Near-Field Warping Sampling Scheme for Broad-Side Antenna Characterization

Abstract

In this paper the problem of sampling the field radiated by a planar source observed over a finite planar aperture located in the near-field is addressed. The problem is cast as the determination of the spatial measurement positions which allow us to discretize the radiation problem so that the singular values of the radiation operator are well-approximated. More in detail, thanks to a suitably warping transformation of the observation variables, the kernel function of the relevant operator is approximated by a band-limited function and hence the sampling theorem applied to achieved discretization. It results in the sampling points having to be non-linearity arranged across the measurement aperture and their number can be considerably lowered as compared to more standard sampling approach. It is shown that the proposed sampling scheme works well for measurement apertures that are not too large as compared to the source’s size. As a consequence, the method appears better suited for broad-side large antenna whose radiated field is mainly concentrated in front of the antenna. A numerical analysis is included to check the theoretical findings and to study the trade-off between the field accuracy representation (over the measurement aperture) and the truncation error in the estimated far-field radiation pattern.

Efficient Planar Near-Field Measurements for Radiation Pattern Evaluation by a Warping Strategy

“…In order to devise the sampling scheme, in [23] we considered finding a discrete approximation of the following eigenvalue problem…”

“…In this section, we introduce the mathematical formulation and the related notation to be used throughout the paper. Also, the field sampling scheme based on the warping transformations, presented in [23], is briefly detailed in order to establish the starting point from which to proceed ahead.…”

“…Recently, we have introduced an approach that is somehow in between the two mentioned ones. Basically, we cast the determination of the sampling points as the ones that allow to approximate the kernel function of the operator consisting of the composition of the radiation operator and its adjoint [23]. In particular, thanks to suitable variable transformations, that warp the spatial observation variables, such a kernel function is approximated as a band-limited function and then the Shannon sampling theorem is used for the discretization.…”

“…Also, it generalizes the point of view of bandlimited approximation approaches, since it does not require splitting the 2D problem into two 1D problems, along the so-called meridian and azimuth curves, since the outset. Indeed, it was shown that the sampling can be factorized (i.e., independently achieved along each dimension) only when the size of the measurement aperture is at most equal to the one of the source [23].…”

“…The first contribution of this paper is the generalization of the warping procedure, that in [23] has been derived only for magnetic source currents, to any type of currents. In particular, in the case of electric currents, there are some further technical difficulties to be tackled.…”