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ECEN 301 Discussion #24 – DAC 1
Date Day ClassNo.
Title Chapters HWDue date
LabDue date
Exam
24 Nov Mon 24 DAC 15.4
25 Nov Tue Recitation HW 10
26 Nov Wed Thanksgiving
27 Nov Thu Thanksgiving
28 Nov Fri Thanksgiving
29 Nov Sat
30 Nov Sun
1 Dec Mon Final ReviewLAB 8
2 Dec Tue
Schedule…
ECEN 301 Discussion #24 – DAC 2
ConversionLuke 22:32 32 But I have prayed for thee, that thy faith fail not: and
when thou art converted, strengthen thy brethren.
ECEN 301 Discussion #24 – DAC 3
Lecture 24 – Digital to Analog Converters (DACs)
ECEN 301 Discussion #24 – DAC 4
ADC/DAC Power coming from the wall is analog, but most devices (appliances,
computers, etc.) are digital thus there must be a conversion Analog to digital (ADC) – coming into a device Digital to analog (DAC) – going out of a device
DeviceADC DAC
DigitalAnalog Analog
ActuatorSensor
ECEN 301 Discussion #24 – DAC 5
ADC/DAC
ADC DAC
DigitalAnalog Analog
001110011…2.23094… 2.23094…
Power coming from the wall is analog, but most devices (appliances, computers, etc.) are digital thus there must be a conversion Analog to digital (ADC) – coming into a device Digital to analog (DAC) – going out of a device
ECEN 301 Discussion #24 – DAC 6
Digital to Analog Converter (DAC)DAC: converts a binary word to an analog
output voltage or current
Word length (n): the number of bits in the sequence of 1s and 0s representing an output
• EX: 0110 – 4-bit word length100101 – 6-bit word length
Binary word (B): a sequence of n 1s and 0s B = bn-1bn-2…b2b1b0
• EX: B = 10100101 (n = 8)
ECEN 301 Discussion #24 – DAC 7
Digital to Analog Converter (DAC)DAC: converts a binary word to an analog
output voltage or current
Resolution δv: minimum step size by which the output voltage (or current) can increment
Output voltage va: the analog value represented by the binary word B
• EX: let n=4va = (23·b3 + 22·b2 + 21·b1 + 20·b0)δv
Max output voltage vaMax: the maximum analog value
• EX: let n=4vaMax = (23 + 22 + 21 + 20)δv
= (2n – 1) δv
Example: δv = 1V, B = 10110 (n = 5)Find vaMax and va
vaMax = (2n – 1) δv = (25 – 1) ∙ 1
= 31va = (24·b4 + 23·b3 + 22·b2 + 21·b1 + 20·b0)δv = (16·1 + 8·0 + 4·1 + 2·1 + 1·0) · 1 = (16 + 4 + 2) = 22
ECEN 301 Discussion #24 – DAC 8
Digital to Analog Converter (DAC)Building a DAC:
use a summing amplifier
–
+ +vo
–
+–
+–
+–
RSn
RS2
RS1
vSn
vS2
vS1
RF
–
+ +va
–R1
Rn-2
Rn-1RF
R0
vin
bn-1
bn-2
b1
b0
Summing amplifier DAC
ECEN 301 Discussion #24 – DAC 9
Digital to Analog Converter (DAC)Building a DAC:
the analog output (va) is proportional to the binary word B
1
00
2n
ii
iin
Fa bv
RRv
–
+ +va
–R1
Rn-2
Rn-1RF
R0
vin
bn-1
bn-2
b1
b0
1
0
n
iini
i
Fa vb
RRv
iiRR2
0Choose
THUS
vsi in summing amplifier
ECEN 301 Discussion #24 – DAC 10
Digital to Analog Converter (DAC)Example1: vin = 5V, B = 1011, R0 = 32kΩ, RF = 64kΩFind Rn and va
–
+ +va
–R1
Rn-2
Rn-1RF
R0
vin
bn-1
bn-2
b1
b0
ECEN 301 Discussion #24 – DAC 11
Digital to Analog Converter (DAC)Example1: vin = 5V, B = 1011, R0 = 32kΩ, RF = 64kΩFind Rn and va
–
+ +va
–R1
R2
R3RF
R0
5 V
b3 = 1
b2 = 0
b1 = 1
b0 = 1
k
k
RR
162
3221
01
k
k
RR
84
3222
02
k
k
RR
48
3223
03
V
bbbbkk
bvRRv
n
ii
iin
Fa
1101110
1112041810
222253264
2
00
11
22
33
1
00
ECEN 301 Discussion #24 – DAC 12
Digital to Analog Converter (DAC)Building a DAC:
the analog output (va) has a step-like appearance because of the discrete nature of a binary signal
The resolution (coarseness of the “staircase”) can be adjusted by changing the word length (the number of bits)
Approximated using 2-bits
Approximated using 3-bits
δv
δv
ECEN 301 Discussion #24 – DAC 13
Digital to Analog Converter (DAC)Example2: find the smallest resolution δv of an 8-bit DAC
vaMax = 12V
–
+ +va
–R1
Rn-2
Rn-1RF
R0
vin
bn-1
bn-2
b1
b0
ECEN 301 Discussion #24 – DAC 14
Digital to Analog Converter (DAC)Example2: find the smallest resolution δv of an 8-bit DAC
vaMax = 12V
mV
vvv
vv
naa
na
1.4712012
12
12
8
minmax
max
–
+ +va
–R1
Rn-2
Rn-1RF
R0
vin
bn-1
bn-2
b1
b0
ECEN 301 Discussion #24 – DAC 15
Digital to Analog Converter (DAC)Example3: find an expression for the number of bits required in a
DAC for a given range and resolutionrange = vaMax – vaMin
resolution = δv
–
+ +va
–R1
Rn-2
Rn-1RF
R0
vin
bn-1
bn-2
b1
b0
ECEN 301 Discussion #24 – DAC 16
Digital to Analog Converter (DAC)Example3: find an expression for the number of bits required in a
DAC for a given range and resolutionrange = vaMax – vaMin
resolution = δv
–
+ +va
–R1
Rn-2
Rn-1RF
R0
vin
bn-1
bn-2
b1
b0
2log1/)(log
1log
12
12
12
10
minmax10
minmax2
minmax
minmax
minmax
vvvn
vvvn
vvvvvv
vvv
aa
aa
aan
aan
naa
ECEN 301 Discussion #24 – DAC 17
Digital to Analog Converter (DAC)Example4: find the number of bits required in a DAC given that:
range = 10Vresolution = 10 mV
–
+ +va
–R1
Rn-2
Rn-1RF
R0
vin
bn-1
bn-2
b1
b0
ECEN 301 Discussion #24 – DAC 18
Digital to Analog Converter (DAC)Example4: find the number of bits required in a DAC given that:
range = 10Vresolution = 10 mV
–
+ +va
–R1
Rn-2
Rn-1RF
R0
vin
bn-1
bn-2
b1
b0
10
97.92log
1001log
2log110/10log
2log1/)(log
2
minmax
vvvn aa
ECEN 301 Discussion #24 – DAC 19
Digital to Analog Converter (DAC)Example5: find the resistor values for a DAC with:
range = 15V δv = 1Vvin = 5V RF = 2kΩ
–
+ +va
–R1
Rn-2
Rn-1RF
R0
vin
bn-1
bn-2
b1
b0
ECEN 301 Discussion #24 – DAC 20
Digital to Analog Converter (DAC)Example5: find the resistor values for a DAC with:
range = 15V δv = 1Vvin = 5V RF = 2kΩ
–
+ +va
–R1
Rn-2
Rn-1RF
R0
vin
bn-1
bn-2
b1
b0
44
2log11/15log
2log1/)(log minmax
vvvn aa
ECEN 301 Discussion #24 – DAC 21
Digital to Analog Converter (DAC)Example5: find the resistor values for a DAC with:
range = 15V δv = 1Vvin = 5VRF = 2kΩ
–
+ +va
–R1
Rn-2
Rn-1RF
R0
vin
bn-1
bn-2
b1
b0
k
vvRR
vRRv
bvRRv
nin
a
F
nin
Fa
n
ii
iin
Fa
10
125152
12
12
2
4
max0
0max
1
00
ECEN 301 Discussion #24 – DAC 22
Digital to Analog Converter (DAC)Example5: find the resistor values for a DAC with:
range = 15V δv = 1Vvin = 5VRF = 2kΩ
iiRR2
0–
+ +va
–R1
Rn-2
Rn-1RF
R0
vin
bn-1
bn-2
b1
b0
k
RR
52
102
3
10
1
k
RR
5.24
102
3
20
2
k
RR
25.18
102
3
30
3
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