
Analog Output Voltage
• Differential
– Worst case deviation from the ideal VLSB step for an
increment of LSB
• Integral
– Worst case deviation from the line between the
endpoint (zero and full scale) voltages
2VLSB
VLSB
Integral
Non-linearity
Digital Input
Introduction to Mechatronics
Student Lecture – 10/23/06
Digital Input
Gain Error
• Also called Full-Scale Error
• Deviation from the ideal full scale voltage due to a higher
or lower gain than expected.
High Gain
Analog Output Voltage
Desired/Ideal Output
Low Gain
Introduction to Mechatronics
Digital
Student Lecture – 10/23/06
Input
Offset Error
• Also called Zero Error
• Difference between ideal voltage output and actual
voltage output for a digital input of zero.
Output Voltage
Ideal Output
Digital Input
Introduction to Mechatronics
Student Lecture – 10/23/06
Monotonicity
Analog Output Voltage
• Increases or decreases of the digital value must
correspond to increases or decreases of the
voltage output.
Desired Output
Non-monotonic
behavior
Digital Input
Introduction to Mechatronics
Student Lecture – 10/23/06
Resolution Error
• For matching curves over time or simply outputting
accurate values a proper resolution must be selected
• Resolution must be high enough for the desired
precision (½ VLSB)
Vout
Desired Analog
signal
11
10
01
00
Introduction to Mechatronics
Time
Student Lecture – 10/23/06
Applications – Audio
Many audio signals are stored as binary
numbers (on media such as CDs and in
computer files such as MP3s). Therefore
computer sound cards, stereo systems,
digital cell phones, and portable music
players contain DAC to convert the digital
representation to an analog signal.
Introduction to Mechatronics
Student Lecture – 10/23/06
Example DAC
• AD 7224 –
– Manufactured by Analog Devices
– Type: R-2R Voltage Output
– Reference voltage: Non-Multiplier
– 2 – 12.5 Volts
– 8-bit Input
– Settling Time: 7 μs
– Cost: about $4.00
Introduction to Mechatronics
Student Lecture – 10/23/06
Example DAC
18 Pin integrated circuit
including output amplifier
Introduction to Mechatronics
Student Lecture – 10/23/06
Applications – Video
Video signals from digital sources, such as a
computer or DVD must be converted to
analog signals before being displayed on an
analog monitor. Beginning on February 18th,
2009 all television broadcasts in the United
States will be in a digital format, requiring
ATSC tuners (either internal or set-top box)
to convert the signal to analog.
Introduction to Mechatronics
Student Lecture – 10/23/06
References
Previous Student Lectures
http://en.wikipedia.org/
http://allaboutcircuits.com
Introduction to Mechatronics
Student Lecture – 10/23/06
Questions
Introduction to Mechatronics
Student Lecture – 10/23/06