# Low-Cost Temperature Logger for a Polymerase Chain Reaction Thermal Cyler
## 2 Materials and Methods  
### Probe and Local System Implementation  
Figure 1 illustrates the cross-sectional view of the probe presented in this paper. An aluminum bolt was used to attach the NTC thermistor (standard precision interchangeable thermistor, US Sensors, Orange, CA, USA) to the aluminum head. The empty space between the aluminum head and the NTC thermistor was filled with thermal grease, which was also used when assembling bolts to the aluminum head to allow proper thermal conduction. The exterior of the aluminum head was designed to achieve satisfactory thermal-coupling with the well by matching the slope of the cone to that of the thermal cycler well. Components other than the aluminum head which are completely inserted into the well, are made with a plastic material (acrylonitrile butadiene styrene, ABS) to minimize heat radiation of the material. The heat radiation will result in creating a temperature gradient between the well and the sensor, hence effecting the efficiency of the measurement and calibration. The height from the probe cap to the aluminum head was equal to that of a 25 mL PCR tube to perform the measurement under the same environment as the actual run of a PCR reaction, where the thermal cycler's lid heater was closed. The leg of the NTC thermistor was fixed using a Teflon tube. A high-end earphone cable (Nobunaga Labs MMCX TR-SE3, WiseTech Inc., Taito, Japan) which was well known for low frequency noises, was used to connect the thermistor and reader. The assembled probe and the temperature reader is shown in Figure 2. The earphone cable is connected to the proposed probe (Figure 2a), and the probe is connected to the temperature reader through the stereo earphone jack at the other end (Figure 2b). The temperature reader was configured to connect two earphone cables where each cable carries two probes, enabling simultaneous measurement of four probes in total. Figure 1: Cross-sectional view of probe (Al: aluminum, ABS: Acrylonitrile butadiene styrene). Figure 2: Assembled local system with probe and temperature reader. (**a**) probe; (**b**) temperature reader. The reader in Figure 2b was implemented using an 8 bit microcontroller (PIC18F4553, Microchip Chip Technology Inc., Chandler, AZ, USA) with an imbedded analog-digital converter (ADC) and universal serial bus interface (USB). The thermistor resistance was calculated (Figure 3) by measuring the voltages divided from the precision reference resistor without a buffer amplifier, and connected to the imbedded 12 bit ADC inside the microcontroller. By calibrating the input impedance of the ADC in the microcontroller, long term precision and accuracy were ensured using a simple circuit [25]. The precision reference resistance value was set to receive maximum resolution in the temperature range mainly used during PCR. A long-term median filter and a short-term average filter were placed to manage noise filtering. To control short-term average filtering, all divided voltages measured in each channel were summed over the number of the filter tap, and thereafter sent to the host. The host divided the delivered sum by the number of filter taps to complete the average filter of the measured voltages. The filtered value of the divided voltage was converted to the thermistor resistance, and the resistance was converted to temperature based on the Steinhart-Hart equation:  
\[\frac{1}{T}=A+B+\log R+C(\log R)^{3}, \tag{1}\]  
where \(R\) and \(T\) are the thermistor resistance and absolute temperature, respectively. The calibration constants are shown in the equation as \(A\), \(B\), and \(C\). Among the various calibration methods developed, the most widely used Steinhart-Hart equation was adopted in this study which provides sufficient accuracy with simplicity in the temperature range of the thermal cycler application (50-98 \({}^{\circ}\)C). The thermistor employed in this paper was calibrated at 4 points (50, 60, 72, 95 \({}^{\circ}\)C) and the maximum error from the resistance-temperature table provided from the vendor was 1.7 mK [26].