Measurement Technique for Interface and Surface Conductivities at Millimeter-Wave Frequencies Using Dielectric Rod Resonator Excited by Nonradiative Dielectric Waveguide

Abstract

Herein, we propose a new technique for measuring interface and surface conductivities, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sigma _{i}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sigma _{s}$ </tex-math></inline-formula> , of circuit substrates separately at millimeter-wave frequencies using a TE <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$_{0m\delta }$ </tex-math></inline-formula> ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$m =1$ </tex-math></inline-formula> , 2, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$3, \ldots, \delta &lt; 1$ </tex-math></inline-formula> ) mode single-crystal sapphire rod resonator excited via nonradiative dielectric waveguide (NRD guide). Here, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sigma _{i}$ </tex-math></inline-formula> represents an effective conductivity of conductor at the dielectric side. On the other hand, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sigma _{s}$ </tex-math></inline-formula> represents an effective conductivity at the shiny side of the conductor. Evaluating <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sigma _{i}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sigma _{s}$ </tex-math></inline-formula> separately is essential for high-precision circuit design at microwave and millimeter-wave frequencies and the development of low-loss circuit substrates. The superiority of NRD guide excitation compared with the conventional loop antenna excitation was confirmed through both experiments and simulations for the dielectric resonator at millimeter-wave frequencies. The feasibility of the proposed technique was verified by measuring <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sigma _{i}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sigma _{s}$ </tex-math></inline-formula> of the two types of commercially available copper-clad substrates, which were liquid-crystal-polymer-based and polytetrafluoroethylene-based substrates, at approximately 62, 74, and 80 GHz. In addition, we confirmed that these data were consistent with respect to the frequency with the measured results obtained using the conventional technique via loop antenna excitation at microwave frequencies, demonstrating the validity of the proposed technique. The measured results from 2 to 80 GHz showed that <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sigma _{i}$ </tex-math></inline-formula> had a smaller value than <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sigma _{s}$ </tex-math></inline-formula> and their values decreased with increasing frequency. Furthermore, it was found that the frequency dependence of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sigma _{i}$ </tex-math></inline-formula> was very different for the two types of substrates.