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# Dac

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### Dac

1. 1. ME 4447: Introduction to Mechatronics1 Digital to Analog Converters (DAC) Jesse Barton Hyun Gyu Kim Christopher Neel
2. 2. ME 4447: Introduction to Mechatronics2 What is a DAC? A digital-to-analog converter (DAC) is a circuit that produces an analog current or voltage that is proportional to an analog reference (voltage or current) and an N-bit binary word. Vout = k x Vref x (Binary Word)
3. 3. ME 4447: Introduction to Mechatronics3 In English • DACs generate piecewise continuous signals from digital code. OR • DAC converters are devices that receive a binary word from the microprocessor and convert it to a scaled analog voltage (or current).
4. 4. ME 4447: Introduction to Mechatronics4 DAC Configuration
5. 5. ME 4447: Introduction to Mechatronics5 DAC Types Multiplying DAC - reference source is external to the DAC package Nonmultiplying DAC - reference source is inside the DAC package
6. 6. ME 4447: Introduction to Mechatronics6 Multiplying DAC advantages • External ref. can be time-varying analog voltage that multiplies binary function  fixed programmable byte scales continuous output instead of using time-varying bytes w/ fixed VR to produce discrete output • External reference can be fixed  less likely to produce error from reference voltage drift with temperature than internal reference
7. 7. ME 4447: Introduction to Mechatronics7 DAC Circuit Types Two types of DAC Circuits: 1. Binary weighted 2. R-2R ladder
8. 8. ME 4447: Introduction to Mechatronics8 N-Bit Binary Weighted DAC
9. 9. ME 4447: Introduction to Mechatronics9 Binary Weighted Principles ( ) MSBb bitsinputofnumberN MSBtoingcorrespondresistanceR junctionleavingcurrentsofsumI 2 1 0 1 10 = = = = = ∑= − N i i i R R b VI
10. 10. ME 4447: Introduction to Mechatronics10 Principles Cont’d V0 = -RfI0 V0 = voltage output from amplifier Rf = feedback resistance Resolution= VR/2N Note: For a gain of 1, R = 2Rf
11. 11. ME 4447: Introduction to Mechatronics11 Example Find output voltage and current for a binary weighted resistor DAC of 4 bits where : R = 10 k Ohms, Rf = 5 k Ohms and VR = 10 Volts. Applied binary word is 1001.
12. 12. ME 4447: Introduction to Mechatronics12 Solution Rf = (R/2) R2R4R8R Vo VR 1-bit MSB 2-bit3-bit4-bit ∑ iI
13. 13. ME 4447: Introduction to Mechatronics13 Solution Cont’d V625.5)A001125.0)(5( IR-V A0.001125- 10*2 1 10*2 0 10*2 0 10*2 1V10 3 0 0f0 0 43424140 =−Ω−= = =     +++ Ω −= V I Io
14. 14. ME 4447: Introduction to Mechatronics14 Solution Cont’d Binary input = 1001 = 9 From example, V0 = 5.625V V0/VR= 5.625V/10V = 9/16
15. 15. ME 4447: Introduction to Mechatronics15 Limitations of the Binary Weighted DAC Has problems if bit length is longer than 8 bits For example, if R = 10 k Ohms R8 = 28-1 (10 k Ohms) = 1280 k Ohms If VR = 10 Volts, I8 = 10V/1280 k Ohms = 7.8 µA Op-amps to handle those currents are expensive because this is usually below the current noise threshold.
16. 16. ME 4447: Introduction to Mechatronics16 Limitations Cont’d If R = 10 Ohms and Vref= 10 V I = VR/R = 10V/10 Ohms = 1 A This current is more than a typical op-amp can handle.
17. 17. ME 4447: Introduction to Mechatronics17 Limitations Cont’d Intuitively, the resistance values must be accurate to less than one part in 2N for the RN input to be meaningful. This is difficult to do, especially in IC’s.
18. 18. ME 4447: Introduction to Mechatronics18 R/2R ladder DAC • Most popular single package DAC • Resolves BWL problems • Only two resistor values
19. 19. ME 4447: Introduction to Mechatronics19 Equations governing R/2R bitsofnumberisNwhere; 2 Resolution N RV = MSBisbwhere; 2 1 1 ∑= −= N i i i Ro b VV ( ) bitsofnumberisNwhere; 2 1 1       −−= NRfso VV ( ) MSBisbwhere; 22 1 1 1∑∑ = − = N i i iR i b R V I
20. 20. ME 4447: Introduction to Mechatronics20 Principles of Operation • Binary Switch  true ground w/ LOW input • Binary Switch  op- amp virtual ground w/ HI input • Splits current at each bit • After multiplication of binary word  Io • Inverting Op-amp used to generate analog output voltage • Performed many times per second  semi- continuous DAC
21. 21. ME 4447: Introduction to Mechatronics21 Specifications of DAC’s • Resolution – Increases (improves) as number of bits increases – Most microcontrollers use 8 bit DAC – Some 12 bit DAC used in high end applications • Linearity – Max deviation over full range of output @ room temp. • Settling Time – Time for DAC to come w/in 0.5 LSB {Vo± 0.5*(VR /2N )} of new voltage after binary change – Typ. current output DAC’s conversion times (10 ns to 1 μs) • Reference Voltage – Internal / external
22. 22. ME 4447: Introduction to Mechatronics22 DAC Errors • Resolution:  more bits = more precise • Overshoot & Settling Time:  String of amplifiers w/ feedback loops = very rapid response or very slow response depending on system properties • Absolute Accuracy Error:  Difference between theoretical and actual output • Conversion Speed:  Rapidly fluctuating inputs require high conversion speed to be interpreted accurately
23. 23. ME 4447: Introduction to Mechatronics23 DAC Errors Cont’d • Non-Monotonicity:  Certain conditions where increased input results in decrease Vo • Differential Non-Linearity:  Deviation of actual converter step size from the ideal predicted wave step • Gain Error:  Gain too low = same analog output; gain too high = too large an output • Offset Error:  Constant error of DAC
24. 24. ME 4447: Introduction to Mechatronics24 DAC Errors Cont’d • Resistance Error:  Pertains mainly to BWR DAC since large variety of resistors used  error varies greatly disturbing DAC performance • Saturation:  Use of op-amps requires that input voltage and scaling voltages be bounded to the specifications of the op-amp.
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31. 31. ME 4447: Introduction to Mechatronics31 Applications of DAC • Control Systems • Digital Audio • Digital Telephones • Cruise Control • Waveform Generation
32. 32. ME 4447: Introduction to Mechatronics32 Discussion