EECS 247 Lecture 13: Data Converters © 2005 H.K. Page 1EE247Lecture 13• Administrative issues§ To avoid having EE247 & EE 142 midterms on the same day, EE247 midterm moved from Oct. 20thto Tues. Oct. 25tho You can only bring one 8x11 paper with noteso No books, class handouts, calculators, computers, cell phones....EECS 247 Lecture 13: Data Converters © 2005 H.K. Page 2EE247Lecture 13• Data Converters0Summary last lecture0ADC & DAC testingú DNL & INL§ Code boundry servo test§ Histogram testingú Spectral testing§ Direct Discrete-Fourier-Transform (DFT) based measurements§ DFT measurements including windowingEECS 247 Lecture 13: Data Converters © 2005 H.K. Page 3Offset and Full-Scale Error-1 0 1 2 3 4 5 6 7 801234567Digital Output CodeADC Input Voltage [LSB]Real ADC characteristicsIdeal converterOffset errorFull-scale errorFor DNL, INL measurementsneed to elliminate offset and full-scale erroràconnect endpoints & deriving ideal codes based on non-ideal endpointsEECS 247 Lecture 13: Data Converters © 2005 H.K. Page 4-1 0 1 2 3 4 5 6 7 8 9012345678ADC characteristicsideal converterADC Differential NonlinearityDNL = deviation of code width from ∆ (1LSB)+0.4 LSB DNL error-0.4 LSB DNL errorà Endpoints connectedà Ideal characteriscticsderived à DNL measured0 LSB DNL errorDigital Output CodeADC Input Voltage [∆]EECS 247 Lecture 13: Data Converters © 2005 H.K. Page 5DAC Differential NonlinearityEECS 247 Lecture 13: Data Converters © 2005 H.K. Page 6ADC Integral Nonlinearity• A straight line through the endpoints used as reference à offset and full scale errors ignored in INL derivation• Ideal converter steps is found for the endpoint line, then INL is measured• Note that INL errors can be much larger than DNL errors and vice-versa-1 0 1 2 3 4 5 6 7 80167Digital Output CodeADC Input Voltage [∆]INL = deviation of code transition from its ideal location-1 LSB INL2345EECS 247 Lecture 13: Data Converters © 2005 H.K. Page 7DAC Integral NonlinearityEECS 247 Lecture 13: Data Converters © 2005 H.K. Page 8DAC DNL and INL* Ref: “Understanding Data Converters,” Texas Instruments Application Report SLAA013, Mixed-Signal Products, 1995.EECS 247 Lecture 13: Data Converters © 2005 H.K. Page 9Example: INL & DNLLarge INL & Small DNLLarge DNL & Small INLEECS 247 Lecture 13: Data Converters © 2005 H.K. Page 10Monotonicity• Monotonicity guaranteed if| INL | = 0.5 LSBThe best fit straight line is taken as the reference for determining the INL.• This implies| DNL | =1 LSB• Note: these conditions are sufficient but not necessary for monotonicityEECS 247 Lecture 13: Data Converters © 2005 H.K. Page 11How to measure DNL/INL?• DAC:– Apply codes and use a good voltmeter to measure output• ADC– Not as simple as DACà need to find "decision levels", i.e. input voltages at all code boundaries• One way: Adjust voltage source to find exact code trip points "code boundary servo"• More versatile: Histogram testingàApply a signal with known distibution and analyze digital code distribution at ADC outputEECS 247 Lecture 13: Data Converters © 2005 H.K. Page 12Code Boundary ServoC1ADCInputR2C2ADCUnder TestVREFi1i2DigitalComp.A<BBA≥BAInputDigitalCodeADCOutputfSEECS 247 Lecture 13: Data Converters © 2005 H.K. Page 13Code Boundary ServoADC Digital OutputADC Analog Input111110101 100011010001000∆ 2∆ 3∆ 4∆ 5∆ 6∆ 7∆• i1 and i2 are small, and C1 is large, so the ADC analog input moves a small fraction of an LSB each sampling period• For a code input of 101, the ADC analog input settles to the code boundary shownEECS 247 Lecture 13: Data Converters © 2005 H.K. Page 14Code Boundary ServoGood DVMC1R2C2ADCVREFi1i2DigitalComp.A<BBA≥BAInputDigitalCodeADCOutputfSEECS 247 Lecture 13: Data Converters © 2005 H.K. Page 15Code Boundary Servo• A very good digital voltmeter (DVM) measures the analog input voltage corresponding to the desired code boundary• DVMs have some interesting properties– They can have very high resolutions (8½ decimal digit meters are inexpensive)– To achieve stable readings, DVMs average voltage measurements over multiple 60Hz ac line cycles to filter out pickup in the measurement loopEECS 247 Lecture 13: Data Converters © 2005 H.K. Page 16Code Boundary Servo• ADCs of all kinds are notorious for kicking back high-frequency, signal-dependent glitches to their analog inputs• A magnified view of an analog input glitch follows …Good DVMR2C2ADCVREFfSEECS 247 Lecture 13: Data Converters © 2005 H.K. Page 17Code Boundary Servo• Just before the input is sampled and conversion starts, the analog input is pretty quiet• As the converter begins to quantize the signal, it kicks back chargetime01/fSanalog inputstart of conversionEECS 247 Lecture 13: Data Converters © 2005 H.K. Page 18Code Boundary Servo• The difference between what the ADC measures and what the DVM measures is not ADC INL, it’s error in the INL measurement• How do we control this error?time01/fSanalog inputADC converts this voltageDVM measures the averageinput including the glitchEECS 247 Lecture 13: Data Converters © 2005 H.K. Page 19Code Boundary Servo• A large C2 fixes this• At the expense of longer measurement timeGood DVMR2C2ADCVREFfSEECS 247 Lecture 13: Data Converters © 2005 H.K. Page 20Histogram Testing• Code boundary measurements are slow– Long testing time– May miss dynamic errors• Histogram testing– Quantize input with known pdf (e.g. ramp or sinusoid)– Measure output pdf– Derive INL and DNL from deviation of measured pdf from expected resultEECS 247 Lecture 13: Data Converters © 2005 H.K. Page 21Histogram Test SetupRamp0VREFADC PCVREF• Slow (wrt conversion time) linear ramp applied to ADC• DNL derived directly from total number of occurrences of each code @ the output of the ADCTimeEECS 247 Lecture 13: Data Converters © 2005 H.K. Page 22A/D Histogram Test Using Ramp SignalDigital OutputAnalog inputRampTimen/fsADCInput/OutputExample:Ramp slope: 10µV/µsec1LSB =10mVEach ADC code à1msecfs =100kHz à Ts=10µsecà n =100 samples/codeEECS 247 Lecture 13: Data Converters © 2005 H.K. Page 23A/D Histogram Test Using Ramp SignalDigital OutputAnalog inputRampTimen/fsADCInput/OutputExample:Ramp slope: 10µV/usec1LSB =10mVEach ADC codeà1msecfs =100kHz à Ts=10µsecà n =100 samples/code# ofSamplesPer codeEECS 247 Lecture 13: Data Converters © 2005 H.K.
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