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.

Hysteresis in power amplifiers is investigated in detail with the aid of an efficient analysis method, compatible with commercial harmonic balance. Suppressing the input source and using, instead, an outer-tier auxiliary generator, together with the Norton equivalent of the input network, analysis difficulties associated with turning points are avoided. The turning point locus in the plane defined by any two relevant analysis parameters is obtained in a straightforward manner, using a geometrical condition. The hysteresis phenomenon is demonstrated to be due to a nonlinear resonance of the device input capacitance under near optimum matching conditions. When increasing the drain bias voltage, some points of the locus degenerate into a large-signal oscillation that cannot be detected with a stability analysis of the dc solution. In driven conditions, the oscillation will be extinguished either through synchronization or inverse Hopf bifurcations in the upper section of the multivalued curves. For an efficient stability analysis, the outer-tier method will be applied in combination with pole-zero identification and Hopf bifurcation detection. Departing from the detected oscillation, a slight variation of the input network will be carried out so as to obtain a high efficiency oscillator able to start-up from the noise level. All the tests have been carried out in a Class-E GaN PA with measured 86.8% PAE and 12.4 W output power at 0.9 GHz.

-Parametric hysteresis in power amplifiers is investigated, studying the causes of this phenomenon and providing an efficient methodology for its prediction and elimination. As will be demonstrated, in MESFET and HEMT devices it is caused by a nonlinear resonance of the device input capacitance under near optimum input matching conditions. Bifurcation loci are used to evaluate the impact of the phenomenon under variation of critical design parameters. All the tests have been carried out in a Class-E GaN PA with measured 86.8% PAE and 12.4 W output power at 0.9 GHz.

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