Digital Information

Objectives:
To understand the operation of some basic types
of D/A converters.
To be able to decide which type is used in which
application.
Digital -to-Analog (D/A) Converters
Digital -to-Analog (D/A) Converters
Computer
D/A
Converter
Voltage, angular motion, or
current
Digital
Information
Continuous
Quantity
Digital -to-Analog (D/A) Converters
D/A
b1
Vout
b2
b3
bN
VRef
Bin
• Bin defined to be an N-bit digital signal (or word)
B
in = b1 2 –1 + b2 2 –2 + . . . + bN 2 –N
• b1 is MSB while bN is LSB
Ideal D/A Converter
Max Vout = V ref ( 1- 2 –N )
Output voltage related to digital input and reference
voltage by:
V
out = V ref (b1 2 –1 + b2 2 –2 + . . . + bN 2 –N )
00 01 10 11
1/4
1/2
3/4
1
V
out/Vref
Bin
2 – bit D/A
converter
VLSB =
V
ref
2N
1 LSB =
1 2
N
Ideal D/A Converter
Example:
An 8-bit D/A converter has V ref = 5V.
a) What is the output voltage when B
in = 10110100?
b) Find V at the LSB .
V
out = V ref (2 –1 + 2 –3 + 2 –4 + 2 –6) = 3.516 V
Solution:
V
LSB = V ref (2 –8 ) = 19.5 mV
Example:
An 8-bit D/A converter has V ref = 12V.
What is the output voltage when B
in = 10100111?
Find V
LSB .
Binary Weighted Resistor D/A Converter
R 2R 4R 8R
S
1
(msb)
S2 S3 S4
I1 I2 I3 I4
(lsb)
I
sum
Vref
I1 = Vref
R
I
2 = Vref
2R
I
3 = Vref
4R
I
4 = Vref
8R
I
sum = I1 + I2 + I3 + I4
S1 S2 S3 S4 Isum
off off off off 0
off off off on V
ref/8R
off off on off 2V
ref/8R
off off on on 3V
ref/8R
. . . . . . . . . . . . . . . . . . . .
on on on on 15V
ref/8R
Difficulties associated with Binary Weighted
Resistance D/A Converter
It would be very difficult to manufacture a set of
resistors of such a wide resistance range that has
accurate ratios and temperature tracking.
The current in the ‘lsb’ position would be very low due
to the high resistance. Such low currents make D/A
converter sensitive to noise currents which may be of
the same magnitude.

Example
• A DAC has a reference voltage of 100 V and
has 6-bit precision. Three successive sampling
instances 0.5 sec apart have the following data
in the data register:
• Output Values:

 Instant Binary Data 1 101000

2 101010
3 101101
E
01 = 100{0.5(1)+0.25(0)+0.125(1)+0.0625(0)+0.03125(0)+0.015625(0)}
E
01 = 62.50V
E
02 = 100{0.5(1)+0.25(0)+0.125(1)+0.0625(0)+0.03125(1)+0.015625(0)}
E
02 = 65.63V
E
03 = 100{0.5(1)+0.25(0)+0.125(1)+0.0625(1)+0.03125(0)+0.015625(1)}
E
03 = 70.31V
Vref

 2R 2R 2R 2R 2R

S1

 (msb) 2 3 (lsb)

SSS4

 S1 S2 S3 S4 Vout

on off off off Vref/3
off on off off (V
ref/3)/2
off off on off (V
ref/3)/4
off off off on (V
ref/3)/8
2R V R R R
out
Computer
Memory CPU
A/D
Converter
Transducer
Physical Quantities
(Temperature, Pressure, etc.)
Electrical signals
Analog-to-Digital (A/D) Converters

 Clock

 filp/flop Q Q

Counter
Ramp Voltage
Generator
C
Clear
Start
The Ramp Voltage Method for A/D Conversion

 Clock

 filp/flop Q Q

4-bit
Counter
C

 Clear

Start
The Simple-Counter Method for A/D Conversion

 D / A Converter Trial signal

Successive Approximation A/D Converter
Example: An analogue signal of +16.25 V is to be digitised for a fullscale range of 0 to +20V. Show graphically how the conversion
can be achieved using the successive approximation method. A
register of 8 bits can be used for storing the digitised value.
0
20 V
15 V
10 V
17.5 V
16.25 V
1 1 0 1 0 0 0 0
Example:
An analogue signal of +1.33 V is to be digitised for a
full-scale range of 0 to +5V. Show graphically how
the conversion can be achieved using the successive
approximation method. A register of 8 bits can be
used for storing the digitised value.
If the conversion time for an analog input of 1 V is
20
s, calculate the conversion time of the +1.33 V.
Flash A/D Converter (also known as parallel A/D)
Flash analog-to-digital converters, also known as parallel
A/D converters, are the fastest way to convert an analog
signal to a digital signal. Flash ADCs are ideal for
applications requiring very large bandwidth, but they
consume more power than other ADC architectures and
are generally limited to 8-bit resolution.

3-bit Flash A/D Converter
𝑉1 =
𝑅
𝑅 + 7𝑅 × 𝑉
𝑅 =
𝑉
𝑅
8
𝑉
1 =
𝑅 + 𝑅
𝑅 + 7𝑅 × 𝑉
𝑅 =
2𝑉
𝑅
8
𝑉
1 =
7𝑅
𝑅 + 7𝑅 × 𝑉
𝑅 =
7𝑉
𝑅
8
3-bit Flash A/D Converter
𝑉𝑅 = 8𝑉
𝑉
𝑖𝑛 = 3.3𝑉
1𝑉
2𝑉
3𝑉
4𝑉
5𝑉
6𝑉
7𝑉
0
0 0 0 1 1 1

Fast A/D
Suitable for large bandwidth applications (Satellite

Disdvantages of Flash A/D Converter:
– High power consumption
– Limited resolution (typically up to 8-bit)
– Large die area (2
n-1 comparators)
– Component matching (comparators and resistors)

Half Flash A/D Converter
8-bit Flash A/D converter:
(2
8 – 1) = 255 Comparator
8-bit Half Flash A/D converter:
2 ×(2
4 – 1) = 30 Comparator