Evaluation of a transfer function model using experimental data and numerical analysis: the case of a pyroelectric sensor

The purpose of this paper is to present an evaluation study of a pyroelectric sensor model implemented in \(\hbox {MATLAB}^{\circledR }/\hbox {SIMULINK}^{\circledR }\) environment. The sensor model consists of some cascaded transfer functions taking into account the material characteristics and geometrical parameters which have been synthesized in the form of thermal and electrical time constants and a global multiplying coefficient. The model was proposed by Odon to serve as an excellent basis for the analysis of the dynamic behavior of a pyroelectric sensor. The study performed is relevant to evaluate the validity of the model by comparing its simulated response to measurement obtained on a pyroelectric sensor prototype. To achieve this evaluation, an optimization algorithm is used to estimate the parameters values of the transfer function model using a succession of tests and adjustments so that the algorithm converges to and reaches the optimal solution giving an acceptable correlation between simulated and measured responses. The semi-experimental evaluation approach has been applied to two prototype sensors with pyroelectric material thicknesses of 9 and \(25\,{\upmu }\hbox {m}\), respectively. In the two cases, the estimated values of the parameters were very interesting in terms of uncertainties (between 1.846 and 6.726 % at \(1{\upsigma }\) level) and setting evidence for the existence of two global solutions, i.e., two deep minima for each prototype sensor.