Fresnel-Zone Focused Antenna Arrays: Tolerance Analysis for Biomedical Applications

Abstract

A detailed tolerance analysis for antenna arrays focused on the Fresnel zone is presented in this work, with the aim to derive the field distribution guaranteeing health safety issues. In particular, random errors related to the amplitudes and phases of the radiators, and random element failures, are considered. As such, the presented tolerance analysis falls within the more prominent theory of random arrays. A particular stochastic function related to the electric field distribution is analyzed and partially characterized by first-and second-order statistics. Subsequently, a discussion is carried out on the estimation of the cumulative distribution function for the squared magnitude of the aforementioned random function. This leads to determine (confidence) level curves inherent to the squared magnitude of the electric field, representing a crucial aspect, in particular for safety issues in biomedical applications. The achieved results confirm the validity of the proposed approach, by extending also the literature for far-field focused arrays.

Tolerance Analysis of Near-Field Focused Arrays to Safe-for-Humans Microwave and RF Applications

“…In light of the above, to somehow take into account the effect of mutual couplings between antenna elements [11], while also considering the effects of possible fluctuations in the feeding network, component tolerances, antenna elements faults, and other possible causes of error, it is assumed that [37]:…”

“…Consequently, it could be set P r R 2 (P) ≤ η q (P) = q% (with 0 ≤ q ≤ 100 and n = 6), η q (P) being the q-th percentile of R 2 (P), and then the q-th ndimensional ellipsoid, associated to f (x, P), can be determined by previously setting r = √ η q and computing all the values of x satisfying (25). Once the vector with the highest Euclidean norm and satisfying ( 25) is identified, the approach in [37] can be generalised to the n-dimensional case. In fact, here, q% is the probability that X(P) lies inside the aforementioned ellipsoid.…”

“…A probabilistic study of random uncorrelated errors in Fresnel-zone focused antenna arrays has recently been presented in [37]. Such work has adapted tolerance theory methodologies for far-field focused arrays to the radiative near-field region, providing a general approach together with some approximations based on recently introduced results [38] for estimating the cumulative distribution function (cd f ) of a particular function, which acts, in a sense, as a kind of array factor.…”

“…A general model for NFFAs, subject to random errors, has been recently proposed by the authors in [39]. Starting from the original development in [39], the present work aims to generalise the methodology in [37], making no assumptions about the geometry of NFFAs to be characterised. Furthermore, the field observation is not restricted to any specific plane, thus fully considering the vector electric field.…”

“…Furthermore, the field observation is not restricted to any specific plane, thus fully considering the vector electric field. By modelling the random errors as in [37], the first-and second-order partial statistical functions of the electric field are first provided. Subsequently, the approach presented in [39] is strongly extended through the following enhancements:…”