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

Abstract

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.