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Digital to Analog Converters. Andrew Gardner Muhammad Salman David Fernandes Jevawn Roberts. Outline. What is a DAC? Different Types of DACs Binary Weighted Resistor R-2R Ladder Specifications Commonly used DACs Application. Introduction - PowerPoint PPT Presentation
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Introduction to Mechatronics
Student Lecture – 10/23/06
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 ResistorR-2R Ladder
SpecificationsCommonly used DACsApplication
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.
0101
0011
0111
1001
1001
1010
1011 DAC
Introduction to Mechatronics
Student Lecture – 10/23/06
IntroductionEach binary number sampled by the DAC
corresponds to a different output level.
10111001 10100111 10000110010101000011001000010000Digital Input Signal
Ana
log
Out
put
Sig
nal
Introduction to Mechatronics
Student Lecture – 10/23/06
Ideally Sampled Signal Output typical of a real, practical DAC due to sample & hold
Typical OutputDACs 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
Introduction to Mechatronics
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
• Vout= -IRf
R
V
R
V
R
V
R
VRIRV
1-nn321
ffout 242
MSB
LSB
I
-+
R
2R
4R
2n-1R
Rf
Vout
Vref
V1
V2
V3
Vn
Introduction to Mechatronics
Student Lecture – 10/23/06
Calculation
R
b
R
b
R
bRVV
nnn
refOUT 2...
42( 021
0122
11 2...22(
2bbbb
VV n
nn
nn
refOUT
Introduction to Mechatronics
Student Lecture – 10/23/06
Cont’d
)2...22(2 012
21
1 bbbbV
V nn
nn
n
refout
refref
out VV
V16
3))1(1)1(2)0(4)0(8(
16
)248(16 0123 bbbbV
V refout
refreffs
nES
ESreffs
VVV
R
RVV
9375.02
12
2/1
4
4
4n
Example:Example:
n = totalbits
Introduction to Mechatronics
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
Bit: 0 0 0 0
4-Bit Converter Vout
Vref
MSB LSB
Introduction to Mechatronics
Student Lecture – 10/23/06
V0V1V2Vref
R-2R DAC Example
• Convert 0001 to analog
Introduction to Mechatronics
Student Lecture – 10/23/06
R-2R DAC Example (cont.)
=V0V1 V0V1
R
RRReq
11 22
1
R
V
R
VV 001
01 2 VV
1 2 21
2
RV V V
R R
2 3 31
2
RV V V
R R
Likewise,
Voltage Divider
Nodal Analysis
Introduction to Mechatronics
Student Lecture – 10/23/06
Conversion Equation
16
1
8
1
4
1
2
10123refout bbbbVV
For a 4-Bit R-2R Ladder
For general n-Bit R-2R Ladder Binary Weighted Resister DAC
i
n
iinbVV
2
1
1refout
Introduction to Mechatronics
Student Lecture – 10/23/06
• Advantages– Only two resistor values– Does not need as precision resistors as Binary weighted
DACs– Cheap and Easy to manufacture
• Disadvantages– Slower conversion rate
R-2R DAC Summary
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
n
refV
2 Resolution
Introduction to Mechatronics
Student Lecture – 10/23/06
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
• Deviation from a linear relationship between digital input and analog output.
Ana
log
Out
put V
olta
ge
Digital Input
Desired Output
Introduction to Mechatronics
Student Lecture – 10/23/06
Non-Linearity
• 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
Digital Input
Ana
log
Out
put V
olta
ge
VLSB
2VLSB
Digital Input
Ana
log
Out
put V
olta
ge
Integral Non-linearity
Introduction to Mechatronics
Student Lecture – 10/23/06
Gain Error
• Also called Full-Scale Error• Deviation from the ideal full scale voltage due to a higher
or lower gain than expected.
Digital Input
Desired/Ideal Output
Ana
log
Out
put V
olta
ge
Low Gain
High Gain
Introduction to Mechatronics
Student Lecture – 10/23/06
Offset Error• Also called Zero Error
• Difference between ideal voltage output and actual voltage output for a digital input of zero.
Digital Input
Ideal Output
Output Voltage
Introduction to Mechatronics
Student Lecture – 10/23/06
Monotonicity
• Increases or decreases of the digital value must correspond to increases or decreases of the voltage output.
Ana
log
Out
put V
olta
ge
Digital Input
Desired Output
Non-monotonic behavior
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
Time
00
01
10
11
Introduction to Mechatronics
Student Lecture – 10/23/06
Applications – AudioMany 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 – VideoVideo 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
ReferencesPrevious Student Lectures
http://en.wikipedia.org/
http://allaboutcircuits.com
Introduction to Mechatronics
Student Lecture – 10/23/06
Questions