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 general, it is the signal level required for a particular quality of received information. In signal processing, sensitivity also relates to bandwidth and noise floor as is explained in more detail below. In the field of electronics different definitions are used for sensitivity. The IEEE dictionary states: "Definitions of sensitivity fall into two contrasting categories." It also provides multiple definitions relevant to sensors among which 1: "(measuring devices) The ratio of the magnitude of its response to the magnitude of the quantity measured.” and 2: "(radio receiver or similar device) Taken as the minimum input signal required to produce a specified output signal having a specified signal-to-noise ratio.”. The first of these definitions is similar to the definition of responsivity and as a consequence sensitivity is sometimes considered to be improperly used as a synonym for responsivity, and it is argued that the second definition, which is closely related to the detection limit, is a better indicator of the performance of a measuring system. To summarize, two contrasting definitions of sensitivity are used in the field of electronics
Sensitivity first definition: the ratio between output and input signal, or the slope of the output versus input response curve of a transducer, microphone or sensor. An example is given in the section below on electroacoustics. Sensitivity second definition: the minimum magnitude of input signal required to produce an output signal with a specified signal-to-noise ratio of an instrument or sensor. Examples of the use of this definition are given in the sections below on receivers and electronic sensors.
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. The sensitivity of a hydrophone is usually expressed as dB relative to 1 V/μPa. The sensitivity of a loudspeaker is usually expressed as dB / 2.83 VRMS at 1 metre. This is not the same as the electrical efficiency; see Efficiency vs sensitivity. This is an example where sensitivity is defined as the ratio of the sensor's response to the quantity measured. One should realize that when using this definition to compare sensors, the sensitivity of the sensor might depend on components like output voltage amplifiers, that can increase the sensor response such that the sensitivity is not a pure figure of merit of the sensor alone, but of the combination of all components in the signal path from input to response. The sensitivity of a powered loudspeaker is defined as the signal level that, when applied to the input, produces maximum output. If the amplifier has variable gain, the gain setting must be specified to make the measurement meaningful.
Receivers 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. It is mathematically defined as the minimum input signal S i {\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:
S i = k ( T a + T r x ) B ⋅ S o N o {\displaystyle S_{i}=k(T_{a}+T_{rx})B\;\cdot \;{\frac {S_{o}}{N_{o}}}}
where
S i {\displaystyle S_{i}} = sensitivity [W]
k {\displaystyle k} = Boltzmann constant
T a {\displaystyle T_{a}} = equivalent noise temperature in [K] of the source (e.g. antenna) at the input of the receiver
T r x {\displaystyle T_{rx}} = equivalent noise temperature in [K] of the receiver referred to the input of the receiver
B {\displaystyle B} = bandwidth [Hz]
S o N o {\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
S i = N i ⋅ F ⋅ S N R o = k T a B ⋅ F ⋅ S N R o {\displaystyle S_{i}=N_{i}\;\cdot \;F\;\cdot \;SNR_{o}=kT_{a}B\;\cdot \;F\;\cdot \;SNR_{o}}
where
F {\displaystyle F} = noise factor
N i {\displaystyle N_{i}} = input noise power
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