Variational Formulation of Open-Ended Coaxial Line in Contact with LayeredBiological Medium

摘要

Open-ended coaxial probe designed to measure layered biological media is analyzedwith a new method. The probe is considered as an electrostatic circuit element whose capacitance is solved using a stationary functional. The fundamental TEM-mode and the series of evanescent wavemodes in the coaxial cable are accounted as basis functions. The field outside the probe is solved using Hankel transform. The capacitance is calculated for one and two-layer cases and results are compared with values measured with a phantom model. The method can be easily extended for structures with an arbitrary number of layers. A practical approximation for two-layer cases, originally developed to compensate the effect of subcutaneous fat in skin measurements, is presented and its validity for all combinations of dielectric constants and the thickness of the first layer is demonstrated. The static approximation limits the frequency range, but it covers the whole range of interest in biological measurements up to 500 MHz. Furthermore, the method developed here is accurate and easy to adopt in practice.