# Sensitivity (electronics)

The sensitivity of an electronic device, such as a communications system receiver, or detection device, such as a PIN diode, is the minimum magnitude of input signal required to produce a specified output signal having a specified signal-to-noise ratio, or other specified criteria.

In signal processing, sensitivity also relates to bandwidth and noise floor.

Sensitivity is sometimes improperly used as a synonym for responsivity.[citation needed][1]

## Electroacoustics

The sensitivity of a microphone is usually expressed as the sound field strength in decibels (dB) relative to 1 V/Pa (Pa = N/m2) or as the transfer factor in millivolts per pascal (mV/Pa) into an open circuit or into a 1 kiloohm load.[citation needed]

The sensitivity of a loudspeaker is usually expressed as dB / 2.83 VRMS at 1 metre.[citation needed] This is not the same as the electrical efficiency; see Efficiency vs sensitivity.

The sensitivity of a hydrophone is usually expressed as dB re 1 V/μPa.[2]

Sensitivity in a receiver, such a radio receiver, indicates its capability to extract information from a weak signal, quantified as the lowest signal level that can be useful.[3] It is mathematically defined as the minimum input signal ${\displaystyle S_{i}}$  required to produce a specified signal-to-noise S/N ratio at the output port of the receiver and is defined as the mean noise power at the input port of the receiver times the minimum required signal-to-noise ratio at the output of the receiver:

${\displaystyle S_{i}=k(T_{a}+T_{rx})B\;\cdot \;{\frac {S_{o}}{N_{o}}}}$

where

${\displaystyle S_{i}}$  = sensitivity [W]
${\displaystyle k}$  = Boltzmann constant
${\displaystyle T_{a}}$  = equivalent noise temperature in [K] of the source (e.g. antenna) at the input of the receiver
${\displaystyle T_{rx}}$  = equivalent noise temperature in [K] of the receiver referred to the input of the receiver
${\displaystyle B}$  = bandwidth [Hz]
${\displaystyle {\frac {S_{o}}{N_{o}}}}$  = Required SNR at output [-]

The same formula can also be expressed in terms of noise factor of the receiver as

${\displaystyle S_{i}=N_{i}\;\cdot \;F\;\cdot \;SNR_{o}=kT_{a}B\;\cdot \;F\;\cdot \;SNR_{o}}$

where

${\displaystyle F}$  = noise factor
${\displaystyle N_{i}}$  = input noise power
${\displaystyle SNR_{o}}$  = required SNR at output.

Because receiver sensitivity indicates how faint an input signal can be to be successfully received by the receiver, the lower power level, the better. Lower power for a given S/N ratio means better sensitivity since the receiver's contribution is smaller. When the power is expressed in dBm the larger the absolute value of the negative number, the better the receive sensitivity. For example, a receiver sensitivity of −98 dBm is better than a receive sensitivity of −95 dBm by 3 dB, or a factor of two. In other words, at a specified data rate, a receiver with a −98 dBm sensitivity can hear signals that are half the power of those heard by a receiver with a −95 dBm receiver sensitivity.[citation needed]

## References

1. ^ Book: Sensors and Transducers Characteristics, Applications, Instrumentation, Interfacing M..J. Usher and D.A. Keating
2. ^ "Underwater Acoustics". resource.npl.co.uk. Retrieved 2020-12-04.
3. ^ Layne, Dennis. "Receiver Sensitivity and Equivalent Noise Bandwidth". High Frequency Electronics. Archived from the original on 2020-08-23. Retrieved 2020-08-23.

This article incorporates public domain material from Federal Standard 1037C. General Services Administration. (in support of MIL-STD-188).