Digital to Analog Converter
[Pages:20]Digital to Analog Converter
Jungchul Lee Kamran Jeelani Jonathan Beckwith
Topics of Discussion
? What is a DAC? ? Types of DAC Circuits
? Resistor-string DAC ? N-Bit Binary weighted DAC ? R-2R Ladder DAC
? Specifications of DAC ? Applications
What is a DAC?
? Digital-to-Analog Converter: An electronic device, often an integrated circuit, that converts a digital number into a corresponding analog voltage or current.
? Relation between analog signal and digital equivalent
n
Va = bi 2-i ? Vref i=1
? AD conversion ? Va -> bi (encoder) ex) Transducer interface ? DA conversion ? bi -> Va (decoder) ex) motor, heater control
DAC configurations
? Assume the analog signal is a voltage
N-bit digital word Analog voltage signal
... DN-1, DN-2 ...
D1, D0
VRef
=VDrVefAO*DCut /2N VOut
Types of DAC Circuits
1. Resistor-string 2. N-Bit Binary Weighted Resistor 3. R-2R Ladder
V Ref
R
1
R
0
R
1
R
0
R
1
R
0
R
1
R
0
B2
A Resistor-string DAC
1 0
1 0
B1
1 0
B0
Example of 3 bit resistor-string DAC Required component
- a resistor string - a set of switches ? select output to use - opamp ? buffer
Vo
V0
=
VRe f
b N-1 i 2i+1 i=0
Resistor String DAC Example
? How many resistors and switches would be required to implement an 8 bit resistor-string DAC?
Ans)
# of resistors = 2N=28=256
N -1
# of switches = 2i = 28 -1 = 255
i=0
Impractical for converters with more than a few bits of
resolution
N-Bit Binary Weighted Resistor
R
MSB 1
2
I0
2R
1
2
4R
1
2
8R
1
2
... ...
LSB
1
2^(N-1)R 2
V Ref
3
+ -
R/2
1 4
2
V out
I0
=
VR
N i=1
bi 2(i-1) R
5
V0 = -Rf I0
N-bit binary weighted Example
? Find output voltage, current, and resolution for a binary weighted resistor DAC of 4 bits - given condition R = 10 k, Rf = 5 k, VR = -10 V Applied binary word is 1001
Example Solutions
-10 V VR
1 2
3 3
2 1 3
2 1 1
2 3
Rf=R/2 5 k
3
R 1
4 2
? Vout
+ -
5
8R
4R
2R
R
10 k
0 Bit
1 Bit
2 Bit
3 Bit
1 0 0 1 ? binary input
Example Solutions (Cont.)
Ans)
I0
=
-10
V
20
1 ?104
+
0 21 ?104
+
22
0 ?104
+
23
1 ?104
= - 0.001125 A
V0 = - Rf I0 = -(5?103) ? (-0.001125A) = 5.625V
Resolution
=
LSB=
VRef 2n
=
10V 24
=
0.625V
Example Solutions (Cont.)
... DN-1, DN-2 ...
D1, D0
VRef
=VDrVefAO*DuCt /2N
VOut
? Binary Word input = 10012 = 910 ? # of input combination : 24 =16 ? Vout = Vref * D/2N = 10*9/16 =5.625 V
Limitations of the Binary Weighted DAC
1. If R = 10 k, 8 bits DAC, and VRef = 10 V R8 = 28-1*(10 k) = 1280 k I8 = VRef/R8 =10V/1280 k = 7.8 ?A
Op-amps that can handle those currents are rare and expensive.
2. If R = 10 and VRef = 10 V R1 = 21-1*(10 ) = 10 I1 = VRef/R1 = 10V/10 = 1 A
This current is more than a typical op-amp can handle.
R-2R Resistor Ladder DAC
Vs
R
R
R
2R
2R
2R
2R
2R
Bit 3
Bit 2
Bit 1
Bit 0
R
Vout
+ -
?Simplest type of DAC
?Requires only two precision resistance value (R and 2R)
R-2R Resistor Ladder DAC
V3
V2
V1
V0
Vs
R
R
R
2R
2R
2R
2R
2R
Bit 3
Bit 2
Bit 1
Bit 0
Each Bit controls a switch between ground and the inverting input of the op amp
The switch is connected to ground if the corresponding bit = 0
R
Vout
4 Bit Converter
+ -
+ -
R-2R DAC Example
Ex. Convert 0001 to analog
V3
V2
V1
V0
Vs
R
R
R
2R
2R
2R
2R
2R
Bit 3
Bit 2
2R Bit 1
2R Bit 0
Switch for bit 0 is connected to op amp input. All other switches connected to ground
R
Vout
Digital Value: O O O 1
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