The Arithmetic of 1/f Noise in a Phase Locked Loop

Frequency countings close to a phase locked zone in an electronic receiver show a 1/f power spectral density. The noise scaling versus the frequency deviation and the open loop gain is found from Adler’s model of the phase locked loop. This fully agrees with experiments performed at 5 MHz on a receiver with a Schottky diode mixer and a low pass filter. The 1/f amplitude and frequency noise due to the whole set of (sub)harmonics is explained from a nonlinear mapping, with a coupling coefficient related to the structure of prime numbers. The number theoretical approach of 1/f noise and the link to the generalized Riemann hypothesis is explained.