VCO sweep-rate limit for a phase-lock loop   总被引：1，自引：0，他引：1  

John Stensby 《Journal of The Franklin Institute》2009,346(3):223-236

Phase-lock loops (PLLs) serve important roles in phase-lock receivers, coherent transponders, and similar applications. For many of these uses, the bandwidth of the loop must be kept small to limit the detrimental influence of noise, and this requirement makes the natural PLL pull-in phenomenon too slow and/or unreliable. For each such case, the phase-lock acquisition process can be aided by the application of an external sweep voltage to the loop voltage controlled oscillators (VCOs). The goal is to have the applied sweep voltage rapidly decrease the closed-loop frequency error to a point where phase lock occurs quickly. For a second-order loop containing a perfect integrator loop filter, there is a maximum VCO sweep-rate magnitude, denoted here as R_m rad/s², for which phase lock is guaranteed. If the applied VCO sweep rate is less than R_m, the loop cannot sweep past a stable phase-lock point, and it will phase lock. On the other hand, for an applied sweep-rate magnitude that is greater than R_m, the PLL may sweep past a lock point and fail to phase lock. In the existing PLL literature, only a trial-and-error approach has been described for estimating R_m, given values of loop damping factor ζ and natural frequency ω_n. Furthermore, no plots exist of computed versus ζ and versus ζ (B_L denotes loop-noise bandwidth). These deficiencies are dealt with in this paper. A new iterative numerical technique is given that converges to the maximum sweep-rate magnitude R_m. It is used to generate data for plots of and versus ζ, the likes of which have never appeared before in the PLL literature.  相似文献   

Null controllability of some nonlinear degenerate 1D parabolic equations     

M.M. Cavalcanti  E. Fernández-Cara  A.L. Ferreira 《Journal of The Franklin Institute》2017,354(14):6405-6421

The main goal of the present paper is twofold: (i) to establish the well-posedness of a class of nonlinear degenerate parabolic equations and (ii) to investigate the related null controllability and decay rate properties. In a previous step, we consider an appropriate regularized system, where a small parameter α is involved. More precisely, the usual nonlinear term b(x)uu_x is replaced by b(x)zu_x, where $z={(\text{Id}.?{\alpha }^{2}A)}^{?1}u$ and A is a Poisson–Dirichlet operator. We investigate the behavior of the null controls and their associated states as α → 0.  相似文献   

On certain meromorphic p-valent starlike functions     

Muhammet Kamali 《Journal of The Franklin Institute》2007,344(6):867-872

A certain differential operator D^n+p is introduced for functions of the form