Using bifurcations in the determination of lock-in ranges for third-order phase-locked loops

2009 ◽  
Vol 14 (5) ◽  
pp. 2328-2335 ◽  
Author(s):  
José Roberto Castilho Piqueira
Keyword(s):  
Phase Locked Loops ◽  
Third Order ◽  
Lock In

scholarly journals Models for Master-Slave Clock Distribution Networks with Third-Order Phase-Locked Loops

2007 ◽  
Vol 2007 ◽  
pp. 1-17 ◽  
Author(s):  
José Roberto Castilho Piqueira ◽  
Marcela de Carvalho Freschi
Keyword(s):  
Numerical Experiments ◽  
Phase Synchronization ◽  
Distribution Networks ◽  
Phase Locked Loops ◽  
Clock Distribution ◽  
Third Order ◽  
Clock Distribution Networks ◽  
Priority Scheme ◽  
Geographically Distributed ◽  
Lock In

The purpose of this work is to study the processing and transmission of clock signals in networks of geographically distributed nodes, in order to derive conditions for frequency and phase synchronization between the nodes. The focus is on the master-slave architecture, which presents a priority scheme of clock distribution. One-way master-slave (OWMS ) and two-way master-slave (TWMS) chains are studied, considering that the slave nodes are third-order phase-locked loops (PLLs). Third-order PLLs are chosen to improve the transient response but, if their parameters are not well adjusted, stability problems and chaotic behaviors appear, restricting the lock-in range of the network. Lock-in range for third-order PLLs with Sallen-Key filter is determined and it is verified whether this range is reduced when the PLLs are connected to a network. Numerical experiments show how chain size changes the lock-in ranges and the acquisition times.

scholarly journals On the Gardner Problem for the Phase-Locked Loops

2019 ◽  
Vol 489 (6) ◽  
pp. 541-544
Author(s):  
N. V. Kuznetsov ◽  
M. Y. Lobachev ◽  
M. V. Yuldashev ◽  
R. V. Yuldashev
Keyword(s):  
Phase Space ◽  
Order System ◽  
Phase Locked Loops ◽  
Stability Criteria ◽  
Third Order ◽  
Classical Stability ◽  
Cylindrical Phase ◽  
Lock In ◽  
Cylindrical Phase Space

This report shows the possibilities of solving the Gardner problem of determining the lock-in range for multidimensional phase-locked loops systems. The development of analogs of classical stability criteria for the cylindrical phase space made it possible to obtain analytical estimates of the lock-in range for third-order system.

A multitechnique investigation of the second order NLO response of a 10,20-diphenylporphyrinato nickel(II) complex carrying a phenylethynyl based push-pull system in the 5- and 15-positions

2004 ◽  
Vol 08 (11) ◽  
pp. 1311-1324 ◽  
Author(s):  
Maddalena Pizzotti ◽  
Elisabetta Annoni ◽  
Renato Ugo ◽  
Silvia Bruni ◽  
Silvio Quici ◽  
...  
Keyword(s):  
Ab Initio ◽  
Planar Structure ◽  
Third Order ◽  
Incident Wavelength ◽  
Pull System ◽  
Nlo Response ◽  
Self Consistent ◽  
Order Of Magnitude ◽  
Zero Frequency

A multitechnique investigation of the determination of the order of magnitude of the second and third order NLO response of [5-[(4-dimethylaminophenyl)ethynyl]-15-[(4-nitrophenyl)ethynyl]-10,20-diphenylporphyrinato]nickel(II) (1) is reported with the aim to produce self consistent evidence for a significant NLO response of this kind of push-pull porphyrin chromophore. The experimental multitechnique approach is based on the EFISH technique, working with a non-resonant incident wavelength of 1.907 μm, on the solvatochromic method and finally on a vibrational method, avoiding any fluorescence or resonance interference. A theoretical MNDO-TDHF evaluation of the zero-frequency quadratic and cubic hyperpolarizabilities of an ab initio optimized planar structure is also reported. The order of magnitude of the quadratic hyperpolarizability of (1) at zero frequency (β0), was found to be significantly lower than that reported for the corresponding Cu (II) or Zn (II) complexes with the same push-pull porphyrin chromophore.

scholarly journals DETERMINATION OF THE ENERGY GAP OF C60 MOLECULE USING THIRD-ORDER DERIVATIVE ABSORPTION SPECTROSCOPY

1998 ◽  
Vol 47 (2) ◽  
pp. 208
Author(s):  
ZHAO MING-SHAN ◽  
DAI ZUO-XIAO ◽  
LI YI ◽  
LI GUO-HUA ◽  
BU YU-XIANG ◽  
...  
Keyword(s):  
Absorption Spectroscopy ◽  
Energy Gap ◽  
Order Derivative ◽  
Third Order

scholarly journals Computation of the lock-in ranges of phase-locked loops with PI filter

2016 ◽  
Vol 49 (14) ◽  
pp. 36-41 ◽  
Author(s):  
Konstantin D. Aleksandrov ◽  
Nikolay V. Kuznetsov ◽  
Gennady A. Leonov ◽  
Pekka Neittaanmäki ◽  
Marat V. Yuldashev ◽  
...  
Keyword(s):  
Phase Locked Loops ◽  
Lock In

scholarly journals A NEW VALIDATED THIRD ORDER DERIVATIVE SPECTROSCOPIC METHOD FOR SIMULTANEOUS ESTIMATION OF METOPROLOL SUCCINATE AND RAMIPRIL IN TABLET DOSAGE FORM

2020 ◽  
pp. 54-59
Author(s):  
ALEKHYA B. ◽  
M. SINDHUSHA ◽  
SORAJ K. RAUL ◽  
GOPAL K. PADHY
Keyword(s):  
Quantitative Analysis ◽  
Dosage Form ◽  
Spectroscopic Method ◽  
Simultaneous Estimation ◽  
Third Order ◽  
Metoprolol Succinate ◽  
Zero Crossing ◽  
Ich Guidelines ◽  
Tablet Dosage

Objective: The objective of the present work is to develop and validate a new UV derivative spectrophotometric method for simultaneous estimation of metoprolol succinate and ramipril in methanol: water (50:50v/v). Methods: “Zero crossing technique” was chosen for quantitative determination. The zero-crossing points (ZCP’s) were found to be 209 nm where metoprolol succinate was quantified and 211 nm where ramipril was quantified. This method was then subjected to accuracy, linearity, sensitivity and reproducibility according to ICH guidelines to ensure and confirm its validity. Results: The method was found to be obeying Beer’s law in the range of 10-50 µg/ml and 5-25 µg/ml for metoprolol succinate and ramipril, respectively. The % recoveries were observed between the range of 99.2-100.2 for metoprolol succinate and 99.57-99.86 for ramipril. The intra-day and inter-day results showed reproducibility. Conclusion: It can be concluded that the developed third-order UV derivative spectroscopic method for the simultaneous determination of metoprolol succinate and ramiprilcan be recommended for routine quantitative analysis.

Determination of Nonchaotic Behavior for Some Classes of Polynomial Jerk Equations

2020 ◽  
Vol 30 (08) ◽  
pp. 2050117
Author(s):  
Marcelo Messias ◽  
Rafael Paulino Silva
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Simple Form ◽  
Chaotic Dynamics ◽  
Third Order ◽  
Algebraic Criterion

In this work, by using an algebraic criterion presented by us in an earlier paper, we determine the conditions on the parameters in order to guarantee the nonchaotic behavior for some classes of nonlinear third-order ordinary differential equations of the form [Formula: see text] called jerk equations, where [Formula: see text] is a polynomial of degree [Formula: see text]. This kind of equation is often used in literature to study chaotic dynamics, due to its simple form and because it appears as mathematical model in several applied problems. Hence, it is an important matter to determine when it is chaotic and also nonchaotic. The results stated here, which are proved using the mentioned algebraic criterion, corroborate and extend some results already presented in literature, providing simpler proofs for the nonchaotic behavior of certain jerk equations. The algebraic criterion proved by us is quite general and can be used to study nonchaotic behavior of other types of ordinary differential equations.

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