# Analytical methods for computation of phase-detector characteristics and PLL design

@article{Kuznetsov2011AnalyticalMF, title={Analytical methods for computation of phase-detector characteristics and PLL design}, author={Nikolay V. Kuznetsov and Gennady A. Leonov and Marat V. Yuldashev and Renat V. Yuldashev}, journal={ISSCS 2011 - International Symposium on Signals, Circuits and Systems}, year={2011}, pages={1-4} }

An effective analytical methods for computation of phase detector characteristics are suggested. For high-frequency oscillators new classes of such characteristics are described. Approaches to a rigorous nonlinear analysis of PLL are discussed.

## 16 Citations

Analytical Method for Computation of Phase-Detector Characteristic

- Computer ScienceIEEE Transactions on Circuits and Systems II: Express Briefs
- 2012

Approaches to a rigorous nonlinear analysis of analog PLL with multiplier phase detector (classical PLL) and linear filter and an effective analytical method for computation of multiplier/mixer phase-detector characteristics is proposed.

Phase-frequency Domain Model of Costas Loop with Mixer Discriminator

- Physics, Computer ScienceICINCO
- 2013

The analytical method for phase detectors characteristics computation is proposed and new classes of phase detector characteristics are computed for the first time.

Simulation of phase-locked loops in phase-frequency domain

- Computer Science2012 IV International Congress on Ultra Modern Telecommunications and Control Systems
- 2012

Simulation of classical phase-locked loop in phase space for general types of signal waveforms is done based on new analytical method for computation of phase detector characteristics (PD), which enables to avoid a number of numerical problems in the simulation of PLL in signal.

Nonlinear analysis of classical phase-locked loops in signal's phase space

- Mathematics
- 2014

Abstract Discovery of undesirable hidden oscillations, which cannot be found by the standard simulation, in phase-locked loop (PLL) showed the importance of consideration of nonlinear models and…

Nonlinear Analysis of Costas Loop Circuit

- Computer ScienceICINCO
- 2012

The analytical method for phase detector characteristics computation is proposed and new c lasses of phase detectors characteristics are computed for the first time.

Nonlinear Analysis of Phase-Locked Loop with Squarer

- Mathematics, Computer SciencePSYCO
- 2013

For various waveforms of high-frequency signals new classes of phase detector characteristics are computed for the first time in a classical phase-locked loop with squarer based carrier recovery circuit.

Nonlinear mathematical models of Costas Loop for general waveform of input signal

- Computer Science2012 IEEE 4th International Conference on Nonlinear Science and Complexity (NSC)
- 2012

This article provides mathematical model of Costas Loop circuit for wide range of signal waveforms using nonlinear phase domain model of PLL with special phase detector characteristics to avoid a number of numerical problems in the simulation of costas Loop in signal domain.

Differential equations of Costas loop

- 2012

It is well known, that to effectively simulate and investigate PLL systems, nonlinear mathematical model has to be derived. This article provides mathematical model of Costas Loop circuit for wide…

Hidden oscillations in SPICE simulation of two-phase Costas loop with non-linear VCO

- Engineering
- 2016

Abstract Simulation is widely used for analysis of Costas loop based circuits. However it may be a non-trivial task, because incorrect choice of integration parameters may lead to qualitatively wrong…

Tutorial on dynamic analysis of the Costas loop

- Computer Science, MathematicsAnnu. Rev. Control.
- 2016

The lock-in range of the Costas loop for the case where a lead-lag filter is used for the loop filter is analyzed and equations for the above mentioned key parameters are derived.

## References

SHOWING 1-10 OF 30 REFERENCES

Asymptotic Analysis of Phase Control System for Clocks in Multiprocessor Arrays

- Computer ScienceICINCO
- 2010

New method for the rigorous mathematical analysis of electronic synchronization systems is suggested. This method allows to calculate the characteristics of phase detectors and carry out a rigorous…

Nonlinear analysis of the Costas loop and phase-locked loop with squarer

- 2012

This work is devoted to the nonlinear analysis of the Costas loop and phase-locked loop with squarer. By using the special asymptotical methods for analysis of high-frequency harmonic and impulse…

Stability and bifurcations of Phase-Locked Loops for Digital Signal Processors

- Computer ScienceInt. J. Bifurc. Chaos
- 2005

For continuous and discrete floating phase-locked loops, conditions of local and global stability are obtained and the results obtained are applied to the solution of the problem of eliminating the clock skew in digital signal processors.

Phase Locked Loops Design and Analysis

- Mathematics, Computer ScienceICINCO-SPSMC
- 2008

The rigorous mathematical formulation of the Costas loop for the clock oscillators are obtained and the block diagram of oating PLL for the elimination of clock skew and that of frequency synthesizer is proposed.

Phase synchronization: Theory and applications

- Mathematics
- 2006

The state-of-the-art of the phase synchronization theory was reviewed. Consideration was given to its applications to the synchronous and induction electrical motors, phase locked loops, and…

Stability Analysis of Nonlinear Microwave Circuits

- Physics
- 2003

Steady-State Solutions on Nonlinear Circuits. Nonlinear Analysis Techniques. Global Stability Analysis of Nonlinear Circuits. Global Stability Analysis of Microwave Circuits. Bifurcation Routes to…

Phase-locked loops: a control centric tutorial

- Computer ScienceProceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301)
- 2002

Presents a tutorial on phase-locked loops from a control systems perspective. It starts with an introduction of the loop as a feedback control problem, with both the similarities and differences to…

Analysis and Design of Computer Architecture Circuits with Controllable Delay Line

- Computer ScienceICINCO-SPSMC
- 2009

In the work it is mathematically strictly shown that RC-chain can be used as a controllable delay line for different problems of circuit engineering if the chain is sequentially connected with hysteretic relay.

Algorithm for constructing counterexamples to the Kalman problem

- Mathematics
- 2010

The method of harmonic linearization and describing function method, numerical methods, and the applied bifurcation theory together discover new opportunities for analysis of hidden periodic…

Theory of the Non-linear Analog Phase Locked Loop

- Computer Science
- 2004

This chapter discusses First Order PLL Components, which consists of the Following: First Order Loop Main Synchronization Third Harmonic Synchronized, Second Order Type-I PLL, and Third order Type-II PLL.