1. Analogue to Digital Conversion

2. 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

3. Step (discrete) approximation
“stair-step” approximation of original signal
sample
level
more samples give greater accuracy
time
hold time for sample

4. This Lecture Methods of analogue to digital conversion
flash
counter ramp
successive approximation
Sample interval and aliasing problems
Sample and hold circuits

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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.

12. 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.

13. 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%

14. 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

15. 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

16. 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

17. Conversion of a.c. signals
Sampling too slowly can cause information to be lost

18. Sample Time vs Frequency
Consider what happens when the signal frequency is higher than the sampling frequency.
sample frequency is number of samples / second

19. 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).

20. 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.

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

22. 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

23. 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

24. 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.