INSTRUMENTATION
Advisory Panel Jonathan W . Amy Glenn L. Booman Robert L. Bowman
Jack W . Frazer G. Phillip Hicks Donald R. Johnson
Howard V. Malmstadt Marvin Margoshes William F. Ulrich
TEMPERATURE COMPENSATION USING THERMISTOR NETWORKS Ray Harruff and Charles Kimball Yellow Springs Instrument Co., Inc., P.O. Box 279, Yellow Springs, Ohio 45387
In temperature compensation, it is usually possible to tailor a ther mistor's response to match a needed correction. The complex interrela tionships involved make a trial-and-error procedure often the simplest. Examples are given to show just how these networks can be designed
M
OST PHYSICAL and chemical pro
cesses exhibit variations in their behavior as a function of their tempera ture. Those processes involved in creating electrical "signals" may be amenable to using electrical correc tions for their temperature artifacts. Thermistors offer several advantages over other temperature transducers for such applications. Some of the thermistor characteris tics that create these advantages are speed of response, negative tempera ture coefficient of resistance, small size, high sensitivity, wide range of resis tance values, rugged construction, and interchangeability if needed. In many situations any one of these characteris tics may be surpassed by another trans ducer, but often the thermistor offers the best compromise among them. The following are the most common difficulties in applying thermistors: lack of knowledge about specific data, how to design for the extremely non linear (approximately exponential) slope characteristic, and if more than one is needed, how to achieve repeatable results from unit to unit. The rest of this article will try to deal with these problems. Thermistors have a temperature vs. resistance characteristic that can be grossly approximated by the equation
Rt = R0 (eB/T) where R = resistance at desired temperature, R0 = resis tance at the temperature for which Β is evaluated (usually 25°C, Β is pre sumed constant for any particular ma terial and is a slope or sensitivity term), and Τ = absolute temperature (de grees Kelvin) at which the resistance is desired. Often a more useful num ber is alpha {a) which is the slope of the resistance vs. temperature curve at the temperature specified. A better equation for approximat ing thermistor behavior is Rt = R0e(B/r
+ C>/T*)_
β
h a s a b o u t
t h e
same meaning as above and C can be thought of as a correction. This im proved equation becomes important when tight tolerance thermistors are used. Β and C are not usually pub lished because it is normally easier for the user to work with resistance vs. temperature tables directly. The power that can be dissipated is a function of many things: size and style of thermistor, surrounding environment including mounting, "thermal runaway" prevention, and the loss of accuracy that is tolerable. The standard industry technique for comparing one thermistor to another is to measure the temperature rise above surrounding still air when a known power is dissipated in the
thermistor while it is suspended by its leads. Since this is the most extreme (except vacuum) case, it is often use ful to have another situation described, and some manufacturers use the same measurement with the thermistor im mersed in a liquid. Since every use is different, the vendor can only provide these guidelines, and the specific use will have to be evaluated by the user. The values in Table I are improved about 10 times with well-stirred liquids for unmounted thermistors, and from 4 to 20 times for various mounting configurations. If the current is limited so that the maximum allowable temperature is never exceeded, only the error due to temperature rise need be considered. The test for current limiting is as follows : •· a m b
^amb / R rmas
' =
* •"! " o
*~ -* m a x
maximum ambient tempera ture around thermistor = current through thermistor if thermistor were a t maxi mum allowable temperature = resistance of thermistor at maximum allowable tem perature = maximum allowable tempera ture
Time constants and dissipation con stants are both an indication of the
ANALYTICAL CHEMISTRY, VOL. 42, NO. 7, JUNE 1970 ·
73 A
Instrumentation
Table I. Β & toi., % @Z5°C
%/°'c @25°C
—25
Specific Data: Typical Range of Values
α
R (ohm) vs. T(°C) 25 50
75
100
Resis. toi., % @25°C
TC, sec.
Pa, IWW/°C
Max. temp.. °C
Small beads
2800 ± 8 4300 ± 8
-3.2 -4.8
68 Κ 10M
2.4K 3M
IK 1M
480 350K
250 130K
140 54K
5 to 20% 0.5 t o i
0.1
300 best 600 max
Large beads Glass probes
2800 ± 10 3900 ± 10 5100 ± 10
-3.2 -4.4 -5.7
680 103K 438M
240 32K 70M
100 48 10K 3700 17.5M 3.9M
25 1500 1.1M
14 700 350K
5 to 20% 2 beads 25 prbs.
1
300 best 600 max
1
100 best 150 max
10
Close 2750 ± 1.0 tolerance 3300 ± 1 . 0 3640 ± 0 . 5 disks 4600 ± 1 . 0
- 3 . 1 627.9 - 3 . 7 8489 - 4 . 1 102.9K -5.2
232.7 2691 29.49K 3.966IVI
100 IK 10K 1M
48.5 423.9 389.3 295.9K
25.9 200.4 1700 100.3K
15.0 103.6 816.8 38.2K
1% 1% 1/2% 1%
3400 ± 3 to 5 Wide tolerance 3900 ± 3 to 5 disks
-3.8 -4.4
12 31K
5 10K
2.1 3.7K
1 1.5K
0.5 700
5 to 20% 150 10
Special mounts
45 103K
ability to effect a heat transfer between the medium and the thermistor. Thus, again the user must evaluate his sys tem and the vendor can only provide some guidelines. One factor to con sider with the thermistor time constant is the time constant of the element being compensated. With the ther mistor in its final position, they should either match or a sufficient waiting period should be allowed for both to come to equilibrium. Most thermistors are available with resistance vs. temperature accuracy of ±10 to ± 2 0 % at 25°C. Additionally the sensitivity values are ± 5 to ± 1 0 % . Beads are available with special match ing to tighter tolerances. Small disks are readily available in accuracies to ± V 2 % over the range of 0 to 75°C, gradually changing to ± 5 % at —80°C, and ± 2 % at 150°C. This corresponds to an equivalent temperature error of ±0.05°C at 25°C. With all these different facets and such wide ranges of values within each, designing to use the thermistor is some what complex. Also, there is enough versatility to cover a wide range of problems. There are some guidelines to help overcome the complexities. A simple compensation problem for thermistors is a resistor with a posi tive temperature coefficient needing to be compensated to yield a constant re sistance. One example of this is a 74 A
•
Up to 30 min.
Any above
meter being used to measure a voltage in a direct reading Wheatstone bridge. The current through the meter (for any particular value of Rt) is a func tion of the resistance in series with the meter and the resistance of the meter itself (Figure 1). Many Wheatstone bridges use microammeters as detectors to maximize the sensitivity. These meters have significantly large resis tance. For example, one 50 μΑ ± 2%
25 3.5
100 to 200
Up to 10 X above
meter has a 1712 ohm ± 10% at 25°C coil resistance. Because this is a copper wire coil, the resistance at different temperatures is calculated by RT = # 2 5 (1 + 0.00385 T). To compensate for this effect some additional data are required. What temperature range is important, how much error is allowable, what can the worst-case voltage sensitivity be, and what compensation component values
m Ç »
Figure 1. A resistor with a positive temperature coefficient needs compensation to yield a constant resistance. Example is a meter used to measure a voltage in a direct reading Wheatstone bridge
ANALYTICAL CHEMISTRY, VOL. 42, NO. 7, JUNE 1970
Instrumentation
are available? For this example, some typical values are: 0 to 50°C ± 2% error due to imperfect temperature compensation and no more than 130 mV required from the bridge output. Com pensation components will be chosen from standard values after the first trial designs. The maximum voltage required by the meter is that needed by the meter with the maximum current and the maximum coil resistance. Thus 51 μΑ Χ 1883 ohms = mV. The maximum voltage available in this example is 130 mV: 130 mV - 96 mV = 34 mV that can be dropped in the compensa tion network and 34 mV/51 ^A = 666 ohms maximum series resistance. The nominal rate of change of re sistance is calculated by multiplying the meter resistance by its coefficient. Thus, 1712 ohms X 0.00385 ohms/ ohm/°C = 6.6 ohms/°C. If a thermistor and a fixed value resistor are paralleled and are placed in series with the meter, a circuit with the tendencies shown in Figure 2 is produced. As the temperature in creases, the meter resistance increases, the thermistor resistance decreases greatly, and the shunt resistor dimin ishes the thermistor decrease. Since the network must have about 6.6 ohms/ °C change and since the fixed resistor is going to reduce the effect of the thermistor, the thermistor must have a change of more than 6.6 ohms/°C at the highest temperature to be com pensated. To keep the total added re sistance as low as possible and to avoid the very large change per degree of the thermistor at low temperatures, the lowest value thermistor having about twice the needed change at high temperatures should be chosen.
Figure 2. A thermistor and fixed value resistor are paralleled and placed in series with the meter
It can be seen in Table I that the 1 Κ disk shows a change of 576 ohms from 25 to 50 and 224 ohms from 50 to 75. This is an average of 400 ohms for 25°C change or 16 ohms/°C at 50°C. The 1 Κ bead is 520 ohms and 230 ohms or 15 ohms/°C. To satisfy the sensitivity requirement either would be acceptable for the first try. The allowable temperature compensation error of 2% dictates the tighter tol erance one. Since the meter changes 6.6 ohms/°C and the range of interest is 0 to 50°C, the total meter change is 330 ohms. The compensation network should also change 330 ohms. When the thermistor to try has been selected, the approxi mate value of shunt resistor can be calculated. The resistance of the thermistor and resistor in parallel at 0°C must be 330 ohms larger than at 50°C. 2691 R
=330+
424Λ
2691 + R 424 + R R = (See Figure 2) 1937 R2 - 1.03 Χ 106 R 0.377 Χ 109 = 0 R = 783 Trying this value with actual thermistor data shows the worst error, for a nominal meter of 1712 ohms, to be 0.21%. Trial and error attempts with standard value 1% resistors show 768 to yield the worst case of 0.13%. To use the same components for meters with ± 1 0 % from 1712 causes a com pensation error with the 783 to be 0.59 to 0.75%. In addition to these errors are the errors associated with the 1% resistor tolerance and the thermistor tolerances. With tight tolerance thermistors, it is feasible to compensate meter circuits to a few per cent over wide temperature ranges. At 25°C, the thermistor is 1000 ohms and the resistor is 768. This yields 434 ohms as the compensation resistance. If no manual resetting is used each time the temperature changes, the maximum voltage required would oc cur at 50 °C with a maximum resis tance and current meter. The meter re sistance is 1712 ohms + 10% X 1712 + 6.6 ohms/°C X 25°C change = 2048 ohms; 2048 ohms X 51 μΑ = 105 mV. The maximum voltage required with the automatic compensation is the same 105 mV plus the voltage drop across the compensation network. With both the thermistor at 50 °C and the 768-ohm resistor at their + 1 % tolerance with 51 μΑ, this is 14.1 mV + 105 mV = 119.1 mV. This meets the original re quirements for a maximum of 130 mV
* WÊÊÉ
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ANALYTICAL CHEMISTRY, VOL. 42, NO. 7, JUNE 1970
•
75 A
Instrumentation
iliïBi
!ll» ; f;jptK5fl|| I»|lJÎÉ3ïlSi:
6K »25°C
3.2 Κ
Figure 3. Circuit diagram for a Thermilinear network
iiïïllïiliïïlîîllî ilfll «ïlïflillftlEï» ÎJÎI...
ilSP
pJïîa;:«lîfflîïiÎ v ίΐϊϊϊ'ίίίΐ*
β.·??.;;
lïïïlil Figure 4. Revised network of Figure 3 produced by computer calculation
ïplllltl» iiiliiiiajjawfjijiisar Bi::#;j 6Κ
«Sis
@25°C tt^^fen 2.61 Κ iiiiîfi!ii:i!ïîï!ï(*, y?J5llïiilliiï:;S ïlilllïïïl :iiiiii Illlllî «isiifSilirriS îîîiïlliiiiift :iillsll(lfil|lil:| BfÎ:ffP(l|:I:tïlïS
111iijiii msmi ïlïsl ÏÏÏËifiΐίΐίϊ? Illaïl iilïiSilBSB'?.:ï ï l l l l «flip? i*lllll!!iSf!
Figure 5. Revised network of Figure 4 with the addition of a 1110-ohm series resistor 78 A ·
ANALYTICAL CHEMISTRY, VOL. 42, NO. 7, JUNE 1970
and shows t h a t automatic compens cost 14.1 m V or a 1 3 % reduction ' sensitivity compared to ideal. The resistance variation of thermistor can also be used to other variations t h a n resistance, transducers generate a current as the desired signal. If this current is passed through a resistor t o develop a voltage, then the resistor can include a thermistor. One example of this is t h e membranecovered polarographic electrode. T h e membrane permeability is temperature sensitive. T h e coefficient of T F E Teflon membranes is approximately + 4 % / ° C , while t h e thermistor is a p proximately — 4 % / ° C . Thus, just using a thermistor of the right value to derive t h e desired voltage will give a "first-order" correction. Resistor a n d thermistor combinations, as in t h e meter coil problem, can be applied to modify the fit. Remember t h a t either series or shunt resistance with the thermistor will reduce its temperature coefficient. Similarly a thermistor can be used to variably shunt a current around a circuit when currents are being used or derived from voltages. The ability to compensate with thermistors can be improved b y the use of more t h a n one thermistor. A t Yellow Springs I n s t r u m e n t Co. ( Y S I ) , we have exploited this concept and produced a commercial product, T h e r m i linear Components, consisting of two thermistors and two resistors which will produce linear current a n d voltage or resistance information for specific temperature ranges. I n addition, it is possible to produce other curve shapes by proper manipulation of t h e two resistors. This concept then is a powerful tool for compensating a number of temperature phenomena. F o r example, assume a test instrument with an ordinary panel meter in a Wheatstone bridge circuit with t h e meter exposed to a temperature variation of 0 to 100°C. Furthermore t h e coil resistance of t h a t meter is 3520 ohms a t 25 °C a n d t h e coil is made of copper. Then the coil resistance will change from 3190 ohms a t 0 ° C to 4510 ohms a t 100°C. This could cause an error in the meter indicated value of as much as 3 0 % . A solution to this problem can be found b y first returning to t h e instrument to determine if a n additional compensating resistance can be tolerated. F o r this example, assume a total of 6600 ohms ± 1% of meter coil; compensation resistance is t h e goal. F o r compensation, then, a network whose r e sistance is 3410 ohms a t 0 ° C and 2090 ohms at 100°C a t a rate of —13.2 o h m s / ° C is needed.
Instrumentation
An investigation of what is available to satisfy the network needs discloses t h a t a Thermilinear Component for 0 to 100°C with a sensitivity of —17.115 o h m s / ° C and a resistance level of 2768 ohms at 0 ° C is the closest thing. T h e circuit diagram for the Thermilinear network is shown in Figure 3. T h e difficult p a r t of the problem is to decrease the sensitivity of the network of Figure 3. T h e resistance level can be adjusted with series resistance. Since sensitivity is to be decreased, the 3200-ohm resistor must be decreased, b u t if the resistance change with temperature is to remain reasonably linear, the 6250-ohm resistor must also be altered. The best way to find these changes is an "educated cut and t r y " method. W e have developed a computer p r o gram which cycles the thermistors through their range of values while allowing an operator to change the fixed resistor values a t the beginning of each cycle. The revised network developed b y this method is shown in Figure 4. This network will produce a resistance of 2309 ohms a t 0 ° C , and 972 ohms at 100°C. When an 1110-ohm series resistor is added, Figure 5, the total at 0 ° C is 3419 ohms, at 100°C 2082 ohms. Table I I gives results every 5° for the entire 0-100°C range. Another fairly common compensation area is the feedback loop of an amplifier—for instance, the circuit shown in block diagram Figure 6. I t
Table I I . °c 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
Results of Figure Network
Desired resistance, ohms
Actual resistance ohms
3410 3344
3419 3361 3299
3278 3212 3146 3080 3014 2948 2882 2816 2750 2684 2618 2552 2486 2420 2354 2288 2222 2156 2090
3235 3170 3103 3037 2971 2905 2840 2775 2708 2642 2574 2505 2435 2364 2293 2222 2152 2082
Feedback Signal cond circuit
Sensor
Figure 6.
Indicator
Amplifier
Block diagram of feedback loop of an amplifier
mSB-
WM'Ï
llillpWiiiK;·:
»m«
• K l i i e i f i :: ' " ! " " · * ma I j : :
fiffSmi
ÎJf-lliiiKif ÎnSiiSSi,! Si!
itiï'fKmi^f
mmm
ftiffli
Figure 7.
e out
Circuit of an operational amplifier used in an inverting mode
is quite common for each element in Figure 6 to have a temperature coefficient. A composite coefficient m a y be determined b y exposing the entire circuit of Figure 6 to the expected temperature variations. At the same time, b y varying the feedback it is normally possible to compensate for sensitivity changes in the circuit. If this feedback circuit requires decreasing resistance with increasing temperature, a thermistor network is a natural. T h e circuit of Figure 7 is a common operational amplifier used in an inverting mode. Suppose t h a t a linear-with-temperature gain change (the ratio of Rf to R^ of —10% in going from 0 to 50°C is needed. A Y S I Thermilinear Component with a resistance of 12,175 ohms at 0 ° C and 5820 ohms a t 50°C at —127.096 o h m s / ° C is available as a standard p a r t . This component was chosen merely for the example. Other available components might be chosen for a more specific problem: Let Rt
RL
Rz< -f-
R
RT = thermilinear network resistance Then (5820 + R) = 0 g (12,175 + R) Ri Ri R = required unknown R = 51,375
initial gain required. Likewise if the gain change needed was say — 5 % for 0 to 50°C, then: (5820 + Ri
R)
0.95
(12,175 + Ri
R)
R = 114,920 ohms Therefore : Rf
= 127,095
Rf @ 50° = 120,740 Again Rx is chosen to produce the initial gain required. Shown above are some of the possible techniques of temperature compensation using thermistors. A thermistor has a large negative temperature coefficient of resistance. Since this coefficient is larger than most other devices' coefficients, it is usually possible to tailor the thermistor's response to match the needed correction. Because of the complex nature of thermistor's temperature relationship, as well as the relationships of the devices t ° be compensated, a trial-and-error procedure is usually the simplest. If the volume of Use is large, then spending the initial time on a long mathematical analysis might be warranted. Because it takes m a n y words to describe, the trial and error methods shown sound laborious. However, the design of these networks goes quickly after a little practice; especially if the best compensation is not needed or if the temperature range is narrow.
Therefore : Rf @ 0° = 63,550 Rf @ 50° = 57,195 Ri
is then chosen to produce the
EDITORS' NOTE: Manufacturers of t h e r m i s t o r s are listed in ANALYTICAL CHEMISTRY'S 1969-70 Laboratory Guide to Instruments, Equipment, and Chemicals, page 2 5 8 LG
ANALYTICAL CHEMISTRY, VOL. 4 2 , NO. 7, JUNE 1970
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