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Name
Solution
Real Time Computing Systems
EE 4770
Midterm Examination
17 March 1999,
8:409:30 CST
Alias
Problem 1
(50 pts)
Problem 2
(50 pts)
Exam Total
(100 pts)
Good Luck!
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View Full DocumentProblem 1:
The partially designed circuit below is to be used to convert temperature
x
∈
[

20
◦
C
,
40
◦
C] to a ﬂoatingpoint number
H
(
x
)=
x/
K to be written into variable
temp
. The circuit
uses an RTD, its model function is
H
t1
(
x
)=
R
0
(1+
α
1
x
), where
R
0
= 100 Ω and
α
1
=0
.
00398
/
◦
C.
The RTD is connected to a

7V source as shown. The ADC response is
H
ADC(10V
,
16b)
.
+

v
1
v
2
R
2
R
3
7 V
ADC
B
I
RTD
(
a
) Complete the design (choose values for
v
2
,
R
2
and
R
3
), so that the ADC input is in
[0
.
5V
,
9
.
5V] over the range of temperatures
to be measured. (20 pts)(For
reduced
credit
[
<
20 pts] make full use of the ADC dynamic
range.)
First, ﬁnd the voltage at the ADC input:
H
c
(
H
t1
(
x
)) =

R
3
±
v
1
H
t1
(
x
)
+
v
2
R
2
²
Call the resistance at the minimum temperature
R
min
and the resistance at the maximum temperature
R
max
.U
s
i
n
g
the boundaries of the temperature range
R
min
=
H
t1
(

20
◦
C) = 92
.
04 Ω
and
R
max
=
H
t1
(40
◦
C) = 115
.
92 Ω
.
As stated in the problem, the ADC input should be a minimum of
0
.
5V
this occurs at the maximum temperature:
H
c
(
H
t1
(40
◦
C)) = 0
.
5V=

R
3
±
v
1
R
max
+
v
2
R
2
²
.
Similarly the ADC input must be
9
.
5V
at

20
◦
C
or
H
c
(
H
t1
(

20
◦
C)) = 9
.
5V=

R
3
±
v
1
R
min
+
v
2
R
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