Analog to Digital ConversionIn These Notes . . .From Analog to DigitalADC Basic FunctionalityADC Transfer FunctionA/D – Flash ConversionADC - Dual Slope IntegratingSlide 8ADC - Successive Approximation ConversionA/D - Successive ApproximationA/D - Sigma / DeltaSlide 12ADC Performance MetricsWaveform Sampling and QuantizationSampling ProblemsQuantizationInputsSample and Hold DevicesM30626P ADC PeripheralInput Mux (262, but 626 similar)ADC Conversion SpeedM30262 Converter Overview (626P similar)Conversion ModesOne Shot - Setting Control RegistersSlide 25One Shot-Setting Control InterruptsSetting Control Registers & InterruptRepeated ADCADC as a Temperature SensorConverting ADC ValuesD-to-A ConversionSlide 32Slide 338-1Embedded SystemsAnalog to Digital ConversionLecture 8Embedded Systems 8-2In These Notes . . . Analog to Digital Converters–ADC architectures–Sampling/Aliasing–Quantization–Inputs –M30262 ADC PeripheralReference: M30626 ADC: Hardware Manual, pp. 187-202Embedded Systems 8-3From Analog to DigitalEmbedded systems often need to measure values of physical parametersThese parameters are usually continuous (analog) and not in a digital form which computers (which operate on discrete data values) can processA Comparator is a circuit which compares an analog input voltage with a reference voltage and determines which is larger, returning a 1-bit numberAn Analog to Digital converter [AD or ADC] is a circuit which accepts an analog input signal (usually a voltage) and produces a corresponding multi-bit number at the output.0101VinVrefClock0Vin0Vin1ComparatorA/D ConverterEmbedded Systems 8-4ADC Basic Functionalityn = converted codeVin = sampled input voltageV+ref = upper end of input voltage rangeV-ref = lower end of input voltage rangeN = number of bits of resolution in ADC int2/112refrefNrefinVVVVn int2/112 refNinVVn i f V- r e f = 0 v 675int2/151230.310vvnEmbedded Systems 8-5ADC Transfer FunctionThe ideal output from an A/D converter is a stair-step function (see right)–Ideal worst case error in conversion is 1/2 bit.–Missing codes or the imperfections where increasing voltage does not result in the next step being output are described as non-monotonicity.–Errors in A/D conversion may be significant particularly if the full range of the analog signal is significantly less than the range of the analog input of the A/D.Output CodeInput Voltage00000001001000110100010101100111100010011010101111001101Output CodeMissing Code-10 V1 LSBNominal Quantizedvalue + 1/2 LSB10 VEmbedded Systems 8-6A/D – Flash ConversionA multi-level voltage divider is used to set voltage levels over the complete range of conversion.A comparator is used at each level to determine whether the voltage is lower or higher than the level.The series of comparator outputs are encoded to a binary number in digital logic (an encoder)+-Encoder+-+-+-+-+-+-1VVinComparators3R2R2R2R2R2R2RR31/16 V3/16 V5/16 V7/16 V9/16 V11/16 V13/16 VEmbedded Systems 8-7ADC - Dual Slope IntegratingOperation–Input signal is integrated for a fixed time–Input is switched to the negative reference and the negative reference is then integrated until the integrator output is zero–The time required to integrate the signal back to zero is used to compute the value of the signal–Accuracy dependent on Vref and timingCharacteristics–Noise tolerant (Integrates variations in the input signal during the T1 phase)–Typically slow conversion rates (Hz to few kHz)210011TrefTindtVCdtVC12TTVVrefinSlope proportionalto input voltageEmbedded Systems 8-8ADC - Dual Slope IntegratingControl LogicCounterStart of ConversionStatusClockAnalog Input (Va)Digital Output12+-Comparator output+--VreferenceComparatorIntegratorEmbedded Systems 8-9ADC - Successive Approximation ConversionSuccessively approximate input voltage by using a binary search and a DACSA Register holds current approximation of resultRepeat –Set next bit input bit for DAC to 1–Wait for DAC and comparator to stabilize–If the DAC output (test voltage) is larger than the input then set the current bit to 1, else clear the current bit to 0VoltageTimeStart of ConversionTest voltage(DAC output)T1T2T3T4T5T6000000111111100000100100AnalogInput1xxxxx10xxxx100xxx1001xx10011x100110100110Embedded Systems 8-10A/D - Successive ApproximationConverter SchematicD/A ConverterSuccessiveApproximationRegisterStart of ConversionStatusClockAnalog InputDigital Output12+-Comparator outputConverter SchematicEmbedded Systems 8-11A/D - Sigma / DeltaOperation–Comparator feedback signal is subtracted from analog input and the difference is integrated.–The average value of VF is forced to equal Va.–VF is a digital pulse stream whose duty cycle is proportional to Va –This pulse stream is sampled digitally and averaged numerically (decimation) giving a numerical representation of Va –The error in the average or mean is:–The greater the number of samples averaged, the greater the accuracy–The greater the number of samples averaged, the greater the time between the start of gathering samples and the output of the mean (group delay)–This A/D does not work well if switched from channel to channel because of the delay until a valid resultnEmbedded Systems 8-12A/D - Sigma / DeltaSigma / DeltaDigitalFilterStart of ConversionStatusAnalog Input (Va)Digital Output+-Comparator output+-ComparatorIntegratorDecimationControlLogic-+Bit streamVFEmbedded Systems 8-13ADC Performance MetricsLinearity measures how well the transition voltages lie on a straight line.Differential linearity measure the equality of the step size.Conversion time:between start of conversion and generation of resultConversion rate = inverse of conversion timeEmbedded Systems 8-14Waveform Sampling and QuantizationA waveform is sampled at a constant rate – every t–Each such sample represents the instantaneous amplitude at the instant of sampling–“At 37 ms, the input is 1.91341914513451451234311… V”–Sampling converts a continuous time signal to a discrete time signalThe sample can now be quantized (converted) into a digital value–Quantization represents a continuous (analog) value with the closest discrete (digital) value–“The sampled input voltage of 1.91341914513451451234311… V is best represented by the code
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