Analog to Digital (A/D) ConversionA/D fundamentalsSlide 3Transfer FunctionA/D Converter TypesSlide 6A/D Converter Types – D to A conversionSlide 8Slide 9Sample and hold devicesSlide 11Slide 12Slide 135/4/2006 BAE 5413 1Analog to Digital (A/D) ConversionAn overview of A/D techniques5/4/2006 BAE 5413 2A/D fundamentals•A / D conversion is a process where an analog signal is converted into a numeric representation.–Analog input is normally classified into one of two types and a voltage range•Types and typical ranges–Uni-polar (0 -1 V, 0 - 5V, 0 - 10V)–Bi-polar (-1 to 1V, -5 to 5V, -10 to 10V)–Digital output is normally binary at the hardware level and typically decimal at the software interface level. Hardware generally controls observed voltage resolution.•Primary critical specifications for A/D conversions–Resolution (voltage resolution)–Conversion rate (time resolution)–Elements contributing to inaccuracy (non-linearity, offset/bias, missing codes, non-monotonicity)5/4/2006 BAE 5413 3A/D fundamentals•Resolution–Normally specified in terms of the number of binary digits that the analog value is converted to:•eg. 8 bit conversion, 12 bit conversion, 16 bit conversion–Analog resolution can be computed from the specified resolution:•analog resolution = analog range / [2^(binary digits in result)]•example: a bi-polar A/D converter set to input a range of -10 to +10 V with a 12 bit conversion•analog resolution = 20V / [2^12] = 20/4096 V / bit = 4.9 mV/bit•Conversion Rate–The rate at which an A/D converter can make sequential a conversions. In general higher resolutions require greater time or greater cost or both.–Typically specified in samples per second (sometimes MSPS)5/4/2006 BAE 5413 4Transfer FunctionOutput CodeInput Voltage00000001001000110100010101100111100010011010101111001101Output CodeMissing Code01 LSBNominal Quantizedvalue + 1/2 LSB•The 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.5/4/2006 BAE 5413 5A/D Converter Types•Dual Slope Integrating5/4/2006 BAE 5413 6A/D Converter Types•Operation•Reference signal is integrated for a fixed time•Input is switched to the analog input and is 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 timing•Characteristics•Noise tolerant (Integrates variations in the input signal during the T1 phase)•Typically slow conversion rates (Hz to few kHz)21002111TVTVdtVCdtVCareferenceTaTreference21TTVVreferencea5/4/2006 BAE 5413 7•Successive Approximation (Digital to Analog Conversion + null balancing)–4 bit D/A using a summing amplifier and switch–4 bit D/A using R-2R ladder•Digital value (D1, D2, D3 etc.) is converted to an analog valueA/D Converter Types – D to A conversion+-2R4R8RR1VRD0D1D2D3+-R2RR2R2R2RR R1V2RD0D1D2D3i=1/2R i=1/4R i=1/8R i=1/16Rå+8141outV5/4/2006 BAE 5413 8A/D Converter Types•Successive Approximation–The input signal must be “held at a single level during conversion. (A sample and hold circuit is required on the input.–Note that conversion time depends on the input level and the convergence method.D/A ConverterSuccessiveApproximationRegisterStart of ConversionStatusClockAnalog InputDigital Output12+-Comparator outputConverter Schematic5/4/2006 BAE 5413 9•Conversion–At start of conversion, the clock is used to cycle a counter that drives the D/A converter.–When the D/A output is larger than the input then the count is reduced otherwise it is increased using an algorithm to home in on the matching value.–When the counter step size is within the tolerance desired (usually 1 count) then conversion is stopped and the digital value being output to the D/A is outputAnalog levelTimeStart of ConversionT1T2T3T4T5T6T7Analog InputD/A Converteroutput5/4/2006 BAE 5413 10Sample and hold devices•Some A/D converters require the input analog signal to be held constant during conversion, (eg. successive approximation devices)•In other cases, peak capture or sampling at a specific point in time necessitates a sampling device.•This function is accomplished by a sample and hold device as shown to the right:•These devices are incorporated into some A/D convertersAnalog InputSignalSamplingswitchHoldCapacitorOutputSignal5/4/2006 BAE 5413 11A/D Converter Types•Flash Conversion–A 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+-+-+-+-+-+-1VVinComparators3R2R2R2R2R2R2RR35/4/2006 BAE 5413 12A/D Converter Types•Sigma / DeltaDigitalFilterStart of ConversionStatusAnalog Input (Va)Digital Output+-Comparator output+-ComparatorIntegratorDecimationControlLogic-+Bit streamVF5/4/2006 BAE 5413 13A/D Converter Types•Operation–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 is known as Delta modulation–This pulse stream is sampled digitally and averaged numerically (decimation) Giving a numerical representation of the voltage in.–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 till valid