Transcript EE302: Lesson 2 Gain and decibels

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.
1.00
0.75
0.50
Voltage (V)

0.25
0.00
-0.25
-0.50
-0.75
-1.00
0
1
2
3
4
Time (ms)
5
6
0110
0111
1000
1010
1100
1110
1111
1111
1111
1110
1100
1010
0111
0101
0011
Analog-to-digital conversion
A/D conversion

A modern A/D converter is a single-chip IC
[ADC IC picture]
which performs the following processes.
Anti-aliasing
filter
Sample-and-hold
(S/H) circuit
A/D
converter
0110
0111
1000
1010
1100
1110
1111
1111
1111
1110
1100
1010
0111
0101
0011
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
Sampling and aliasing (frequency)

The frequency spectrum resulting from sampling looks
like:
We get a carrier and upper
and lower sidebands at
multiples of the sampling
frequency: fs, 2fs, 3fs , etc.

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

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
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
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
 Flash
converter
converter
Anti-aliasing
filter
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.
+Vcc= +5 V
A
B
+

-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 successiveapproximations 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.
Number of Comparators Required for an n-bit Flash ADC
1200
1000
Number of compartors (2 n)

800
600
400
200
0
0
1
2
3
4
5
6
n-bits
7
8
9
10
11
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.
1.00
0.75
0 1 1 1 0 0 1 1 0 1 1 1 1 1 1 1 1 0 0 1 1 0 0 1
D/A
conversion
Voltage (V)
0.50
0.25
0.00
-0.25
-0.50
-0.75
-1.00
0
1
2
3
4
Time (ms)
Analog-to-digital conversion
5
6
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 .
 Rf  bn bn1
Vo  VRef 1   1  2 
R  2
2

b1 
 n
2 
Vo
Vref
b0
b1
b2
b3
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. 00002
b. 00012
c. 01012
d. 11112
Vo
e. What is the resolution
of this D/A converter.
b
0
Vref
b1
b2
b3