1. Digital to Analog Converter (DAC)
Trayvon Leslie
Orlando Carreon
Zack Sosebee
ME 6405
Intro to Mechatronics
March 14, 2008

2. Outline Overview Choosing a DAC Specifications Types of DAC
Resolution
Speed
Linearity
Settling Time
Reference Voltages
Errors
Types of DAC
Binary Weighted Resistor
R-2R Ladder
Multiplier DAC
Non-Multiplier DAC
Applications
References
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3. Overview Digital to Analog Converter (DAC)
A digital to analog converter (DAC) is a device that converts digital numbers (binary) into an analog voltage, current, or electric charge output.
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4. Overview Digital to Analog Converter (DAC)
Generate piecewise continuous signals from digital code.
Typically generates a piecewise continuous function
Step Functions
The function is continuous between each of the open intervals
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5. Overview
Each binary number sampled by the DAC corresponds to a different output level.
Normally a linear function
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6. Overview
What a DAC Looks Like
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7. Overview Example of DAC Trayvon Leslie Specifications:
An example of a DAC would be the Analog Devices AD 7224 D/A Converter. The AD7224 is a precision 8-bit, voltage-output, digital-to-analog converter with an output amplifier.
Specifications:
DAC Type – R-2R Voltage Out
Input – Dual 8 Bit
Reference voltage – Non-Multiplier
2v – 12.5v
Settling Time - 7μs
Cost - Under $4.00
AD 7224
8-Bit Voltage Output
R-2R
Output Amplifier
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8. Overview Examples of DAC AD7224 Trayvon Leslie 8 input pins
Reference Voltage
Variable Resistors
Helps to meet the output signal requirements
Helps to adjust input signal
Offset: Decreasing the offset Decreases the Output Voltage
Gain:
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9. Choosing a DAC
There are six(6) main specifications that should be considered when choosing a DAC for a particular project.
Reference Voltage
Resolution
Linearity
Speed
Settling Time
Error
When it comes to your project…
There are 6 main specification for choosing your DAC
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10. Specifications Reference Voltage
To a large extent the output properties of a DAC are determined by the reference voltage.
Multiplier DAC – The reference voltage is constant and is set by the manufacturer.
Non-Multiplier DAC – The reference voltage can be changed during operation.
The out of the DAC is largely determined by the reference voltage
Usually changes with the types of DAC
Multiplier: (Internal Reference)
Fixed Reference Voltage
Less Error
Non-Multiplier: (External Reference)
Multiplies binary functions
Scales Continuous
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11. Specifications Resolution
The resolution is the amount of voltage rise created by increasing the LSB (Least Significant Bit) of the input by 1. This voltage value is a function of the number of input bits and the reference voltage value.
1 bit DAC is designed to reproduce 2 (21) levels while an 8 bit DAC is designed for 256 (28) levels.
Increasing the number of bits results in a finer resolution
Most DACs are in the bit range
Similar to the ADC
Will be shown from the linear specifications
Function of the Reference Voltage and the Number of Bits
Increasing the bits decreases the resolution (finer)
Number of bits representing an analog signal -- generally ranging from 6 to 24. The higher the number of
bits, the higher the resolution of the converter. Generally more accurate too.
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12. Specifications Linearity
The linearity is the relationship between the output voltage and the digital signal input.
Depending on the binary number that
How well the device's actual performance across a specified operating range approximates a straight line.
Maximum deviation of actual performance relative to a straight line, located such that it minimizes the maximum deviation
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13. Specifications
Speed
Usually specified as the conversion rate or sampling rate.
It is the rate at which the input register is updated.
High speed DACs are defined as operating at greater than 1 MHz.
Some state of the art bit DAC can reach speeds of 1GHz
The conversion of the digital input signal is limited by the clock speed of the microprocessor and the settling time of the DAC.
The rate at which the input digital or binary number are cycled through the DAC
The number of conversions per second the DAC is producing.
Clock speed: the speed at which the CPU operates.
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14. Specifications Settling Time
Ideally a DAC would instantaneously change its output value when the digital input would change.
In a real DAC it takes time for the DAC to reach the actual expected output value.
Ideally
Usually updated at uniform sampling intervals
Each number latched in sequence
The time required for the output to reach and remain within a specified error band about its final value,
measured from the start of the output transition.
Ideal Sampled Signal
Real DAC Output
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15. Specifications
Error
There are multiple sources of error in computing the analog output.
Gain Error
Offset Error
Full Scale Error
Linearity
Non-Monotonic Output Error
Settling Time and Overshoot
Resolution
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16. Errors
Gain Error Deviation in the slope of the ideal curve and with respect to the actual DAC output
High Gain Error: Step amplitude is higher than the desired output
Low Gain Error: Step amplitude is lower than the desired output
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17. Errors
Offset Error
Occurs when there is an offset in the output voltage in reference to the ideal output.
This error may be detected when all input bits are low (i.e. 0).
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18. Errors Full Scale Error
Occurs when there is an offset in voltage form the ideal output and a deviation in slope from the ideal gain.
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19. Errors
Non-Linearity Differential Non-Linearity: Voltage step size differences vary as digital input increases. Ideally each step should be equivalent.
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20. Errors
Non-Linearity Integral Non-Linearity: Occurs when the output voltage is non linear. Basically an inability to adhere to the ideal slope.
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21. Errors Non-Monotonic Output Error
Occurs when the an increase in digital input results in a lower output voltage.
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22. Errors Settling Time and Overshoot
Settling Time: The time required for the voltage to settle within +/- the voltage associated with the VLSB. Any change in the input time will not be reflected immediately due to the lag time.
Overshoot: occurs when the output voltage overshoots the desired analog output voltage.
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23. Errors
Settling Time and Overshoot
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24. Errors Resolution Inherent errors associated with the resolution
More Bits = Less Error and Greater Resolution
Less Bits = More Error and Less Resolution
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25. Errors Resolution Poor Resolution (1 Bit)
Does not accurately approximate the desired output due large voltage divisions.
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26. Errors Resolution Better Resolution (3 Bit)
Better approximation of the of the desired output signal due to the smaller voltage divisions.
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27. Types of DAC Binary Weighted Resistor Basic Ideas: Assumptions:
Use a summing op-amp circuit
Use transistors to switch between high and ground
Use resistors scaled by two to divide voltage on each branch by a power of two
Assumptions:
Ideal Op-Amp
No Current into Op-Amp
Virtual Ground at Inverting Input
Vout = -IRf
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28. Types of DAC 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
Vn is least significant bit
MSB
LSB
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29. Types of DAC Binary Weighted Resistor If Rf=R/2 Zack Sosebee
For example, a 4-Bit converter yields
Where b3 corresponds to Bit-3, b2 to Bit-2, etc.
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30. Types of DAC Binary Weighted Resistor Zack Sosebee Summing op-Amp:
Example
Vref = -2V
Digital Word = 1010
V1 = -2V
V2 = 0V
V3 = -2V
V4 = 0V
Rf = R/2
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31. Types of DAC Limitations of Binary Weighted Resistor
1. If R = 10 kΩ, 8 bits DAC, and VRef = 10 V
R8 = 2(8-1)*(10 kΩ) = 1280 kΩ
I8 = VRef/R8 =10V/1280 kΩ = 7.8 μA
Op-amps that can handle those currents are rare and expensive.
2. If R = 10 Ω and VRef = 10 V
R1 = 2(1-1)*(10 Ω) = 10 Ω
I1 = VRef/R1 = 10V/10 Ω = 1 A
This current is more than a typical op-amp can handle.
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32. Types of DAC Binary Weighted Resistor Summary Advantages Disadvantages
Simple
Fast
Disadvantages
Need large range of resistor values (2000:1 for 12-bit) with high precision in low resistor values
Need very small switch resistances
Summary
Use in fast, low-precision converter
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33. Types of DAC R-2R Ladder Zack Sosebee Each bit corresponds
to a switch:
If the bit is high,
the corresponding
switch is connected to
the inverting input of
the op-amp.
If the bit is low, the
corresponding switch
is connected to ground.
Zack Sosebee

34. Types of DAC R-2R Ladder Zack Sosebee 2R V3 Vref V2 V1 V3 Ideal Op-amp34

35. Types of DAC R-2R Ladder I Zack Sosebee V2 V3 R Vref V2 V1 V3 Vout
Likewise,
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36. Types of DAC R-2R Ladder Results: Zack Sosebee Vref V2 V1 V3
Where b3 corresponds to bit 3,
b2 to bit 2, etc.
If bit n is set, bn=1
If bit n is clear, bn=0
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37. Types of DAC R-2R Ladder For a 4-Bit R-2R Ladder
For general n-Bit R-2R Ladder or Binary Weighted Resister DAC
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38. Types of DAC R-2R Ladder Summary Advantages Summary
Only 2 resistor values
Summary
Better than weighted resistor DAC
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39. Types of DAC
Binary Weighted Resistor vs. R-2R Ladder
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40. Applications Generic Use Circuit Components Audio and Video
Oscilloscopes/Generators
Motor Controllers
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41. Applications Generic Use
Used when a continuous analog signal is required.
Signal from DAC can be smoothed by a Low pass filter
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42. Applications Circuit Components Voltage controlled Amplifier
Digital input, External Reference Voltage as Control
Digitally operated attenuator
External Reference Voltage as Input, Digital Control
Programmable Filters
Digitally Controlled Cutoff Frequencies
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43. Applications Audio Video
Most modern audio signals are stored in digital form and in order to be heard through speakers they must be converted into an analog signal.
CD Players - Digital Telephones
MP3 Player - Hi-Fi Systems
Video
Video signals from a digital source must be converted to analog form if they are to be displayed on an analog monitor
- Computers - Digital Video Player
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44. Applications Oscilloscopes/Generators Digital Oscilloscopes
Digital Input
Analog Output
Signal Generators
Sine wave generation
Square wave generation
Triangle wave generation
Random noise generation
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45. Applications Motor Controllers Cruise Control Valve Control
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46. References http://en.wikipedia.org/wiki/Digital-to-analog_converter
Alciatore, “Introduction to Mechatronics and Measurement Systems,” McGraw-Hill, 2003
Horowitz and Hill, “The Art of Electronics,” Cambridge University Press, 2nd Ed
02.pdf df
Past student lectures

47. Questions