Design of a New Step-like Frame FBAR for Suppression of Spurious Resonances

Film bulk acoustic wave resonators (FBARs) are of great interest for wireless applications due to its inherent advantages at microwave frequencies. However, the presence of spurious modes near the main resonance degrades the performance of resonators and requires development of new methods to suppress such unwanted modes. Different techniques are used to suppress these spurious modes. In this paper, we present design of a new step-like frame structure film bulk acoustic wave resonator operating near 1.5 GHz. The simulated results are compared with simple frame-like structure. The spurious resonances are eliminated effectively and smooth pass band is obtained with effective coupling coefficient of 5.68% and quality factor of 1800. The equivalent electrical mBVD model of the FBAR based on impedance response is also presented. These highly smooth phase response and passband skirt steepness resonators are most demanding for the design of low cost, small size and high performance filters, duplexers and oscillators for wireless systems

Dark sector interaction: a remedy of the tensions between CMB and LSS data

The well-known tensions on the cosmological parameters $H_0$ and $\sigma_8$ within the $\Lambda$CDM cosmology shown by the Planck-CMB and LSS data are possibly due to the systematics in the data or our ignorance of some new physics beyond the $\Lambda$CDM model. In this letter, we focus on the second possibility, and investigate a minimal extension of the $\Lambda$CDM model by allowing a coupling between its dark sector components (dark energy and dark matter). We analyze this scenario with Planck-CMB, KiDS and HST data, and find that the $H_0$ and $\sigma_8$ tensions disappear at 68\% CL. In the joint analyzes with Planck, HST and KiDS data, we find non-zero coupling in the dark sector up to 99\% CL. Thus, we find a strong statistical support from the observational data for an interaction in the dark sector of the Universe while solving the $H_0$ and $\sigma_8$ tensions simultaneously.Comment: 5 pages, 3 figure

On Rational Sets in Euclidean Spaces and Spheres

IFor a positive rational $l$, we define the concept of an $l$-elliptic and an $l$-hyperbolic rational set in a metric space. In this article we examine the existence of (i) dense and (ii) infinite $l$-hyperbolic and $l$-ellitpic rationals subsets of the real line and unit circle. For the case of a circle, we prove that the existence of such sets depends on the positivity of ranks of certain associated elliptic curves. We also determine the closures of such sets which are maximal in case they are not dense. In higher dimensions, we show the existence of $l$-ellitpic and $l$-hyperbolic rational infinite sets in unit spheres and Euclidean spaces for certain values of $l$ which satisfy a weaker condition regarding the existence of elements of order more than two, than the positivity of the ranks of the same associated elliptic curves. We also determine their closures. A subset $T$ of the $k$-dimensional unit sphere $S^k$ has an antipodal pair if both $x,-x\in T$ for some $x\in S^k$. In this article, we prove that there does not exist a dense rational set $T\subset S^2$ which has an antipodal pair by assuming Bombieri-Lang Conjecture for surfaces of general type. We actually show that the existence of such a dense rational set in $S^k$ is equivalent to the existence of a dense $2$-hyperbolic rational set in $S^k$ which is further equivalent to the existence of a dense 1-elliptic rational set in the Euclidean space $\mathbb{R}^k$.Comment: 20 page