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This paper presents an analysis of a simple oscillator designed for stabilized frequency divider application. The oscillator combines some of the characteristics of sinusoidal and relaxation oscillators to provide a high degree of frequency stability while allowing sufficient tendency for synchronization. The analytical results are obtained in a graphical form which is easy to handle and which could be used as a design procedure for stabilized frequency dividers. Synchronization of the oscillator is described for the case of an input signal consisting of narrow pulses. It is shown that the circuit can maintain a given frequency division ratio regardless of variations in, the amplitude of such a synchronization signal. The results of the graphical analysis are confirmed by experimental observations. Performance data are presented indicating that the circuit is capable of frequency division ratios of 30 to 40 without requiring close control of the power supply voltage.