1/f spectrum in a nonlinear electronic loop: consequences in frequency standards and signal processing

We study an electronic loop in which we can observe two different behaviors: the frequency locking and the free-run mode. Two ultrastable RF oscillators are compared in an electronic loop whose phase error follows the Adler model. This model presents a separatrix yielding a chaotic behavior under small perturbations. We study experimentally and numerically the effects of perturbations given by the intermodulation products generated by the mixer, or by the intrinsic instability of oscillator under measurement. Power spectral density and Allan variance measurements are in agreement with theoretical results which predict an increasing instability close to the separatrix. Furthermore, we find that the most important noise contribution follows a 1/f dependence. In our experiment we attribute the 1/f fluctuations to the presence of nonlinear effects predicted from the Adler equation under time depending perturbations.