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.[1]
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[2] [3] 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,[4] [5] 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.[6]
To summarize, two contrasting definitions of sensitivity are used in the field of electronics
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 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. The sensitivity of a hydrophone is usually expressed as dB relative to 1 V/μPa.[7]
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.
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.[8] It is mathematically defined as the minimum input signal
Si
Si=k(Ta+Trx)B ⋅
| So | |
| No |
where
Si
k
Ta
Trx
B
| So | |
| No |
The same formula can also be expressed in terms of noise factor of the receiver as
Si=Ni ⋅ F ⋅ SNRo=kTaB ⋅ F ⋅ SNRo
where
Ni
SNRo
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..
For electronic sensors the input signal can be of many types, like position, force, acceleration, pressure, or magnetic field. The output signal for an electronic analog sensor is usually a voltage or a current signal . The responsivity of an ideal linear sensor in the absence of noise is defined as , whereas for nonlinear sensors it is defined as the local slope
dSo/dSi
SNRo=So/Noi
S
SNRo
S=
| S | |
| i,SNRo |
=
| Noi | |
| R |
SNRo
This equation shows that sensor sensitivity can be decreased (=improved) by either reducing the intrinsic noise of the sensor or by increasing its responsivity . This is an example of a case where sensivity is defined as the minimum input signal required to produce a specified output signal having a specified signal-to-noise ratio. This definition has the advantage that the sensitivity is closely related to the detection limit of a sensor if the minimum detectable SNRo is specified (SNR). The choice for the SNRo used in the definition of sensitivity depends on the required confidence level for a signal to be reliably detected (confidence (statistics)), and lies typically between 1-10. The sensitivity depends on parameters like bandwidth BW or integration time τ=1/(2BW) (as explained here: NEP), because noise level can be reduced by signal averaging, usually resulting in a reduction of the noise amplitude as
Noi\propto1/\sqrt{\tau}
\tau
Si,So,Noi
Noi,tot
Noi,PSD=Noi,tot/BW
Noi,ASD=\sqrt{Noi,PSD
In some instruments, like spectrum analyzers, a SNRo of 1 at a specified bandwidth of 1 Hz is assumed by default when defining their sensitivity. For instruments that measure power, which also includes photodetectors, this results in the sensitivity becoming equal to the noise-equivalent power and for other instruments it becomes equal to the noise-equivalent-input[9]
NEI=Noi,ASD/R
D=R/Noi
As an example, consider a piezoresistive force sensor through which a constant current runs, such that it has a responsivity
R=1.0~V/N
Noi,rm{ASD
Si,ASD=NEI=10~nN/\sqrt{Hz
(10~nN/\sqrt{Hz