Variational formulation of open-ended coaxial line in contact with layered biological medium

An open-ended coaxial probe designed to measure layered biological media is analyzed with a new method. The probe is considered as an electrostatic circuit element whose capacitance is solved using a stationary functional. The fundamental transverse electric and magnetic field (TEM)-mode and the series of evanescent wavemodes in the coaxial cable are used as basis functions. The field outside the probe is solved using a Hankel transform. The capacitance is calculated for homogeneous materials and two-layer structures and the 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 take into account the effect of subcutaneous fat in skin measurements, is presented and its validity for different combinations of dielectric constants and the thickness of the first layer is demonstrated. The static approximation limits the frequency range, but it covers biological measurements up to 500 MHz. The developed method is accurate and easy to adopt in practice.