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A model is presented for an injection-locked oscillator. It is derived from a perturbation of the free-running oscillator steady state, which is accurately determined from a harmonic balance (HB) simulation. As a first application, the proposed model is used to trace the existing solutions of the injection-locked system and their stability. It is then extended to include the effect of noise on the stability. Finally, the injection-locked system performance is studied under phase modulation. Sinusoidal phase modulation is considered and the stability of the modulated solutions is examined by Floquet theory. The validity of the model is verified for a 4.422-GHz oscillator, by HB and envelope transient simulations, as well as measurements. Index Terms--Angle modulation, envelope transient (ET), harmonic balance (HB), injection-locked oscillator, stochastic differential equations.

The time-domain modeling of the operation of a 94-GHz pulsed silicon IMPATT oscillator, based on a physical approach, is described in this paper. It relies on the coupling of electrical, thermal, electromagnetic, and carrier transport physical models. The model has been used to study the high-power stable operation of a 94-GHz oscillator. The results of a comparison between simulations, using two different types of passive radio-frequency load circuits, including experimental measurements, are presented and discussed. They tend to demonstrate that it is now possible to develop accurate millimeter-wave-circuit predictive models even for application based on a nonlinear thermal and electrical transient operation such as IMPATT oscillators. Index Terms - Millimeter-wave pulsed IMPATT oscillator, time-domain global modeling.

A new type of 94-GHz pulsed silicon impact avalanche and transit time (IMPATT) oscillator numerical modeling is described. It consists of a set of three models of increasing complexity; namely, a pure sine model, time-domain isothermal model, and time-domain electro-thermal model, which basically rely on a diode one-dimensional bipolar drift-diffusion model embedded in a time-domain circuit modeling. In this paper, they are first used to investigate the 94-GHz diode intrinsic operation and performance. Secondly, the load-impedance level has been optimized. In each case, the thermal behavior is especially considered. Thirdly, pulse-operation-simulation results are compared with experiments performed at Thomson CSF, Radars et Contre-Mesures, Elancourt, France. Finally, some improvements of the present modeling are discussed in Section VI. Index Terms - Macroscopic modeling, millimeter waves, pulsed IMPATT oscillator.

The modified Bethe theory is applied to the waveguide-to-resonator transition, which is used for output coupling in an orotron oscillator designed for operation at 94 GHz. The finite thickness of the coupling hole between output waveguide and resonator is taken into account. The approach results in an equivalent circuit, which describes the reflection-type resonator, with respect to the output waveguide. Its equivalent circuit parameters are given in closed-form expressions. The calculated reflection coefficients are compared to experimental results. The assumed single-mode operation in the resonator is demonstrated by field-profile measurements. Index Terms: Electromagnetic coupling, optical resonator, Q measurements.

Previous investigations of noise in mutually synchronized coupled-oscillator systems are extended to include the effects of phase noise introduced by externally injected signals. The analysis is developed for arbitrarily coupled arrays and an arbitrary collection of coherent injected signals, and is illustrated with the specific case of linear chains of nearest neighbor coupled oscillators either globally locked (locking signal applied to each array element) or with the locking signal applied to a single-array element. It is shown that the general behavior is qualitatively similar to a single injection-locked oscillator, with the output noise tracking the injected noise near the carrier, and returning to the free-running array noise far from the carrier, with intermediate behavior significantly influenced by the number of array elements and injection strength. The theory is validated using a five-element GaAs MESFET oscillator array operating at X-band. Index Terms: Array noise, globally locked, injection locked, injection strength, noise admittance, noise offset frequency, phase noise, power spectral density, single element locked, synchronization.