Extending Leeson's Equation

Abstract

The oscillator phase noise is one of the key limitations in several fields of electronics. An electronic oscillator phase noise is usually described by the Leeson's equation. Since the latter is frequently misinterpreted and misused, a complete derivation of the Leeson's equation in modern form is given first. Second, effects of flicker noise and active-device bias are accounted for. Next the complete spectrum of an electronic oscillator is derived extending the result of the Leeson's equation into a Lorentzian spectral line. Finally the spectrum of more complex oscillators including delay lines is calculated, like opto-electronic oscillators.