Ultra-compact programmable arbitrary power splitter

AbstractIn this paper, a balanced-to-balanced (BTB) branch-slotline directional coupler (DC) is firstly presented, which can realize an arbitrary power division ratios (PDRs). The coupler is composed by microstrip-to-slotline (MS) transition structures and branch-slotline coupled structures. The single-ended to balanced-ended conversion is simplified and easy to implemented by the MS transition structures, which intrinsically leads to the differential-mode (DM) transmission and common-mode (CM) suppression. Moreover, the different PDRs which are controlled by the widths of branch-slotlines can be achieved. In order to verify the feasibility of the proposed design method, two prototype circuits of the proposed coupler with different PDRs are fabricated and measured. The return loss and the isolation of two designs are all better than 10 dB. Moreover, the CM suppressions are greater than 35 dB. A good agreement between the simulation and measurement results is observed.

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Abundance of Primordial Black Holes in Peak Theory for an Arbitrary Power Spectrum

Progress of Theoretical and Experimental Physics ◽

10.1093/ptep/ptaa155 ◽

2020 ◽

Author(s):

Chul-Moon Yoo ◽

Tomohiro Harada ◽

Shin’ichi Hirano ◽

Kazunori Kohri

Keyword(s):

Mass Spectrum ◽

Power Spectrum ◽

Environmental Effect ◽

Window Function ◽

Radial Coordinate ◽

Primordial Black Holes ◽

Scale Invariant ◽

Curvature Perturbation ◽

Arbitrary Power ◽

Nonlinear Relation

Abstract We modify the procedure to estimate PBH abundance proposed in Ref. [1] so that it can be applied to a broad power spectrum such as the scale-invariant flat power spectrum. In the new procedure, we focus on peaks of the Laplacian of the curvature perturbation △ ζ and use the values of △ ζ and △ △ ζ at each peak to specify the profile of ζ as a function of the radial coordinate while the values of ζ and △ ζ are used in Ref. [1]. The new procedure decouples the larger-scale environmental effect from the estimate of PBH abundance. Because the redundant variance due to the environmental effect is eliminated, we obtain a narrower shape of the mass spectrum compared to the previous procedure in Ref. [1]. Furthermore, the new procedure allows us to estimate PBH abundance for the scale-invariant flat power spectrum by introducing a window function. Although the final result depends on the choice of the window function, we show that the k-space tophat window minimizes the extra reduction of the mass spectrum due to the window function. That is, the k-space tophat window has the minimum required property in the theoretical PBH estimation. Our procedure makes it possible to calculate the PBH mass spectrum for an arbitrary power spectrum by using a plausible PBH formation criterion with the nonlinear relation taken into account.

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