The heat diffusion related f(-1/2) slow decay in the frequency domain transfer function of thermoelectric devices introduces a bias in figure of merit measurement methods that do not take it into account. The bias can range from less than 1% to more than 20% depending on the device. Harman type methods are not immune. Neither is the simple single measurement procedure proposed here on the basis of a complex thermal impedance analysis of the device, but in this case the supporting theory allows evaluating and correcting for the bias with documented accuracy. To this aim, both a theoretical approach based on a priori knowledge of the device and an experimental one based on theory guided measurements are possible and are described in the paper. Typical residual Type B uncertainties after correction can be below 10% of the bias.
A half-pole can be expected in the transfer function of a Peltier device because proportionality between the diffusion length and the square root of the diffusion time is intrinsic in the diffusion equation. The resulting -1∕2 bilogarithmic slope (10 dB∕dec) is, however, easily masked by the thermal time constant of the load, which makes it elusive. The goal of this work is to identify the arrangements which can reveal and make usable the half-pole, because the latter can be instrumental in a servo control to increase the open-loop gain without risking instability. The diffusion equation was solved in a sine wave regime for a one-dimensional model of a Peltier device. The Laplace transform method was used, and the periodic solution was obtained using Cauchy's theorem and the method of residues. The -1∕2 slope of the half-pole appeared observable in a frequency range which can be several decades wide, depending on details of device configuration and considered position within. Amplitude and phase of temperature and heat flux in various spots are discussed with emphasis on the physical meaning, and a comparison is provided with solutions yielded by the lumped model, which cannot show the half-pole. An experimental check of the theoretical approach and analysis was made taking into account the deviations from one-dimensionality occurring in a real Peltier device. Given a constant amplitude sine wave injected current, the quadrature component of the Seebeck voltage across the whole series of junctions was identified as the most easily measurable quantity related to the thermal response of the device. Experimental results for the latter turned out in good agreement with analytical solutions.
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