Analytical Expressions For Reflection Coefficients Research Articles

Spread Spectrum Time Domain Reflectometry With Lumped Elements on Asymmetric Transmission Lines

Spread spectrum time domain reflectometry (SSTDR) has been traditionally used to detect hard faults (open and short circuit faults) in transmission lines. Prior work has focused on loads at the end of the line with little research on impedances from circuit elements located in the middle of the line (i.e., not at the load) or on only one wire of the line. In this work we consider cases of transmission lines with different impedances on each wire. We refer to lines with the same impedance on both wires (positive and negative) as symmetric. Lines with different impedances on each wire are asymmetric. For highly localized impedances (approximately infinitesimal in length, i.e. with a length significantly smaller than the wavelength of the incident signal), the reflections and their effects on the propagating wave become difficult to describe with traditional transmission line theory. We provide analytical expressions for reflection coefficients for symmetric and asymmetric transmission lines and show that these formulae describe experimental measurements of capacitors and resistors to about 99% accuracy for the magnitudes and 75% for the phases.

Perfect anomalous reflection using a compound metallic metagrating.

Metagrating is a new concept for wavefront manipulation that, unlike phase gradient metasurfaces, does not suffer from low efficiency and also has a less complicated fabrication process. In this paper, a compound metallic grating (a periodic metallic structure with more than one slit in each period) is proposed for anomalous reflection. We propose an analytical method for analyzing the electromagnetic response of this grating. Closed-form and analytical expressions are presented for the reflection coefficients of zeroth diffracted order and also higher diffracted orders. The proposed method is verified against full-wave simulations and the results are in excellent agreement. Thanks to the geometrical asymmetry of compound metallic grating, it can be used for designing anomalous reflection at the normal incidence. Given analytical expressions for reflection coefficients, we design a perfect anomalous reflector for a TM polarized plane wave via transferring all the incident power to ( - 1) diffraction order . The structure designed in this study has an unprecedented near-to-unitary efficiency of 99.9%. Finally, a multi-element compound metallic grating is proposed for reflecting the normal incidence to angles of below 30°, which is a challenging accomplishment. This excellent performance of compound metallic grating shows its high potential for microwave and terahertz wavefront manipulation applications.

Analytical expressions for reflection coefficients of artificially soft and hard surfaces: dielectric slab loaded with a periodic array of strips over a ground plane

Simple and closed form expressions for plane wave reflection coefficients of a dielectric slab loaded with a periodic array of strips over a ground plane are presented for use in antenna applications. In the analysis, a set of integral equations for the fields between the strips and dielectric slab are derived from the three-dimensional boundary value problem. Using the low frequency approximation, closed form expressions were obtained for the reflection coefficients. Numerical comparison with the point matching method shows that the accuracy is excellent in practical uses. The frequency bandwidth of the surfaces at the artificially soft and hard boundaries is discussed.