RF Spectrum of a Signal after Frequency Multiplication; Measurement and Comparison with a Simple Calculation

A novel experimental technique is introduced and used to measure the effect of frequency multiplication on the RF spectrum of an oscillator. This technique makes it possible to produce the RF spectrum at X band-where measurements are relatively straightforward-that would have been produced by frequency multiplication of the 5-MHz source to any frequency from 9.2 GHz to 100 THz (1014 Hz). A simplified theory is developed and shown to reproduce the experimental results for the relative power in the carrier and noise pedestal, and the shape and the width of the carrier and noise pedestal, to within the measurement uncertainty of 2 or 3 dB, from 5 MHz to 10 THz. The calculations are easily made using analytical techniques from the measurement of the spectral density of phase fluctuations of the source, the effective input spectrum density and the bandwidth of the multiplier chain, and the frequency multiplication factor. It is shown that present 5-MHz-crystal-controlled oscillators are useful as a precision source to ~500 GHz. Suggestions for extending their range to ~100 THz are made.