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Transcript
Digital to Analog Converters (DAC) 15 March 2006 Doug Hinckley Lee Huynh Dooroo Kim What is a DAC? A digital to analog converter (DAC) converts a digital signal to an analog voltage or current output. 100101… DAC Analog Output Signal What is a DAC? 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 Digital Input Signal Types of DACs Many types of DACs available. Usually switches, resistors, and opamps used to implement conversion Two Types: Binary Weighted Resistor R-2R Ladder Binary Weighted Resistor Utilizes a summing op-amp circuit Weighted resistors are used to distinguish each bit from the most significant to the least significant Transistors are used to switch between Vref and ground (bit high or low) Binary Weighted Resistor Assume Ideal Op-amp No current into op-amp Virtual ground at inverting input Vout= -IRf Vref R 2R I Rf 4R + 2nR Vout 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 Vref V1 R V2 2R V3 4R I Rf + Vn is least significant bit Vn 2n-1R MSB Vout Vn V1 V2 V3 IRf Rf n -1 2 R R 2R 4R LSB Vout Binary Weighted Resistor If Rf=R/2 Vout Vn V1 V2 V3 IRf n 2 2 4 8 For example, a 4-Bit converter yields Vout 1 1 1 1 Vref b3 b2 b1 b0 4 8 16 2 Where b3 corresponds to Bit-3, b2 to Bit-2, etc. Binary Weighted Resistor Advantages Simple Construction/Analysis Fast Conversion Disadvantages Requires large range of resistors (2000:1 for 12-bit DAC) with necessary high precision for low resistors Requires low switch resistances in transistors Can be expensive. Therefore, usually limited to 8-bit resolution. R-2R Ladder Each bit corresponds to a switch: Vref If the bit is high, the corresponding switch is connected to the inverting input of the op-amp. Bit: 0 0 0 4-Bit Converter 0 Vout If the bit is low, the corresponding switch is connected to ground. R-2R Ladder Vref V1 V2 V3 V3 Ideal Op-amp 2R 2R 2 R 2 R Req R 2R 2R R-2R Ladder Vref V1 V2 V2 V3 V3 R R 1 R V3 V V2 2 2 RR I Likewise, Vout 1 V1 2 1 V1 Vref 2 Vout IR V2 R-2R Ladder Results: Vref V1 V2 V3 1 1 1 V3 Vref , V2 Vref , V1 Vref 8 4 2 Vout Vref Vref Vref Vref R b3 b2 b1 b0 4R 8R 16 R 2R Where b3 corresponds to bit 3, b2 to bit 2, etc. Vout If bit n is set, bn=1 If bit n is clear, bn=0 R-2R Ladder For a 4-Bit R-2R Ladder Vout 1 1 1 1 Vref b3 b2 b1 b0 4 8 16 2 For general n-Bit R-2R Ladder or Binary Weighted Resister DAC n Vout Vref bn i i 1 1 i 2 R-2R Ladder Advantages Only two resistor values (R and 2R) Does not require high precision resistors Disadvantage Lower conversion speed than binary weighted DAC Specifications of DACs • • • • • • Resolution Speed Linearity Settling Time Reference Voltages Errors Resolution Smallest analog increment corresponding to 1 LSB change An N-bit resolution can resolve 2N distinct analog levels Common DAC has a 8-16 bit resolution Vref Resolution VLSB N 2 where N number of bits 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. Linearity Analog Output Signal The difference between the desired analog output and the actual output over the full range of expected values 0000 0001 0010 0011 Digital Input Signal 0100 0101 Linearity Ideally, a DAC should produce a linear relationship between the digital input and analog output 0000 Analog Output Signal Non-Linearity Analog Output Signal Linearity (Ideal) 0001 0010 0011 Digital Input Signal 0100 0101 0000 0001 0010 0011 Digital Input Signal 0100 0101 Settling Time Time required for the output signal to settle within +/- ½ LSB of its final value after a given change in input scale Limited by slew rate of output amplifier Ideally, an instantaneous change in analog voltage would occur when a new binary word enters into DAC Reference Voltages Used to determine how each digital input will be assigned to each voltage division Types: Non-multiplier DAC: Vref is fixed Multiplier DAC: Vref provided by external source Types of Errors Associated with DACs Gain Offset Full Scale Resolution Non-Linearity Non-Monotonic Settling Time and Overshoot Analog Output Occurs when the slope of the actual output deviates from the ideal output . Gain Error Digital Input Ideal Output Positive Offset Errorr Negative Offset Error Analog Output Occurs when there is a constant offset between the actual output and the ideal output . Offset Error Digital Input Ideal Output Positive Offset Errorr Negative Offset Error Analog Output Occurs when the actual signal has both gain and offset errors . Full Scale Error Digital Input Ideal Output Full Scale Error Error Resolution Error Poor representation of ideal output due to poor resolution Size of voltage divisions affect the resolution Non-Linearity Error Occurs when analog output of signal is non-linear Two Types Differential – analog step-sizes changes with increasing digital input (measure of largest deviation; between successive bits Integral – amount of deviation from a straight line after offset and gain errors removed; on concurrent bits Non-Linearity Error, cont. Non-Monotonic Error Occurs when an increase in digital input results in a decrease in the analog output Settling Time and Overshoot Error Analog Settling Time – Output +1/2*VLSB time required for Ideal the output to fall Output with in +/- ½ VLSB -1/2*VLSB Overshoot – occurs when analog output overshoots Settling the ideal output Time Time Applications Digital Motor Control Computer Printers Sound Equipment (e.g. CD/MP3 Players, etc.) Electronic Cruise Control Digital Thermostat References Callis, J. B. “The Digital to Analog Converter.” 2002. http://courses.washington.edu/jbcallis/lectures/C464_Le c5_Sp-02.pdf. 14 March 2006 “DAC.” 2006. http://en.wikipedia.org/wiki/Digital-toanalog_converter#DAC_types. 14 March 2006. Johns, David and Ken Martin. “Data Converter Fundamentals.” © 1997. http://www.eecg.toronto.edu/~kphang/ece1371/chap11 _slides.pdf. 14 March 2006 Goericke, Fabian, Keunhan Park and Geoffrey Williams. “Digital to Analog Converter.” © 2005. http://www.me.gatech.edu/mechatronics_course/DAC_F 05.ppt. 14 March 2006 QUESTIONS?