I
INSTRUMENTATION
Advisory Panel Jonathan W. Amy Glenn L. Booman Robert L. Bowman
Jack W. Frazer G. Phillip Hicks Donald R. Johnson
I
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 thermistor’s response to match a needed correction. The complex interrelationships involved make a trial-and-error procedure often the simplest. Examples are given to show just how these networks can be designed
M
and chemical processes exhibit variations in their behavior as a function of their temperature. Those processes involved in creating electrical “signals” may be amenable to using electrical corrections for their temperature artifacts. Thermistors offer several advantages over other temperature transducers for such applications. Some of the thermistor characteristics that create these advantages are speed of response, negative temperature coefficient of resistance, small size, high sensitivity, wide range of resistance values, rugged construction, and interchangeability if needed. I n many situations any one of these characteristics may be surpassed by another transducer, 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 nonlinear (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 OST PHYSICAL
Rt = R, ( e B I T ) where R = resistance at desired temperature, Ro = resistance at the temperature for which B is evaluated (usually 25OC, B is presumed constant for any particular material and is a slope or sensitivity term), and T = absolute temperature (degrees Kelvin) a t which the resistance is desired. Often a more useful number is alpha (a)which is the slope of the resistance vs. temperature curve at the temperature specified. A better equation for approximating thermistor behavior is Rt = Roe(B/T+ @ I T a ) . B has about the same meaning as above and C can be thought of as a correction. This improved equation becomes important when tight tolerance thermistors are used. B and C are not usually published because it is normally easier for the user to work with resistance us. 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 useful to have another situation described, and some manufacturers use the same measurement with the thermistor immersed 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 vell-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 :
+ Z2RP0 T,*x Tarn,, = maximum ambient temperature around thermistor I = current through thermistor if thermistor were at maximum allowable temperature R = resistance of thermistor at maximum allowable temperature T,,, = maximum allowable temperature Time constants and dissipation constants are both an indication of the Tamb
ANALYTICAL CHEMISTRY, VOL. 42, NO. 7, JUNE 1970
73A
Instrumentation
Table I. Specific Data: Typical Range of Values B&tol % @ 25.2
82% -25
R 0
(ohm) vs. T ("c) 25 50
Resis. 75
100
Max. temp.,
TCr
$kg*%
sec.
OC
Small beads
2800 f 8 4300 f 8
-3.2 -4.8
68K 10M
2.4K 3M
1K 1M
480 350K
250 130K
140 54K
5to20% 0.5 t o 1
0.1
300 best 600 max
Large beads Glass probes
2800 f 10 3900 f 10 5 1 0 0 f 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
5to20% 2 beads 25 prbs.
1
300 best 600 max
-3.1 -3.7 -4.1 -5.2
627.9 8489 102.9K
232.7 2691 29.49K 3.966M
100 1K 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
12 31K
5 10K
2.1 3.7K
1 1.5K
0.5 700
5to20% 150 10
...
...
...
Close 2750 f 1.0 tolerance 3300 f 1.0 disks 3640f0.5 4600 f 1.0
..,
Wide 3400 f 3 t o 5 -3.8 tolerance 3900 f 3 t o 5 -4.4 disks
45 103K
.. .
...
Special mounts
Any above
ability to effect a heat transfer between the medium and the thermistor. Thus, again the user must evaluate his system and the vendor can only provide some guidelines. One factor to consider with the thermistor time constant is the time constant of the element being compensated. With the thermistor in its final position, they should either match or a sufficient waiting period should be allowed for both t o come t o equilibrium. Most thermistors are available with resistance vs. temperature accuracy of *IO to 220% a t 25OC. Additionally the sensitivity values are f 5 to +IO%. Beads are available with special matching to tighter tolerances. Small disks are readily available in accuracies to +1/2% over the range of 0 to 75OC, gradually changing to +5% a t -8O"C, and f2% a t 15OOC. This corresponds to an equivalent temperature error of -CO.O5OC a t 25OC. With all these different facets and such wide ranges of values within each, designing t o use the thermistor is somewhat complex. Also, there is enough versatility t o 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 positive temperature coefficient needing to be compensated to yield a constant resistance. One example of this is a 74A
...
...
meter being used to measure a voltage in a direct reading Wheatstone bridge. The current through the meter (for any particular value of R,) is a function 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 resistance. For example, one 50 p4 f 2%
10
100 best
150 max
1% 1/2%
1%
...
Up to 30 min.
25 3.5
Up to 10 Xabove
100 to 200
...
meter has a 1712 ohm -C 10% at 25OC coil resistance. Because this is a copper wire coil, the resistance at different temperatures is calculated by RT = R25 (1 0.00385 7'). 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
+
Figure 1. A resistor with a positive temperature coefficient needs compensation t o yield a constant resistance. Example is a meter used t o measure a voltage i n a direct reading WheatBtone bridge
ANALYTICAL CHEMISTRY, VOL. 42, NO. 7, JUNE 1970
are available? For this example, some typioal values are: 0 to 5OoC t 2% error due to imperfect temperature compensation and no more than 130 mV required from the bridge output. Compensation 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 PA x 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 compensation network and 34 mV/51 pA = 666 ohms maximum series resistance. The nominal rate of change of resistance is calculated by multiplying the meter resistance by its coefficient. Thus, 1712 ohms x 0.00385 ohms/ ohm/OC = 6.6 ohms/OC. 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 increases, the meter resistance increases, the thermistor resistance decreases greatly, and the shunt resistor diminishes the thermistor decrease. Since the network must have about 6.6 ohms/ "C change and since the fixed resistor is going t o reduce the effect of the thermistor, the thermistor must have a change of more than 6.6 ohms/OC a t the highest temperature to be compensated. To keep the total added resistance as low as possible and to avoid the very large change per degree of the thermistor a t low temperatures, $he lowest value thermistor having about twice the needed change a t high temperatures should be chosen.
It can be seen in Table I that the 1 K disk shows a change of 576 ohms from 25 to 50 and 224 ohms from 50 t o 75. This is an average of 400 ohms for 25OC change or 16 ohms/OC a t 50°C. The 1 K 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 tolerance one. Since the meter changes 6.6 ohms/OC 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 approximate value of shunt resistor can be calculated. The resistance of the thermistor and resistor in parallel a t O°C must be 330 ohms larger than a t 50°C. 2691 R 424 R = 330 2691 R 424 R R = (See Figure 2)
+
+
1937 Rz
- 1.03 X R
~
lo6 R 0.377
=
x
lo9
= 0
Compare
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 t o yield the worst case of 0.13%. To use the same components for meters with +-lo% from 1712 causes a compensation error with the 783 to be 0.59 t o 0.75%. I n 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 occur a t 50°C with a maximum resistance and current meter. The meter resistance is 1712 ohms 10% x 1712 6.6 ohms/"C X 25'C change = 2048 ohms; 2048 ohms x 51 ,A = 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 a t 50°C and the 768-ohm resistor a t their +1% tolerance with 51 PA, this is 14.1 mV 105 mV = 119.1 mV. This meets the original requirements for a maximum of 130 mV
+
Figure 2. A thermistor and fixed value resistor are paralleled and placed in series with the meter
+
+
+
You can, with the E-C Vertical Gel Electrophoresis unit. A s many as 30 samples at the same time. All run under identical conditions: same gel, same temperature, same voltage. Want more versatility? The E-C Vertical Gel system accepts all types of gel, including starch, agar, silica, and polyacrylamide. Its design makes possible both continuous and discontinuous electrophoresis. And, because you're using a flat gel slab, you can do twodimensional separations too. For simplicity of operation and consistent results, nothing else compares with the E-C Electrophoresis system.
To get more detailed information for your application, call our Technical Service collect, at (215) 382-9100, o r write E-C Apparatus Corporation, 755 St. M a r k s Street, University City, Philadelphia, Pennsylvania 19104.
E-C Apparatus Corporation A Milton Roy Company
Circle No. 41 on Readers' Service Card
ANALYTICAL CHEMISTRY, VOL. 42, NO. 7, JUNE 1970
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75A
The HP model 7670A automaticsampler uses a GC syringe the same way you doBBBexcept that it comple&ly unattended
The 7670A Automatic Sampler completely automates the measurement and injection of a sample into a GC. After loading it with as many as 36 samples, you push the RUN button-and then go do something useful for the next few days. Meanwhile the 7670A, under the foolproof and continuous direction of its Control Unit, performs the complete job, completely unattended: 1-washes the syringe by aspirating a full bore of new sample 5 or 11 times as desired, and dumps the washings into a waste tray , . , to minimize sample carryover-and pumps the pre-selected sample volume in and out of the syringe 5 times,, , to eliminate bubbles 2-measures the desired sample volume with machine-reproducibility , . . t o improve precision 3-injects the sample into the GC as a ‘slug’ . . . to improve reproducibility
4-indexes the carousel-like tray to the next sample (or repeats the previous sample, if you prefer) and re-starts the procedure . , , for full automation As you can see, the 7670A does the job the same way that a good chromatographer does . . . but with two exceptions. It is consistently more precise than even a skilled technician because it does everything with machinereproducibility. . . and it is substantially more economical because it operates completely unattended all day, all night, all week-end long. Priced at $2850, the 7670A can be installed directly on HP Series 7620, 5750 and 810 GC’s, . . another reason why most chromatographers choose HP for all GC instruments and accessories, Hewlett-Packard, Route 41, Avondale, Pa. 19311. In Europe: 1217 MeyrinGeneva, Switzerland .
A N A LYTI C A L
I N STR U M E NTS
Circle NO. 61 on Readers’ Service Card
If the acids you're using now don't have all of these features, better look to Eastman. Dripless spout under a color-coded cap
C o m p l e t e , actual lot analysis on each bottle
-
Each bottle individually packed in impact-absorbing polystyrene
-Color - coded labels
And some other interesting features. photographic f i l m , and ethanol is a story a l l by itself.)
A quantity-rate price schedule that allows you t o obtain the best price by mixing full cases of ACS Reagent acids, solvents, and N H 4 0 H .
Some interesting, attractive freight terms, like FOB destination on combined acid, solvent, and N H 4 0 H orders totaling $200 or more.
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Get the whole story complete with prices, freight terms, availability, and ordering information. Use the coupon t o request Kodak Publication No. JJ-163,"ACS Acids, Solvents, a n d ",OH."
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I I 1 I I
Dept. 41 2L, Eastman Organic Chemicals Eastman Kodak Company, Rochester, N.Y. 14650 Please send me Kodak Publication No. JJ-163, "ACS Acids, Solvents, and NH40H."
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Name
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Firm Name
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Circle NO. 40
on Readers' Service Card
ANALYTICAL CHEMISTRY, VOL. 42, NO. 7, JUNE 1970
77A
Instrumentation
An investigation of what is availahle
ohms/OC and a resistance level of 2768
~~~~
~~
~~
~"
_." ~
Table II. Results of Figure 5 Network resistance, ohms
Actual resistance, Ohms
3410 3344 3278 3212 3146 3080 3014 2948 2882 2816 2750 2684 2618 2552 2486 2420 2354 2288 2222 2156 2090
3419 3361 3299 3235 3170 3103 3037 2971 2905 2840 2775 2708 2642 2574 2505 2435 2364 2293 2222 2152 2082
Desired
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
~.____-
._____-. ..__l_l.~
~
ure 3. The resistance level can he a i justed with series resistance. Since sensitivity is to be decreased, the 3200-ohm resistor must be decreased, but 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 try" method. We have developed a computer program 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 by this method is shown in Figure 4. This network will produce a resistance of 2309 ohms a t OC ' , and 972 ohms at 100°C. When an 1110-ohm series resistor is added, Figure 5, the total a t 0°C is 3419 ohms, a t 100°C 2082 ohms. Table I1 gives results every 5O for the entire Ck100"C range. Another fairly common compensation area is the feedback loop of an amplifier-for instance, the circuit shown in block diagram Figure 6. It
QC
3
Figure 6. BIoc k diagram of feedback loop of an amplifier
is quite common for each element in Figure 6 to have a temperature eoefficient. A composite coefficient may be determined by exposing the entire circuit of Figure 6 to the expected temperature variations. At the same time, by 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. The circuit of Figure 7 is a common operational amplifier used in an inverting mode. suppose that a linear.&h.temperature gain change (the ratio of R, to R,) of -10% in going from 0 to 5 0 0 ~is needed. A y s ~Themilinear cornponentwith a resistanee of 12,175 ohms at ooc and 5820 ohms at 5 0 0 ~at -127.096 ohms/oc is available as a standard part. This component was chosen merely for the example. Other available components might be chosen for a more specific problem: Let
R,= R T + R R, = thermilinear network resistance Then (5820
+ R) = o,9 (12,175 + R )
7,
7,
n,
n*
R = required unknown R
=
51,375
:
OI,lYD
R, is then chosen to produce the
initial gain required. Likewise if the gain change needed was say -5% for 0 to 50°C, then: (5820
f
R,
= 0.95 (12,175 f
R1
R,
R, R = 114,920 ohms
Therefore:
R, = 127,095 R, @ 50' = 120,740 Again RI is chosen to Produce the initial gain required. Shown above are some of the possible techniques of temperature cornpensation 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 t,ailor the thermistor's response to match the needed correction. Because of the complex nature of themistor's temperatnre relationship, as well as the relationshius of the devices to 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 he warranted. Because i t takes many words t o describe, the trial and error methods shown sound laborious. However. the desien of these networks goes quickly after a little practice; especially if the best compensation is not needed or if the temperature range is narrow. I
..
Guide to Instruments. Eouioment. and Chemicals, page 258 LG
