Measuring Thermistors in a Half-Bridge

Publish Date: Feb 23, 2011 | 6 Ratings | 3.17 out of 5 |  PDF | Submit your review

Overview

A thermistor is a type of resistor whose resistance varies significantly with temperature. Thermistors are typically desirable for applications that require a very accurate temperature measurement over a relative narrow temperature range. Thermistors are available for temperatures between -50°C to 100 °C. Many thermistors have a sensitivity of 3-6%/°C which means that they may vary in resistance by more than +/- 500% of their nominal value over their full measurement range. This wide range presents a measurement challenge that can be addressed by making a half bridge measurement with a correctly chosen reference resistor.

Table of Contents

1. The Measurement Circuit (Half-Bridge)
2. Choosing a Reference Resistor
3. Scaling the Data to Resistance and Temperature
4. Example Temperature Measurement Accuracy Calculation

1. The Measurement Circuit (Half-Bridge)

From page 19 of the NI 9219 Operating Instructions and Specifications we can see the input circuitry for full and half bridge configurations.  With slight modifications to this image, here is the circuit used to measure thermistors:

Figure 1:  Dotted lines indicate circuitry connected inside the NI 9219 module.  Only the Thermistor, Rtherm, reference resistor, Rref, the two wires connecting to EX+ and EX-, and the wire connected to HI are external.

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2. Choosing a Reference Resistor

In order to maximize the accuracy of your measurement, the reference resistor should be chosen such that the min and max resistances are centered around the NI 9219’s input range.  That is, when your thermistor and reference resistor are placed in a voltage divider, you should choose the reference resistor so that the min and maximum thermistor values will create equal, but opposite imbalances from a nominally balanced voltage divider.  This will keep the measurement error to a minimum because the resistance measurement error becomes larger as Vout approaches ground or Vex.  Here’s an example to make things more clear:

Figure 2:  Circuit diagram used for the derivation of the optimal reference resistor value.

Let’s say that we have chosen the PR103J2 thermistor from US Sensor and we are interested in measuring -8 C to 65C.  Using this sensors data sheet, we can see that -8 C corresponds to a thermistor resistance of ~50 kΩ and 65 °C corresponds to thermistor resistance of ~2 kΩ.    This means that we want to optimize Rref to allow Rtherm to vary between 2 and 50 kΩ.  In order to do this, we can solve a system of voltage divider equations with the assumption that we want the min and max Rtherm values to provide equal but opposite imbalances from a balanced bridge (balanced bridge condition is equivalent to Vout = ½ Vex which is equivalent to Rtherm = Rref) in our voltage divider.

Eq. 1:      

Eq. 2:     

We can set Eq. 1 equal to (-1) * Eq. 2 to solve the system of equations for Rref.

Eq. 3:     

Since Vex cancels out, we can solve the following quadratic equation for Rreference,

Eq. 4:     

Taking the positive value, we find that Rref should be 10000 Ω.

Eq. 5:     

Given the above thermistor resistance measurement range and target reference resistor value, the next step is to choose a reference resistor.  In order to maintain excellent accuracy, a high accuracy resistor with a very low temperature coefficient of drift should be used.  One example of such a resistor is the Vishay, Z201T 10K000 B, A, or Q for 0.1%/0.05%/0.02% resistor with 0.6 ppm/C drift. 

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3. Scaling the Data to Resistance and Temperature

Since the NI 9219 half bridge mode can only return data in units of mV/V we must scale the data to resistance and then temperature.  The scaling from mV/V to Ω can be derived from the voltage divider equation with the knowledge that the reading returned by the NI 9219 in half bridge mode when wired as shown in Figure 1 is equal to Vout/Vex – 0.5 V/V. 

Eq. 6:    

Then, solving Eq. 6 for Rtherm we can get the following scaling equation for Rtherm in terms of the NI9219 Reading and Rref.

Eq. 7:  

You can use Eq. 7 to scale the NI9219 Reading from mV/V to Ω.  From this point you can use the scaling equation provided by your thermistor manufacturer to scale the data from Ohms to temperature.

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4. Example Temperature Measurement Accuracy Calculation

First of all, we’ll calculate our measurement range in the units that the 9219 measures which are mV/V.  We can do this by plugging Rref = 10000 Ω into equations 1 and 2 and solving for Vout/Vex.

For Eq. 1 & 2 with Rref = 10000 Ω:

                                        

This corresponds to a maximum reading of ± 333 mV/V for the NI 9219, and we can use this to calculate the measurement accuracy using the formula:

Eq. 8:     

Using Eq. 8, we can compute the max error in high resolution mode at the desired full scale ( ±333.33 mV/V) over the full operating temperature range -40°C to 70 °C in units of mV/V,

Eq. 9:  

Now that we know the mV/V measurement error as well as the reference resistor tolerance, we can compute the Max % Error in Resistance using the scaling equation (Eq. 7).  In order to determine the maximum error you must check the effect of ±Measurement Error and ±Reference Resistor Error.  In the circuit configuration shown, with the reference resistor as the lower leg of the bridge and a reference resistor that has been chosen to be in the middle of the range, the max error case is for opposite signs (i.e. +0.68 mV/C measurement error and -0.1% resistor tolerance).

Eq. 10:  

Solving Eq. 10 for a 333.33 mV/V reading and a ±0.1% reference resistor we can determine that the maximum error is 13.7 Ω, or ±0.68% at Rtherm = 2000 Ω.  Since most thermistors have sensitivities in the range of 3%/°C to 6%/°C, 0.68% error in resistance corresponds to 0.11°C to 0.23°C error.  In this case, the thermistor referenced above has a sensitivity of 3.46%/°C at Rtherm = 2000Ω so the total error is ±0.20°C.