Power Spectral Density

Power spectral density, abbreviated PSD, describes how power is distributed with frequency. It is power per unit bandwidth. In RF work it may be reported in dBm/Hz or dBW/Hz. In instrumentation and vibration work it may appear as squared engineering units per hertz, such as V^2/Hz, g^2/Hz or Pa^2/Hz.

PSD is useful because bandwidth changes the total power. A broadband noise source can have a low density but large integrated power over a wide band. A narrow spur can have high peak amplitude but small integrated power over a wide channel. Engineers use PSD to avoid confusing a per-hertz value with channel power, noise floor or a single FFT marker.

Density Definition

If total power P is distributed over frequency, power spectral density can be written as:

The integrated power over a band from f_1 to f_2 is:

If PSD is approximately flat across bandwidth B, the integrated power is:

In decibel form, with PSD in dBm/Hz:

This equation is the common bridge between density and channel power.

Worked RF Example

A spectrum measurement estimates wanted-signal PSD:

over a channel bandwidth:

The integrated channel power is:

If the receiver noise density is:

the integrated noise over the same bandwidth is:

The resulting SNR is:

If the noise bandwidth is narrowed to:

the same noise density gives:

The density did not change. The integrated noise changed because the bandwidth changed.

RBW and FFT Scaling

Spectrum analyzers and FFT tools often display values over a finite resolution bandwidth or bin. If a displayed bin power is:

over equivalent noise bandwidth:

then a first-pass density estimate is:

For example, a noise bin at -114 dBm measured over 10 kHz corresponds to:

This correction is only valid when the measured content is noise-like over the bin. A narrow coherent tone should normally be reported as integrated tone power, not as a density spread over an arbitrary RBW.

Boundary With Noise Floor and Channel Power

Noise floor is an integrated or displayed level over a stated bandwidth and detector. PSD is the per-hertz density behind that level when the spectrum is treated as density. Channel power is the integrated power inside a named frequency boundary. Eb/N0 uses noise power spectral density as a denominator so bit-energy comparisons can remain meaningful when bit rate changes.

PSD also differs from an amplitude spectrum. An FFT amplitude plot, a power spectrum and a power spectral density plot can show the same data with different scaling. The report must state which form is used.

When the density is not flat, a single average PSD can be misleading. Band-limited noise, shaped transmit spectra, vibration resonances and filtered sensor outputs may require integration over each relevant frequency region rather than multiplying one representative density by the full bandwidth.

Validation Evidence

A defensible PSD statement includes reference plane, units, one-sided or two-sided convention, bandwidth or bin basis, window, ENBW, RBW, detector mode, averaging, sample rate, record length, calibration, impedance or engineering-unit scaling, and whether the measured signal is stationary enough for a density interpretation.

For RF measurements, state whether PSD is conducted at a connector, referred to antenna input, or derived from radiated field strength. For sensors and vibration, state calibration factors and whether the value is power, amplitude-squared density or amplitude spectral density.

Common Mistakes

Common mistakes include comparing dBm/Hz with dBm, integrating dBm values directly, treating a narrow spur as broadband PSD, forgetting one-sided versus two-sided convention, using FFT bin spacing instead of ENBW, reporting PSD without window settings, and hiding bandwidth changes inside a noise-floor comparison.

The practical rule is to use PSD when the question is power per hertz, and integrate it explicitly when the decision depends on total power in a band.