O. De Feo

Observations Concerning the Locking Range in a Complementary Differential

The use of resonant injection-locked frequency dividers in frequency synthesizers has increased in recent years due to their lower power consumption compared to conventional digital prescalers. Numerous circuit ideas have been proposed, but there are few and sometimes contradictory estimates of the locking ranges (LRs) in these dividers. Despite several attempts, there is still no accurate analytical method to predict the LR. In this paper, we present a nonlinear approach based on the application of bifurcation theory to predict where the LR is wider rather than to say precisely how wide it is. The results presented have been derived by numerical bifurcation analysis using AUTO and have been verified by circuit simulations and experiments. In Part II, we will show how the insights developed in this paper lead to a rigorous design methodology.

LC

Objective:u2002 To reveal the EEG correlates of resting hypofrontality in schizophrenia (SZ).

Injection-Locked Frequency Divider—Part I: Qualitative Analysis

An intuitive approach to analyze the behavior of an Injection-Locked Frequency Divider was presented in Part I of this work; that paper provided insight into the locking behavior in the valid design area of the circuit. In this paper, we present a rigorous design methodology which provides a closed form equation showing where the locking range is wider. Theoretical predictions of the locked regions are verified by simulations of the circuit in Spectre RF using 0.35-CMOS technology models.

Alpha rhythm and hypofrontality in schizophrenia

Injection-locked frequency dividers (ILFDs) are versatile analog circuit blocks used, for example, within phase-locked loops (PLLs). With respect to their digital counterparts, they have the advantages of a low power consumption and division ratios greater than two. The price for these advantages is believed to be a limited locking range. Here we show that this is not the case; indeed, by combining nonlinear systems theory (bifurcation analysis) with optimization techniques, we have significantly increased the locking range of a classical (LC oscillator-based) injection-locked frequency divider, predicting a locking range that is about twenty times greater than what has been reported in the literature to date. The wider locking range predicted by the theory has been confirmed by SPICE simulations.

Observations Concerning the Locking Range in a Complementary Differential

We address here an aspect of the problem concerning circuit implementations of nonlinear dynamical systems that depend on control parameters. In particular, the problem of the identification of such systems is addressed in two steps. The first step uses the state-space reconstruction (through time delay reconstruction associated with principal component analysis) on the basis of scalar time series measured in the systems to be identified. The second step deals with the approximation of the flow in the reconstructed space (through a piecewise-linear approximation technique). The proposed method is first validated with two examples concerning known systems and then applied successfully to two realistic cases.

LC

The possible dynamics of a model of a hysteresis-based circuit oscillator are analyzed when varying its characteristics parameters. By combining brute-force simulations with continuation methods it is shown that the complexity of the scenario obtained through brute-force simulation is largely justified by the presence of a few codimension-2 bifurcation points, which organize the whole bifurcation scenario.