Search results for "Linear analysis"

The Egan problem on the pull-in range of type 2 PLLs

2021

In 1981, famous engineer William F. Egan conjectured that a higher-order type 2 PLL with an infinite hold-in range also has an infinite pull-in range, and supported his conjecture with some third-order PLL implementations. Although it is known that for the second-order type 2 PLLs the hold-in range and the pull-in range are both infinite, the present paper shows that the Egan conjecture may be not valid in general. We provide an implementation of the third-order type 2 PLL, which has an infinite hold-in range and experiences stable oscillations. This implementation and the Egan conjecture naturally pose a problem, which we will call the Egan problem: to determine a class of type 2 PLLs for …

3D Data Acquisition and Numerical Analysis of a Footwear in Walking

2004

The aim of the paper is to set a procedure to study the load history of a footwear during a step with non-linear FE analysis. The geometric model tested was reconstructed from a real shoe by means of Reverse Engineering process, starting from dense point clouds acquired by non-contact scanning system. For each phase of the walk, the pressure values are obtained by a pressure distribution platform when tester is walking along the platform. The Finite Element model is easily generated by Hypermesh software using the CAD model. Ansys software is used to perform non-linear analyses. The procedure can be employed for improving the product performance in terms of durability, flexibility and comfo…

Numerical seismic performance of a rammed earth dwelling considering the use of a textile reinforced mortar system

Rammed earth buildings represent a considerable portion of the existing vernacular building stock of several countries and they are very common in the southern region of Portugal. The historical and architectural values of these constructions, along with their recognized high seismic vulnerability, have made the structural rehabilitation of earthen buildings a priority among the scientific community. Despite some recent studies, the prediction of the seismic response of these buildings is still a challenging task. This paper presents the results of a numerical investigation on the seismic behaviour of a representative rammed earth building located in Alentejo (South of Portugal). Numerical …

Pattern formation driven by cross-diffusion

2009

In this work we are interested in describing the mechanism of pattern formation for a reaction-diffusion system with nonlinear diffusion terms (which take into account the self and the cross-diffusion effects). The reaction terms are chosen of the Lotka-Volterra type in the competitive interaction case. The cross-diffusion is proved to be the key mechanism of pattern formation via a linear stability analysis. A weakly nonlinear multiple scales analysis is carried out to predict the amplitude and the form of the pattern close to the bifurcation threshold. In particular, the Stuart-Landau equation which rules the evolution of the amplitude of the most unstable mode is found. In the subcritica…

Seismic Behavior of Lisbon Mixed Masonry-RC Buildings With Historical Value: A Contribution for the Practical Assessment

2018

The fact that linear analysis is still the most used procedure in the design engineering offices, studies which addresses issues associated to the estimation of the structural behavior factor values are relevant. In this study, the behavior factor of a particular type of mixed masonry-reinforced concrete buildings in Lisbon is estimated. The typology chosen in this study represents 30% of building stock in Lisbon; these buildings were built between 1930 and 1960 and thus were designed without considering the seismic-design requirements proposed in current codes. The evaluation of the behavior factors was based on the use of nonlinear static analyses, performed in the form of the sensitivity…

Cross-diffusion driven instability for a nonlinear reaction-diffusion system

2008

In this work we investigate the possibility of the pattern formation for a system of two coupled reaction-diffusion equations. The nonlinear diffusion terms has been introduced to describe the tendency of two competing species to diffuse faster (than predicted by the usual linear diffusion) toward lower densities areas. The reaction terms are chosen of the Lotka-Volterra type in the competitive interaction case. The system is supplemented with the initial conditions and no-flux boundary conditions. Through a linear stability analysis we find the conditions which allow a homogeneous steady state (stable for the kinetics) to become unstable through a Turing mechanism. In particular, we show h…

Harmonic balance analysis of pull-in range and oscillatory behavior of third-order type 2 analog PLLs

2020

The most important design parameters of each phase-locked loop (PLL) are the local and global stability properties, and the pull-in range. To extend the pull-in range, engineers often use type 2 PLLs. However, the engineering design relies on approximations which prevent a full exploitation of the benefits of type 2 PLLs. Using an exact mathematical model and relying on a rigorous mathematical thinking this problem is revisited here and the stability and pull-in properties of the third-order type 2 analog PLLs are determined. Both the local and global stability conditions are derived. As a new idea, the harmonic balance method is used to derive the global stability conditions. That approach…

Computation of lock-in range for classic PLL with lead-lag filter and impulse signals

2016

For a classic PLL with square waveform signals and lead-lag filter for all possible parameters lock-in range is computed and corresponding diagrams are given. peerReviewed

Hold-in, Pull-in and Lock-in Ranges for Phase-locked Loop with Tangential Characteristic of the Phase Detector

2019

In the present paper the phase-locked loop (PLL), an electric circuit widely used in telecommunications and computer architectures is considered. A new modification of the PLL with tangential phase detector characteristic and active proportionally-integrating (PI) filter is introduced. Hold-in, pull-in and lock-in ranges for given circuit are studied rigorously. It is shown that lock-in range of the new PLL model is infinite, compared to the finite lock-in range of the classical PLL. peerReviewed

Non-linear analysis of a modified QPSK Costas loop

2019

A Costas loop is one of the classical phase-locked loop based circuits, which demodulates data and recovers carrier from the input signal. The Costas loop is essentially a nonlinear control system and its nonlinear analysis is a challenging task. In this article for a modified QPSK Costas loop we analyze the hold-in, pull-in and lock-in ranges. New procedure for estimation of the lock-in range is considered and compared with previously known approach. peerReviewed