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Digital to Analog Converter (DAC)

Digital to Analog Converter (DAC). Trayvon Leslie Orlando Carreon Zack Sosebee. ME 6405 Intro to Mechatronics March 14, 2008. Overview Choosing a DAC Specifications Resolution Speed Linearity Settling Time Reference Voltages Errors Errors Types of DAC Binary Weighted Resistor

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Digital to Analog Converter (DAC)

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

  2. Overview • Choosing a DAC • Specifications • Resolution • Speed • Linearity • Settling Time • Reference Voltages • Errors • Errors • Types of DAC • Binary Weighted Resistor • R-2R Ladder • Multiplier DAC • Non-Multiplier DAC • Applications • References Outline Trayvon Leslie

  3. 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. Overview Trayvon Leslie

  4. Digital to Analog Converter (DAC) • Generate piecewise continuous signals from digital code. Overview Trayvon Leslie

  5. Overview Each binary number sampled by the DAC corresponds to a different output level. Trayvon Leslie

  6. Overview What a DAC Looks Like Trayvon Leslie

  7. Overview Example of DAC 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 Trayvon Leslie

  8. Overview Examples of DAC AD7224 Trayvon Leslie

  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 Trayvon Leslie

  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. Trayvon Leslie

  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 12-18 bit range Trayvon Leslie

  12. Specifications Linearity The linearity is the relationship between the output voltage and the digital signal input. Trayvon Leslie

  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 12-16 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. Trayvon Leslie

  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. Ideal Sampled Signal Real DAC Output Trayvon Leslie

  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 Trayvon Leslie

  16. Errors HighGain Error: Step amplitude is higher than the desired output LowGain Error: Step amplitude is lower than the desired output Orlando Carreon Gain ErrorDeviation in the slope of the ideal curve and with respect to the actual DAC output

  17. Errors This error may be detected when all input bits are low (i.e. 0). Orlando Carreon Offset Error Occurs when there is an offset in the output voltage in reference to the ideal output.

  18. Errors Occurs when there is an offset in voltage form the ideal output and a deviation in slope from the ideal gain. Orlando Carreon Full Scale Error

  19. Errors Orlando Carreon Non-LinearityDifferential Non-Linearity: Voltage step size differences vary as digital input increases. Ideally each step should be equivalent.

  20. Errors Orlando Carreon Non-LinearityIntegral Non-Linearity: Occurs when the output voltage is non linear. Basically an inability to adhere to the ideal slope.

  21. Errors Orlando Carreon Non-Monotonic Output Error Occurs when the an increase in digital input results in a lower output voltage.

  22. Errors 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. Orlando Carreon Settling Time and Overshoot

  23. Errors Orlando Carreon Settling Time and Overshoot

  24. Errors Orlando Carreon Resolution Inherent errors associated with the resolution • More Bits = Less Error and Greater Resolution • Less Bits = More Error and Less Resolution

  25. Errors Does not accurately approximate the desired output due large voltage divisions. Orlando Carreon ResolutionPoor Resolution (1 Bit)

  26. Errors Better approximation of the of the desired output signal due to the smaller voltage divisions. Orlando Carreon ResolutionBetter Resolution (3 Bit)

  27. Binary Weighted Resistor • Basic Ideas: • 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 Types of DAC Zack Sosebee

  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 Zack Sosebee

  29. Types of DAC • Binary Weighted Resistor If Rf=R/2 For example, a 4-Bit converter yields Where b3 corresponds to Bit-3, b2 to Bit-2, etc. Zack Sosebee

  30. Types of DAC Summing op-Amp: • Binary Weighted Resistor • Example • Vref = -2V • Digital Word = 1010 • V1 = -2V • V2 = 0V • V3 = -2V • V4 = 0V • Rf = R/2 Zack Sosebee

  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. Zack Sosebee

  32. Types of DAC • Binary Weighted Resistor Summary • Advantages • 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 Zack Sosebee

  33. R-2R Ladder 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. Types of DAC Zack Sosebee

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

  35. Types of DAC V2 V3 Vref V1 V2 V3 R R Vout • R-2R Ladder I Likewise, Zack Sosebee

  36. Vref V1 V2 V3 Types of DAC • R-2R Ladder Results: 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 Zack Sosebee

  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 Zack Sosebee

  38. Types of DAC • R-2R Ladder Summary • Advantages • Only 2 resistor values • Summary • Better than weighted resistor DAC Zack Sosebee

  39. Types of DAC • Binary Weighted Resistor vs. R-2R Ladder Zack Sosebee

  40. Applications • Generic Use • Circuit Components • Audio and Video • Oscilloscopes/Generators • Motor Controllers Orlando Carreon

  41. Applications • Generic Use • Used when a continuous analog signal is required. • Signal from DAC can be smoothed by a Low pass filter Orlando Carreon

  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 Orlando Carreon

  43. Applications • Audio 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 Orlando Carreon

  44. Applications Oscilloscopes/Generators • Digital Oscilloscopes • Digital Input • Analog Output • Signal Generators • Sine wave generation • Square wave generation • Triangle wave generation • Random noise generation Orlando Carreon

  45. Applications • Motor Controllers • Cruise Control • Valve Control • Motor Control Orlando Carreon

  46. 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. 1995 • http://products.analog.com/products/info.asp?product=AD7224 • http://courses.washington.edu/jbcallis/lectures/C464_Lec5_Sp-02.pdf • http://www.eecg.toronto.edu/~kphang/ece1371/chap11_slides.pdf • Past student lectures References

  47. Questions

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