4.1. Transient Behaviors
a illustrates the experimental setup for measuring the behaviors of the proposed thermal oscillator. In order to carefully control the boundary temperature for better characterization, the device was mounted on a thermoelectric cooler (TEC1-12706, Hebei I.T. Co.). The hot side of the thermoelectric cooler was water-cooled. The temperature of the cold side of the cooler could be adjusted by the applied voltage.
Three K-type thermocouples were used to measure the temperatures at the regions close to the PTC composite sensor (), the heater (), and the cold side of the thermoelectric cooler (), respectively.
The outputs of the thermocouples were acquired by a temperature input module (NI-9212, National Instruments Co.). The voltage drop across the divider resistor (
) was measured by a data acquisition device (USB-6341, National Instruments Co.). By using Figure 1
can be easily evaluated because
are given values. Figure 6
b shows a photo of the measurement of the thermal oscillator with the thermocouples and cooler.
The initial resistances of the PTC composite sensor () and the microheaters (at 25 °C) were measured by using a multimeter. To confirm the fabrication reproducibility of the thermal oscillator, these measurements were repeated for two other PTC composite sensors and two microheaters from separate batches of fabrication. The results show that the initial resistances of the PTC composite sensors range from 310 Ω to 450 Ω, and the resistances of microheaters range from 24 Ω to 26 Ω.
The resistance vs. temperature curves for the devices with PTC films of different OA concentrations are shown in Figure 7
. The graphite concentration was fixed at 25 wt%. Obviously, the resistivity of the material remained almost constant in the low-temperature region, but suddenly began to increase sharply when the temperature exceeded its
. In addition, as shown in Figure 7
of acrylate-based PTC materials is a strong function of OA concentration.
A PTC material with a lower than room temperature must be cooled to below room temperature in order to make a semicrystalline-to-amorphous transition, although heating is not required to make an amorphous-to-semicrystalline transition. On the other hand, a PTC material with a higher than room temperature can reach semicrystalline-to-amorphous transition with the assistance of the environment’s temperature.
It is quite simple to implement microheaters with other MEMS components monolithically, while active cooling devices are usually either bulky or difficult to integrate. Therefore, in order to avoid using an external highly efficient cooler, a PTC material with 80 mol% OA was chosen for the studies in the subsequent experiments.
shows the typical transient behavior of the proposed device with three consecutive cycles.
were 8.5 V and 7 V, respectively.
was 25 °C, and
was 400 Ω. As the device reached periodical steady state,
oscillated from 40.7 °C to 92.5 °C. The temperature behaviors of the PTC temperature sensor lagged behind that of the heater by about 1/5 of a period, and
stably oscillated between 26.8 °C to 27.6 °C. In addition, the corresponding
, which was calculated by using the given values of
, is also shown in the figure. The oscillation period was 12.35 s.
A typical thermal oscillation cycle with a period (
) of 10.55 s is shown in Figure 9
. The rising time (
) and the falling time (
) are defined as the time interval from the lowest temperature to the highest temperature and that from the highest temperature to the lowest temperature, respectively.
We also studied the repeatability and drift of the proposed device by measuring the long-term transient responses for over 1000 cycles. Figure 10
a represents a 1000 s (about 85 cycles) subset of the long-term test. As shown in the figure, the amplitude of thermal oscillation is about 51.7 °C, and the variation between each cycle is approximately 1.5%. Additionally, the figure shows that the drift was not obvious. These results indicate that the stability of the thermal oscillator was reasonably good.
b–c show the measured
and the calculated
. It was observed that the phase transition of the PTC thermal sensor on the proposed thermal oscillator was accurately controlled for this long-term repeatability testing.
4.2. Discussions on Divider Resistance and Active Cooling
shows the relationship between the average maximum/minimum temperatures in an oscillation cycle and the ,
varied from 400 Ω to 2100 Ω. Note that the initial resistance of the PTC composite sensor at room temperature is about 400 Ω. By adjusting
, the initial gate-to-source voltage (at 25 °C) of the MOSFET can be maintained at 4.2 V, which is slightly above the threshold voltage of the MOSFET to ensure that the MOSFET is in the saturation region at the beginning of the heating.
As shown in the figure, the minimum and maximum temperatures of each cycle increase as increases. The explanation is as follows. As is relatively small (e.g., around , or 400 Ω), a minor increase in during heating can significantly decrease , which rapidly switches the MOSFET from the saturation region to the cut-off region. Therefore, the heating time is relatively short, which results in less heating, and the minimum and maximum temperatures are therefore relatively lower. As increases, the required change in for reducing to the value below the MOSFET threshold voltage becomes larger, and, therefore, a longer heating time is required, and the minimum and maximum temperatures become higher.
shows the minimum heating voltages (
) required to initialize oscillation for different
. The conditions of the measurement are the same as those in Figure 11
. As shown in Figure 12
. This is because a relatively larger
requires a larger
to turn off the heater, which requires greater temperature variation on the PTC material, and therefore the required heating voltage (
) becomes larger.
and Figure 14
show the effects of cooling by using a thermoelectric cooler. The relationships of
are shown in Figure 13
. Both relationships are quite linear. As
decreases, the active cooling effect will be enhanced, and, therefore,
will increase because more heating is required. However, it is worth mentioning that the absolute value of the slopes of
is larger than that of
. This phenomenon leads to the results shown in Figure 14
, which indicate that