77,252 research outputs found

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

    Get PDF
    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

    On Rational Sets in Euclidean Spaces and Spheres

    Full text link
    IFor a positive rational ll, we define the concept of an ll-elliptic and an ll-hyperbolic rational set in a metric space. In this article we examine the existence of (i) dense and (ii) infinite ll-hyperbolic and ll-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 ll-ellitpic and ll-hyperbolic rational infinite sets in unit spheres and Euclidean spaces for certain values of ll 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 TT of the kk-dimensional unit sphere SkS^k has an antipodal pair if both x,xTx,-x\in T for some xSkx\in S^k. In this article, we prove that there does not exist a dense rational set TS2T\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 SkS^k is equivalent to the existence of a dense 22-hyperbolic rational set in SkS^k which is further equivalent to the existence of a dense 1-elliptic rational set in the Euclidean space Rk\mathbb{R}^k.Comment: 20 page

    Friedmann model with viscous cosmology in modified f(R,T)f(R,T) gravity theory

    Get PDF
    In this paper, we introduce bulk viscosity in the formalism of modified gravity theory in which the gravitational action contains a general function f(R,T)f(R,T), where RR and TT denote the curvature scalar and the trace of the energy-momentum tensor, respectively within the framework of a flat Friedmann-Robertson-Walker model. As an equation of state for prefect fluid, we take p=(γ1)ρp=(\gamma-1)\rho, where 0γ20 \leq \gamma \leq 2 and viscous term as a bulk viscosity due to isotropic model, of the form ζ=ζ0+ζ1H\zeta =\zeta_{0}+\zeta_{1}H, where ζ0\zeta_{0} and ζ1\zeta_{1} are constants, and HH is the Hubble parameter. The exact non-singular solutions to the corresponding field equations are obtained with non- viscous and viscous fluids, respectively by assuming a simplest particular model of the form of f(R,T)=R+2f(T)f(R,T) = R+2f(T), where f(T)=αTf(T)=\alpha T ( α\alpha is a constant). A big-rip singularity is also observed for γ<0\gamma<0 at a finite value of cosmic time under certain constraints. We study all possible scenarios with the possible positive and negative ranges of α\alpha to analyze the expansion history of the universe. It is observed that the universe accelerates or exhibits transition from decelerated phase to accelerated phase under certain constraints of ζ0\zeta_0 and ζ1\zeta_1. We compare the viscous models with the non-viscous one through the graph plotted between scale factor and cosmic time and find that bulk viscosity plays the major role in the expansion of the universe. A similar graph is plotted for deceleration parameter with non-viscous and viscous fluids and find a transition from decelerated to accelerated phase with some form of bulk viscosity.Comment: 19 pages, 3 figures, the whole paper has been revised to improve the quality of paper. Some references added. arXiv admin note: text overlap with arXiv:1307.4262 by other author