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1 Digital to Analog Converter Nov. 1, 2005 Fabian Goericke, Keunhan Park, Geoffrey Williams

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2 Outline What is a DAC? Types of DAC Circuits Resistor-string DAC Binary weighted DAC R-2R Ladder DAC Specifications of DAC Errors Applications

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3 A digital to analog converter (DAC) is a device that converts digital numbers (binary) into an analog voltage or current output. 01010101 00110011 01110111 10011001 10011001 10101010 10111011 DAC What is a DAC?

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4 1011 1001101001111000011001010100 0011001000010000 Digital Input Signal Analog Output Signal

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5 Types of DAC Circuits 1. Resistor String 2. Binary Weighted Resistor 3. R-2R Ladder

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6 Components of a String DAC Resistor String supply discrete voltage levels Selection Switches connect the right voltage level to op-amp according to input bits Op-amp amplifies the discrete voltage levels to desired range, keeps the current low Resistor String DAC

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7 Resistor String Example Resistor String DAC

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8 1 1 0 6V1 1 1 7V 1 0 0 4V 0 0 0 0V Selection Switches Resistor String DAC

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9 Advantages: simple fast for < 8 bits Disadvantages: high element count for higher resolutions, reason: number of resistors: number of switches: slow for > 10 bits Resistor String DAC

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10 Basic Idea: 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 - + R 2R 4R 2nR2nR Rf V out Binary Weighted Resistor DAC

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11 non-inverting input on ground virtual ground at inverting input KIRCHHOFF’s current law and no input current into op-amp I1 + I2 = 0 I1 = V1 / R + V2 / (2R) + V3 / (4R) + … Binary Weighted Resistor DAC

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12 Binary Weighted Resistor DAC Terms have less influence Most significant bit Least significant bit Vn = Vref, if bit is set Vn = 0, if bit is clear Rf = R / 2

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13 Advantages Simple Fast Disadvantages Needs large range of resistor values (2000:1 for 12- bit) with high precision in low resistor values Needs very small switch resistances Binary Weighted Resistor DAC

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14 R-2R Resistor Ladder DAC Simplest type of DAC Requires only two precision resistance valuce (R and 2R) Each bit controls a switch between ground and the inverting input of the op amp. The switch is connected to ground if the corresponding bit is zero. 0 0 00 4 bit converter V ref

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15 R-2R DAC Example Convert 0001 to analog V0V0 V1V1 V2V2 V3V3 V0V0 V1V1 V0V0 V1V1 = V ref

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16 R-2R DAC Example Convert 0001 to analog 2R R V0V0 V ref

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17 R-2R DAC Summary Conversion results for each bit Conversion equation for N-bit DAC Digital bitAnalog Conversion 0001 0010 0100 1000 for

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18 Advantages Only two resistor values Does not need the kind of precision as Binary weighted DACs Easy to manufacture Faster response time Disadvantages More confusing analysis R-2R DAC Summary

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19 Specification of DAC Resolution Speed Settling time Linearity Reference voltage

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20 The amount of variance in output voltage for every change of the LSB in the digital input. How closely can we approximate the desired output signal(Higher Res. = finer detail=smaller Voltage divisions) A common DAC has a 8 - 16 bit Resolution N = Number of bits Specification - Resolution

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21 Rate of conversion of a single digital input to its analog equivalent Conversion Rate depends on clock speed of input signal settling time of converter When the input changes rapidly, the DAC conversion speed must be high. Specification - Speed

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22 The time required for the input signal voltage to settle to the expected output voltage (within +/- ½ of V LSB ). Ideally, an instantaneous change in analog voltage would occur when a new binary word enters into DAC Fast converters reduce slew time, but usually result in longer ring time. Specification – Settling Time t delay t slew t ring

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23 The difference between the desired analog output and the actual output over the full range of expected values. Specification – Linearity

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24 Specification – Linearity Linearity(Ideal Case) Digital Input Perfect Agreement Desired/Approximate Output Analog Output Voltage NON-Linearity(Real World) Analog Output Voltage Digital Input Desired Output Miss-alignment Approximate output Ideally, a DAC should produce a linear relationship between a digital input and the analog output, this is not always the case.

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25 A specified voltage used to determine how each digital input will be assigned to each voltage division. Types: Non-multiplier DAC: V ref is fixed (specified by the manufacturer) Multiplier DAC: V ref is provided via an external source Specification – Reference Voltage

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26 Full Scale Voltage Defined as the output when digital input is all 1’s. Specification – Reference Voltage

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27 Errors Common DAC Errors: Gain Error Offset Error Full Scale Error Non Linearity Non-Monotonic Resolution Errors Settling Time and Overshoot There are a multiple sources of error associated with DAC

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28 Gain Error: Deviation in the slope of the ideal curve and with respect to the actual DAC output. Gain Error High Gain Error: Step amplitude is higher than the desired output Low Gain Error: Step amplitude is lower than the desired output Digital Input Desired/Ideal Output Analog Output Voltage Low Gain High Gain

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29 Offset Error: Occurs when there is an offset in the output voltage in reference to the ideal output. Offset Error Digital Input Desired/Ideal Output Output Voltage Positive Offset Negative Offset This error may be detected when all input bits are low (i.e. 0).

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30 Full Scale Error 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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31 Differential Non-Linearity: Voltage step size changes vary with as digital input increases. Ideally each step should be equivalent. Differential Non-Linearity Digital Input Ideal Output Analog Output Voltage V LSB 2V LSB Diff. Non-Linearity = 2V LSB

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32 Integral Non-Linearity: Occurs when the output voltage is non linear. Basically an inability to adhere to the ideal slope. Integral Non-Linearity Digital Input Ideal Output 1V LSB Int. Non-Linearity = 1V LSB Analog Output Voltage

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33 Non-Monotonic Output Error: Occurs when the an increase in digital input results in a lower output voltage. Non-Monotonic Output Error Analog Output Voltage Digital Input Desired Output Monotonic Non-Monotonic

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34 Resolution Errors Poor Resolution(1 bit) V out Desired Analog signal Approximate output 2 Volt. Levels Digital Input 0 0 1 Does not accurately approximate the desired output due large voltage divisions.

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35 Resolution Errors Better Resolution(3 bit) Digital Input V out Desired Analog signal Approximate output 8 Volt. Levels 000 001 010 011 100 101 110 111 110 101 100 011 010 001 000 Better approximation of the of the desired output signal due to the smaller voltage divisions.

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36 Settling Time and Overshoot Analog Output Voltage Expecte d Voltage +V LSB -V LSB Settling time Time Settling Time: The time required for the voltage to settle within +/- the voltage associated with the V LSB. 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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37 Common Applications Audio: Most modern audio signals are stored in digital form (for example MP3s and CDs) and in order to be heard through speakers they must be converted into an analog signalMP3sCDs Video:Video signals from a digital source, such as a computer, must be converted to analog form if they are to be displayed on an analog monitor. http://en.wikipedia.org/wiki/Digital-to-analog_converter

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38 References Alciatore, “Introduction to Mechatronics and Measurement Systems,” McGraw-Hill, 2003 Horowitz and Hill, “The Art of Electronics,” Cambridge University Press, 2 nd Ed. 1995 http://products.analog.com/products/info.asp?product=AD7224 http://courses.washington.edu/jbcallis/lectures/C464_Lec5_Sp- 02.pdf http://courses.washington.edu/jbcallis/lectures/C464_Lec5_Sp- 02.pdf http://www.eecg.toronto.edu/~kphang/ece1371/chap11_slides.pd f http://www.eecg.toronto.edu/~kphang/ece1371/chap11_slides.pd f Previous students’ lectures on DAC

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39 Questions?

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