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The present extent of the number of radio communications has led to an overcrowding of transmitting frequencies. It is therefore desirable, especially in variable frequency transmitters or receivers, to be able to make, according to circumstances, a swift choice of the proper working frequency. On the other hand, in phase shift telegraphy and in single sideband transmitters, a very high long-term accuracy in the carrier wave is needed. Hence, the main problem is the design of an easily tunable, high-precision variable oscillator with, of course, a limited number of crystals. In this respect, probably the most famous present technique consists in the use of a variable oscillator frequency synchronized on pulse harmonics issued by a quartz oscillator. This system is referred to, hereafter, as an "Impulse Governed Oscillator" (IGO). This paper gives a mathematical analysis of the above system together with its circuits. The main difficulties met in its design as well as the way to overcome them are examined.