1. Digital to Analog Converters
Andrew Gardner
Muhammad Salman
David Fernandes
Jevawn Roberts
Introduction to Mechatronics
Student Lecture – 10/23/06

2. 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

3. 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.
1001
0101
0011
0111
1001
1010
1011
DAC
Introduction to Mechatronics
Student Lecture – 10/23/06

4. Introduction
Each binary number sampled by the DAC corresponds to a different output level.
Digital Input Signal
Analog Output Signal
Introduction to Mechatronics
Student Lecture – 10/23/06

5. Ideally Sampled Signal
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.
Output typical of a real, practical DAC due to sample & hold
Ideally Sampled Signal
DAC
Introduction to Mechatronics
Student Lecture – 10/23/06

6. 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

7. 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

8. Binary Weighted Input DAC- + R 2R 4R
2n-1R Rf
Vout
Vref V1 V2 V3 Vn
Ideal Op-amp
No current into
op-amp
Virtual ground at
inverting input
Vout= -IRf I - + R 2R 4R
2n-1R Rf
Vout
Vref V1 V2 V3 Vn
MSB
LSB
Introduction to Mechatronics
Student Lecture – 10/23/06

9. Calculation
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10. Cont’d Example: n = totalbits Introduction to Mechatronics
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11. Advantages and Disadvantages
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

12. R-2R Resistor Ladder DAC
Vref
MSB
LSB
Bit:
Vout
4-Bit Converter
Introduction to Mechatronics
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13. R-2R DAC Example Convert 0001 to analog V2 V1 V0 Vref
Introduction to Mechatronics
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14. R-2R DAC Example (cont.) = Nodal Analysis Likewise, Voltage Divider V1
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15. Conversion Equation For a 4-Bit R-2R Ladder
For general n-Bit R-2R Ladder
Binary Weighted Resister DAC
Introduction to Mechatronics
Student Lecture – 10/23/06

16. R-2R DAC Summary Advantages Disadvantages 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

17. DAC Specification Resolution Reference Voltage Speed Settling Time
Linearity
Introduction to Mechatronics
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18. 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
Introduction to Mechatronics
Student Lecture – 10/23/06

19. 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

20. 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

21. 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

22. Linearity
Represents the relationship between digital values and analog outputs.
Should be related by a single proportionality constant. (constant slope)
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Student Lecture – 10/23/06

23. DAC Error Non-Linearity Differential Integral Gain Error Offset Error
Monotonicity
Resolution
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24. Non-linearity
Deviation from a linear relationship between digital input and analog output.
Analog Output Voltage
Digital Input
Desired Output
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Student Lecture – 10/23/06

25. 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
Analog Output Voltage
VLSB
2VLSB
Digital Input
Analog Output Voltage
Integral
Non-linearity
Introduction to Mechatronics
Student Lecture – 10/23/06

26. 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
Desired/Ideal Output
Analog Output Voltage
Low Gain
Introduction to Mechatronics
Student Lecture – 10/23/06
Digital Input

27. 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

28. Monotonicity
Increases or decreases of the digital value must correspond to increases or decreases of the voltage output.
Analog Output Voltage
Digital Input
Desired Output
Non-monotonic behavior
Introduction to Mechatronics
Student Lecture – 10/23/06

29. 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
Student Lecture – 10/23/06
Time

30. 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

31. 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

32. Example DAC 18 Pin integrated circuit including output amplifier
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33. 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

34. References Previous Student Lectures http://en.wikipedia.org/
Introduction to Mechatronics
Student Lecture – 10/23/06

35. Questions
Introduction to Mechatronics
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