Harmonic and Intermodulation Performance of the Semiconductor Bolometer
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Harmonic and Intermodulation Performance of the Semiconductor Bolometer Muhammad Taher Abuelma’atti
Received: 25 March 2007 / Accepted: 5 June 2007 / Published online: 27 June 2007 # Springer Science + Business Media, LLC 2007
Abstract A mathematical model for the temperature dependence of the bolometer semiconductor resistance is presented. The model, basically a sine-series function, can easily yield closed-form expressions for the harmonic and intermodulation performance of the acquired interferogram voltage with large-amplitude multisinusoidal variations in the incident radiation. The special case of two-tone equal-amplitude incident radiation is considered in detail. The results show that the intermodulation components are always higher than the harmonic components of the same order. The results also show that the second-order intermodulation is always dominant and is higher than the second-harmonic component by about 6 dB. Moreover, the results show that for relatively small incident amplitudes of the incident radiation the ratio between the second- and third-harmonic components is almost equal to the ratio between the second-harmonic component and the fundamental. The results also show that the ratio between the amplitudes of the second- and third-order intermodulation components is almost equal to the ratio between the amplitudes of the second-order intermodulation component and the fundamental. Keywords Infrared detectors . Intermodulation distortion . Harmonic distortion . Interferometry
1 Introduction The semiconductor bolometer is the most sensitive wideband detectors for far-infrared and millimeter wavelengths. This is attributed to the strong temperature dependence of their electrical resistance that makes detection of the heating effects of the incident radiation feasible. While a variety of theoretical models can be used for representing the electrical resistances of the semiconductors at low temperature, it appears that the semi-empirical
M. T. Abuelma’atti (*) King Fahd University of Petroleum and Minerals, Box 203, Dhahran, 31261, Saudi Arabia e-mail: [email protected]
742
Int J Infrared Milli Waves (2007) 28:741–749
relation of equation (1) is widely accepted to represent the semiconductor resistance at or below helium temperatures [1]. R ¼ R1 exp ððδ=T Þm Þ
ð1Þ
where R∞ is equal to the asymptotic value of the resistance for T >> δ, δ =10 – 20K depending on the material, and m = 0.25,0.5 or 1 depending on the doping and the temperature range. The model of equation (1) describes the bolometer resistance not only when it is at the bath temperature but also under dynamic equilibrium with the bolometer heated above the bath temperature to T, through the combined effects of Joule heating from the bias current and the power absorbed from the radiation background [1]. In equation (1), R∞,δ and m are fitting parameters that can be obtained using the least-square fitting technique to fit the measured zero-background electrical resistance versus temperature data. In an interferometer using a bol
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