RTD TEMPERATURE MEASUREMENT (C, F)
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RTD Measurement with the i100

The i100xx box provides 8 differential analog input voltage channels (14bit) and 8 voltage output channels (i.e. for excitation) that can be used for RTD measurement with the help of one user-supplied external shunt resistor. For i100 analog input specifications, click here.

Temperature measurement using a voltage divider circuit involves connecting an RTD in series with a shunt resistor of known value, applying a voltage across the pair and measuring the voltage across the RTD, as illustrated below.  The voltage across the RTD is measured between a pair of instruNet Vin+ and Vin- input terminals while the excitation voltage for the divider is supplied by the instruNet Vout terminal.  instruNet calculates the temperature of the RTD device using the equations shown below, and returns "degrees C" engineering units.

Fig 3.13 - Temperature Measurement (RTD)  Voltage Divider Circuit

Alpha is the temperature coefficient of the RTD at 0°C and delta is the Callendar-Van Dusen delta constant.  These constants are often supplied by the manufacturer of the RTD, and are described in more detailbelow.  Temperatures below 0°C are supported by instruNet software (iNet32.dll) version ≥ 3.0; yet not in early versions.

To do temperature measurement using an RTD in a voltage divider circuit you must:

1.   Set the Sensor field in the Hardware settings area to RTD.

2.   Set the Wiring field in the Hardware settings area to Voltage Divider .

3.   Set the Voltage Range field in the Hardware settings area to something similar to Vout * (RTD_Max / (Rshunt + RTD_Max )), where RTD_Max is the RTD resistance at 0°C times 4.

4.   Set the Rshunt field in the Constants settings area to Rshunt. 1, 3, 6

5.   Set the Ro field in the Constants settings area to the resistance of the RTD at 0°C, in ohms units.

6.   Set the Vout field in the Constants settings area to specify the excitation voltage that is to be applied to the divider.   In high current cases (e.g. >2mA), it is often helpful to alternate the polarity of the excitation voltages to evenly burden the +/-12V supplies. 11

7.   Set the alpha field in the Constants settings area to the alpha value of your RTD.

8.   Set the delta,Rlead field in the Constants settings area to the delta value of your RTD.

9.   Wire your voltage source per figure 3.13, click here if you need more guidance setting up the software, and click here if the measured value is not correct.  To reduce noise, 0.001 seconds of integration is often helpful (i.e. set the Integrate field in the Hardware setting area to 0.001). 5, 10

RTD Self Heating Vs. Excitation Voltage

Many RTD manufacturers recommend that RTD resistance be measured with a 1mA current source since this often dissipates several milliwatts, and therefore does not cause noticeable "self" heating of the RTD device.  An example would be a 100 ohm RTD (which will vary from 100 to 214 ohms as the temperature varies from 0°C to 300°C), a 3.3V excitation voltage (i.e. Vout) and a 10K ohm shunt resistor.  The average current and power dissipation of the RTD at 0°C would be:

Current (Amps) = Volts / Resistance = 3.3V / [10000 + 100] = .32mA

Power (W) = Current  * Current  * Resistance  = .00032 ^ 2 * 10100 = 1mW

The voltage across the RTD would vary from 32mV to 69mV as the resistance across the RTD changed from 100 to 214 ohms (corresponding to a temperature change of 0 to +300 Celsius); therefore, an input Voltage Range of ±80mV would be ideal with a 100 ohm RTD, 3.3V excitation voltage, and 10K ohm shunt resistor.

Typical RTD's

The table below shows several standard RTD's. R_xxC refers to the resistance (Ω) across the RTD device when it is at xx °C; whereas Ro refers to the resistance (Ω) across the RTD when it is at 0°C. The A/B/C and the alpha/delta/beta coefficients describe the temperature vs. resistance curve as noted below.

RTD Temperature Vs. Resistance Math

Resistance as a function of Temperature
There are 2 big equations that described the relationship between the temperature of an RTD device and the resistance across the device. One is for temperatures above 0 °C and the other is for temperatures below 0 °C:

Temp > 0°C:   R (Ω) = R_0C * { 1 + A*t + B*(t^2) }
Temp < 0°C:   R (Ω) = R_0C * { 1 + A*t + B*(t^2) + -100*C*(t^3) + C*(t^4) }

Where:

R (Ω) = resistance across the RTD in ohms units, when the RTD is at temperature t °C
t = temperature of RTD device, in °C units
R_0C = resistance across the RTD in ohms units, when the RTD is at 0 °C
A, B = coefficients that described the temperature vs. Ω's curve for all temperatures
C = coefficient that describes the RTD temperature vs. Ω's curve for temperatures < 0 °C

Temperature as a Function Of Resistance
If one solves the above R = function(T) equation in the reverse direction, for temperatures above 0 °C, they get the following (temperatures < 0 °C are more complex):

R_RTD (Ω) = Rshunt * (Vin+ - Vin-) /  (Vout - (Vin+ - Vin-))
Ro_A = Ro_0C * alpha (1.0 + (delta / 100.0))
Ro_B = Ro_0C * -1.0 * alpha * delta / (100.0 * 100.0)
diff = Ro_0C -  R_RTD 
t (°C) = diff / (-0.5 * (Ro_B + sqrt((Ro_B*Ro_B) - (4.0 * Ro_A * diff))))

Where:

R_RTD (Ω) = resistance across the RTD in ohms units, at temperature t
t (°C) = temperature of RTD, in degrees C units
Rshunt = resistance of fixed shunt resistor (voltage divider wiring), in ohms units
R_0C = resistance across the RTD in ohms units, when the RTD is at 0 °C
Vout = excitation voltage
Vin+ = voltage at Vin+ screw terminal
Vin- = voltage at Vin- screw terminal
alpha, delta = coefficients that described the temp vs. Ω's curve for all temperatures
beta = coefficient that describes the temp vs. Ω's curve for temperatures < 0 °C

RTD Coefficients
RTD manufacturers supply coefficients that describe the temperature vs. resistance relationship of their device. There are two sets of coefficents: alpha/delta/beta and A/B/C. Either can describe the T vs. R curve. alpha and delta are typically defined using several temperature points, as shown below:

alpha = (R_100C - R_0C) / (100 * R_0C)
delta = { [ R_0C * (1 + alpha * 260.0)] - R_260C } / (4.16 * R_0C * alpha)

Where:

R_0C = resistance across the RTD in ohms units, when the RTD is at 0 °C
R_100C = resistance across the RTD in ohms units, when the RTD is at 100 °C
R_260C = resistance across the RTD in ohms units, when the RTD is at 260 °C

The equations below show the relationship between alpha/delta/beta and A/B/C:

alpha = [ A + 100*B ]
delta = [ B * ( 100.0 ^ 2) * -1 ] / alpha
beta = [ C * ( 100.0 ^ 4) * -1 ] / alpha

Troubleshooting Your RTD Temperature Vs. Resistance Curve

To learn more about the T (°C) vs. R (Ω) curve being used by instruNet to calculate your RTD's temperature: Press the Script Tab at the bottom of the window, type "print_rtd! = 1" (without the quotes) into the window, press the "Execute" button, press the Network tab at the bottom of the window, click on your RTD channel to open it's settings dialog, press the "Update" button, click on the "Test" tab at the bottom of the window, and then view your RTD's internal parameters in the 2nd column of the resulting table. This is supported with instruNet software (iNet32.dll) version ≥ 3.0.

Also note that temperatures below 0°C are supported by instruNet software (iNet32.dll) version ≥ 3.0; yet not in early versions.