An estimate of the error caused by the elongation of the wavelength in a focused beam in free-space electromagnetic parameters measurement

摘要

A pair of spot-focusing horn lens antenna is the key component in a free-space measurement system. The electromagnetic constitutive parameters of a planar sample are determined using transmitted and reflected electromagnetic beams. These parameters are obtained from the measured scattering parameters by the microwave network analyzer, thickness of the sample, and wavelength of a focused beam on the sample. Free-space techniques introduced by most papers consider the focused wavelength as the free-space wavelength. But in fact, the incident wave projected by a lens into the sample approximates a Gaussian beam, thus, there has an elongation of the wavelength in the focused beam and this elongation should be taken into consideration in dielectric and magnetic measurement. In this paper, elongation of the wavelength has been analyzed and measured. Measurement results show that the focused wavelength in the vicinity of the focus has an elongation of 1%–5% relative to the free-space wavelength. Elongation's influence on the measurement result of the permittivity and permeability has been investigated. Numerical analyses show that the elongation of the focused wavelength can cause the increase of the measured value of the permeability relative to traditionally measured value, but for the permittivity, it is affected by several parameters and may increase or decrease relative to traditionally measured value.