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Methods for facilitating the design of phase-shift oscillators at extreme frequencies of a fraction of a cycle to a few megacycles are discussed. It is shown that, if the input impedance of each section of a lumped resistance-capacitance network is made K times that of the previous section, the gain required for oscillation can be reduced to a theoretical minimum of 8 for a three-section network with K high, as against 29 for a K of unity. A new circuit element called the "resistance-capacitance transmission line," consisting of a resistance covered by a well-insulated and grounded metal surface, is introduced and is analyzed as a phase-shifting network to give reliable operation in a phase-shift oscillator at frequencies up to a few megacycles. Curves are presented to facilitate the design of the latter type of oscillator. Various configurations of the resistance-capacitance transmission line are discussed and experimental results are presented.