1. EET260: A/D and D/A converters

2. Analog-to-digital conversion
A/D conversion
We will consider process and circuits required to convert an analog waveform into a digital output.
0110
0111
1000
1010
1100
1110
1111
0101
0011
Analog-to-digital conversion

3. Sample-and-hold (S/H) circuit
A/D conversion
A modern A/D converter is a single-chip IC
which performs the following processes.
[ADC IC picture]
0110
0111
1000
1010
1100
1110
1111
0101
0011
Anti-aliasing
filter
Sample-and-hold (S/H) circuit
A/D converter

4. Sampling and aliasing 
Sampling is basically a multiplication process, and it gives rise to sidebands just like AM modulation does. 
analog input
sampled output
sampling pulses

5. Sampling and aliasing (frequency)
The frequency spectrum resulting from sampling looks like:
Decreasing the sampling frequency ( fs ), we get:
If we continue to decrease fs to a value less than the Nyquist rate, aliasing (overlapping of the spectra) occurs:
We get a carrier and upper
and lower sidebands at
multiples of the sampling
frequency: fs, 2fs, 3fs , etc.

6. Sample-and-hold (S/H) circuit
Sampling and aliasing
To eliminate the problem, a low-pass filter called an anti-aliasing filter is included at the input of the A/D converter to block any frequencies higher than one-half the sampling frequency.
Anti-aliasing
filter
Sample-and-hold (S/H) circuit
A/D converter

7. Sample-and-hold circuit
A/D conversion begins with sampling, which is carried out by a sample-and-hold (S/H) circuit.
The S/H circuit takes a precise measurement of the analog voltage at specified intervals.
Anti-aliasing
filter
Sample-and-hold (S/H) circuit
A/D converter

8. Sample-and-hold circuit
A sample-and-hold (S/H) circuit accepts the analog input signal and passes it through, unchanged, during its sampling mode.
In the hold mode, the amplifier remembers or memorizes a particular voltage level at the instant of sampling.
The output is a fixed DC level whose amplitude is the value at the sampling time.

9. Sample-and-hold (S/H) circuit
Conversion
The constant S/H output during the sampling interval permits accurate quantization.
The last step is the conversion from an analog voltage into a binary number.
Two common converters are:
Successive-approximation converter
Flash converter
Anti-aliasing
filter
Sample-and-hold (S/H) circuit
A/D converter

10. Comparator Comparators are found in both types of A/D converters.
A comparator compares two analog inputs and produces a binary output.
+Vcc= +5 V
inputs
outputs
if A > B
C is true (+5 V)
if A < B
C is false (0 V) A + C B 
-Vcc= 0 V

11. Successive-approximation converter
This converter contains an 8-bit successive-approximations register (SAR).

12. Successive-approximation converter
Special logic in the register causes each bit to be turned on one at a time from MSB to LSB until the closest binary value is stored in the register.
At each clock cycle, a comparison is made.
If the D/A output is greater than the analog input, that bit is turned off (set to 0)
If the D/A output is less than the analog input, that bit is left on (set to 1).
Process repeats until 8 bits are checked.

13. Successive-approximation converter
If the clock frequency is 200-kHz, how long does it take to complete the conversion for an 8-bit D/A converter?

14. Successive-approximation converter
Successive-approximation converters are fast and consistent.
Conversion times range from 0.25 to 200 ms and 8-, 10-, 12-, and 16-bit versions are available.

15. Flash converter
A flash converter uses a large resistive voltage divider and multiple analog comparators.

16. Flash converter
The encoder logic circuit converts the 7-bit input from the comparators into a 3-bit binary output.
The flash converter produces an output as fast as the comparators can switch and the signals can be translated to binary levels by the logic circuits.
Flash converters are the fastest type of A/D converter.

17. Flash converter
The number of comparators is equal to 2N – 1, where N is the number of desired output bits.

18. Flash converter
Flash A/D converters are complicated and expensive but are the best choice for high-speed conversions.
Conversion speeds < 100 ns are typical.
Speed less than 0.5 ns are possible.
6-, 8-, 10-bit flash converters are available.

19. Digital-to-analog (D/A) conversion
We will consider a circuit which convert a digital signal into and analog output.
D/A conversion
Analog-to-digital conversion

20. Digital-to-analog (D/A) conversion
One of the most popular D/A circuits is the R-2R ladder shown below

21. R-2R ladder DAC
The output voltage is given . b0 b1 b2 b3
Vref Vo

22. Example Problem 1
Assume the R-2R ladder DAC circuit below as the following values: R = 50 k and Rf = 100 k. Assume Vref = 1 V. Determine the D/A converter output for the following binary inputs. a b c d
e. What is the resolution of this D/A converter. b0 b1 b2 b3
Vref Vo