Investigation into spectrum shape fluctuations of oscillators and signal sources

A standard SDR receiver with digital FFT type spectrum analysis software and a time waterfall display is used to investigate spectrum shape and `spur´ fluctuations in LC and crystal oscillators. Oscillator start-up spectra are found to narrow exponentially in time towards the expected Leeson model `bell´ shape, with a time constant inversely proportional to the resonator bandwidth. Spurs can be seen most prominent around the 3dB bandwidth frequencies of the oscillator resonator. The spur frequencies in general are a constant fixed offset from the carrier frequency and do not drift. Spur amplitude fluctuations appear to be random but with an average periodicity inversely proportional to spacing from the carrier. Some theory for the fluctuations is under development.