In this paper, a microstrip lowpass filter using rectangular resonators is designed. To weaken the undesired harmonics from 10 to 20 GHz, a stair-shaped suppressing cell and also high impedance elements at the edges are utilized. It should be noted that for analyzing the proposed filter, an LC model is used and the design is done in such a way that the coupling effects of the close-up lines are reduced as much as possible, so that they are ignored in the circuit analysis. The designed filter has a cut-off frequency of 1.01 GHz and the transition band is only 0.1 GHz. In addition to compression of dimensions, the stopband bandwidth is 18.7 times the cut-off frequency (18.7 × fc). The attenuation rate in the passband reaches 0.081 dB which indicates that the passband is flat. In the stopband, disturbing harmonics have been dampened to −23.5 dB and a good bandwidth is achieved. The figure of merit of the proposed filter is 180 387 and it is a good benchmark for the overall comparison of the proposed filter with the previous works.

A function has been proposed to evaluate the electron density model constructed by inverse Fourier transform using the observed structure amplitudes and trial phase set. The strategy of this function is applying an imaginary electron density modification to the model, and then measuring how well the calculated structure amplitudes of the modified model matches the expected structure amplitudes for the modified correct model. Since the correct model is not available in advance, a method has been developed to estimate the structure amplitudes of the modified correct model. With the estimated structure amplitudes of the modified correct model, the evaluation function can be calculated approximately. Limited tests on simulated diffraction data indicate that this evaluation function may be valid at the data resolution better than 2.5 Å.

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.

A lattice metric singularity occurs when unit cells defining two (or more) lattices yield the identical set of unique calculated d-spacings. The existence of such singularities, therefore, has a practical impact on the indexing of powder patterns. Lattice metric singularities often involve lattices that are in a derivative relationship one to another. A variety of types of singularities are possible depending on the number of different lattices involved (i.e., binary, ternary, quaternary), on the nature of the derivative lattice relationship (i.e., subcell/supercell, composite), on the Bravais type of each of the lattices, and on the the volume ratio(s) of primitive cells defining the lattices. In the laboratory, an encounter with a singularity can lead one into a trap; viz., the investigator using an indexing program, or by other means, may determine only one of the lattices with a high figure of merit. When this happens, it is critical to recognize that there exists more than one indexing solution. In a previous work, a binary singularity was described involving a monoclinic and a rhombohedral lattice. In the present work, we describe a second type of singularity—a ternary singularity—in which the two of the three lattices are in a derivative composite relationship.