This article presents the modeling and realization of a compact substrate integrated coaxial line (SICL) based butler matrix operating at 5 GHz for beam-forming applications. The proposed 4 × 4 butler matrix is developed using SICL-based hybrid coupler, crossover, and phase shifter. A compact 90∘ coupler comprising of center tapped unequal stubs is designed to enhance the size reduction as well as to extend the out of band rejection. Wideband SICL-based crossover operating from DC to 10 GHz is conceived for the proposed butler matrix using a plated through hole as transition. The SICL crossover features very high measured isolation of 65 dB owing to the reduction in coupling between the two signal paths within a lateral footprint of only 0.034 $\lambda_g^2$. A meandered SICL-based line is used in order to provide the necessary 45∘ and 0∘ phase shift to realize the butler matrix. The fully shielded and self-packaged compact 4 × 4 SICL-based butler matrix is fabricated and experimentally validated to operate at 5 GHz.

A simple and compact three-way planar power divider, which avoids the floating common node of the isolation resistors, is presented. The proposed structure exhibits a wideband operation (measured frequency range of 1.6–3.3 GHz and bandwidth of 69.4%) with good return loss and isolation characteristics. Transmission line theory is used for the mathematical analysis and extraction of design equations, followed by simulations and experimental measurements that confirm the predicted results. The proposed divider achieves an equal power split (∼32%, −4.9 ± 0.4 dB insertion loss) between the input and each output port. The measured return loss is better than −10 dB at all ports, and the measured maximum isolation is close to −30 dB. The proposed design exhibits a fully planar structure, thus eliminating the need for a floating common node for the isolation resistors. Additionally, its structure is much simpler (i.e., no coupled lines, crossovers, or lumped capacitors are required) than other designs, achieves wideband operation, and provides design simplicity, flexibility, and easy implementation. Despite its simple noncomplicated structure, the proposed three-way planar divider achieves similar (or in some cases, better) performance and size than other more complicated structures. Furthermore, it can be expanded to an n-way structure.

A significant measureable development of inductance gain per unit of space in loop fractals for a suite of inductors which occupy the same layout space and require only a single-fabrication layer is investigated. All structures are fabricated on a borofloat glass substrate with dielectric constant loss tangent of 0.004. A chrome layer of 30 nm for adhesion followed by a 180 nm gold layer were sputtered and etched. To increase the surface area is implemented a simple geometrical strategy through fractalization and consequently the inductive performances is improved. Also, the higher fractal orders can be developed the inductive performance over 9 times from 0th to 3rd order. The fractal derivations of the original loop due to its space filling properties are examined and it suggests that although the effective electrode length increases, overall, the arrangement still essentially occupies the same space. In terms of design space for 0th, 3O-5O-7O of 1st, 2nd, and 3rd orders of fractals, 0, 26.2, 34.6, 38.6, 65.5, and 75.8% of occupied conductor surface area are saved. The measured inductances and resistances for aforementioned orders of fractals are 4.6 nH and 5 Ω, 8.6 nH and 10.5 Ω, 12 nH and 11.6 Ω, 12.8 nH and 17.3 Ω, 19.2 nH and 23.2 Ω, and 44.7 nH and 63.5 Ω, respectively.

We prove that every finite distributive lattice can be represented as the congruence lattice of a finite (planar) semimodular lattice.

Recent collections of Sawdonia ornata have been made from the Strathmore Group which crops out in the Midland Valley of Scotland. The sediments are Lower Devonian, probably Emsian, in age. New morphological features discovered include planar branching of vegetative and fertile axes, abaxial emergences close to branch points and H branching. Well preserved cuticles have permitted reinterpretation of the structure of stornata, rosettes (hair bases), papillae and spines, and striated cuticle is identified as S. ornata. The morphology of sporangia and in situ spores is described. Pyritised axes have revealed details of xylem shape, maturation, changes in the vicinity of branching, tracheidal structure and the arrangement of xylem and cortex in deformed axes.