#### Phase noise

Phase noise is a term used in the frequency domain to refer to the amount of unwanted, statistically occurring phase changes of a generator as a signal source. It is also called short-term stability and is an important characteristic of signal sources. Phase noise is typically measured in dBc/Hz (decibel carrier per Hertz) and represents the noise power in relation to the carrier, contained in a bandwidth of 1 Hz and localized at a certain distance from the carrier frequency. In the time domain, phase noise is the difference between the theoretical and actual zero crossings of a harmonic oscillation. The fluctuations in the deviations are referred to as jitter.

An ideal oscillating circuit operated with superconducting properties at a temperature of absolute zero (0K or -273.15°C) without inherent noise would also generate an ideal periodic signal, which can be described as follows:

(1)

- A
_{ }= amplitude of the signal - f
_{0}= frequency of the signal - 2πf
_{0}t = phase of the signal

Inherent noise is a result of basic physical processes that cannot be prevented during normal operations. This noise, also known as thermal or flicker noise, causes variations in the amplitude and phase of the oscillator. To represent this, a stochastic process denoted by the symbol φ is added to the signal, giving it a phase noise. (We can ignore the effect on the amplitude in this context.)

(2)

The simplest and quickest method to determine the phase noise of an oscillator
is to measure it directly with a
spectrum analyzer.
However, the phase noise of the internal oscillators of the spectrum analyzer must be sufficiently small
so that the properties of the measurement object are not superimposed by the phase noise of the spectrum analyzer.
This is because the measurement does not display the phase noise of the device under test (DUT) alone,
but the sum of the power of the phase noise of the DUT, the phase noise of the internal oscillators, and the thermal noise.

Figure 1: The power density spectrum of flicker noise as a function of frequency

Figure 1: The power density spectrum of flicker noise as a function of frequency

While a constant background noise in the range between -125 to -130 dB can be observed for high-frequency components, the phase noise increases towards lower frequency components, initially with a 1/f ² dependence and from a circuit-specific corner frequency with a 1/f ³ dependence due to flicker noise contributions. In Figure 1, the double logarithmic plot of the power density versus frequency results in a straight line with a slope of -2 for the 1/f ² noise and a slope of -3 for the 1/f ³ noise. From the UHF band onwards, only the frequency-independent “white” noise has an effect.