eet260: a/d and d/a converters. a/d conversion we will consider process and circuits required to...

EET260: A/D and D/A converters

A/D conversion We will consider process and circuits required to

convert an analog waveform into a digital output.

011001111000101011001110111111111111111011001010011101010011

Analog-to-digital conversion

0 1 2 3 4 5 6

-1.00

-0.75

-0.50

-0.25

0.00

0.25

0.50

0.75

1.00

Time (ms)

Vol

tage

(V

)

A/D conversion A modern A/D converter is a single-chip IC

which performs the following processes.

[ADC IC picture]

Anti-aliasingfilter

Sample-and-hold(S/H) circuit

A/D converter

011001111000101011001110111111111111111011001010011101010011

Sampling and aliasing Sampling is basically a multiplication process,

and it gives rise to sidebands just like AM modulation does.

analog input

sampling pulses

sampled output

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:

Sampling and aliasing (frequency)

We get a carrier and upper and lower sidebands at multiples of the sampling frequency: fs, 2fs, 3fs , etc.

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-aliasingfilter

Sample-and-hold(S/H) circuit

A/D converter

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-aliasingfilter

Sample-and-hold(S/H) circuit

A/D converter

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.

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-aliasingfilter

Sample-and-hold(S/H) circuit

A/D converter

Comparator Comparators are found in both types of A/D

converters. A comparator compares two analog inputs and

produces a binary output.

+A

B

+Vcc= +5 V

-Vcc= 0 V

C

inputs outputs

if A > B C is true (+5 V)

if A < B C is false (0 V)

Successive-approximation converter

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

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.

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?

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.

Flash converter A flash converter uses a large resistive voltage

divider and multiple analog comparators.

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.

Flash converter The number of comparators is equal to 2N – 1,

where N is the number of desired output bits.

0 1 2 3 4 5 6 7 8 9 10 110

200

400

600

800

1000

1200

n-bits

Num

ber

of c

ompa

rtor

s (2

n )

Number of Comparators Required for an n-bit Flash ADC

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.

Digital-to-analog (D/A) conversion We will consider a circuit which convert a digital

signal into and analog output.

Analog-to-digital conversion

0 1 1 1 0 0 1 1 0 1 1 1 1 1 1 1 1 0 0 1 1 0 0 1

0 1 2 3 4 5 6

-1.00

-0.75

-0.50

-0.25

0.00

0.25

0.50

0.75

1.00

Time (ms)

Vol

tage

(V

)

D/Aconversion

D/Aconversion

Digital-to-analog (D/A) conversion One of the most popular D/A circuits is the R-2R

ladder shown below

R-2R ladder DAC The output voltage is given .

f 1 1Ref 1 2

12 2 2

n no n

R b b bV V

R

b0

b1

b2

b3Vref

Vo

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. 00002

b. 00012

c. 01012

d. 11112

e. What is the resolution of this D/A converter. b0

b1

b2

b3Vref

Vo

Example Problem 1