Analysis of bias-shift effects in free-running and injection-locked negative resistance oscillators

In this paper, the interaction between DC and RF in quasi-sinusoidal free-running and injection-locked oscillators is addressed. To account for and illustrate in a user-friendly manner the bias-shift related effects stemming from such interaction, a frequency-domain method of analysis has been developed for a rather wide class of negative-resistance circuits. Grounding on a first-approximation exact perturbation-refined approach, it permits computationally efficient simulation of the oscillator behavior directly in terms of the DC and RF signals evolutions (dynamical complex envelopes). In fact, it allows the investigation of both steady-state and transient operation of the shifting-bias driven/undriven oscillator, including the phase-lock/dynamical stability evaluation. The circuit presented as example of application (a cubic-nonlinearity single-tuned resonator ILO configuration), though simple and standard, evidences a number of interesting and unusual phenomena. This confirms the importance of carefully accounting for such DC/RF interaction effects during the circuit design phase, and the convenience of having at one´s disposal a convenient analysis tool as the one here proposed.