Modelling Miniature Incandescent Light Bulbs for Thermal Infrared ‘THz Torch’ Applications
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The ‘THz Torch’ concept is an emerging technology that was recently introduced by the authors for implementing secure wireless communications over short distances within the thermal infrared (20-100 THz, 15 μm to 3 μm). In order to predict the band-limited output radiated power from ‘THz Torch’ transmitters, for the first time, this paper reports on a detailed investigation into the radiation mechanisms associated with the basic thermal transducer. We demonstrate how both primary and secondary sources of radiation emitted from miniature incandescent light bulbs contribute to the total band-limited output power. The former is generated by the heated tungsten filament within the bulb, while the latter is due to the increased temperature of its glass envelope. Using analytical thermodynamic modelling, the band-limited output radiated power is calculated, showing good agreement with experimental results. Finally, the output radiated power to input DC power conversion efficiency for this transducer is determined, as a function of bias current and operation within different spectral ranges. This modelling approach can serve as an invaluable tool for engineering solutions that can achieve optimal performances with both single and multi-channel ‘THz Torch’ systems.
KeywordsTHz Torch thermal infrared thermodynamics band-limited blackbody source
The thermal infrared frequency bands, from 20 to 40 THz (15 μm to 7.5 μm) and 60 to 100 THz (5 μm to 3 μm), are best known for applications in thermography. There has been little in the way of enabling technologies within this part of the electromagnetic spectrum to support wireless communications. However, this largely unused spectral range offers opportunities for the development of secure communications. To this end, the ‘THz Torch’ concept was recently introduced by the authors [1-6]. The ‘THz Torch’ technology fundamentally exploits engineered blackbody radiation, by partitioning thermally-generated noise power into pre-defined frequency channels. The band-limited power in each channel is then independently pulsed-modulated, transmitted and detected, creating a robust form of short-range secure communications in the thermal infrared. In this paper, the radiation mechanisms associated with the basic transducer within the ‘THz Torch’ transmitter will be investigated, leading to the calculation of output radiated power and then output radiated power to input DC power conversion efficiency for this transducer.
The first incandescent light bulb to employ a tungsten filament was patented in 1904 by Just and Hanaman , offering greater luminosity in the visible spectrum, when compared to carbon filaments. Since then, a great deal of research has been undertaken to investigate the optical, electrical, chemical and thermal properties of tungsten materials; as well as the characteristics of tungsten light bulbs [8-14]. More recently, due to advances in materials and nanotechnology, higher luminous efficiency has been achieved by improving the emissivity of the filaments or reducing the infrared radiation contribution to the blackbody spectrum without reducing the radiation at visible wavelengths [15-17].
With traditional incandescent light bulb applications, only output radiated power within the visible spectrum is considered useful, while the remaining energy is considered to be lost. This explains why they are highly inefficient when compared to white light-emitting diodes (LEDs). Fortunately, these bulbs represent a low cost far/mid-infrared thermal source, which has been exploited by the authors to implement secure short range wireless communications. However, for the thermal infrared, the modelling approaches used for the visible spectral range is insufficient for predicting the band-limited output power from incandescent light bulbs. Therefore, an analytical thermodynamic modelling approach needs to be developed, so that the performance of both single and multi-channel ‘THz Torch’ thermal infrared systems can be optimised.
In the thermal infrared, technologies have also been developed to improve the emission efficiency of thermal sources at specific wavelengths by modifying the blackbody radiation using periodic microstructures [18-22]. However, most of these studies are based on sophisticated and time-consuming technologies, such as electron beam lithography or a repetitive etching-and-deposition process . Therefore, these devices cannot be easily mass produced. Most of the thermal infrared sources on the market still rely on untrimmed blackbody radiation using materials with high emissivity. It should be noted that although such thermal-based sources offer many benefits (e.g., simplicity, ease of tuning and affordability), the main drawback is that there is no signal coherency, as with all unmodulated noise sources. Thus, only the intensity of band-limited output power can be controlled.
The thermal analysis of incandescent light bulbs involves all three fundamental methods of heat transfer: radiation, conduction and convection. This analysis is inherently complex, as it requires the study of a number of interacting mechanisms: (a) primary radiation from the filament (which appears mostly in the frequency spectrum between millimeter-wave and beyond visible); (b) absorption of primary radiation by the glass envelope, causing it to heat up; (c) thermal convection inside the glass envelope, causing the filament to heat up the glass envelope; (d) thermal conduction within the glass envelope and also within the two electrical leads to the outside world, which act as poor heat sinks; (e) secondary radiation from the glass envelope (which appears mostly in the thermal infrared spectral region, due to a much lower outside surface temperature); (f) thermal conduction from the glass envelope to the contacting environments on both sides; and (g) thermal convection outside the glass envelope. Due to this inherent complexity, it is not possible to individually quantify the effects of all the mechanisms.
The output radiated power contributed by the primary source of radiation lies in the spectral region dominated by high transmittance through the glass envelope; while that from secondary radiation lies in the spectral region dominated by high absorptance within the glass envelope. The power transmittance for typical (soda lime silica) window glass will first be calculated, and the band-limited output radiant intensity due to primary radiation will be determined. Then, the outside surface temperature of the glass envelope will be measured directly and the band-limited output radiant intensity due to secondary radiation will be determined. The combined band-limited output radiated power is then measured, using a calibrated thermal detector, which verifies our modelling of the two radiation sources for this basic transducer.
2 Primary Radiation Modelling
Primary radiation is defined as the output power that is generated directly from the tungsten filament and passes through the glass envelope. When a bias electrical current is applied, the temperature of the filament increases, due to Joule heating. In theory, the filament will radiate electromagnetic energy across the whole frequency spectrum. An inert gas (e.g., argon) is normally used to fill the inside of the bulb; to prevent the tungsten filament from oxidizing, which would otherwise result in the catastrophic failure of the transducer.
2.1 Filament Working Temperature Estimation
At room temperature, ρ(288 K) = 5.14 × 10-6 Ω.cm . The combined resistance of five Eiko 8666-40984 bulbs connected in series is directly measured to be 23.6 Ω at room temperature. Therefore, if the parasitic resistances of the short electrical leads are considered negligible (which is a good assumption), this gives an average value of R(288 K) = 4.72 Ω for each bulb filament. As a result, the effective ratio of cross-sectional area to length can be extracted using (1) and (2), to give a value of (CSA/l) eff = 10.9 nm, which is assumed to be temperature independent. By indirectly measuring the resistance of a bulb, at a specific bias current, the working temperature can now be estimated to an acceptable degree of accuracy.
2.2 Ideal Spectral Radiance Estimation
With the earliest experiments, the Eiko 8666-40984 bulbs had a quiescent DC biasing current of 44 mA, which gives an estimated filament working temperature of 772 K and a corresponding spectral radiance peak at 80 THz (3.75 μm), as shown in Fig. 3(b). This peak frequency can be easily adjusted by changing the bias current. With a larger bias current, one can obtain higher spectral radiance levels, yielding an increased integrated output power for transmission. However, the penalty for this is a decrease in the band-limited output radiated power to input DC power conversion efficiency for this transducer; which may be an issue where available DC supply power is at a premium (e.g., coin battery powered security key fob applications).
2.3 Bulb Filament Emissivity Estimation
2.4 Band-limited Radiant Intensity from Primary Radiation
By applying (16) to (9)-(12), ρ 1, ρ 2, τ 1 and τ 2 can be obtained. As a result, S 21 and S 11 can then be calculated using (13) and (14). The overall power transmittance and reflectance are determined from |S 21|2 and |S 11|2, respectively, while power absorptance is given by 1 − |S 11|2 − |S 21|2.
It can also be seen from Fig. 6 that typical window glass can be considered opaque below ~60 THz (5 μm). For most conventional applications, this would only allow its use in its transparent region above ~70 THz (4.3 μm). However, for our ‘THz Torch’ applications, the high absorptance will contribute to the secondary source of radiation (due to the increase in outer surface temperature).
2.5 Filament Thermal Time Constants
Filament thermal time constants are also important parameters for ‘THz Torch’ applications having transient behaviour in the electrical stimulus of the transducer (e.g., direct modulation); this will set fundamental limits on signalling rates. When the bulb is in the ON state, having a step response function, at its initial temperature T(0), there is a large injection of current and the temperature of the filament increases. Since the resistivity of tungsten has a positive temperature coefficient, the instantaneous bulb resistance also increases; from its initial value of R(T(0)) until a steady-state value is reached, at thermal equilibrium, where the input power is exactly balanced out by all of the dissipative (i.e., heat transfer) loss mechanisms.
3 Secondary Radiation Modelling
3.1 Band-limited Radiant Intensity from Secondary Radiation
With our particular 5-bulb array configuration, the radiant intensity from secondary radiation can be further separated out into two parts: the central higher temperature region and its surrounding lower temperature region, as shown in Fig. 10.
The outer surface temperature of the glass envelope depends on the filament’s emissivity, emitting area, temperature, position and shape. Instead of using complex thermodynamic modelling to simulate its outer surface temperature distribution, a more direct approach is to measure its temperature using a thermal camera. An experiment using a FLIR E60 thermal camera was performed. This camera uses an uncooled microbolometer focal plane array with 320×240 pixels. Note that the THz band-pass filter and associated aperture were removed, in order obtain the actual temperature distribution for the 5-bulb array.
Measured outer surface temperatures for the 5-bulb array at different bias currents
Bias Current (mA)
Measured Temperatures (K)
Outer Bulb Centre
3.2 Glass Envelope Thermal Time Constants
4 Calculated and Measured Band-limited Output Radiated Power
5 Band-limited Output Radiated Power to Input DC Power Conversion Efficiency Calculations
In this section, the band-limited output radiated power and conversion efficiency for both single and multi-channel ‘THz Torch’ transmitters, employing the same 5-bulb array configuration described previously, can be calculated. The spectral range for the first proof-of-concept single-channel ‘THz Torch’ system was defined over the 25 to 50 THz (12 μm to 6 μm) octave bandwidth [1,3,4], while four non-overlapping spectral ranges for the 4-channel multiplexing systems are: 15 to 34 THz (20 μm to 8.8 μm) for Channel A; 42 to 57 THz (7.1 μm to 5.3 μm) for Channel B; 60 to 72 THz (5 μm to 4.2 μm) for Channel C; and 75 to 89 THz (4 μm to 3.4 μm) for Channel D [2,4-6].
The ‘THz Torch’ concept was recently proposed as a low cost means of establishing secure communications over short distances. In order to accurately characterize the thermal infrared transmitter and, in turn, predict the band-limited output radiated power for each channel, a detailed investigation of the associated radiation mechanisms has been given here for the first time. It is found that, with the use of incandescent light bulbs, the output radiated power has contributions from both the primary and secondary radiation sources. At a fixed bias current of 44 mA, these two radiation mechanism can generate similar band-limited (1-100 THz) output radiation power levels. In addition, the thermal time constants for both the tungsten filaments and glass envelopes have been investigated. For channels above ~70 THz (4.3 μm), where primary radiation dominates, the cooling thermal time constant of the filaments dictates switching speed. For channels below ~60 THz (5 μm), where secondary radiation dominates, the cooling thermal time constant of the glass envelope dictates switching speed; this is two to three orders of magnitude slower than those associated with the filaments.
Low cost near-infrared LEDs can provide even higher efficiency and switching speeds, but their output spectral frequency cannot be tuned. In contrast, the spectral peak of thermal sources can be continuously tuned over a vast spectral range, simply by changing the quiescent DC bias current.
The thermodynamic modelling approach reported here can accurately estimate the band-limited output radiated power of the thermal sources, and this has been verified by experimental results. Our modelling approach can serve as an invaluable tool for engineering solutions that can achieve optimal performances with both single and multi-channel ‘THz Torch’ systems. Moreover, the modelling methodology presented in this paper can be further extended to other incandescent light bulbs or more bespoke thermal sources, having different material systems, to predict the band-limited output power in the spectrum of interest.
This work was partially supported by the China Scholarship Council (CSC).
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