The Complex World of Oscillator Noise: Modern Approaches to Oscillator (Phase and Amplitude) Noise Analysis

The study of fluctuations in oscillators has been a classical research topic in mathematics, physics, and engineering since the first half of the 20th century [1]-[4]. Besides the intellectual fascination for mathematically difficult problems, the importance of the topic is deeply rooted in practical applications, mainly in the fields of RF and microwave electronics and also telecommunications. In fact, defining a precise frequency reference is fundamental for many applications, both electrical (e.g., transmitters and receivers) and optical (e.g., lasers). The broadening of the generated spectral line is mainly due to the phase-noise component of oscillator fluctuations, which consequently is the most commonly studied feature of oscillator noise (see [5] for a recent and exhaustive review). In a dual perspective, the definition of a precise time reference is also extremely important for digital applications, thus implying the necessity to keep under control the time jitter in clocked and in sampled systems. From a theoretical standpoint, phase noise and time jitter are simply two sides of the same coin, a manifestation of the oscillator's noisy behavior. As the microwave engineer is more often interested in the phase-noise characterization, we discuss only the latter. The time-jitter estimation is discussed, for instance, in [6].