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# Noise-equivalent Power

Acronym: NEP

Definition: the input power to a detector which produces the same signal output power as the internal noise of the device

German: äquivalente Rauscheingangsleistung

Units: W or W / Hz1/2

Author:

When a photodetector does not get any input light, it nevertheless produces some noise output with a certain average power, which is proportional to the square of the r.m.s. voltage or current amplitude. The noise-equivalent power (NEP) of the device is the optical input power which produces an additional output power identical to that noise power for a given bandwidth (see below). If the input is interpreted as a signal, the output signal and noise powers are then identical, i.e., the signal-to-noise ratio would be 1.

The inverse of the noise-equivalent power is called the detectivity.

The possible signal-to-noise ratio of a measurement (for a 1-Hz bandwidth) can be estimated simply as the available input power divided by the noise-equivalent power. For that purpose, one does not need to know the detector's responsivity.

Note that the noise-equivalent power depends on the optical wavelength, since that influences the responsivity of the detector. The lowest NEP is achieved for those wavelengths where the responsivity is the highest.

## Influence of the Bandwidth

The noise power and thus also the noise-equivalent power depends on the measurement bandwidth. (For white noise, it is proportional to that bandwidth.) At a first glance, one may find it most natural to use the full detection bandwidth of the device. Then, however, the NEP would not allow a fair comparison of detectors with different bandwidth; it would be reduced if additional electronic filtering, reducing the detection bandwidth, would be applied. Therefore, it is common to assume a bandwidth of 1 Hz, which is usually far below the detection bandwidth.

Some authors specify the NEP in units of W / Hz1/2 rather than W (watts), as would be the usual units for a power. Effectively, they base the NEP on a power spectral density (PSD) rather than on a power. The numerical results are not changed, as the power in a 1-Hz bandwidth arises from multiplying the PSD with the bandwidth of 1 Hz.

## Measurement of Noise-equivalent Power

For experimentally obtaining the noise-equivalent power, one first needs to measure the power spectral density of the instrument output without any optical input. That result has to be divided by the responsivity.

For example, if a photodiode produces a photocurrent with a PSD of 1 nA / Hz1/2, and its responsivity is 0.5 A/W, the NEP is 1 nA / Hz1/2 / 0.5 A/W = 2 nW / Hz1/2.

## Optimization

Obviously, a low noise-equivalent power is desirable, because that power level is about the minimum input power level which can be detected easily when averaging the signal over a time of the order of one second. Using advanced methods such as lock-in detection, one can actually detect much weaker signals, provided that these have a bandwidth far below the detection bandwidth. In effect, one restricts the detection bandwidth to a value far below 1 Hz, which also reduces the noise power with which the signal has to compete. The required averaging time is correspondingly longer.

If the responsivity of a photodetector (e.g. a photodiode) can be increased without increasing the delivered noise power, the noise-equivalent power can be reduced. However, by using an avalanche photodiode, for example, where the responsivity can be greatly enhanced due to an internal amplification mechanism, one also obtains substantially more noise, so that the noise-equivalent power may even be increased.

## Questions and Comments from Users

2021-03-03

I would like to understand the relationship between the NEP and the signal-to-noise ratio. If the NEP is large, does the signal-to-noise ratio become small?

Yes, it will. However, the signal-to-noise ratio also depends on the strength of the transmitted signal, while the NEP does not deal with that.

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