Abstract
Low-loss dielectric laminates that are routinely used in the manufacturing of printed circuit boards (PCBs) are known to be anisotropic. The <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in-plane</i> and the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">out-of-plane</i> components of the dielectric permittivity have been so far typically determined using one of several available methods. In this article, we performed measurements of both components of complex permittivity of selected isotropic and anisotropic laminar materials employing a combination of a few split-post dielectric resonators (SPDRs) and one cylindrical cavity supporting several TM <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$_{0n0}$ </tex-math></inline-formula> modes in the microwave band. Based on obtained data a novel, more precise approach to measuring the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">out-of-plane</i> component of complex permittivity of laminar samples has been proposed. Additionally, a detailed analysis of several sources of measurement uncertainty (e.g., due to finite tolerances of manufacturing of the sample) has been performed and some recommendations formulated.
Highlights
L OW-LOSS dielectric laminates that are routinely used in the manufacturing of printed circuit boards (PCBs) for the microwave and millimeter-wave circuits are known to be anisotropic [1] with two major diagonal components of a permittivity tensor ε defined as
The circumferential wall of the cavity is made of aluminum, but lids are made of silver-plated copper in order to reduce the conduction losses within the resonator
By employing (2) and the measurement procedure described in Section II, we have measured the out-of-plane complex permittivity of several materials which are known to be isotropic, and materials that are known to be anisotropic
Summary
L OW-LOSS dielectric laminates that are routinely used in the manufacturing of printed circuit boards (PCBs) for the microwave and millimeter-wave circuits are known to be anisotropic [1] with two major diagonal components of a permittivity tensor ε defined as. The permittivity component perpendicular to the substrate (the out-of-plane component) is the most often measured in a strip-line transmission set-up [10], different microstrip or standardized strip-line resonators [11], [12], on doubly metalized substrates creating a full sheet resonator [13], re-entrant cavities [9]–[14] or using a whispering gallery mode resonator (WGM) [15]–[17] All these measurement methods allow us to determine the real part of permittivity. They require either a relatively complicated measurement setup (e.g., the re-entrant cavity with an adjustable air-gap reported in [9] or the methods based on the clamped strip-line like the IPC-TM-650 approach in [11]), or they provide the in-plane component of permittivity only (like the SPDRs), or require a well-trained personnel in order to properly identify resonant modes (i.e., full-sheet resonator or WGMs). No similar characterization campaign covering several frequencies has been reported in the literature to the best of our knowledge
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