Analyzing the effect of the phase-jitter in the operation of second order phase-locked loops

Phase-locked loops (PLLs) are designed to extract timing signals in telecommunication networks. Noise, cross-talk, inter-symbol interference, quantization noise, and signal distortion are responsible for oscillations in the time between two successive transitions of the clock or data signal. It appears as an accidental phase modulation superposed to the original signal. This phenomenon is called timing jitter and affects the integrity of the data recovering process and, as a consequence, the error bit rate is increased. This problem has been studied by treating the jitter as a band limited noise process and tolerance masks for the jitter amplitude and frequency are recommended for several network architectures. Here, we develop a simple model with the continuous phase deviations of the clock signals considered as periodic signals in the band of the real disturbances. Comparisons with the stochastic approach are presented.     

Conditional targeting for communication

In this work we propose the use of a targeting method applied to chaotic systems in order to reach special trajectories that encode arbitrary sources of messages. One advantage of this procedure is to overcome dynamical constraints which impose limits in the amount of information that the chaotic trajectories can encode. Another advantage is the message decoding, practically instantaneous and independent of any special technique or algorithm. Furthermore, with this procedure, information can be transmitted with no errors due to bounded noise.     

Synchronous states in time-delay coupled periodic oscillators: A stability criterion

There are several works showing that nonzero time delay between nodes in an oscillator network can be responsible for several kinds of behavior as synchronization and chaos. Here, by using the Lyapunov linearizing method, in a system of two coupled oscillators derived as a particular case of the full connected network, it is shown that the time delay parameter has two sets of values: one that destabilizes the whole system and other that implies stability. Besides, there is a set of time delay values responsible for chaotic behaviors, even in a simple coupled oscillators system.     

A non-ideal portal frame energy harvester controlled using a pendulum

A model of energy harvester based on a simple portal frame structure is presented. The system is considered to be non-ideal system (NIS) due to interaction with the energy source, a DC motor with limited power supply and the system structure. The nonlinearities present in the piezoelectric material are considered in the piezoelectric coupling mathematical model. The system is a bi-stable Duffing oscillator presenting a chaotic behavior. Analyzing the average power variation, and bifurcation diagrams, the value of the control variable that optimizes power or average value that stabilizes the chaotic system in the periodic orbit is determined. The control sensitivity is determined to parametric errors in the damping and stiffness parameters of the portal frame. The proposed passive control technique uses a simple pendulum to tuned to the vibration of the structure to improve the energy harvesting. The results show that with the implementation of the control strategy it is possible to eliminate the need for active or semi active control, usually more complex. The control also provides a way to regulate the energy captured to a desired operating frequency.     

Architectures,stability and optimization for clock distribution networks

Synchronous telecommunication networks, distributed control systems and integrated circuits have its accuracy of operation dependent on the existence of a reliable time basis signal extracted from the line data stream and acquirable to each node. In this sense, the existence of a sub-network (inside the main network) dedicated to the distribution of the clock signals is crucially important. There are different solutions for the architecture of the time distribution sub-network and choosing one of them depends on cost, precision, reliability and operational security. In this work we expose: (i) the possible time distribution networks and their usual topologies and arrangements. (ii) How parameters of the network nodes can affect the reachability and stability of the synchronous state of a network. (iii) Optimizations methods for synchronous networks which can provide low cost architectures with operational precision, reliability and security.     

Modeling and measuring double-frequency jitter in one-way master–slave networks

The double-frequency jitter is one of the main problems in clock distribution networks. In previous works, some analytical and numerical aspects of this phenomenon were studied and results were obtained for one-way master-slave (OWMS) architectures. Here, an experimental apparatus is implemented, allowing to measure the power of the double-frequency signal and to confirm the theoretical conjectures.     

Optimized network structure for full-synchronization

A network of Kuramoto oscillators with different natural frequencies is optimized for enhanced synchronizability. All node inputs are normalized by the node connectivity and some important properties of the network structure are determined in this case: (i) optimized networks present a strong anti-correlation between natural frequencies of adjacent nodes; (ii) this anti-correlation should be as high as possible since the average path length between nodes is maintained as small as in random networks; and (iii) high anti-correlation is obtained without any relation between nodes natural frequencies and the degree of connectivity. We also propose a network construction model with which it is shown that high anti-correlation and small average paths may be achieved by randomly rewiring a fraction of the links of a totally anti-correlated network, and that these networks present optimal synchronization properties.     

Two-way master-slave double-chain networks: limitations imposed by linear master drift for second order PLLs as slave nodes

Distribution of precise time signals among the nodes of a network is a fundamental requirement for digital transmission and switching systems in telecommunication and control. Cideciyan et al., (1987) conjectured that two-way master-slave (TWMS) networks present, in the general case, a better performance than one-way master-slave (OWMS) considering the long term linear master frequency drift. In this work we study the TWMS case using dynamical system theory showing that, due to the effects of long-term clock instabilities, the steady-state frequency-error is unstable for a number of slaves higher or equal than four, limiting the use of this kind of architecture.     

Estimating the critical number of slave nodes in a single-chain PLL network

The existence and stability conditions for the synchronous state in telecommunication networks with single-chain master-slave clock distribution architecture are determined. The slave nodes are modeled as first-order phase-locked loops (PLLs) and the signal processing and propagation delays are taken into account. We analytically show that if the number of slaves exceeds a critical value, synchronization is unreachable.     

Extending SDL and LMC complexity measures to quantum states

An extension of SDL (Shiner, Davison, Landsberg) and LMC (López-Ruiz, Mancini, Calbet) complexity measures is proposed for the quantum information context, considering that Von Neumann entropy is a natural disorder quantifier for quantum states. As a first example of application, the simple qubit was studied, presenting results similar to that obtained by applying SDL and LMC measures to a classical probability distribution. Then, for the Werner state, a mixture of Bell states, SDL and LMC measures were calculated, depending on the mixing factor γ$\gamma$, providing some conjectures concerning quantum systems.