Now showing 1 - 10 of 17
  • 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.
      248
  • 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.
      581Scopus© Citations 29
  • 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.
      304Scopus© Citations 32
  • 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.
      388Scopus© Citations 18
  • 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.
      252Scopus© Citations 5
  • 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.
      299Scopus© Citations 2
  • Publication
    Mode-locking in a network of kuramoto-like oscillators
    In this paper we consider a network of phase oscillators. We develop the equations that model the time evolution of the phase of each oscillator in the network. The oscillator represents a modified Kuramoto oscillator and in this study we discuss how these modifications are obtained. In the context of this study, we use this network to model a network of PLLs for distributed clock applications. We analyse analytically and numerically the synchronisation modes of this system for different types of the coupling function. We show that depending on the properties of the coupling function, the network displays either multiple coexisting synchronisation modes or only a single synchronisation mode. While in the context of clock generation, multiple synchronisation modes coexisting in the system at the same parameters are a parasitic phenomenon. However in the context of other application such as associative memory models, mode-locking can be seen a useful phenomenon. The results provide a deeper understanding of globally synchronised clock networks with applications in microprocessor design.
      302Scopus© Citations 2
  • Publication
    Generation of a Clocking Signal in Synchronized All-Digital PLL Networks
    In this brief, we propose a discrete-time framework for the modeling and studying of all-digital phase-locked loop (ADPLL) networks with applications in clock-generating systems. The framework is based on a set of nonlinear stochastic iterating maps and allows us to study a distributed ADPLL network of arbitrary topology. We determine the optimal set of control parameters for the reliable synchronous clocking regime, taking into account the intrinsic noise from both local and reference oscillators. The simulation results demonstrate very good agreement with experimental measurements of a 65-nm CMOS ADPLL network. This brief shows that an ADPLL network can be synchronized both in frequency and phase. We show that for a large Cartesian network the average network jitter increases insignificantly with the size of the system.
      263Scopus© Citations 7
  • Publication
    Limit on Converted Power in Resonant Electrostatic Vibration Energy Harvesters
    Based on the formal analysis of a resonant electrostatic vibration energy harvester operating in constant-charge mode with a gap-closing transducer, we show that the system displays universal behaviour patterns. In this paper, we treat the harvester as a nonlinear forced oscillator and bound the area of control parameters where the system displays regular harmonic oscillations allowing the conditioning circuit to operate in the most effective mode. Before the system exhibits irregular behaviour, there exists a universal optimal value of normalised converted power regardless of the system design and control parameters.
      365Scopus© Citations 14
  • 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.
      224Scopus© Citations 13