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Small offsets in frequency from a given reference can be generated in a single sideband mixer employing a PLL. It is shown that the output frequency stability depends linearly on the fractional shift of the offset frequency generated, and on the coherence of the VCO. For the typical digital phase-locked loop synthesizer techniques, employing a crystal-stabilized VCO at 5 MHz, a 500-Hz offset can be realized with a 1-s frequency stability no better than a few parts in 107. An improved design is described which employs a pair of analog multipliers as an instantaneous phase detector together with feedback in quadrature. In laboratory tests this design demonstrated one second frequency stability of better than 1 part in 1010 when synthesizing the frequency 4.9995776 MHz from a 5.0-MHz cesium reference.