Complete Meniscus Removal Method for Broadband Liquid Characterization in a Semi-Open Coaxial Test Cell

Abstract

We present a new technique for broadband liquid characterization using a semi-open, vertically oriented test cell that is measured with a calibrated vector network analyzer in three states: the empty one and filled with two different volumes of the liquid under test. Using the measurements, we de-embed a transfer matrix representing a volume increment of the liquid sample and determine its column height with a novel closed-form formula. Thanks to the de-embedding, the method enables one, for the first time, to completely remove effects caused by a reproducible meniscus forming the top surface of a liquid tested in the cell and determine not only the propagation constant, but also characteristic impedance of the liquid sample, from which its permittivity and permeability are calculated. The results are highly consistent, because all the measurements are performed without disassembling the cell. We validate experimental results of the meniscus removal method by comparing them with reference data and outcomes of the Nicolson–Ross–Weir method.

Errors in Broadband Permittivity Determination Due to Liquid Surface Distortions in Semi-Open Test Cell

“…As the surface of a liquid in a semi-open cell is not ideally flat, but distorted with a meniscus, the measured sample generally becomes asymmetrical. Therefore, we have proposed a new method dealing with the asymmetry of the distorted sample in [25]. It employs three measurement states: the empty cell and the cell with two different volumes of a liquid for which we assume the reproducible shape of the meniscus, as presented in Figure 3.…”

“…In Section 2.1 we present a classical approach for permittivity calculation with one state of liquid using the NRW algorithm [26,27] and Somlo's method [15] for the sample height determination. In Section 2.2 we summarize our meniscus removal (MR) method, presented in [25], that uses two volumes of liquid.…”

“…For this goal, we simulated the measurements performed in our 7 mm coaxial fixture employed in [16,25], as shown in Figure 4, at frequencies up to 18 GHz. The fixture was filled with vacuum, as a good substitute for air, and with the liquid sample (the blue layer).…”

“…To overpass problems with the meniscus in semi-open cells, which are more universal, we have proposed a new method [25] that can remove systematic errors caused by the meniscus in the broadband permittivity measurements. Its high performance has been confirmed experimentally [25].…”

“…To overpass problems with the meniscus in semi-open cells, which are more universal, we have proposed a new method [25] that can remove systematic errors caused by the meniscus in the broadband permittivity measurements. Its high performance has been confirmed experimentally [25]. However, due to the finite uncertainty of the scattering parameters measurement with a calibrated VNA, it was uneasy to get deeper into errors that occur when the conventional techniques as [15,16,26] are applied to this goal.…”