Note: Parameter extraction of samples without the direct application of the passivity principle from reference-plane-invariant measurements.

An extraction algorithm has been proposed for explicit complex permittivity and complex permeability determination of samples using reference-plane-invariant scattering parameters without resorting to the application of the passivity principle. The algorithm relies on the definition of new odd and even reflection coefficients which result in no-crossing of the negative real axis for the argument of the square-root functions. Permittivity measurements of two low-loss samples were performed for validation of our algorithm.

Determination of full S-parameters of a low-loss two-port device from uncalibrated measurements.

A procedure has been proposed for the determination of full scattering (S-) parameters of a low-loss two-port device using uncalibrated waveguide measurements of four configurations (thru, non-reflecting line, device, and reflection-line with the device). It is shown that to uniquely determine forward and backward reflection S-parameters of the device, S-parameters of a reflecting line (reflection-symmetric or reflection-asymmetric) in series with the device should be used. We first validated our proposed method from simulated S-parameters and then extracted full S-parameters of three different two-port devices [waveguide cells partially loaded by low-loss dielectric samples-polyethylene, polyvinyl chloride, and alumina (with 99.5% concentration) samples] using symmetric and asymmetric reflecting lines. Next, we also compared the complex permittivities of the polyethylene and polyvinyl chloride samples inside two different devices using extracted S-parameters from our formalism with the complex permittivities of the same samples measured by a calibration-dependent method. A good agreement between measured and extracted complex permittivities is observed, demonstrating the accuracy of our proposed method. Finally, we carried out ten independent measurements to determine at each frequency the average and maximum and minimum values (thus changes from the average) of extracted full S-parameters of a low-loss two-port device to evaluate the total uncertainty in measuring these parameters by our method. We note from this analysis that if the S-parameters of a low-loss two-port device will be determined using a reflecting line with symmetric reflections, then attention should be paid in implementing a reflecting line with symmetric reflections since any deviation from the symmetric property of the reflecting line could increase the overall uncertainty.

Calibration-free extraction of constitutive parameters of magnetically coupled anisotropic metamaterials using waveguide measurements.

A calibration-free method for extraction of electromagnetic properties of magnetically coupled anisotropic biaxial metamaterial (MM) slabs from waveguide measurements is proposed. It relies on three measurement steps (thru, empty line, and the same line arbitrarily loaded by the MM slab) to extract electromagnetic properties. It is evaluated against another calibration-dependent method for retrieval of electromagnetic properties of a MM slab constructed by C-shaped resonators. From evaluation analysis, we note that our method, as compared to the calibration-dependent method, not only accurately extracts electromagnetic properties without requiring the use of expensive calibration standards but also is reference-invariant.

Phase-ambiguity-free and accurate permittivity determination from waveguide measurements.

A microwave method has been proposed for accurate and unique extraction of relative complex permittivity (εr) of dielectric materials from 2π phase-ambiguity-free amplitude-only two-port and one-port scattering parameter measurements. Improved accuracy has been shown by the applied uncertainty analysis. For the validation of our method, εr of low-loss and lossy samples was extracted.

Comment on "Calibration-independent measurement of complex permittivity of liquids using a coaxial transmission line" [Rev. Sci. Instrum. 86, 014704 (2015)].

In this letter, we comment on the applicability of the derived characteristic equation (Eq. (7)) in a recently published article of Guoxin [Rev. Sci. Instrum. 86, 014704 (2015)]. To validate our comment, we first derive another characteristic function for determination of complex permittivity of dielectric materials for the configurations considered in the above article using calibration-independent uncorrected S-parameters for transmission-line measurements (coaxial-line, waveguide, free-space, etc). Unlike the characteristic equation in this article, the characteristic equation derived here for determination of the complex permittivity of liquid samples does not require any knowledge about the complex permittivity of plugs, used for holding liquid samples in place. We then performed 3-D full-wave simulations for the measurement configurations presented in Guoxin's article for substantiation of the characteristic equation derived in this letter.

Microwave method for reference-plane-invariant and thickness-independent permittivity determination of liquid materials.

An attractive transmission-reflection method based on reference-plane invariant and thickness-independent expressions has been proposed for accurate and unique retrieval of complex permittivity of dielectric liquid samples. The method uses both branch-index-independent expressions and a restricted solution set for determining unique and fast complex permittivities. A 2D graphical method has been applied to demonstrate the operation and validation of the proposed method. A uncertainty analysis has been performed to monitor how the accuracy of the proposed method can be improved by a correct selection of sample holder properties. Scattering parameter measurements of two tested reference liquids (distilled water and methanol) have been carried out for comparison of various techniques with the proposed one when the reference-planes and sample thickness are not precisely known. We note from the comparison that whereas other techniques are seriously affected by imprecise knowledge of both reference-planes and sample thickness, the proposed method removes this restriction.

The effect of silicon loss and fabrication tolerance on spectral properties of porous silicon Fabry-Perot cavities in sensing applications.

In this paper, we investigate the effect of non-uniformities (enlargement of current passage, non-equal surface current densities, etc.) in axial as well as transverse directions of a porous silicon Fabry-Perot (FP) cavity as well as loss nature of bulk silicon on spectral properties of this cavity, even that cavity is created with an anisotropic etching process. Without correct and comprehensive characterization of such cavities by incorporating these non-uniformities and inherent lossy nature of a cavity, detection and identification of biological and chemical molecules by that cavity may yield unpredictable and misleading results. From our simulations, we note the following two key points. First, effects of the refractive index and the thickness of microcavity region of a lossless or lossy FP cavity on resonance wavelength is more prevailing than those of first and last layers. Second, the effect of some small loss inside the FP cavity is not detectable by the measurement of resonance wavelength whereas the same influence is noticeable by the measurement of reflectivity. We carried out some measurements from two different regions on the fabricated cavities to validate our simulation results. From a practical point of view in correct detection and/or identification of lossy biological or chemical vapor by FP cavities, we conclude that not only the measurement of resonance wavelength as well as its shift but also the reflectivity value at the resonance wavelength or some specific wavelengths should be utilized.

A microcontroller-based microwave free-space measurement system for permittivity determination of lossy liquid materials.

A microcontroller-based noncontact and nondestructive microwave free-space measurement system for real-time and dynamic determination of complex permittivity of lossy liquid materials has been proposed. The system is comprised of two main sections--microwave and electronic. While the microwave section provides for measuring only the amplitudes of reflection coefficients, the electronic section processes these data and determines the complex permittivity using a general purpose microcontroller. The proposed method eliminates elaborate liquid sample holder preparation and only requires microwave components to perform reflection measurements from one side of the holder. In addition, it explicitly determines the permittivity of lossy liquid samples from reflection measurements at different frequencies without any knowledge on sample thickness. In order to reduce systematic errors in the system, we propose a simple calibration technique, which employs simple and readily available standards. The measurement system can be a good candidate for industrial-based applications.

A calibration-independent method for accurate complex permittivity determination of liquid materials.

This note presents a calibration-independent method for accurate complex permittivity determination of liquid materials. There are two main advantages of the proposed method over those in the literature, which require measurements of two cells with different lengths loaded by the same liquid material. First, it eliminates any inhomogeneity or impurity present in the second sample and decreases the uncertainty in sample thickness. Second, it removes the undesired impacts of measurement plane deterioration on measurements of liquid materials. For validation of the proposed method, we measure the complex permittivity of distilled water and compare its extracted permittivity with the theoretical datum obtained from the Debye equation.