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Digital to Analog Converter. Nov. 1, 2005 Fabian Goericke, Keunhan Park, Geoffrey Williams. Outline. What is a DAC? Types of DAC Circuits Resistor-string DAC Binary weighted DAC R-2R Ladder DAC Specifications of DAC Errors Applications. What is a DAC?.

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## Digital to Analog Converter

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**Digital to Analog Converter**Nov. 1, 2005 Fabian Goericke, Keunhan Park, Geoffrey Williams**Outline**• What is a DAC? • Types of DAC Circuits • Resistor-string DAC • Binary weighted DAC • R-2R Ladder DAC • Specifications of DAC • Errors • Applications**What is a DAC?**• A digital to analog converter (DAC) is a device that converts digital numbers (binary) into an analog voltage or current output. 1001 0101 0011 0111 1001 1010 1011 DAC**What is a DAC?**Analog Output Signal Digital Input Signal**Types of DAC Circuits**1. Resistor String 2. Binary Weighted Resistor 3. R-2R Ladder**Resistor String DAC**• 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**Resistor String Example**Resistor String DAC**Selection Switches 1 1 0 6V 1 1 1 7V 1 0 0 4V 0 0 0 0V**Resistor String DAC**Advantages: • simple • fast for < 8 bits Disadvantages: • high element count for higher resolutions, reason: number of resistors: number of switches: • slow for > 10 bits**R**2R 4R 2nR Rf - Vout + Binary Weighted Resistor DAC • 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**Binary Weighted Resistor DAC**• 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**Most significant bit Least significant bit Rf = R / 2 Vn = Vref, if bit is set Vn = 0, if bit is clear Terms have less influence**Binary Weighted Resistor DAC**• 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**R-2R Resistor Ladder DAC**Vref Each bit controls a switch between ground and the inverting input of the op amp. • Simplest type of DAC • Requires only two precision resistance valuce (R and 2R) The switch is connected to ground if the corresponding bit is zero. 0 0 0 0 4 bit converter**R-2R DAC Example**• Convert 0001 to analog V0 V1 V0 V1 = V2 V1 V0 V3 Vref**R-2R DAC Example**• Convert 0001 to analog R 2R Vref V0**R-2R DAC Summary**• Conversion results for each bit • Conversion equation for N-bit DAC for**R-2R DAC Summary**• 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**Specification of DAC**• Resolution • Speed • Settling time • Linearity • Reference voltage**Specification - Resolution**• 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 - Speed**• 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 – Settling Time**• The time required for the input signal voltage to settle to the expected output voltage (within +/- ½ of VLSB). • 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. tslew tring tdelay**Specification – Linearity**• The difference between the desired analog output and the actual output over the full range of expected values.**Linearity(Ideal Case)**NON-Linearity(Real World) Desired Output Desired/Approximate Output Approximate output Analog Output Voltage Analog Output Voltage Digital Input Digital Input Miss-alignment Perfect Agreement Specification – Linearity • Ideally, a DAC should produce a linear relationship between a digital input and the analog output, this is not always the case.**Specification – Reference Voltage**• A specified voltage used to determine how each digital input will be assigned to each voltage division. • Types: • Non-multiplier DAC: Vref is fixed (specified by the manufacturer) • Multiplier DAC: Vref is provided via an external source**Specification – Reference Voltage**• Full Scale Voltage • Defined as the output when digital input is all 1’s.**Errors**There are a multiple sources of error associated with DAC Common DAC Errors: • Gain Error • Offset Error • Full Scale Error • Non Linearity • Non-Monotonic • Resolution Errors • Settling Time and Overshoot**High Gain**Desired/Ideal Output Analog Output Voltage Low Gain Digital Input Gain Error 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**Offset Error**Offset Error: Occurs when there is an offset in the output voltage in reference to the ideal output. Output Voltage Desired/Ideal Output • This error may be detected when all input bits are low (i.e. 0). Positive Offset Digital Input NegativeOffset**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.**Ideal Output**Analog Output Voltage Diff. Non-Linearity = 2VLSB 2VLSB VLSB Digital Input Differential Non-Linearity Differential Non-Linearity: Voltage step size changes vary with as digital input increases. Ideally each step should be equivalent.**Integral Non-Linearity**Integral Non-Linearity: Occurs when the output voltage is non linear. Basically an inability to adhere to the ideal slope. Ideal Output Analog Output Voltage Int. Non-Linearity = 1VLSB 1VLSB Digital Input**Non-Monotonic Output Error**Non-Monotonic Output Error: Occurs when the an increase in digital input results in a lower output voltage. Desired Output Non-Monotonic Monotonic Analog Output Voltage Digital Input**Poor Resolution(1 bit)**Vout Desired Analog signal 1 2 Volt. Levels 0 0 Digital Input Approximate output Resolution Errors Does not accurately approximate the desired output due large voltage divisions.**Better Resolution(3 bit)**Vout Desired Analog signal 111 110 110 8 Volt. Levels 101 101 100 100 011 011 010 010 001 001 000 000 Digital Input Approximate output Resolution Errors Better approximation of the of the desired output signal due to the smaller voltage divisions.**Analog Output Voltage**+VLSB Expected Voltage -VLSB Time Settling time 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.**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 signal • 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**References**• 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 • Previous students’ lectures on DAC

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