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Static calibration of bridge and voltage divider circuits forTemperature Measurement
Venkata Rohith Reddy Matli
Group member: Arpit Thyagi
Date: September 9th, 20!"
#age $%
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Introduction
Theory
&ne o' the mo(t important part( o' thi( e)periment i( *heat(tone bridge" A *heat(tone bridge i(
an ele+tri+al +ir+uit u(ed to mea(ure an unkno*n ele+tri+al re(i(tan+e by balan+ing t*o leg( o' a
bridge +ir+uit, one leg o' *hi+h in+lude( the unkno*n +omponent" &ne o' the adantage( o' u(ing
a *heat(tone bridge *hen +ompared to a oltage diider +on'iguration i( the a++ura+y a((o+iated
*ith the re(ult(" The re(ult( obtained 'rom *heat(tone bridge +on'iguration are more a++urate*hen +ompared to tho(e obtained 'rom oltage diider"
Motivation/Objective
Thermi(tor( are ery ine)pen(ie, highly (en(itie temperature mea(urement dei+e(" Thi(
e)periment *a( done in order to determine the a++ura+y o' the alue( mea(ured by thermi(tor by
+omparing it *ith a true alue o' temperature *hi+h i( mea(ured a+ro(( a TM# -% (en(or" The
e)periment *a( +ondu+ted by +onne+ting the thermi(tor in t*o di''erent tran(du+er
+on'iguration( in order to ob(ere the di''eren+e in alue( obtained" The(e alue( *ere then
+ompared to determine the relatie a++ura+y o' the tran(du+er (y(tem( u(ed and to determine the
ne+e((ity to +alibrate thermi(tor"
MethodsA .heat(tone bridge *a( (etup on the breadboard in the +on'iguration (ho*n in /ig" u(ing the
'i)ed re(i(tor(, potentiometer and a thermi(tor" The bridge output *a( +onne+ted to the +hannel(
indi+ated in /igure on the bla+k terminal board atta+hed to the ab1a+k u(ing 1umper +able("
Analog input +hannel( that *ere ne)t to ea+h other *ere u(ed to mea(ure di''erential3 potential in
the +ir+uit" TM# -% (en(or i( al(o +onne+ted to the ab1a+k" A "4T 'ile that log( the data 'romTM# -% (en(or and .heat(tone bridge i( +reated in DA5 'a+tory" .heat(tone bridge i( balan+ed
at room temperature" The re(i(tan+e( o' all the +omponent( in the +ir+uit are determined u(ing
multimeter"
TM# -% and thermi(tor are put in hot *ater +olle+ted in a tumbler" The alue read by TM# -%
(en(or i( monitored and on+e the temperature (tabili6e( aboe 70 degree( +entigrade the oltage
alue( a+ro(( the .heat(tone bridge are logged in the "+tl 'ile +reated be'ore" 8+e i( added (tep by
(tep to redu+e the temperature o' *ater in the tumbler and alue( are logged eery time the
temperature (tabili6e(" Thi( i( +ontinued till the *ater in tumbler rea+he( a temperature o' 7degree( +entigrade"
The (ame pro+edure i( repeated 'or a oltage diider +on'iguration"
The de(ign (tage un+ertainty in temperature alue( mea(ured a+ro(( the thermi(tor *a(
determined by +ondu+ting un+ertainty analy(i( u(ing the un+ertainty a((o+iated *ith the ariou(
+omponent( u(ed in the *heatone bridge +ir+uit"
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Figure 1 (adapted from MTU lab materials): Schematic of thermistor/wheatstone bridgeand temperature sensor configuration for simultaneous measurement and calibration
Results/Discussion
Results obtained across the wheatstone bridge
The oltage de'le+tion a+ro(( the *heat(tone bridge and the temperature mea(ured by the TM# -%
are tabulated" (ing the oltage di''eren+e a+ro(( the *heat(tone bridge and the kno*n alue( o'
the 'i)ed re(i(tan+e( and potentiometer3( re(i(tan+e the arying re(i(tan+e o' the thermi(tor
+orre(ponding to ea+h temperature i( +al+ulated" The temperature mea(ured by the thermi(tor at
ea+h point i( determined u(ing the 'ormula "
Formula 1 (adapted from Visha 1!" data sheet): #esistance to absolute temperature$
Table 1: Values obtained from wheatstone bridge$
ThermistorBridge (V)
Temperature
TMP36 (C)
Resistance(ohm)
T(C) Absolute
ΔT
0.9829941 45.70187 4364.336381
45.046
75
0.655120
408
0.9819932 45.68847 4368.463108
45.022
56
0.665906
93
0.6989037 39.34025 5639.474632
38.603
34
0.736912
731
0.6991007 39.23382 5638.511799
38.607
55
0.626266
84
0.1583554 28.84504 8819.872579 27.892 0.952132
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91 38
0.1570471 28.77014 8829.143098
27.868
5
0.901635
154
-0.70894 12.73955 17945.76201
12.140
3
0.599251
658
-0.7156178 12.60789 18050.54585
12.017
09
0.590801
572
-1.020115 6.905376 23836.82076
6.2370
52
0.668324
022
-1.025192 6.905376 23953.62229
6.1372
38
0.768137
968
0.9919397 46.18201 4327.558746
45.263
46
0.918548
903
0.9874393 46.14022 4346.037415
45.154
31
0.985905
754
&n +omparing the alue( mea(ured by the TM# -% (en(or and thermi(tor an ab(olute error o' 0"degree( +entigrade i( ob(ered" A( per the data (heet o' TM# -% (en(or it ha( an a++ura+y o' ; 2
degree( +entigrade" There'ore, the alue( obtained u(ing TM# -% (en(or and thermi(tor (en(or
'all *ithin the (ame range" A( there i( no (y(temati+ error <la+k o' o''(et= a((o+iated *ith the
alue( mea(ured a+ro(( the thermi(tor *hi+h +an be noti+ed 'rom the graph in /igure 2 the errorthat *e noti+ed in the alue( mea(ured +an be attributed to random error <hy(tere(i(, linearity
et+"="
Figure % & Voltage across wheatstone bridge VS Temperature
#age 7$%
T e m p e r a t u r e < o 4 =
Voltage <V=
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Results obtained across the Voltage Divider
(ing the oltage drop mea(ured a+ro(( the arying re(i(tan+e i"e" the thermi(tor in thi( +a(e the
re(i(tan+e in ea+h +a(e i( determined" (ing thi( re(i(tan+e the alue o' temperature 'or ea+h +a(e
i( determined by u(ing the (ame pro+edure 'ollo*ed to determine re(ult( a+ro(( *heat(tone
bridge"
Table %: Values obtained from wheatstone bridge$
ThermistorVolatage drop
(V)
Temperature
TMP36(C)
Resistanceo
thermistor(ohm)
T(C) ΔT (C)Absolute ΔT(C)
0.4509747 44.16054 4574.319 43.8480
8
-0.3124
6
0.3124
65
0.4542387 44.39312 4496.561 44.2844
9
-
0.1086
3
0.1086
25
0.4584803 44.19129 4527.346 44.1106
9
-
0.0806
0.0805
98
0.174178 35.96326 5351.357 39.9028
6
3.9396
04
3.9396
04
0.1779825 35.96668 5363.825 39.845 3.8783
17
3.8783
17
0.1849678 35.91937 5374.478 39.7956
7
3.8763
01
3.8763
01
0.02362121 2.836431 29763.42 1.76348
-
1.0729
5
1.0729
51
0.03038571 2.871909 29815.32 1.72886
5
-
1.1430
4
1.1430
44
0.3129807 46.11736 4375.508 44.9813
3
-
1.1360
3
1.1360
25
0.3233639 46.12682 4358.322 45.08204
-
1.0447
8
1.044775
&n +omparing the alue( o' temperature obtained 'rom thermi(tor *ith the temperature read by
the TM# -% (en(or an aerage ab(olute error o' about degree +entigrade <"9>& 4= i( ob(ered" A(
the TM# -% (en(or ha( an a++ura+y o' ; 2 degree( +entigrade the alue( mea(ured a+ro(( the
thermi(tor 'all *ithin the range o' alue( that a TM# -% (en(or might read" A( there i( no
noti+eable o''(et in the alue( obtained a( noti+ed 'rom the graph there i( no (y(temati+ error
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a((o+iated *ith the (en(or" There'ore the error noti+ed in the +al+ulated alue( +an be attributed to
random error a((o+iated *ith the tran(du+er +on'iguration and the (en(or u(ed"
Figure ': Voltage across oltage diider VS Temperature$
Comparing values obtained from wheatstone bridge to those across Voltage divider
?en though the ma)imum error in the +al+ulated alue( *a( about the (ame in both +a(e( *hi+h
+an be noti+ed in the table( and 2, the alue( mea(ured a+ro(( the *heat(tone bridge *ere 'ound
to be (lightly more a++urate than the alue( mea(ured u(ing the oltage diider *hi+h +an be
noti+ed in the 'igure( 2 and -" Thi( i( to be e)pe+ted a( *heat(tone bridge i( a re'ined er(ion o'
the oltage diider" The random error a((o+iated *ith the reading( 'rom both the tran(du+er
+on'iguration( +an be attributed to hy(tere(i( by ob(ering 'igure( 2 and -"
Design stage uncertainty!
The de(ign (tage un+ertainty o' the temperature mea(ured a+ro(( the thermi(tor in *heat(tone
bridge +on'iguration *a( determined 'or a range o' output oltage( and graph *a( plotted"
#age %$%
Voltage <V=
T
e m p e r a t u r e < o 4 =
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Figure : Temperature across output oltage across wheatstone bridge transducer sstem
Conclusions@a(ed on the alue( obtained +alibration o' thermi(tor i( not reuired a( the alue( mea(ured
a+ro(( the thermi(tor lie *ithin the a++ura+y limit( (pe+i'ied by the TM# -% data(heet" The alue(
mea(ured a+ro(( *heat(tone bridge *ere 'ound to be more a++urate than the alue( mea(ure
a+ro(( the oltage diider a( the random error a((o+iated *ith the alue( mea(ured a+ro(( the
oltage diider +on'iguration *a( 'ound to be (lightly larger than the alue( obtained a+ro((
*heat(tone bridge"
Appendix
Design "tage #ncertainity $nalysis
Table ': Uncertainit in Vout and temperatures oer a range of Vout
Vout(V)
ResistanceThermistor(ohm)
T(C) !ncertainit"in Vout
T(min) T(ma#)
-2.2 638.2979 102.02
54 0.273381342
79.064
4
209.36
74
-2.1 869.5652 91.671
2 0.278914409
73.234
3
137.23
68
-2 1111.111 83.822
71 0.28452581
68.261
59
114.36
17
#age >$%
T e m p e r a t u r e < & 4 =
Voltage <V=
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-1.9 1363.636 77.494
93 0.290185346
63.912
62
100.85
13
-1.8 1627.907 72.181
78 0.295868273
60.035
52
91.306
65
-1.7 1904.762 67.589
9 0.301554199
56.526
09
83.931
33
-1.6 2195.122 63.534
54 0.307226298
53.309
76
77.913
71
-1.5 2500 59.891
98 0.312870734
50.331
31
72.820
34
-1.4 2820.513 56.575
42 0.318476203
47.548
65
68.393
42
-1.3 3157.895 53.521
61 0.324033569
44.928
88
64.467
58
-1.2 3513.514 50.683
01 0.329535562
42.445
79
60.930
54
-1.1 3888.889 48.022
98 0.33497653 40.078
57.702
72
-1 4285.714 45.512
6 0.340352236
37.807
84
54.725
6
-0.9 4705.882 43.128
61 0.345659675
35.620
4
51.954
96
-0.8 5151.515 40.851
96 0.350896935
33.502
94
49.356
49
-0.7 5625 38.666
8 0.356063062
31.444
35
46.903
05
-0.6 6129.032 36.559
72 0.361157958
29.434
81
44.572
73
-0.5 6666.667 34.519
2
0.366182284 27.465
51
42.347
54
-0.4 7241.379 32.535
23 0.371137381
25.528
35
40.212
51
-0.3 7857.143 30.598
95 0.376025199
23.615
81
38.154
98
-0.2 8518.519 28.702
4 0.380848236
21.720
74
36.164
1
-0.1 9230.769 26.838
33 0.385609483
19.836
19
34.230
44
0 10000 25.000
04 0.390312378
17.955
31
32.345
7
0.1 10833.33
23.181
19 0.395214923
16.066
57
30.507
35
0.2 11739.13 21.375
71 0.400057549
14.167
46
28.703
48
0.3 12727.27 19.577
68 0.404841266
12.250
42
26.927
93
0.4 13809.52 17.781
18 0.409567601
10.307
23
25.174
98
0.5 15000 15.980 0.414238579 8.3288 23.439
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2 4 21
0.6 16315.79 14.168
51 0.418856724
6.3049
73
21.715
42
0.7 17777.78 12.339
52 0.423425057
4.2237
66
19.998
51
0.8 19411.76
10.486
12 0.427947095
2.0711
74
18.283
44
0.9 21250 8.6004
54 0.432426855
-
0.1698
1
16.565
06
1 23333.33 6.6737
01 0.436868862
-
2.5203
2
14.838
11
1.1 25714.29 4.6957
4 0.441278154
-
5.0073
2
13.097
04
1.2 28461.54
2.6547
15 0.445660295
-
7.66626
11.335
9
1.3 31666.67 0.5364
4 0.450021394
-
10.545
5
9.5482
49
1.4 35454.55
-
1.6764
3
0.45436812
-
13.713
9
7.7269
12
1.5 40000
-
4.0056
5
0.458707736
-
17.274
9
5.8637
95
1.6 45555.56
-
6.47918
0.463048127
-
21.3957
3.9495
86
1.7 52500
-
9.1341
5
0.467397856
-
26.375
1
1.9733
67
1.8 61428.57
-
12.021
6
0.471766219
-
32.839
7
-
0.0779
1
1.9 73333.33
-
15.215
1
0.476163342
-
42.547
9
-
2.2201
5
2 90000
-
18.8263
0.480600315
-
67.8673
-
4.47322
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%heatstone &ridge
Table : Temperature and absolute difference in temperature at arious output oltages in
wheatstone bridge configuration
thermistor$bridge (V)
Temp$TMP36 (C)
Resistance(ohm)
T(C) Absolute
ΔT
0.9887555 45.95495 4340.62815 45.18621
0.768740089
0.9869428 45.79175 4348.078972 45.142
29
0.649461
997
0.9857133 45.69477 4353.137059 45.112
52
0.582250
022
0.9829941 45.70187 4364.336381 45.046
75
0.655120
408
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0.9819932 45.68847 4368.463108 45.022
56
0.665906
93
0.9790376 45.59149 4380.662974 44.951
21
0.640277
458
0.9762554 45.54182 4392.166079 44.884
14
0.657675
574
0.9759874 45.53 4393.275109 44.877
69
0.652311
101
0.7331726 39.93944 5473.754158 39.341
3
0.598144
166
0.7112146 39.40648 5579.532764 38.867
38
0.539104
527
0.7019696 39.55785 5624.503568 38.668
98
0.888867
054
0.6989037 39.34025 5639.474632 38.603
34
0.736912
731
0.6991007 39.23382 5638.511799 38.607
55
0.626266
84
0.6897295 39.1873 5684.445266 38.407
34
0.779964
706
0.6832036 39.06352 5716.592347 38.268
3
0.795216
971
0.6787348 38.92161 5738.682266 38.173
28
0.748328
242
0.1589781 28.92467 8815.463382 27.904
52
1.020145
85
0.1583554 28.84504 8819.872579 27.892
91
0.952132
38
0.1570471 28.77014 8829.143098 27.868
5
0.901635
154
0.1117088 27.96057 9156.156712 27.025
82
0.934746
96
-0.7025539 12.86964 17846.28581 12.258
02
0.611619
918
-0.70894 12.73955 17945.76201 12.140
3
0.599251
658
-0.7156178 12.60789 18050.54585 12.017
09
0.590801
572
-0.7186452 12.53772 18098.3095 11.961
19
0.576527
111
-0.7206399 12.50461 18129.86921
11.924
35
0.580258
779
-0.7221615 12.48253 18153.99139 11.896
24
0.586289
432
-0.7330493 12.46204 18327.81342 11.694
91
0.767125
238
-0.7416429 12.2468 18466.53355 11.535
78
0.711016
877
-0.7572533 12.02211 18722.03115 11.246 0.775923
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19 056
-1.006743 6.961352 23532.99876 6.4992
85
0.462067
222
-1.01026 6.906164 23612.37715 6.4304
06
0.475757
76
-1.013106 6.905376 23676.88701
6.3746
21
0.530754
908
-1.020115 6.905376 23836.82076 6.2370
52
0.668324
022
-1.025192 6.905376 23953.62229 6.1372
38
0.768137
968
0.9820326 45.90528 4368.300616 45.023
51
0.881765
067
0.9921683 46.13628 4326.621387 45.269
01
0.867268
084
0.9919397 46.18201 4327.558746 45.263
46
0.918548
903
0.9874393 46.14022 4346.037415 45.15431
0.985905754
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Voltage Divider
Table : Temperature and absolute difference in temperature at arious output oltages inVoltage *iider configuration
VolatageThermistor(%olt)
Temp$TMP36 (C)
Resistance o thermistor(oh
m)T(C) ΔT
2.213574 29.84 7944.133453 30.339
35
0.4993
48
2.076022 32.94315 7099.99186 33.006
29
0.0631
38
2.059899 33.28217 7006.218494 33.324
63
0.0424
55
2.056848 33.46823 6988.589104 33.385
01
-
0.0832
2
2.0609 33.54076 7012.010479 33.304
82
-
0.2359
4
2.062051 33.45325 7018.675273 33.282
06
-
0.1711
9
2.061618 33.36495 7016.167401 33.290
62
-
0.0743
3
2.138897 31.81731 7475.777698 31.776
87
-
0.0404
4
2.242059 30.28624 8129.466874 29.796
87
-
0.4893
7
2.314159 29.11704 8616.142951 28.436 -
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65 0.6803
9
2.369796 28.1205 9009.932309 27.398
34
-
0.7221
6
2.260106 30.35956 8248.881161 29.45472
-
0.9048
4
1.682215 42.3346 5070.295393 41.249
76
-
1.0848
4
1.569308 44.16054 4574.319117 43.848
08
-
0.3124
6
1.550906 44.39312 4496.560546 44.284
49
-
0.1086
3
1.547847 44.37499 4483.714945 44.35742
-
0.0175
7
1.550938 44.33399 4496.695043 44.283
73
-
0.0502
6
1.553989 44.23623 4509.530004 44.211
11
-
0.0251
2
1.554675 44.22756 4512.419003 44.194
79
-
0.0327
7
3.067438 14.70189 15872.39116 14.76 0.058112
3.279565 11.03109 19062.41735 10.867
22
-
0.1638
7
3.403605 8.693472 21320.56916 8.5317
65
-
0.1617
1
3.505104 7.912954 23447.14281 6.5740
79
-
1.3388
8
3.587421 6.941642 25396.2504
4.9477
51
-
1.99389
3.632778 4.973002 26570.50574 4.0343
18
-
0.9386
8
3.657131 3.97173 27233.71379 3.5382
53
-
0.4334
8
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3.682754 3.460057 27957.98203 3.0117
92
-
0.4482
7
3.701857 3.020917 28516.55788 2.6161
3
-
0.4047
9
3.716482 2.805683 28955.43343 2.3113
17
-
0.4943
7
3.726866 2.77257 29273.1637 2.0938
64
-
0.6787
1
3.734072 2.718171 29496.71703 1.9424
47
-
0.7757
2
3.738092 2.710287 29622.53984 1.8577
91
-
0.8525
3.742563 2.836431 29763.42354 1.76348
-
1.0729
5
3.744202 2.871909 29815.32062 1.7288
65
-
1.1430
4
1.661638 44.04701 4977.405087 41.713
71
-
2.3333
1.541509 45.51029 4457.172218 44.508
86
-
1.0014
3
1.521862 46.11736 4375.507815
44.981
33
-
1.13603
1.517699 46.12682 4358.32227 45.082
04
-
1.0447
8
1.517581 46.10711 4357.835746 45.084
9
-
1.0222
1
1.519173 46.10159 4364.402483 45.046
36
-
1.0552
3
1.518101 46.07636 4359.979999
45.072
31
-
1.00405
1.517825 46.0464 4358.841816 45.078
99
-
0.9674
1
1.518235 45.98569 4360.532661 45.069
07
-
0.9166
2
#age !$%
7/21/2019 EMDA Lab Report 1
http://slidepdf.com/reader/full/emda-lab-report-1 16/16
1.518606 45.90922 4362.063013 45.060
08
-
0.8491
4
#age %$%