unit

root hertz

A unit of measurement for noise spectral density, indicating sensitivity per square root of bandwidth.
30 related articles

Description

The hertz (Hz) is the standard unit of frequency, measuring cycles per second. In the context of noise spectral density, the unit is often expressed as "per square root hertz" (1/√Hz). This notation describes how the amplitude of noise scales with the bandwidth of a measurement: a detector's sensitivity to a signal is quoted in units of signal amplitude per √Hz, meaning that the noise floor is proportional to the square root of the measurement bandwidth. This allows engineers and physicists to compare the intrinsic sensitivity of different instruments regardless of how fast they sample data.

History

The unit is named after Heinrich Hertz, who experimentally confirmed the existence of electromagnetic waves in the 1880s. The formal adoption of "hertz" as a unit occurred in 1930 by the International Electrotechnical Commission.

How it works

When measuring a weak signal, noise accumulates over time. If you integrate a measurement for longer, the signal adds up linearly, but random noise adds up in quadrature (as the square root of the number of samples). Thus, the noise spectral density, expressed in units like volts per √Hz, tells you the noise amplitude in a 1 Hz bandwidth. To find the total noise in a measurement, you multiply this density by the square root of the bandwidth. This scaling is fundamental to optimizing detectors, from gravitational wave observatories to atomic magnetometers.

In practice

Used universally in specifying the sensitivity of sensors, including gravitational wave detectors (strain per √Hz), magnetometers (tesla per √Hz), and optical frequency combs (phase noise per √Hz).

Fun fact

The square-root-hertz notation is so ubiquitous in experimental physics that it is often read aloud as "per root hertz," and it appears in the specifications of nearly every precision measurement device.

Concept graph →

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