scholarly journals Fully Connected PLL Networks: How Filter Determines the Number of Nodes

2009 ◽  
Vol 2009 ◽  
pp. 1-13 ◽  
Author(s):  
Átila Madureira Bueno ◽  
André Alves Ferreira ◽  
José Roberto C. Piqueira

Synchronization plays an important role in telecommunication systems, integrated circuits, and automation systems. Formerly, the masterslave synchronization strategy was used in the great majority of cases due to its reliability and simplicity. Recently, with the wireless networks development, and with the increase of the operation frequency of integrated circuits, the decentralized clock distribution strategies are gaining importance. Consequently, fully connected clock distribution systems with nodes composed of phase-locked loops (PLLs) appear as a convenient engineering solution. In this work, the stability of the synchronous state of these networks is studied in two relevant situations: when the node filters are first-order lag-lead low-pass or when the node filters are second-order low-pass. For first- order filters, the synchronous state of the network shows to be stable for any number of nodes. For second-order filter, there is a superior limit for the number of nodes, depending on the PLL parameters.

2008 ◽  
Vol 2008 ◽  
pp. 1-13 ◽  
Author(s):  
José R. C. Piqueira ◽  
Maurízio Q. de Oliveira ◽  
Luiz H. A. Monteiro

Synchronization is an essential feature for the use of digital systems in telecommunication networks, integrated circuits, and manufacturing automation. Formerly, master-slave (MS) architectures, with precise master clock generators sending signals to phase-locked loops (PLLs) working as slave oscillators, were considered the best solution. Nowadays, the development of wireless networks with dynamical connectivity and the increase of the size and the operation frequency of integrated circuits suggest that the distribution of clock signals could be more efficient if distributed solutions with fully connected oscillators are used. Here, fully connected networks with second-order PLLs as nodes are considered. In previous work, how the synchronous state frequency for this type of network depends on the node parameters and delays was studied and an expression for the long-term frequency was derived (Piqueira, 2006). Here, by taking the first term of the Taylor series expansion for the dynamical system description, it is shown that for a generic network withNnodes, the synchronous state is locally asymptotically stable.


2014 ◽  
Vol 986-987 ◽  
pp. 377-382 ◽  
Author(s):  
Hui Min Gao ◽  
Jian Min Zhang ◽  
Chen Xi Wu

Heuristic methods by first order sensitivity analysis are often used to determine location of capacitors of distribution power system. The selected nodes by first order sensitivity analysis often have virtual high by first order sensitivities, which could not obtain the optimal results. This paper presents an effective method to optimally determine the location and capacities of capacitors of distribution systems, based on an innovative approach by the second order sensitivity analysis and hierarchical clustering. The approach determines the location by the second order sensitivity analysis. Comparing with the traditional method, the new method considers the nonlinear factor of power flow equation and the impact of the latter selected compensation nodes on the previously selected compensation location. This method is tested on a 28-bus distribution system. Digital simulation results show that the reactive power optimization plan with the proposed method is more economic while maintaining the same level of effectiveness.


Perception ◽  
10.1068/p5348 ◽  
2005 ◽  
Vol 34 (4) ◽  
pp. 501-510 ◽  
Author(s):  
Mark E McCourt

The magnitudes of two suprathreshold lateral spatial-interaction effects—grating induction and contrast–contrast—were compared with regard to their dependence upon inducing-grating spatial frequency. Both effects cause the contrast of target stimuli embedded in surrounding patterns to be matched nonveridically. The magnitudes of each effect were measured in a common unit that indexed the degree of nonveridical contrast matching across a large range of target-grating contrasts (±0.80). Grating induction was a low-pass effect with respect to spatial frequency, whereas contrast–contrast was bandpass, peaking at approximately 4.0 cycles deg−1. The magnitude of grating induction exceeded that of contrast – contrast, both overall and at their optimal frequencies (0.03125 and 4.0 cycles deg−1, respectively); the two effects are equipotent at an inducing-grating spatial frequency of 1.0 cycle deg−1. A significant negative correlation between the magnitudes of the two effects suggests a link whereby activation of second-order normalization mechanisms may inhibit first-order mechanisms.


VLSI Design ◽  
2001 ◽  
Vol 13 (1-4) ◽  
pp. 257-264
Author(s):  
Magnus Willander ◽  
Yevgeny Mamontov ◽  
Jonathan Vincent

The second-order nonrandom ordinary differential equation (ODE) system derived as the noise-source-aware model for expectations of solutions of Itô's stochastic differential equation (ISDE) system is discussed in connection with large-scale integrated circuits (ICs). The work explains the reason why the new model consistently allows for the noise-induced phenomena in the expectations, namely, stochastic resonance, stochastic linearization, stochastic self-oscillations and stochastic chaos. The case of stochastic resonance is considered as an example. In spite of the fact that the above second-order model is more complex than the nonrandom first-order IC ODE system for the expectations commonly used in engineering, an efficient practical technique for its implementation is proposed. The corresponding predicted computing time is only in 2.5 times greater than in the case of the first-order model which does not include any noise-source influence upon the expectations of the modelled IC responses.


Author(s):  
Átila Madureira Bueno ◽  
Angelo Marcelo Tusset ◽  
Diego Paolo Ferruzzo Correa ◽  
José Roberto Castilho Piqueira ◽  
José Manoel Balthazar

Synchronization plays an important role in telecommunication systems and integrated circuits. The Master-Slave is a commonly used strategy for clock signal distribution. However, due to the wireless networks development and the higher operation frequency of integrated circuits, the Mutually-Connected clock distribution strategies are becoming important, and the Fully-Connected strategy appears as a convenient engineering solution. The main drawback of the Fully-Connected architecture is the definition of control algorithms that assure the stability of the network sinchronization. In hybrid synchronization techniques groups of nodes synchronized by the Fully-Connected architecture are synchronized with network master clocks by using the Master-Slave tecnique. In this arrangement, if a route of clock signal distribution becomes inoperative, the group of Fully-Connected nodes retain for some time the original phase and frequency received from the network. The Fully-Connected architecture complexity imposes difficulties to satisfy both stability and performance requirements in the control system design. For that reason the multi-variable LQG/LTR and the SDRE control techniques are applied in order to fulfill both stability and performance requirements. The performance of both techniques are compared, and the results seems to confirm the improvement in the transient response and in the precision of the clock distribution process.


2006 ◽  
Vol 2006 ◽  
pp. 1-12 ◽  
Author(s):  
J. R. C. Piqueira ◽  
M. Q. Oliveira ◽  
L. H. A. Monteiro

Fully connected phase-locked networks are built with all nodes exchanging phase and frequency signals. The nodes are phase-locked loops (PLLs) with slightly different free-running frequencies. The synchronous state emerges from a dynamic process with the phase interactions generating a common frequency steady state. In this work, an estimation is analytically obtained for the synchronous state in a genericN-node network. Numerical experiments complete the analysis of the fully connected network relating free-running frequencies, node gains, and propagation delays.


2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
José Roberto C. Piqueira

Since phase-locked loops (PLLs) were conceived by Bellescize in 1932, their presence has become almost mandatory in any telecommunication device or network, being the essential element to recover frequency and phase information. As the technology developed, PLL appeared in several applications, such as, dense communication networks, smart grids, electronic instrumentation, computational clusters, and integrated circuits. In all of these practical cases, isolated or networked PLLs are responsible for recovering the correct time basis and synchronizing the processes. According to the application needs, different clock distribution strategies were developed, with the master-slave being the simplest and most used choice. Considering that the master clock is obtained from a stable periodic oscillator, two topologies are studied: one-way, not considering clock feedback; and two-way master-slave, with the slave nodes providing clock feedback to the master. Here, these two cases are studied by using simulation strategies, presenting results about the clock signal recovery process in the presence of disturbances, indicating that master-slave clock distribution networks can be useful for networks with few nodes and a stable master oscillator with the one-way topology presenting better results than the two-way arrangement.


1997 ◽  
Vol 36 (04/05) ◽  
pp. 315-318 ◽  
Author(s):  
K. Momose ◽  
K. Komiya ◽  
A. Uchiyama

Abstract:The relationship between chromatically modulated stimuli and visual evoked potentials (VEPs) was considered. VEPs of normal subjects elicited by chromatically modulated stimuli were measured under several color adaptations, and their binary kernels were estimated. Up to the second-order, binary kernels obtained from VEPs were so characteristic that the VEP-chromatic modulation system showed second-order nonlinearity. First-order binary kernels depended on the color of the stimulus and adaptation, whereas second-order kernels showed almost no difference. This result indicates that the waveforms of first-order binary kernels reflect perceived color (hue). This supports the suggestion that kernels of VEPs include color responses, and could be used as a probe with which to examine the color visual system.


2017 ◽  
Vol 9 (3) ◽  
pp. 17-30
Author(s):  
Kelly James Clark

In Branden Thornhill-Miller and Peter Millican’s challenging and provocative essay, we hear a considerably longer, more scholarly and less melodic rendition of John Lennon’s catchy tune—without religion, or at least without first-order supernaturalisms (the kinds of religion we find in the world), there’d be significantly less intra-group violence. First-order supernaturalist beliefs, as defined by Thornhill-Miller and Peter Millican (hereafter M&M), are “beliefs that claim unique authority for some particular religious tradition in preference to all others” (3). According to M&M, first-order supernaturalist beliefs are exclusivist, dogmatic, empirically unsupported, and irrational. Moreover, again according to M&M, we have perfectly natural explanations of the causes that underlie such beliefs (they seem to conceive of such natural explanations as debunking explanations). They then make a case for second-order supernaturalism, “which maintains that the universe in general, and the religious sensitivities of humanity in particular, have been formed by supernatural powers working through natural processes” (3). Second-order supernaturalism is a kind of theism, more closely akin to deism than, say, Christianity or Buddhism. It is, as such, universal (according to contemporary psychology of religion), empirically supported (according to philosophy in the form of the Fine-Tuning Argument), and beneficial (and so justified pragmatically). With respect to its pragmatic value, second-order supernaturalism, according to M&M, gets the good(s) of religion (cooperation, trust, etc) without its bad(s) (conflict and violence). Second-order supernaturalism is thus rational (and possibly true) and inconducive to violence. In this paper, I will examine just one small but important part of M&M’s argument: the claim that (first-order) religion is a primary motivator of violence and that its elimination would eliminate or curtail a great deal of violence in the world. Imagine, they say, no religion, too.Janusz Salamon offers a friendly extension or clarification of M&M’s second-order theism, one that I think, with emendations, has promise. He argues that the core of first-order religions, the belief that Ultimate Reality is the Ultimate Good (agatheism), is rational (agreeing that their particular claims are not) and, if widely conceded and endorsed by adherents of first-order religions, would reduce conflict in the world.While I favor the virtue of intellectual humility endorsed in both papers, I will argue contra M&M that (a) belief in first-order religion is not a primary motivator of conflict and violence (and so eliminating first-order religion won’t reduce violence). Second, partly contra Salamon, who I think is half right (but not half wrong), I will argue that (b) the religious resources for compassion can and should come from within both the particular (often exclusivist) and the universal (agatheistic) aspects of religious beliefs. Finally, I will argue that (c) both are guilty, as I am, of the philosopher’s obsession with belief. 


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