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Recent articles in the literature have described voltage-controlled square-wave oscillators using transistors and square-loop magnetic cores and generally incorporating four windings. These oscillators give output frequency directly proportional to applied voltage; hence they are useful as solid-state dc to dc converters, telemetering oscillators, and many other devices. Each application is based on the fact that the volt seconds applied to a core are proportional to the flux switched, which is essentially constant for the core. This paper is primarily devoted to the fundamentals and applications of a novel two-winding transistor-core oscillator and derived circuits. The two-winding circuit is capable of true square-wave output at 700 kc, the upper frequency limit being determined by the present state of the art of transistor and core development. A review is given first of the usual four-winding oscillator, tracing its operating cycle step by step and showing the circuit to be derivable directly from a fundamental transistor-core switching circuit. Then, the two-winding oscillator is discussed. With this circuit, the two separate base windings are elimated through cross-coupling of each collector to the base of the opposite transistor. During switching time, the collector winding of the OFF transistor supplies the necessary regenerative voltage to the base of the ON transistor. A parallel RC in each base circuit speeds up the turn-off action by application of inverse current to the ON base. Direct electrical cross-connection from the ON base to the OFF collector means that at switchover the inverse transient voltage, due to flyback, will momentarily place the OFF transistor into inverse saturated conduction, thereby presupplying it with holes so that it can take on its load in the forward direction extremely rapidly when the ON transistor shuts off. In this circuit, self-starting is inherent, due to the direct connections from base to negative supply. The circuit operation is analyzed in detail and worst-case design equations are derived. A bibliography of the literature is included.