Generalization of the thermal model of infrared radiation sensors

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Abstract

In many theories and applications, generalized models can give a good head start for further research where the implementation of new elements and/or boundary conditions could become quite complex. In this paper the development of a compact thermal model of an infrared sensor will be presented. This thermal model includes not only the thermal resistances and capacitances of the sensor structure itself but the radiative and convective thermal resistances to the ambience and between the sensor plate and the heat source (thermal transfer impedance) which is important when the heat source and the sensor are in close proximity. Limitations and the applicability of the proposed model are also discussed. We also aim to present how the proposed model can be used for other IR sensor structures as well.

Introduction

The infrared sensor card (Fig. 1) presented in paper [1] enables temperature mapping of different circuits and assembled boards. With the presented method the infrared (IR) radiation-distribution of boards from the close proximity of the sensor card can be monitored, enabling in situ IR measurement between operating cards of a system e.g. in a rack, ATX or BTX type systems. Using this contactless temperature mapping method the temperature distribution and the locations of hot-spots in an operating assembled printed circuit board can be identified in a dense rack system, where only a thin measurement board could be inserted between the operating cards. Determining the exact place of the hot-spots the reliability of an electronic system can be improved.

In the previous work presented in paper [2] our main goals were to reduce the thermal time constant of the sensor card and to minimize the thermal crosstalk effect between the adjacent sensor pixels. The thermal time constant was successfully reduced by decreasing the thermal capacitance of a sensor pixel. Lowering the thermal time constant allows better time resolution of real time transient detection of hot spots. Reduced thermal crosstalk allows more accurate spatial detection of hot-spots.

Although a detailed lumped element model was presented in [2] and can be seen in Fig. 2, the analytically calculated time constant differed from the results of the measurements of a real situation. The difference was more than 40%. This error was caused by the total negligence of the radiative thermal transfer impedance between the heat source and the sensor. The stimuli in case of the simulations and of the initial measurements were a power step which was applied on the diode of the adequate pixel. This method supposes the total absorbance of the radiated thermal radiation of a distant source. This way only the thermal time constant of the pixel itself can be determined but not the exact time constant of the entire measurement setup.

Additionally, measurements in electrical system are typically carried out in close proximity arrangement. In our case close proximity means that the side length of the pixel can be compared to the distance of the sensor and the heat source. In this case the parasitic effects (e.g.: conductance of the filling gas, convective and radiative heat transfer between the sensor pixel and the measured unit) should be taken into account in the model. In [2] the thermal radiation was considered only when the crosstalk effect between pixels was determined and it was neglected in the model and when the time constant was calculated.

In this paper a new thermal compact model is presented which consists of the radiative thermal transfer impedance between the heat source and the sensor. Limitations and the applicability of this model are also discussed. Since the radiative thermal transfer impedance depends on the temperature of the heat source and the distance between the heat source and the sensor pixel so this model is applicable to determine the thermal behaviour and the time constant of the whole measurement arrangement. The analytical calculation of the time constant was verified by simulations and measurements. The results and comparison to the analytical calculation are also presented.

Section snippets

Sensors for contactless thermal measurement

The thermal emission described by the Planck relationship is a function of the temperature of the bodies and the emissivity. The intensity of the radiation and the peak wavelength (λmax)decrease with the temperature (T) as it is described byWien׳s displacement law:λmax⋅T=2897.8[μmK]The temperature of the terrestrial objects are typically about 300 K which results in a peak emission in far infrared (FIR) with wavelengths near 10 µm.

The two principal types of far infrared (FIR) detectors are photon

The infrared sensor card

In previous papers [2], [10] the development and characterization of a macroscopic infrared sensor card realized on a PCB were introduced (Fig. 1). In the case of these sensor cards the thermal isolation between the pixels was not optimized and the measurement results suggested that there was crosstalk between the adjacent pixels. The neighbouring pixels were heated up to 25% of the temperature of the pixel which was situated in front of the hot-spot of the measured boards due to mainly the

Modelling and analytical calculation

Recent simulation and measurement results showed that the characteristic time constant of the entire measurement setup depends on the distance between the heat source and the sensor card beside the temperature of the heat source. It highlights the importance of the radiative thermal resistance between the source and the sensor plate. For the precise determination of thermal time-constant the calculation with radiative thermal transfer impedance is demanded.

Therefore analytical calculations are

Simulation

The analytical results are compared and verified by CFD simulations [17]. The applied numerical and analytical input parameters are summarized in Table 2.

The simulation setup and the steady-state solution can be seen in Fig. 10 where a black-painted hot-spot was placed in front of a 3×3 sensor card. The radiative heat transfer values among the pixels and between the pixels and the source were predetermined by the CFD tool (configuration factor calculation step) and used as an initial variable

Measurements

The aim of the measurements was to validate the analytical calculations and the simulation using the prototype of the sensor card. The measurement setup consisted of a variable temperature, black painted heat source and thermal transient tester equipment. For this purpose the Mentor Graphics® T3Ster® measurement environment [18], [19] was used. With this instrument the forward voltage change of the silicon diode can be logged and thus the temperature change of the PN junction can be determined.

Conclusion

Throughout our paper we have presented the thermal generalization of an infrared sensor card, which is based on the insertion of some neglected effects into the lumped model. With these effects we showed certain limitations of the thermal time constants of the infrared sensor card. For the demonstrations analytical calculations, state-of-the-art simulation tools and different measurement setups were utilized. The results are in good agreement with each other thus supporting the presented ideas.

Acknowledgement

The authors would like to express their gratitude to Prof. Vladimír Székely, the member of Hungarian Academic of Science for his continuous guidance and help throughout the research.

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