** Using an
oscillator with fast startup allows shorter wake-up cycles and longer battery life compared to MEMS devices.
In general, there are various methods available to reduce the output noise of a ring
oscillator. Some of these methods are intended to lower the effect of a specific noise source while others improve the overall noise characteristics of the circuits.
Kyocera developed the Z-Series clock
oscillators to meet these demands while providing unprecedented flexibility in a standardized, quick-fulfillment solution.
Among the
oscillators presented in Table I [3], the Microcomputer Compensated Crystal
Oscillator (MCXO) seems to be the one that best fits with the frequency stability requirements, and also with the very low consumption demand.
where a is the periodic unit size, qaj is the j periodic phase factor, and [A.sub.1.sup.(0)][A.sub.2.sup.(0)] are the steady-state amplitude of shell and
oscillator, respectively.
The authors are also grateful to Professor Michael Rosenblum for drawing their attention to the fact that, in paper [47], along with the suppression of synchrony in an ensemble of interacting units, stabilization of an active
oscillator by means of a passive
oscillator, included in the feedback loop, is also described.
For an ideal
oscillator, [G.sub.T] ([G.sub.R]) boils down to the identity matrix [I.sub.N].
The frequency of the noise spur induced by the EMI occurs at offset frequencies that are aliases of the
oscillator frequency.
These correspond to the period bifurcation cascades observed at the mentioned angles and, making a parallel with a common
oscillator, it results evident that the extremes of the amplitude oscillations are far from being symmetrical at both sides of the equilibrium position of the chaotic
oscillator.
From these system of equations, one can obtain approximate frequency-amplitude relationship of a nonlinear
oscillator up to higher order.
In order to verify the theoretical analysis, the proposed
oscillator has been simulated using HSPICE program by using TSMC 0.18 [micro]m CMOS process technology process parameters.
where [[psi].sub.j] is the phase of the
oscillator number j; [[OMEGA].sub.1] and [[OMEGA].sub.2] are characteristic frequencies of excitatory and inhibitory neural
oscillators population, respectively; [S.sub.1] ([[psi].sub.j]) and S2([[psi].sub.j]) are the external stimulations on excitatory and inhibitory neural
oscillators, respectively; [M.sub.11]([[psi].sub.j] - [[psi].sub.k]) is the mutual coupling interactions between excitatory coupling
oscillators; and inhibitory coupling
oscillators [M.sub.12]([[psi].sub.j] - [[psi].sub.k]), [M.sub.22]([[psi].sub.j] [[psi].sub.k]), [M.sub.21] ([[psi].sub.j] - [[psi].sub.k]) [F.sub.j](t) are Gaussian white noise, able to meet the following second-order condition:
