44018

D 

## **Linear Thermistor Components and Probes** 

**OL-705-PP air probe shown with Model 5830, sold separately.** 

Following is a description of why these networks produce linear information. The equation for a voltage divider network, consisting of R and R0 in series, is: R Eout = Ein R + R0 

where Eout is the voltage drop across R. If R is a thermistor, and Eout is plotted versus temperature, the total curve will be essentially non-linear and of a general “S” shape, with linear or nearly linear portions near the ends and in the center. 

## **Linear Response Components** 

For applications requiring thermistors with linear response to temperature change, OMEGA offers linear components. These unique devices consist of a thermistor composite for temperature sensing and an external resistor composite for linearizing. 

Thermistor composites 44018 and 44019 each contain two thermistors packaged in a single sensor (Figures 1A and 1B). Thermistor composite 44020 contains three thermistors packaged in a single sensor (Figure 1C). 

Resistor composites for use with 44018 and 44019 thermistor composites consist of two metal film resistors of the size shown in Figure 2. Resistor composites for use with the 44020 thermistor composite consist of three of the same type metal film resistors. 

Linear components are manufactured with different values for different temperatures ranges. When they are connected in networks shown in Figures 3 (A and B) and 4 (A and B), they produce a varying voltage or resistance which is linear with temperature. 

One of the basic network manifestations is a voltage divider as in Figure 3A for components other than #44212, and as shown in Figure 3B for component #44212. The area within the dashed lines represents the thermistor composite. The network hookup for linear resistance versus temperature is shown in Figure 4A for linear components except #44212, and in Figure 4B for #44212. 

## **Linear Voltage vs. Temperature** 

**==> picture [234 x 88] intentionally omitted <==**

**----- Start of picture text -----**<br>
Eout Eout<br>R1 Positive R1 Positive<br>Slope Slope<br>R2<br>Ein Ein<br>R2 R3<br>Eout Eout<br>Negative Negative<br>Slope Slope<br>T1 T2 T1 T2 T3<br>Figure 3A Figure 3B<br>**----- End of picture text -----**<br>


_**Note:** Model 5830 precision benchtop thermometer includes linearized circuity._ 

**==> picture [204 x 153] intentionally omitted <==**

**----- Start of picture text -----**<br>
Figure 1A 2.0 mm(0.08")<br>Thermistor Max.<br>Composite 44018 OSS 3.8 mm(0.150)Max. (6") Nom.150 mm —<br>Figure 1B (0.110")2.8 mm -<br>Thermistor Max.<br>Composite 44019 OS= 3.8 mm(0.150)Max. (6") Nom.150 mm —<br>3.1 mm :<br>Figure 1C (0.125")<br>Thermistor Max.<br>Composite 44020 == 7.1 mm(0.28'')Max. (6") Nom.150 mm —<br>2.5 mm | 0.63 mm D<br>Figure 2Metal Film (0.100")Max. (0.025")<br>Resistor oe 6.8 mm (0.27")<br>Max.<br>**----- End of picture text -----**<br>


If R is modified by the addition of other thermistors and resistors, linearity of the center section of the curve, where sensitivity is greatest, can be extended to cover a wide range of temperatures. This section follows the general equation for a straight line, y = mx + b or in terms of a linear component: 

For Voltage Mode For Resistance Mode Eout = ±MT + b Rt = MT + b where M is slope where M is slope in volts/ °T, in ohms/°T, T is temperature T is temperature in °C or °F, and in °C or °F, and b is the value of b is the value of the Eout when T = 0° total network resistance, Rt, in ohms when T = 

## **Linear Resistance vs. Temperature** 

**==> picture [249 x 117] intentionally omitted <==**

**----- Start of picture text -----**<br>
R2<br>R2 R3<br>R1 R RL 1* R1 R RL 1*<br>T1 T2<br>T1 T2 T3<br>Figure 4A Figure 4B<br>* (R [RL] 1A1) is selected to satisfy the relationship: [ may be any value as long as a new R] 1 [ value  ] R1A = RRL1 x RL1 – R11<br>**----- End of picture text -----**<br>


**D-42** 

Sensitivity is 400 times greater than an IC thermocouple. Thermistor values as high as 30 mV/°C are common. In addition, output voltage can be applied to a recorder or digital voltmeter to produce a precise, sensitive, direct reading thermometer. 

In other situations, it is frequently desirable to have thermistor composite temperature sensors at more than one location. When this is required, it is not necessary to have a separate resistor composite for each thermistor composite. It is 

possible to multiplex any number of thermistor composites through a single resistor composite for greater design flexibility 

## **Multiplexing** 

The 44018 thermistor composite is used in four of the linear components. The part that changes in each component is the resistor composite, which determines the temperature range. Therefore, the 44018 thermistor composite can be used over the entire -30 to 100°C temperature range by simply changing resistor composites. Its accuracy and interchangeability over the full range is ±0.15°C. It is not mandatory that OMEGA[®] resistor composites be used with the 44018 thermistor composite. Any 0.1% resistors of the proper values and with a temperature coefficient of 30 PPM or less may be substituted. 

|**To Order**|**To Order**|**To Order**|
|---|---|---|
|**Linear Kit†**<br>**Model No.**|**Thermistor**<br>**Composite**<br>**Model No.**|**Resistor**<br>**Composite**<br>**Model No.**|
|**44201**|**44018**|**44301**|
|**44202**|**44018**|**44302**|
|**44203**|**44018**|**44303**|
|**44204**|**44018**|**44304**|
|**44211A**|**44019**|**44311A**|
|**44212**|**44020**|**44312**|



_See the next page for more information._ 

_**Ordering Examples: 44203,** linear kit,_ _**44018** , dual thermistor composite plus_ _**44303,** resistor composite sensor._ _**44202,** linear kit,_ _**44018,** dual thermistor composite plus_ _**44302,** resistor composite sensor._ 

## **Component Specifications** 

|**°C **<br>sD|**°C **<br>sD|**°F **<br>sD|**°C **<br>sD<br>~~QO~~|**°F**<br>sD|
|---|---|---|---|---|
|**† Linear Components**<br>**Kit Model No.**<br>~~ee~~|**44201**<br>~~Re~~||**44202**<br>~~QO~~<br>~~(~~||
|**Range **<br>~~ee~~|0 to 100°C<br>~~Re~~|32 to 212°F|-5 to 45°C|23 to 113°F<br>~~(~~|
|**Thermistor Composite**<br>**Model No.**<br>~~ee~~|**44018**<br>~~Re~~||**44018**<br>~~(~~||
|**Resistor Composite**<br>**Model No.**|**44301**||**44302**||
|**Resistor**<br>**Composite Values**|R1= 3200Ω,<br>R2= 6250Ω||R1= 5700Ω,<br>R2= 12000Ω||
|**Thermistor Accuracy**<br>**& Interchangeability**|±0.15°C<br>-30 to 100°C|±0.27°F<br>-22 to 212°F|±0.15°C<br>-30 to 100°C|±0.27°F<br>-22 to 212°F|
|**E0 Positive Slope**|Eout=<br>(+0.0053483 Ein) T<br>+0.13493 Ein|Eout=<br>(+0.00297127 Ein) T<br>+0.03985 Ein|Eout=<br>(+0.0056846 Ein) T<br>+0.194142 Ein|Eout=<br>(+0.00315851 Ein) T<br>+0.093083 Ein|
|**E0 Negative Slope**|Eout=<br>(-0.0053483 Ein) T<br>+0.86507 Ein|Eout=<br>(-0.00297127 Ein) T<br>+0.96015 Ein|Eout=<br>(-0.0056846 Ein) T<br>+0.805858 Ein|Eout=<br>(-0.00315851 Ein) T<br>+0.906917 Ein|
|**Resistance Mode**<br>~~es~~|Rt=<br>(-17.115)T +2768.23<br>~~Ra~~|Rt=<br>(-9.508)T +3072.48<br>~~Ra~~|Rt=<br>(-32.402)T +4593.39|Rt=<br>(-18,001)T +5169.42|
|***Ein MAX**<br>~~es~~<br>~~ee~~|2.0 Volts<br>~~Ra~~||3.5 Volts||
|***IT MAX**<br>~~es~~<br>~~ee~~|625µA<br>~~Ra~~||615µA||
|*****Load Resistance**<br>**Minimum R.L.**<br>~~ee~~<br>~~ee is~~|3 MΩ<br>~~is~~||10 MΩ||
|**Linearity Deviation**<br>~~ee is~~|±0.216°C<br>~~is~~|±0.388°F|±0.065°C|±0.12°F|



_*** Ein Max** and_ _***IT Max** values have been assigned to control thermistor self-heating errors so they do not enlarge the component error band; i.e., the sum of the linearity deviation plus the probe tolerances. The values were assigned using a thermistor dissipation constant of 8MW/°C in stirred oil. If better heat-sink methods are used or if an enlargement of the error band is acceptable, Ein Max. and IT Max values may be exceeded without damage to the thermistor probe._ 

_******* See Figure 1, example 1 on typical linear component application on next page._ 

_**††** Kit includes thermistor composite and resistors._ 

**D-43** 

D 

|<br>**°C**|<br>**°C**|**°F**|**°C**|**°F**|
|---|---|---|---|---|
|**Linear Components**<br>**Kit Model Number†**|**44203**||**44204**||
|**Range **|-30 to 50°C|-22 to 122°F|-2 to 38°C|+30 to 100°F|
|**Thermistor Composite**<br>**Model Number**|**44018**||**44018**||
|**Resistor Composite**<br>**Model Number**|**44303**||**44304**||
|**Resistor**<br>**Composite Values**|R1= 18,700Ω<br>R2= 35,250Ω||R1= 5700Ω<br>R2= 12,400Ω||
|**Thermistor Accuracy**<br>**& Interchangeability**|±0.15°C<br>-30 to 100°C|±0.27°F<br>-22 to +212°F|±0.15°C<br>-2 to +38°C|±0.27°F<br>-22 to +212°F|
|**E0 Positive Slope**|Eout=<br>(+0.0067966 Ein) T<br>+0.34893 Ein|Eout=<br>(+0.00377588 Ein) T<br>+0.228102 Ein|Eout=<br>(+0.00563179 Ein) T<br>+0.192439 Ein|Eout=<br>(+0.0031289 Ein) T<br>+0.09232 Ein|
|**0**<br> <br> **E0 Negative Slope**|Eout=<br>(-0.0067966 Ein) T<br>+0.65107 Ein|Eout=<br>(-0.00377588 Ein) T<br>+0.771898 Ein|Eout=<br>(-0.00563179 Ein) T<br>+0.807563 Ein|Eout=<br>(-0.0031289 Ein) T<br>+0.90768 Ein|
|**Resistance Mode**|Rt = (-127.096) T<br>+12175|Rt = (-70.608) T<br>+14435|Rt = (-32.1012) T<br>+4603.1|Rt = (-17,834) T<br>+5173.8|
|**Ein MAX***|3.0 Volts||4 Volts||
|**IT MAX*****|475 µA||685 µA||
|**Load Resistance**<br>**Minimum R.L.*****<br>~~ee~~|10 MΩ<br>~~Rsee~~||10 MΩ<br>~~(~~||
|**Linearity Deviation**<br>~~ee~~|±0.16°C<br>~~Rs~~|±0.29°F<br>~~ee~~|±0.03°C<br>~~(~~|±0.055°F|
|**Linear Components**<br>**Kit Model Number†**<br>~~ee~~|**44211A**<br>~~Rsee~~||**44212**<br>~~(~~||
|**Range **|-55 to 85°C|-67 to 185°F|-50 to 50°C|-58 to 122°F|
|**Thermistor Composite**<br>**Model Number**|**44019**||**44020**||
|**Resistor Composite**<br>**Model Number**|**44311A**||**44312**||
|**Resistor**<br> **Composite Values**|R1= 3550Ω,<br>R2= 6025Ω||R1= 23,100Ω<br>R2= 88,200Ω<br>R3= 38,000Ω||
|**Thermistor Accuracy**<br>**& Interchangeability**|±0.4°C,  0 to 85°C<br>±0.8°C,-55 to 0°C|±0.72, 32 to 185°F<br>±1.44,-67 to 32°F|±0.1°C<br>±0.18°F<br>-50 to 50°C<br>- 58 to 122°F||
|**E0 Positive Slope**|Eout=<br>(+0.005068 Ein) T<br>+0.3411 Ein|Eout=<br>(+0.002816 Ein) T<br>+0.2510 Ein|Eout=<br>(+0.00559149 Ein) T<br>+0.40700 Ein|Eout=<br>(+0.00310638 Ein) T<br>+0.30760 Ein|
|**E0 Negative Slope**|Eout=<br>(-0.005068 Ein) T<br>+0.6589 Ein|Eout=<br>(-0.002816 Ein) T<br>+0.7490 Ein|Eout=<br>(-0.00559149 Ein) T<br>+0.59300 Ein|Eout=<br>(-0.00310638 Ein) T<br>+0.69240 Ein|
|**Resistance Mode**|Rt = (-17.99)  T<br>+2339|Rt = (-9.994) T<br>+2658.8|Rt = (-129.163) T<br>+13698.23|Rt = (-71.757) T<br>+15994.5|
|**Ein MAX.***|2.0 Volts||3.5 Volts||
|**IT MAX.*****|833µA||700µA||
|**Load Resistance**<br>**Minimum R.L.*****|10 MΩ||10 MΩ||
|**Linearity Deviation**<br>|±1.1°C|±2°F|±0.15°C (condition A)******<br>±0.08°C (condition B)******|******<br>±0.27°F (A)<br>******<br>±0.15°F (B)|



_******[ The maximum error at any point is the algebraic sum of the thermistor manufacturing tolerances, plus linearity deviation, a fixed network ] behavior. Condition “A” is the worst case linearity deviation of ±0.15°C and may occur with the ±0.1% resistors supplied. Condition “B” exists when the three resistors are whin ±0.02% of nominal, which reduces linearity deviation to ±0.08°C._ 

_**Note:** The time required for a thermistor composite to indicate 63% of a newly impressed temperature is one second in “well stirred” oil and ten seconds in free , still air._ 

_**††** Kit includes thermistor composite and resistors._ 

**D-44** 

**Typical Linear Component Applications Example 1: R1 R3 Ein** To measure and record on a 100 mV recorder temperature in the range 30 to 40°C. **RL R2** 1. Select Part number 44202 (temperature range -5°to +45°C) **Eout2** 2. Calculate Ebasic equation Ein for 10°C equal to 100 mVout1 = (-0.0056846 Ein) T +0.805858 Ein **T1 T2 R4 Figure 1** (Eout, @30°C - Eout1 @ 40°C) = 100 mV [(-0.0056846 Ein) 30°C + 0.805858 Ein] - [(-0.0056846 Ein) 40°C + 0.805858 Ein] = 100 mV 0.056846 Ein = 100 mV Ein = 1.7591 Volts 3. Using the Linear network as two legs of a Wheatstone bridge add the two additional legs, R3 and R4 so that Eout2 = 0 when T = 30°C. (See Figure 1.) R3 and R4 are calculated from five known conditions. (1) The voltage drop across R4 (ER4) should equal Eout1 at 30°C for Eout2 to equal zero. (2) Ein = 1.7591 Volts (3) 1000 ohms ≤ R3 + R4 ≤ 5000 ohms. (If R3 + R4 is less than 1 K, excessive battery drain may occur. If R3 + R4 is more than 5 K, some degradation of linearity will occur.) (4) ER4 = Ein R4 R3 + R4 (5) Eout1 = -0.0056846 (1.7591 Volts) (+30°C) +0.805858 (1.7591 Volts) = 1.1180 Volts ER4 = Eout1 = ER4 = Ein R4 ~~o~~ r 1.1180 =[ R] 4[ 1.7591] and let us choose R3 + R4 i = 1000 ohms. R3 + R3 R3 + R4 Solve for R3 ~~—~~ and R4 1.1180 =[ R] R ~~—~~[4] 4[ 1.7591] + 100-R4 RR43 = 635.55 ohms = 364.45 ohms 4. Apply Eout2 to the recorder input terminals and the result is a direct reading 10°C full scale thermometer. **Example 2:** To make a 4 digit 100 mV sensitivity digital voltmeter into a direct reading differential thermometer whose ambient range is -30 to 40°C; **R1 R1 Ein** 1. Select Part number 44203 (temperature range -30 to 50°C) **RL** basic equation Eout = (-0.0067966 Ein) T +0.65107 Ein **R2 Eout R2** 2. Calculate Ein so that 10 mV equals one degree C. (This is done so that the Digital  Volt Meter will read directly in temperature with 0.01°C readability) **T1 T2 T2 T1** (Eout, @ -30°C - Eout, @ +40°C) = 0.700 Volts [(-0.0067966 Ein)(-30) +0.65107 Ein] - [(-0.0067966 Ein) (40) + 0.65107 Ein] = 0.700 **Figure 2** 0.47576 Ein = 0.700 | Ein = 1.4713 Volts a ~~o~~ n 3. Connect two linear networks (#44203) as shown in Fig. 2. 4. Apply Eout to the Digital Volt Meter input terminals for a direct reading differential thermometer. **Example 3:** To make a 2-wire system from a 3-wire system using any Linear component: 1. For voltage mode, connect R2 to the thermistor composite. (See Figure 3.) This unit can function as the temperature sensor and be located remote from the signal conditioning circuit by up to distance “D”. 2. The resistance mode differs from the voltage mode only by removal of the power source. (See Figure  4.) 3. Acceptable distance “D” varies according to the temperature range. Using #22 wire “D” may be as follows without loss of accuracy in both 2-wire and 3-wire systems. Where distance “D” is greater than indicated, heavier gauge wire may be used. **Temperature Distance R2 A A Figure 4 Range “D” T1 R1 R1 Resistance Mode** 0 to 100°C 30 m (100') -5 to 45°C 91 m (300') -30 to 50°C 91 m (300') **T2 Ein Eout R1** 30 to 100°C 91 m (300') **D B B Example 4: R2** Multiplexing to connect any number of thermistor **SENSOR1 T1 R1** composites to a single signal conditioning circuit. **T2 Ein Eout** (See Figure 5.) Multiplexing can be accomplished much more easily with a two-wire system, such as shown in Figure 5. **SENSORN** Ls **T1 Figure 5 T2** ~~———~~ **Lead Colors:** ~~ee~~ **Green** :  Common to T1 & T2 **Brown** : T1 **Red:** T2 

**D-45**