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

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 Trayvon Leslie

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. Trayvon Leslie

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 Trayvon Leslie

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

Overview What a DAC Looks Like Trayvon Leslie 6

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 Trayvon Leslie 7

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: Trayvon Leslie 8

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 Trayvon Leslie 9

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 Trayvon Leslie 10

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 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. Trayvon Leslie 11

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 Trayvon Leslie 12

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. 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. Trayvon Leslie 13

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 Trayvon Leslie 14

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 15

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 Orlando Carreon 16

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). Orlando Carreon 17

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. Orlando Carreon 18

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

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

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

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. Orlando Carreon 22

Errors Settling Time and Overshoot Orlando Carreon 23

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

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

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

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 Zack Sosebee

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 28

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. Zack Sosebee 29

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 Zack Sosebee 30

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 31

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 Zack Sosebee 32

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

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

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

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 Zack Sosebee

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 37

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

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

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

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

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 42

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 Orlando Carreon 43

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 44

Applications Motor Controllers Cruise Control Valve Control Orlando Carreon 45

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. 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.p df Past student lectures

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