This paper presents a method for effectively characterizing the dielectric permittivity of nematic liquid crystals across a broad frequency range. These materials show significant potential for reconfigurable devices operating in microwave and millimeter-wave frequencies. To achieve this goal, an additive manufacturing technique is used to create a microstrip line that can be filled with liquid that acts as its substrate. The liquid crystal (LC) is then biased to modulate its permittivity. After manufacturing, a time-gating approach is used to extract the permittivity, eliminating the need for in-fixture calibration, such as Thru-Reflect-Line (TRL). Finally, the approach is validated through simulations and experimental results, which closely align with those reported using other methods in the bibliography.

The use of an eigenstate based equivalent circuit topology is proposed for the analysis and modeling of lossless and lossy bi-periodic scatterers. It can significantly simplify the design of this kind of surfaces, since it reduces the number of elements with respect to other general circuits. It contains at most only two admittances and two transformers depending on one unique transformation ratio. The real parts of these admittances can be assured to be non-negative, an interesting aspect in the modeling of lossy surfaces such as those present in asorbers. Moreover, due to the capability of decomposition into the eigenexcitations of the structure, the circuit provides important physical insight. Different cases of scatterers have been analyzed: symmetric and asymmetric, lossy and lossless. In all these cases, the modeling of the circuit admittances has been successfully achieved with a few RLC elements, positive and frequency independent. In the case of structures with symmetries, the transformation ratio directly reflects the physical orientation of the eigenexcitations of the scatterer. Furthermore, in the case of lossy scatterers but without symmetries, the resulting equivalent circuit reveals that their eigenexcitations are not linear polarizations, but elliptic polarizations whose properties are described by the complex transformation ratio.

An equivalent-circuit topology for two-port lossy non-symmetric reciprocal networks is proposed. The circuit topology is based on the eigenstate decomposition. The proposed circuit consists of two immittances and two transformers with a single complex turns ratio, all obtained from the eigenvalues and eigenvectors of the admittance or impedance matrix of the network in a straightforward way. The interconnection of the circuit elements is simple and compact, and the real parts of its immittances are always positive. To verify its behavior, the equivalent circuit of two different leaky-wave antenna unit cells is extracted: a series-fed coupled patch radiating element, and the complementary strip-slot. Simulated and measured data are provided for the study cases, highlighting the satisfactory behavior of the equivalent circuit over a very broad bandwidth. A simple asymmetry model is also proposed that can be used advantageously in the analysis and design of non-symmetric two-ports, like unit cells of leaky-wave antennas.