Theory of Frequency Syntesis

The design of a system for the synthesis of one frequency from another is discussed in terms of mathematical methods of approximating real numbers, the ratio of the frequencies being the number approximated. A general equation describing the frequency synthesis process is derived and it is shown, using charts, how block diagrams for a frequency synthesizer can be developed from the solutions of this equation. Examples are given for a synthesizer which compares the frequency of an ammonia N15H3 maser with a standard frequency of 5 MHz, and for a synthesizer which offsets a standard frequency of 100 kHz by steps of 1×10-5 Hz.