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A simple transistor oscillator circuit is analyzed in an illuminating way. The analysis predicts oscillation in either of two modes and provides a means of determining the maximum frequency of oscillation in each. The two modes are identified as "three-terminal" or "two-terminal" according to whether RF current is required in the base lead to produce the oscillations. The relationship between these modes is developed and visualized in a "frequency portrait" for the transistor which serves to unify the principal results of the paper.