Now showing 1 - 10 of 17
  • Publication
    Averaging Techniques for the Analysis of Event Driven Models of All Digital PLLs
    In this paper, we introduce a statistical approach for studying a special class of nonlinear dynamical systems such as ADPLLs and ADPLL networks, where the process driving the adjustment of the DCO frequency can be seen as ΣΔ modulation. We showed that, by applying the Frobenius-Perron operator to the governing equation, it is possible to find the invariant probability density which is valid for dynamically changing input of ΣΔ modulator. By using this, we show that the average behaviour of the corresponding complex system can be dramatically simplified and studied analytically.
      447Scopus© Citations 2
  • Publication
    Semianalytical model for high speed analysis of all-digital PLL clock-generating networks
    In this paper, we propose the model of a network consisting of All-Digital Phase-Locked Loop Network in application to Clock-Generating Systems. The method is based on a solution of a system of non-linear finite-difference stochastic equations and allows us to perform high speed simulations of a distributed Clock Network on arbitrary topology. The result of our analysis show a good agreement with experimental measurements of a 65nm CMOS All-Digital Phase-Locked Loop Network.
      437Scopus© Citations 3
  • Publication
    A Concept of Synchronous ADPLL Networks in Application to Small-Scale Antenna Arrays
    In this paper, we introduce a reconfigurable oscillatory network that generates a synchronous and distributed clocking signal. We propose an accurate model of the network to facilitate the study of its design space and ensure that it operates in its optimal, synchronous mode. The network is designed and implemented in a fully integrated 65-nm CMOS system-on-chip that utilizes coupled all digital phase locked loops interconnected as a Cartesian grid. The model and measurements demonstrate frequency and phase synchronization even in the presence of noise and random initial conditions. This network is proposed for small-scale multiple input multiple-output systems that require complete synchronization both in frequency and in phase.
      364Scopus© Citations 14
  • Publication
    Bifurcation Scenarios in Electrostatic Vibration Energy Harvesters
    In this paper, we present numerical bifurcation analysis of an electrostatic vibration energy harvester operating in constant-charge mode and using the in-plane gap closing transducer. We show how the system can be represented as a nonlinear oscillator and analysed using methods of nonlinear dynamics. We verify previous analytical theories and explain the behaviour of these energy harvesters, particularly in the regime between the first period doubling bifurcation and chaos.
      321
  • Publication
    Steady-State Oscillations in Resonant Electrostatic Vibration Energy Harvesters
    In this paper, we present a formal analysis and description of the steady-state behavior of an electrostatic vibration energy harvester operating in constant-charge mode and using different types of electromechanical transducers. The method predicts parameter values required to start oscillations, allows a study of the dynamics of the transient process, and provides a rigorous description of the system, necessary for further investigation of the related nonlinear phenomena and for the optimisation of converted power. We show how the system can be presented as a nonlinear oscillator and be analysed by the multiple scales method, a type of perturbation technique. We analyse two the most common cases of the transducer geometry and find the amplitude and the phase of steady-state oscillations as functions of parameters. The analytical predictions are shown to be in good agreement with the results obtained by behavioural modeling.
      734Scopus© Citations 32
  • Publication
    Combined mechanical and circuit nonlinearities in electrostatic vibration energy harvesters
    The aim of this paper is to study an electrostatic vibration energy harvester that utilises a nonlinear resonator. A vibration energy harvester represents a system where a mechanical resonator driven by ambient vibrations is coupled with a conditioning electronic circuit, which acts as a damper and converts mechanical energy into electrical. If a nonlinear resonator is embedded into the conditioning circuit, nonlinearity will appear from both mechanical and circuit components of the system. We expand the analytical approach that we developed in our previous works to the case of combined mechanical and circuit nonlinearities. This allow us to analyze steady-state behavior and compare it with the linear case. In addition, we discuss a specific nonlinear phenomena that is introduced by the discontinuity of the system — the sliding bifurcation. We show that the onset of steady-state quasi-harmonic oscillations occur through the disappearance of sliding motion.
      431Scopus© Citations 7
  • Publication
    Bifurcations and chaos in electrostatic vibration energy harvesters
    In this paper, we present an analysis of an electrostatic vibration harvester operating in the constant-charge mode. The goal of the study is to bound regions of control parameters where the system displays steady-state harmonic oscillations as required for practical use. We show how the system can be presented as a nonlinear oscillator and analysed employing the multiple scales method, Floquet theory and Lyapunov exponents. We determine the conditions for the onset of steady-state oscillations, the period doubling bifurcation and transition to chaos. This allows us to bound regions of control parameters where the system displays desired regular oscillations and, therefore, to identify maximal harvestable power for a particular architecture.
      531Scopus© Citations 10
  • Publication
    Tools for analytical and numerical analysis of electrostatic vibration energy harvesters: application to a continuous mode conditioning circuit
    This paper reports the application of different analytical tools to a basic continuous conditioning (CC) circuit for electrostatic vibration energy harvesters (e-VEHs). We address the fundamental issues of this conditioning circuit and give design advice that enhances the performance of e-VEHs employing this circuit. This circuit is widely used for harvesters with or without an electret layer. Despite its wide use, its fundamental problems have been weakly addressed even for simple configurations of e-VEHs since it is impossible to solve the corresponding equations in closed form. As a consequence, appropriate semi-analytical methods that provide an insight into the physics of the system are required.
      316Scopus© Citations 6
  • Publication
    Capacitive Energy Conversion with Circuits Implementing a Rectangular Charge-Voltage Cycle Part 1: Analysis of the Electrical Domain
    Capacitive kinetic energy harvesters (KEH) employ conditioning circuits which achieve a dynamic biasing of the transducer's variable capacitor. This paper, composed of two articles Part 1 and Part 2, proposes a unified theory describing electrical and electromechanical properties of an important and wide class of conditioning circuits: those implementing a rectangular charge-voltage cycle. The article Part 1 introduces a basic configuration of conditioning circuit implementing an ideal rectangular QV cycle, and discusses its known practical implementations: the Roundy charge pump with different flyback mechanisms, and configurations based on the Bennet's doubler. In Part 1, the analysis is done in the electrical domain, without accounting for electromechanical coupling, while in Part 2, the full electromechanical system is analyzed. An optimization approach common to all configurations is proposed. A comparison is made between different topologies and operation modes, based on the maximal energy converted in one cycle under similar electrical and mechanical conditions. The last section discusses practical implementation of circuits with smart and adaptive behavior, and presents experimental results obtained with state-of-the art MEMS capacitive KEH devices.
      534Scopus© Citations 40
  • Publication
    Capacitive Energy Conversion with Circuits Implementing a Rectangular Charge-Voltage Cycle Part 2: Electromechanical and Nonlinear Analysis
    In this paper, we explore and describe the electromechanical coupling which results in eKEH conditioning circuits implementing a rectangular QV cycle, including but not limited to the charge pump and Bennet’s doubler circuits. We present numerical and semi analytical analyses describing the nonlinear relationship between the oscillating mass and the conditioning circuit. We believe this is a poorly understood facet of the device and, as we will portray, effects the potential harvested energy. An approach to determine the frequency shift due to the electromechanical coupling is presented and compared with novel experimental results. We provide some examples of bifurcation behaviour and show that the only source of nonlinearity is in the coupling between the electrical and mechanical domains. This work continues from the electrical analysis presented in Part 1, providing a full insight into the complex behaviour of the electromechanical coupling.
      525Scopus© Citations 20