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This paper addresses the problem of the stability and the performance analysis of N-nodes cartesian networks of self-sampled all digital phase-locked loops. It can be demonstrated that under certain conditions (such as proper filter coefficient values), a global and a local synchronization can be obtained. Our approach to find the optimal conditions consists of analyzing a corresponding linear average...
This paper considers the analysis and the design of an array of two NMOS differential oscillators coupled through a resistor. A new writing of the nonlinear equations proposed by R. York to describe the oscillators' locked states but limited for the specific case of a resistive coupling is presented. The new system permits the calculation of the free-running frequencies of the oscillators when a specific...
Networks made up of bio-inspired neuron oscillatory circuits with nanoscale memristors may achieve the large connectivity and highly parallel processing power of biological systems. Memristor also has potential to reproduce the behavior of a biological synapse. As in a living creature the weight of a synapse is adapted by ionic flow through it, so the conductance of a memristor is controlled by flux...
FFT-IFFT configuration, or more generally a forward-inverse orthogonal transform pair, offers a way to implement a digital filter whose frequency-domain characteristics can be straightforwardly tuned by adjusting the complex gains of the frequency bins. Using filter banks (FBs) for the transform pair, sharp transition bands can be obtained for low-pass/bandpass/highpass type filter designs. However,...
For designing oscillatory circuit, it is important to simulate and search the characteristics. If we analyze a weakly nonlinear circuit, we often apply averaging method which is one of the approximate solving method. In this study, we combine the averaging method to Newton homotopy method and analyze a circuit by using Spice. By solving Newton homotopy method, we obtain multiple equilibrium points...
A new cyclic ADC structure achieving capacitor mismatch insensitivity is presented. This technique enables cyclic ADC to obtain a very precise residue voltage in cycles independent of matching of capacitors. In addition, this new structure saves the die area of capacitors in the switched capacitor network by 25% and significantly reduces power consumption by up to 40%. A 12-bit 1.67MS/s cyclic ADC...
This paper describes an original experimental procedure to extract the oscillator's phase sensitivity to injected noise perturbations. The proposed method relies on measuring the width of the locking ranges over which the oscillator's response synchronizes with an injected small-amplitude signal. The extraction procedure is applied to a relaxation oscillator which exhibits a strongly nonlinear behavior.
Coupled oscillatory systems are suitable to express synchronization phenomena, and it is important to unveil nonlinear phenomena. In this study, we investigate the synchronization phenomena observed in four coupled van der Pol oscillators as a regular tetrahedron form. We observe the rotation of the phase difference between anti-phase state and asynchonization state. Furthermore, the sojourn time...
In this study, synchronization phenomena observed in coupled polygonal oscillatory networks with frustration is investigated. In this oscillatory system, dilemma is created by the shared branch. We investigate the phase difference between adjacent oscillators when the number of oscillators connected to one side of the polygonal network is increased for considering the large-scale oscillatory networks.
We investigate a system of mutually coupled three neurons in a line with the inhibitory synapses as a basic motif of complex networks. For class I and class II neurons, bifurcation structure is analyzed when we change the external DC current of a middle neuron. In both classes, the neurons have a wide parameter region in which stable 1∶2 cluster synchronous firing is observed as the external DC current...
We present a nonlinear analysis of differential LC injection-locked frequency dividers (ILFDs) operating at high-level injection regime. We derive the general second-order equation which describes their behaviour and its approximate solution in explicit form, by solving the shortened equations for the amplitude and phase of the synchronized oscillation. These equations are obtained by the classical...
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