Thermistor Step Response Characterization
An Ametherm’s Glass Encapsulated DG Series negative temperature coefficient (NTC) thermistor 3934K bead DG103395 sensor has been chosen. It is used to sense temperature and is known for its fast thermal time constants (under 6s), high accuracy, hermetic sealing, small size, and temperature range of function. The sensor could be used for a high density thermal sensor array due to its relatively small size and performance characteristics. The datasheet was noticeably of minimal detail aside from the base parameters needed for the device. No example applications or recommendations are provided.
The sensor may be used between -40 °C and 300 °C and has a resistance at 25 °C of 10 kΩ ± 2% (0.2 kΩ). The thermal time constant is estimated at less than or equal to 6.5s.
The test was performed by reading voltage from the sensor via an Arduino Uno microcontroller communicating via serial to my laptop using its 5V source. The software used to interface the microcontroller was the Arduino Serial Monitor and MATLAB due to the rapid development speed of the software and lack of need for high frequency recording, with Arduino and Teensyduino used for testing purposes outside the experiments. The Arduino was separated from the USB power line noise by means of a USB isolator. Excel was used to plot step response output from the serial monitor.
The three Taylor Compact Instant-Read Pen Style Digital Thermometers were metal thermocouple based sensors. These tend to have generally slow thermal constants but highly accurate measurements but this device was designed to have a fast thermal time constant and has an update rate of the screen of 1 Hz. The glass thermometers were glass mercury thermometers.
Ice was acquired from the BME cell bio labs, as was a hot plate, ice water container, and several 100 mL beakers (minimum of two needed for replication but three were used to see if the temperature measured from room temperature water read differently than room temperature air – the difference was negligible).
Distilled water was acquired from the BME labs and Walgreens.
The expected needed sampling rate was chosen on the basis of being a bit less than one tenth of the expected time constant and proved to be insufficient to observe all step responses but nonetheless was effective enough to observe most of them. Future experiments will use 100 Hz instead of 10 Hz observation. Judging by the number of data points from the experiment for each step response, it seemed notable that further higher frequency recorded testing will be necessary for more accurate 2nd order model parameter estimation.
From air temperature to ice cold, the time constant (t) was 0.322 s. From cold temperature to air, the t was too small to be read due to sampling rate limitation meaning it was smaller than 0.1 s. From air temperature to ice cold, the t was 0.800 s. From air temperature to ice cold, the t was 5.199 s.
The Steinhart-Hart parameters were estimated to give the parameters A, B, and C with values of 31.000, 22.627, and 16.758 using normal equations and 30.444, 19.940, and 19.424 using gradient descent. Both methods gave an R2 of 98% [3,4].
The figures of the step responses (Fig. 1 and 2), temperature vs. resistance (Fig. 3), and voltage vs. temperature (Fig. 4) plots can be found in the Figures section at the end of the document. The iteration curve of the cost function of gradient descent can be seen in Fig. 5 in the same section.
For figures and more detail on the experiment, please refer to the attached documentation.
The sensor may be used between -40 °C and 300 °C and has a resistance at 25 °C of 10 kΩ ± 2% (0.2 kΩ). The thermal time constant is estimated at less than or equal to 6.5s.
The test was performed by reading voltage from the sensor via an Arduino Uno microcontroller communicating via serial to my laptop using its 5V source. The software used to interface the microcontroller was the Arduino Serial Monitor and MATLAB due to the rapid development speed of the software and lack of need for high frequency recording, with Arduino and Teensyduino used for testing purposes outside the experiments. The Arduino was separated from the USB power line noise by means of a USB isolator. Excel was used to plot step response output from the serial monitor.
The three Taylor Compact Instant-Read Pen Style Digital Thermometers were metal thermocouple based sensors. These tend to have generally slow thermal constants but highly accurate measurements but this device was designed to have a fast thermal time constant and has an update rate of the screen of 1 Hz. The glass thermometers were glass mercury thermometers.
Ice was acquired from the BME cell bio labs, as was a hot plate, ice water container, and several 100 mL beakers (minimum of two needed for replication but three were used to see if the temperature measured from room temperature water read differently than room temperature air – the difference was negligible).
Distilled water was acquired from the BME labs and Walgreens.
The expected needed sampling rate was chosen on the basis of being a bit less than one tenth of the expected time constant and proved to be insufficient to observe all step responses but nonetheless was effective enough to observe most of them. Future experiments will use 100 Hz instead of 10 Hz observation. Judging by the number of data points from the experiment for each step response, it seemed notable that further higher frequency recorded testing will be necessary for more accurate 2nd order model parameter estimation.
From air temperature to ice cold, the time constant (t) was 0.322 s. From cold temperature to air, the t was too small to be read due to sampling rate limitation meaning it was smaller than 0.1 s. From air temperature to ice cold, the t was 0.800 s. From air temperature to ice cold, the t was 5.199 s.
The Steinhart-Hart parameters were estimated to give the parameters A, B, and C with values of 31.000, 22.627, and 16.758 using normal equations and 30.444, 19.940, and 19.424 using gradient descent. Both methods gave an R2 of 98% [3,4].
The figures of the step responses (Fig. 1 and 2), temperature vs. resistance (Fig. 3), and voltage vs. temperature (Fig. 4) plots can be found in the Figures section at the end of the document. The iteration curve of the cost function of gradient descent can be seen in Fig. 5 in the same section.
For figures and more detail on the experiment, please refer to the attached documentation.
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