Phase Noise - Background

Background

An ideal oscillator would generate a pure sine wave. In the frequency domain, this would be represented as a single pair of delta functions (positive and negative conjugates) at the oscillator's frequency, i.e., all the signal's power is at a single frequency. All real oscillators have phase modulated noise components. The phase noise components spread the power of a signal to adjacent frequencies, resulting in noise sidebands. Oscillator phase noise often includes low frequency flicker noise and may include white noise.

Consider the following noise free signal:

v(t) = Acos(2πf₀t).

Phase noise is added to this signal by adding a stochastic process represented by φ to the signal as follows:

v(t) = Acos(2πf₀t + φ(t)).

Phase noise is a type of cyclostationary noise and is closely related to jitter. A particularly important type of phase noise is that produced by oscillators.

Phase noise (ℒ(f)) is typically expressed in units of dBc/Hz, and it represents the noise power relative to the carrier contained in a 1 Hz bandwidth centered at a certain offsets from the carrier. For example, a certain signal may have a phase noise of -80 dBc/Hz at an offset of 10 kHz and -95 dBc/Hz at an offset of 100 kHz. Phase noise can be measured and expressed as single sideband or double sideband values, but as noted earlier, the IEEE has adopted the definition as one-half of the double sideband PSD.