Digital to Analog Converters (DAC) and Their Applications
Digital to Analog Converters
(DAC)
What
is
a
DAC?
The Digital to Analog Converter (DAC)
is
used to convert digital signal to
an
analog voltage
or
current
output
.
R
L
>>R
Digital
input
Analog
Output
1- The Weighted
–Resistor
DAC.
Digital
input
M
SB
L
SB
Analog
Output
Load
Resistor
99
The output voltage,
V
A
,
may
be
found using Millman's
theorem:
Assume
that:
Logic "0"
=0
V
Logic "1"=+7
V
*
V
IH
=
V
IN
High
Vo
=
a
o
2
o
+
a
1
2
1
+ ⋯ .
+a
n−1
2
n−1
2
n
−
1
∗
VinH
100
Example
1:
For a 4 input resistive divider
(0=0
V
,
1=10
V
)
find
a.
The full-scale output
voltage.
b.
The output voltage
change
due to the
LSB.
c.
The analog output voltage
for a
digital input
of
1011.
Sol.:
a)
The max. Output voltage occurs when
all
the input (1111)
at
+10V (ignoring the
effects of
RL).
b)
0→15 the LSB
must
be
equal to 1/15
of the
full scale output.
Therefore
the
change
in
the output voltage
due
to the LSB
is
+10 *
1/15
=
+2/3V
c)
Using Millman's theorem,
the
output voltage
for a
digital input
of
1011
is:
Vo
=
a
o
2
0
+
a
1
2
1
+⋯+
a
n−1
2
n−1
2
n
−
1
in
×
V
H
Vo
=
1
∗
2
o
+
1
∗
2
1
+0
∗
2
2
+1
∗
2
3
2
4
−
1
×
10
Vo =110
/
15 =7.33
v
Assume
that
Logic "0"
= 0
v
Logic
"1" =
10v
o
1
n−1
Vo =
a
o
2
+a
1
2
+⋯+a
n−1
2
∗
VIH
2
n
H.W
:
For a five-bit resistive divider,
determine:
a)
The weight assigned to the LSB and also
the
second and the third
LSB.
B)
The change
in
output voltage due to
a
change
in
the
LSB.
C)
The output voltage
for a
digital input
of 10110.
Assume
0= 0V
and
1=
+10V.
101
2- The R-2R Ladder
DAC.
Digital
Input
Analog
Output
3- Feedback
Amplifier
DAC.
V
r
ef
V
o
= −
F.B
Resistor
R
i
1
0
2
For
R
1
= R,
R
2
= 2R,
R
3
= 4R,
R
4
= 8R,
R
i
=
R
o
V
=
V
re
f
R
[
a
1
R+a
2
(
2R
)
+a
3
(
4R
)
+a
4
(8R)
]
V
o
=
V
ref
(a
1
+
2a
2
+
4a
3
+
8a
4
)
Multiplying DAC
[MDAC]
i
a
=
{0
Switch
is
closed
1
Switch
is
open
}
4-
Simple D/A
converter using op-amp
summing
amplifier.
103
Example2
:
So
we shall
assume
that 0 =
0V
and 1 =
8V
When input
DCBA = 0000,
then putting these value
in
above
equation (1) we
get:
When digital input
of the
circuit
DCBA =
0001, then putting these value
in
above
equation (1) we get
:
When digital input
of the
circuit
DCBA =
0010, then putting these value
in
above
equation (1) we get
:
Resolution:
The number
of
bits making up the input data word that will ultimately determine
the
output step voltage
as a
percentage
of
full-scale output voltage.
Example
3
:
Calculate
the resolution
of
an
8-bit
DAC.
Solution:
Resolution
= 8
bits
Percentage resolution
=
1
0
4
Design
of
D/A Converter:
To complete the design
of
the D/A converter, there
must
be a
register
which
can
be
used to store the digital information, there must
be
level
amplifiers between the
register
and
the resistive network to insure that the digital signals presented
to
the
network
are
all
of
the same
level
and
are
constant.
The level amplifiers each have two inputs: one input is the +10v from
the
precision voltage source, and the other
is
from
a
flip-
flop. When the input from
a
flip-
flop is high, the output
of
the amplifier
is
at
+10v. When the input from
the
flip-
flop is low, the output
is
0v.
105
Example
4
:
Design
a four
bit digital to analog converter using
the
Ladder type
as
a
resistive
divider.
Digital
Input
Four Bit Analog
to
Digital
Converter
1
0
6
Digital to Analog Converters (DAC) are essential components used to convert digital signals into analog voltage or current outputs. This article explains the working principle of DACs, provides examples of different types such as Weighted Resistor DAC, R-2R Ladder DAC, Feedback Amplifier DAC, and Simple D/A Converter, and discusses how to calculate output voltages and resolutions. Explore the world of DACs to understand their significance in signal processing and electronic circuits.
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Presentation Transcript
Digital to Analog Converters (DAC) What is a DAC? The Digital to Analog Converter (DAC) is used to convert digital signal to an analog voltage or current output. AnalogOutput Digital input 1- The Weighted Resistor DAC. Digital input MSB LSB AnalogOutput LoadResistor RL>>R
99 The output voltage, VA, may be found using Millman's theorem: Assume that: Logic "0" =0 V * VIH = VIN High Logic "1"=+7V Vo =ao2o + a121 + .+an 12n 1 2n 1 VinH Digital I/P Output Vo 0v 1v 2v 3v 4v 000 001 010 011 100
101 110 111 5v 6v 7v 100 Example 1: For a 4 input resistive divider (0=0V, 1=10V) find a. The full-scale output voltage. b. The output voltage change due to the LSB. c. The analog output voltage for a digital input of 1011. Sol.: a)The max. Output voltage occurs when all the input (1111) at +10V (ignoring the effects of RL). b)0 15 the LSB must be equal to 1/15 of the full scale output. Therefore the change in the output voltage due to the LSB is +10 * 1/15 = +2/3V c) Using Millman's theorem, the output voltage for a digital input of 1011 is: ao20+ a121+ + an 12n 1 2n 1 Vo = V H in 1 2o+ 1 21+0 22+1 23 24 1 Vo = 10 Vo =110 / 15 =7.33v
H.W: For a five-bit resistive divider, determine: a) The weight assigned to the LSB and also the second and the third LSB. B) The change in output voltage due to a change in the LSB. C)The output voltage for a digital input of 10110. Assume 0= 0V and 1= +10V. 101 2- The R-2R Ladder DAC. Digital Input Analog Output Assume that Logic "0" = 0 v Logic "1" = 10v o 1 n 1 Vo = ao2 +a12 + +an 12 VIH 2n
3- Feedback Amplifier DAC. Vo= F.B Resistor Ri Vref 102 For R1 = R, R2 = 2R, R3 = 4R, R4 = 8R, Ri = R [a1R+a2(2R)+a3(4R)+a4(8R)] V = Vref o R Vo = Vref(a1 + 2a2 + 4a3 + 8a4) Multiplying DAC [MDAC] i a = {0 Switch is closed 1 Switch is open} 4- Simple D/A converter using op-amp summing amplifier.
103 Example2: So we shall assume that 0 = 0V and 1 = 8V When input DCBA = 0000, then putting these value in above equation (1) we get: When digital input of the circuit DCBA = 0001, then putting these value in above equation (1) we get :
When digital input of the circuit DCBA = 0010, then putting these value in above equation (1) we get : Resolution: The number of bits making up the input data word that will ultimately determine the output step voltage as a percentage of full-scale output voltage. Example 3: Calculate the resolution of an 8-bit DAC. Solution: Resolution = 8 bits Percentage resolution = 104 Design of D/A Converter: To complete the design of the D/A converter, there must be a register which can be used to store the digital information, there must be level amplifiers between the register and the resistive network to insure that the digital signals presented to the network are all of the same level and are constant.
The level amplifiers each have two inputs: one input is the +10v from the precision voltage source, and the other is from a flip- flop. When the input from a flip- flop is high, the output of the amplifier is at +10v. When the input from the flip- flop is low, the output is 0v. 105 Example 4: Design a four bit digital to analog converter using the Ladder type as a resistive divider.
DigitalInput Four Bit Analog to DigitalConverter 106
