Phase noise to jitter

A phase-noise curve gives noise density at offsets from the carrier. To find the noise within a band, convert the single-sideband (SSB) density $L(f)$ from dBc/Hz to a linear ratio per hertz, then integrate between the selected offset limits:

Here $f$ is separation from the carrier in hertz, and $A$ is the integrated SSB noise-to-carrier power ratio. The displayed integrated SSB noise is $10\log_{10}(A)$ dBc. Between supplied points, the model uses a straight line in dB versus log offset, equivalent to a power law in linear density, and integrates each segment analytically. It does not extrapolate beyond the supplied data.

For small random phase fluctuations, include both noise sidebands and take the square root to obtain RMS phase jitter $\sigma_\phi$ in radians:

The factor of two accounts for the two sidebands. Use random noise density in dBc/Hz; discrete spurs specified in dBc are excluded. The 0.1 rad caution is a reminder of the small-phase assumption, not an accuracy guarantee.

One carrier cycle is $2\pi$ radians. Dividing phase jitter by the carrier’s angular frequency converts it to RMS time jitter $\sigma_t$:

The carrier frequency $f_c$ is in hertz and time jitter is in seconds. This is RMS jitter over the selected offset band, not period jitter, cycle-to-cycle jitter or a peak-to-peak limit. Choose the band for the application; the tool does not fit a PLL response or apply tracking-loop or measurement-filter weighting.

Generated carrier-unit conversions display at most two decimals while retaining full precision until edited. Offset labels use a finer common unit when needed; very narrow windows use explicit edge labels and a span instead of showing identical rounded endpoints. Raw data and copied inputs keep their precision.