Efficient Simulation of Solution Curves and Bifurcation Loci in Injection-Locked Oscillators

Abstract

A new method is presented for the two-level harmonic-balance analysis of multivalued synchronized solution curves in injection-locked oscillators. The method is based on the extraction of a nonlinear admittance function, which describes the circuit response from the input source terminals. It does not require any optimization or parameter switching procedures, this constituting a significant advantage compared with previous analysis techniques. With additional mathematical conditions, it enables a straightforward determination of the turning point and Hopf bifurcation loci that delimit the stable injection-locked operation bands. The codimension two bifurcation point at which the turning point and Hopf bifurcation loci merge is analyzed in detail, as well as the saddle-connection locus. As it is shown, a second intersection of the saddle-connection locus with the turning point locus acts as a boundary between synchronization points and points associated with jumps and hysteresis. The likely observation of chaotic solutions in the neighborhood of the saddle-connection locus is discussed too. The techniques have been validated by application to several injection-locked oscillators, obtaining good agreement with the experimental results.

Growth-rate function for the nonlinear analysis of the transient dynamics of microwave oscillators

“…Note that, in contrast with previous works [4]- [5], equation (4) is nonlinear. This implies that the nonlinear function   [5], [8].…”

Simulation Method for Complex Multivalued Curves in Injection-Locked Oscillators

“…The recent work [33] proposes a new technique for the efficient simulation of fundamentally injection-locked oscillators, in which neither a parameter switching nor optimization is required. The method is based on the calculation of the nonlinear admittance function that models the undriven oscillator response.…”

“…This prevents the direct use of the outer-tier admittance function, modeling the sole oscillator circuit. In fact, for a direct extension of the work [33] to the analysis of a subharmonically injection-locked oscillator, one would need two different outer-tier admittance functions, one at calculated as the ratio between the AG current and voltage, with the current usually entering the circuit, to detect the negative conductance excess (Fig. 3).…”

“…The analysis of the phase sensitivity with respect to the input source will allow an estimation of the input power required to achieve the sub-synchronized state. The intricate synchronizedsolution curves will be obtained with a new method, based on the calculation of a series of phase-dependent admittance-type functions, constituting an outer-tier description of the oscillator response to the injection source, which is different from the undriven oscillator-admittance function proposed in [33].…”

Parametric hysteresis in power amplifiers

“…This required an involved estimation of the determinant threshold to ensure sufficient analysis accuracy. The new method is developed from the recently published procedure [5] for studying injection-locked oscillators. It avoids all of these requirements and is based on the calculation of an outer-tier admittance function in commercial HB.…”