Temperature Measurement System Design

Temperature Measurement System

In this lab we design a temperature measurement system using a thermistor that creates a resistance change. This resistance change is then converted to a voltage change using a wheatstone bridge. Finally the voltage change is amplified using a difference amplifier.

Balancing the Wheatstone Bridge Circuit

The wheatstone bridge circuit was wired according to the diagram above. Measured resistance values are given. Ideally, all the resistors should have equal resistances. Also, they should all have a value close to the nominal resistance of the thermistor, that is, the resistance of the thermistor at room temperature (about 25 °C). A potentiometer is wired in series with resistor R_a to help balance the wheatstone bridge. This is used to fine tune the circuit so that the potential difference between a and b is V_ab = 0 V. 

Here we see the wheatstone bridge circuit, wired according to the diagram above.

A multimeter is used to measure the output voltage V_ab. A constant source voltage V_s of 5 V is then applied using the Analog Discovery. The potentiometer knob is then adjusted until the potential is 0 V +/- 20 mV. When the thermistor is held, its resistance decreases until it reaches body temperature (about 37 °C) to about 10.8 kΩ. This creates a potential difference between nodes a and b. The maximum voltage, after warming up the thermistor between pressed fingers for about 30 seconds, was -244 mV. The negative sign indicates that the node a is at a higher potential than node b.

 Difference Amplifer

According to the design specifications, a rise in output voltage of at least 2 V is required. Since the potential difference V_ab ranged from 0 mV to 244 mV, a difference amplifier with a gain of at least 10 is desired (which would yield an output of 2.44 V theoretically). To be safe, 10 kΩ and 150 kΩ resistors are used (measured resistances above) to give a gain of 15. The gain is the ratio of the feedback resistor R_2 to an input resistor R_1 where R_1 = R_3 and R_2 = R_4. The calculated gain is 149.8 kΩ/ 9.80 kΩ = 15.29. Therefore, the output voltage of the difference amplifier should be 15.29 times the potential difference between V_a and V_b, V_out = 15.29 (V_b - V_a).

The pictures above show the difference amplifier circuit with and without the wires needed for voltage supplies, ground, and measuring channels. 

To test if the difference amplifier is functioning correctly, the output voltage was measured for varying input voltages. V_a was kept constant at 300 mV while V_b was varied from 100 mV to 500 mV in 50 mV increments. The theoretical voltages are shown as well as the measured values. The accuracy of the experiment is reasonable, at a max of 6% error. 

Here is a plot of the output voltage vs difference input voltage, V_out vs V_ab (title on graph should be changed). We see that the slope of the line is -15.34 with a great accuracy (R^2 = 1.00). The measured voltage V_ab was opposite sign than expected indicating that the wires used for measuring voltage must have been reversed. Ommiting the negative sign, our measured gain is 15.34, which has a 0.3 % error.

Putting it all Together

Now that both circuits are functioning properly, the node voltages of the wheatstone bridge V_a and V_b are connected to the inputs of the difference amplifier (long orange wires). This should convert the resistance change in the thermistor into a small voltage change in the wheatstone bridge which is then amplified by the difference amplifier. The voltage should start at 0 V +/- 20 mV and have a change of at least 2 V.

This video shows the voltage changes as the thermistor goes from room temperature to body temperature. Channel 1 is the potential difference coming from the wheatstone bridge V_ab, and Channel 2 shows the output voltage V_out after being amplified by a factor of 15.34. We see that it originally starts at 0 V +/- 20 mV and rises up to about -3.56 V as it goes to body temperature (omitting negative signs). The wheatstone bridge gives a max V_ab of -244 mV (negative because node a is actually at higher potential than b). Theoretically, after this this voltage is amplified it should be -244 mV * 15.29 = -3.73 V, Compared to our measured output voltage of -3.56 V, we see that our percent error is 4.6%.