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**Analogue to Digital Conversion**

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**Digital Signal Processing**

A digital signal is an approximation of an analog one Levels of signal are sampled and converted to a discrete bit pattern. Resistor networks can be used to convert digital signals into analogue voltages

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**Step (discrete) approximation**

“stair-step” approximation of original signal sample level more samples give greater accuracy time hold time for sample

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**This Lecture Methods of analogue to digital conversion**

flash counter ramp successive approximation Sample interval and aliasing problems Sample and hold circuits

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The Comparator Most A-D converters use a comparator as part of the conversion process A comparator compares 2 signals A and B if 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

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Flash Converter Uses a reference and a comparator for each of the discrete levels represented in the digital output Number of comparators = number of quantisation levels Not practical for more than 10 bit converters generally fast but expensive

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**Counter-ramp Converter**

Comprises a D-A converter, a single comparator, a counter, a clock and control logic When a conversion is required A signal (conversion request) is sent to the converter and the counter is reset to zero a clock signal increments the counter until the reference voltage generated by the D-A converter is greater than the analogue input At this point in time the output of the comparator goes to a logic 1, which notifies the control logic the conversion has finished The value of the counter is output as the digital value

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**Counter-ramp Converter**

The time between the start and end of the conversion is known as the conversion time A drawback of the counter-ramp converter is the length of time required to convert large voltages We must assume the worst case when calculating conversion times

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**Successive Approximation Converter**

Counter replaced by a register Contents of register decided by clock and control logic When a conversion is required: contents of register cleared Vd = 0 MSB set to a 1 if Vc = 0 then Vd < Vin => leave MSB set if Vc =1 then Vd > Vin => clear MSB Repeat previous step for other bits in MSB to LSB order Vin Vc Vd

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**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 equivalents Total conversion time = n+1 cycles where n = the number of bits in the code word

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**ADC Conversion Error Assume 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.

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Quantisation Output from an A-D converter can only be one of a limited number of possible codes Hence quantisation errors will arise. Possible to reduce this error to half by adding q/2 to the output of the D-A converter Equivalent of “rounding” decimal numbers.

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Quantisation Quantisation errors can be reduced by increasing the number of bits Common for A-D converters to have 16 bit or better resolution However the accuracy of the reference voltage must be of the same precision Example: Consider a A-D converter where Vref is only accurate to within 1%

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

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

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**Conversion of a.c. signals**

The 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 time Not possible to sample at every instant in time rate at which we take samples is known as the sampling rate sampling too fast can be inefficient

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**Conversion of a.c. signals**

Sampling too slowly can cause information to be lost

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**Sample Time vs Frequency**

Consider what happens when the signal frequency is higher than the sampling frequency. sample frequency is number of samples / second

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**Conversion of a.c. signals**

Effects of under-sampling possible to interpolate high frequency components as low frequency ones these errors are said to be caused by aliasing important to preceed A-D converter with a low pass filter to remove high frequencies known as an anti-aliasing filter voltage time Sample frequency must be at least twice the highest signal frequency (2f is also called the Nyquist Frequency).

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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.

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**Sample-and-hold devices**

Sampling rule tells us at what rate to make conversions, but there is still another problem associated with changing signals

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**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

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**Sample-and-hold devices**

A number of problems exist with the previous sample and hold circuit load placed on the input of the circuit by charging the capacitor during the sample phase current flowing from the capacitor used in the conversion will reduce the voltage stored on the capacitor

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**What you should be able to do**

Explain 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.

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