Analogue to Digital Conversion

Digital Signal ProcessingA digital signal is an approximation of an analog oneLevels of signal are sampled and converted to a discrete bit pattern.Resistor networks can be used to convert digital signals into analogue voltages

Step (discrete) approximationtimelevelsamplestair-step approximation of original signalhold time for samplemore samples give greater accuracy

This LectureMethods of analogue to digital conversionflashcounter rampsuccessive approximationSample interval and aliasing problemsSample and hold circuits

The Comparator Most A-D converters use a comparator as part of the conversion processA comparator compares 2 signals A and Bif A > B the comparator output is in one logic state (0, say)if B > A then it is in the opposite state (1, say)A comparator can be built using an op amp with no feedback

Flash ConverterUses a reference and a comparator for each of the discrete levels represented in the digital outputNumber of comparators = number of quantisation levelsNot practical for more than 10 bit convertersgenerally fast but expensive

Counter-ramp ConverterComprises a D-A converter, a single comparator, a counter, a clock and control logicWhen a conversion is requiredA signal (conversion request) is sent to the converter and the counter is reset to zeroa clock signal increments the counter until the reference voltage generated by the D-A converter is greater than the analogue inputAt this point in time the output of the comparator goes to a logic 1, which notifies the control logic the conversion has finishedThe value of the counter is output as the digital value

Counter-ramp ConverterThe time between the start and end of the conversion is known as the conversion timeA drawback of the counter-ramp converter is the length of time required to convert large voltagesWe must assume the worst case when calculating conversion times

Successive Approximation ConverterCounter replaced by a registerContents of register decided by clock and control logicWhen a conversion is required:contents of register cleared Vd = 0MSB set to a 1if Vc = 0 then Vd < Vin => leave MSB setif Vc =1 then Vd > Vin => clear MSBRepeat previous step for other bits in MSB to LSB orderVinVdVc

The successive approximation A-D converter

Example:A 4-bit successive approximation A-D converter has a full-scale input of +15V. Show how the A-D converter would convert the analogue voltages 10.9V and 3.1V into their digital equivalentsTotal conversion time = n+1 cycles where n = the number of bits in the code word

ADC Conversion ErrorAssume D-A converter output has stepped up to V1.Because Vi > V1, the output has stayed at a logic 0.On the next clock pulse the D-A output rises to V2.V2 > Vi, comparator output becomes logic 1 and conversion is completed.Maximum possible error = q.

QuantisationOutput from an A-D converter can only be one of a limited number of possible codesHence quantisation errors will arise.Possible to reduce this error to half by adding q/2 to the output of the D-A converterEquivalent of rounding decimal numbers.

QuantisationQuantisation errors can be reduced by increasing the number of bitsCommon for A-D converters to have 16 bit or better resolutionHowever the accuracy of the reference voltage must be of the same precisionExample:Consider a A-D converter where Vref is only accurate to within 1%

Summary

One way to reduce quantisation errors is to use a larger number of bits in the codewordabsolute accuracy of conversion may not be as good as the resolution if the error tolerance for reference voltages gets too largeA multiplexer enables one A-D converter to be switched between several signal inputs

MultiplexersThe A-D converters described above have all been single-input devicesIt is often necessary to convert several analogue signals to binary code wordsIntegrated circuit multiplexers are available which can select one of its analogue inputs at a time and present it to a single A-D converter

Conversion of a.c. signalsThe A-D converters that we have looked at present no special problems with d.c.What about a.c. signals?Example consider reading room temperature and plotting against timeNot possible to sample at every instant in timerate at which we take samples is known as the sampling ratesampling too fast can be inefficient

Conversion of a.c. signalsSampling too slowly can cause information to be lost

Sample Time vs FrequencyConsider what happens when the signal frequency is higher than the sampling frequency.

sample frequency is number of samples / second

Conversion of a.c. signalsEffects of under-samplingpossible to interpolate high frequency components as low frequency onesthese errors are said to be caused by aliasingimportant to preceed A-D converter with a low pass filter to remove high frequenciesknown as an anti-aliasing filtertimevoltageSample frequency must be at least twice the highest signal frequency (2f is also called the Nyquist Frequency).

Example What is the maximum frequency of input signal that can be converted by an A-D convertor with a conversion time of 0.25 mS?

samples per second = 1000 / 0.25 = 40,000

Maximum frequency in input signal has to be half this or 20kHz.

Sample-and-hold devicesSampling rule tells us at what rate to make conversions, but there is still another problem associated with changing signals

Sample-and-hold devices To remove the problem a sample and hold device which samples the input and holds this value until the end of the conversion is often used

Sample-and-hold devicesA number of problems exist with the previous sample and hold circuitload placed on the input of the circuit by charging the capacitor during the sample phasecurrent flowing from the capacitor used in the conversion will reduce the voltage stored on the capacitor

What you should be able to doExplain the operation of binary weighted resistor and R-2R ladder networks. Recall their general layout.Calculate the output voltage given an input 4-bit value.Explain quantisation with reference to D-A conversion.Explain the operation of flash, counter ramp and successive approximation A-D convertors. Recall their general layout.Recall their conversion time relative to number of bits required.Explain quantization with reference to A-D conversion.Explain the aliasing problem and the relationship between sample rate and input signal frequency.