Polynomial Computability of Fields of Algebraic Numbers

© 2018, Pleiades Publishing, Ltd. We prove that the field of complex algebraic numbers and the ordered field of real algebraic numbers have isomorphic presentations computable in polynomial time. For these presentations, new algorithms are found for evaluation of polynomials and solving equations of one unknown. It is proved that all best known presentations for these fields produce polynomially computable structures or quotient-structures such that there exists an isomorphism between them polynomially computable in both directions

A compact 3-dB coupler with microstrip cells

Research of the design of a coupler with an operating frequency of 1.8 GHz has been conducted. This construction has a small area and can be used in microwave circuits for power division. Suggested construction, taking into consideration the reduced dimensions, has characteristics comparable to the design in the traditional version. Miniaturization of the device was achieved by using synthesized microstrip cells which were installed instead of ordinary sections. The coupler was modeled and fabricated and the measured characteristics are well coincide with the calculations. © Published under licence by IOP Publishing Ltd

Design of miniature directional coupler with wide bandwidth

Miniature directional coupler with wide bandwidth consisting of compact structures and curved lines has been developed. The type of structures was chosen in such a way as to achieve the greatest possible coincidence of their characteristics in the bandwidth with the characteristics of quarter-wave sections. The area of the developed coupler is 69.8% less than the area of the same device in its standard version. Device modeling was performed in the Cadence AWR program. It is shown that miniaturization of the directional coupler caused deterioration of such characteristics as operating frequencies band, preservation of the phase differences between the outputs in a wide frequencies band, and attenuation in the band. A model of the coupler was made, which allowed us to confirm experimentally the correctness of calculations in AWR. © Published under licence by IOP Publishing Ltd

A compact 3-dB coupler with stubs

High wave resistance line and no-load stubs were used as a tool for reducing the area of directional coupler on microwave substrate. Replacement of all λ/4 sections (segments) that are part of the coupler with the described artificial transmission lines allowed to reduce the area of the device by 76,8% (with frequency 1.9 GHz). Mathematical calculation and analysis of devices was made using Cadence AWR DE. The manufactured layout has comparable characteristics with the characteristics obtained for the model in AWR program. Negative aspects of miniaturization are narrowing of the line and increasing losses at the coupler. © Published under licence by IOP Publishing Ltd