Linear Response Components For applications requiring thermistors with linear response to temperature change, NEWPORT 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 & 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 and 4, 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.



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:

Eout = Ein	R
	R + R0

where E_out is the voltage drop across R. If R is a thermistor, and E_out 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.

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

Figure 3A

Figure 3B

Note: Model 5830 precision benchtop thermometer includes linearized circuity.

Figure 4A

Figure 4B

*RL1 may be any value as long as a new R1 value (R1A) is selected to satisfy the relationship:	R1A =	R1 x RL1
		RL1 – R1

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.

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 NEWPORT® 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. 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: Linear Thermistor Components are manufactured under U.S. Patent #3316765 and Canadian Patent #782790.

To Order (Specify Model Number)

†Kit includes thermistor composite and resistors.

Component Specifications * 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 page. †Kit includes thermistor composite and resistors. ** 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.

Typical Linear Component Applications
Example 1:
To measure and record on a 100 mV recorder temperature in the range 30 to 40°C.
1. Select Part number 44202 (temperature range -5°to +45°C) basic equation E_out1 = (-0.0056846 E_in) T +0.805858 E_in

2. Calculate E_in for 10°C equal to 100 mV

(E_out, @30°C - E_out1 @ 40°C) = 100 mV
[(-0.0056846 E_in) 30°C + 0.805858 E_in] - [(-0.0056846 E_in) 40°C + 0.805858 E_in] = 100 mV
0.056846 E_in = 100 mV
E_in = 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 E_out2 = 0 when T = 30°C. (See Figure 1.) R₃ and R₄ are calculated from five known conditions.

(1) The voltage drop across R₄ (E_R4) should equal E_out1 at 30°C for E_out2 to equal zero.
(2) E_in = 1.7591 Volts
(3) 1000 ohms < or equal to R₃ + R₄ < or equal to 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) E_out1 = -0.0056846 (1.7591 Volts) (+30°C) +0.805858 (1.7591 Volts) = 1.1180 Volts

ER4 = Eout1 = ER4 =

Ein R4 R3 + R4

or 1.1180 =

R4 1.7591 R3 + R4

and let us choose R3 + R4 = 1000 ohms.

Solve for R3 and R4

1.1180 =

R4 1.7591 R4 + 100-R4

R4 = 635.55 ohms R3 = 364.45 ohms

4. Apply E_out2 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;

1. Select Part number 44203 (temperature range -30 to 50°C) basic equation Eout = (-0.0067966 Ein) T +0.65107 Ein

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)

(E_out, @ -30°C - E_out, @ +40°C) = 0.700 Volts
[(-0.0067966 E_in)(-30) +0.65107 E_in] - [(-0.0067966 E_in) (40) + 0.65107 E_in] = 0.700
0.47576 E_in = 0.700
E_in = 1.4713 Volts

3. Connect two linear networks (#44203) as shown in Fig. 2.
4. Apply E_out 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 Range	Distance Range “D”
0 to 100°C	100 ft.
-5 to 45°C	300 ft.
-30 to 50°C	300 ft.
+30 to 100°C	300 ft.

Example 4: Multiplexing to connect any number of thermistor composites to a single signal conditioning circuit. (See Figure 5.) Multiplexing can be accomplished much more easily with a two-wire system, such as shown in Figure 5.

Lead Colors:
Green: Common to T1 & T2
Brown: T1
Red: T2