View source for Sensitivity (electronics)

{{short description|Minimum magnitude of input signal to produce a specified output by an electronic device}}

The '''sensitivity''' of an [[electronic device]], such as a [[communications system]] receiver, or detection device, such as a [[PIN diode]], is the minimum [[magnitude (mathematics)|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.<ref>{{cite book |last1=Hernandez |first1=Marco |last2=Mucchi |first2=Lorenzo |title=Chapter 1 - Survey and Coexistence Study of IEEE 802.15.6™ -2012 Body Area Networks, UWB PHY |url=https://www.sciencedirect.com/science/article/pii/B9780123965202000017 |date=2014 |pages=1–44 |publisher=Academic Press |doi=10.1016/B978-0-12-396520-2.00001-7 |isbn=978-0-12-396520-2 |access-date=19 March 2024 |ref=sensi}}</ref>

In [[signal processing]], sensitivity also relates to [[bandwidth (signal processing)|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<ref name=":0">{{Cite report |url=https://ieeexplore.ieee.org/document/4116787 |title=100-2000 - The Authoritative Dictionary of IEEE Standards Terms, Seventh Edition |date=2000 |doi=10.1109/ieeestd.2000.322230 |isbn=0-7381-2601-2 |language=en}}</ref><ref>{{Cite book |last1=Vig |first1=J.R. |last2=Walls |first2=F.L. |chapter=A review of sensor sensitivity and stability |date=2000 |title=Proceedings of the 2000 IEEE/EIA International Frequency Control Symposium and Exhibition (Cat. No.00CH37052) |publisher=IEEE |pages=30–33 |doi=10.1109/FREQ.2000.887325 |isbn=978-0-7803-5838-6}}</ref> 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]]'',<ref>Book: Sensors and Transducers Characteristics, Applications, Instrumentation, Interfacing M..J. Usher and D.A. Keating</ref><ref name=":1">{{Cite web |title=Lecture 2: Noise processes and measurement sensitivity — Open Quantum Sensing and Measurement Notes |url=https://interactivetextbooks.tudelft.nl/qsm/src/2_noise_types.html |access-date=2024-08-19 |website=interactivetextbooks.tudelft.nl}}</ref> 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.<ref name=":3">{{Cite journal |last1=Ekins |first1=Roger |last2=Edwards |first2=Philip |date=1997-10-01 |title=Point On the meaning of "sensitivity" |url=https://academic.oup.com/clinchem/article/43/10/1824/5640627 |journal=Clinical Chemistry |volume=43 |issue=10 |pages=1824–1831 |doi=10.1093/clinchem/43.10.1824 |issn=0009-9147}}</ref>

To summarize, two contrasting definitions of sensitivity are used in the field of electronics

* [[#Electroacoustics|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.
* [[#Electronic Sensors|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 [[decibel]]s (dB) relative to 1 [[volt|V]]/[[Pascal (unit)|Pa]] (Pa = [[newton (unit)|N]]/[[meter|m]]<sup>2</sup>) or as the transfer factor in millivolts per [[pascal (unit)|pascal]] (mV/Pa) into an [[Open-circuit voltage|open circuit]] or into a 1 kiloohm [[Load impedance|load]].{{Citation needed|date=March 2013}} The sensitivity of a [[hydrophone]] is usually expressed as dB relative to 1 V/μPa.<ref>{{Cite web|title=Underwater Acoustics|url=http://resource.npl.co.uk/acoustics/techguides/concepts/sen.html|access-date=2020-12-04|website=resource.npl.co.uk}}</ref>

The sensitivity of a [[loudspeaker]] is usually expressed as dB / 2.83 V<sub>RMS</sub> at 1 metre.{{Citation needed|date=March 2013}} This is not the same as the [[electrical efficiency]]; see [[Loudspeaker#Efficiency vs. sensitivity|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.

== 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.<ref>{{Cite web|last=Layne|first=Dennis|title=Receiver Sensitivity and Equivalent Noise Bandwidth|url=http://www.highfrequencyelectronics.com/index.php?option=com_content&view=article&id=553:receiver-sensitivity-and-equivalent-noise-bandwidth&catid=94:2014-06-june-articles&Itemid=189|url-status=live|archive-url=https://web.archive.org/web/20200823041810/http://www.highfrequencyelectronics.com/index.php?option=com_content&view=article&id=553:receiver-sensitivity-and-equivalent-noise-bandwidth&catid=94:2014-06-june-articles&Itemid=189|archive-date=2020-08-23|access-date=2020-08-23|website=High Frequency Electronics}}</ref> It is mathematically defined as the minimum input signal <math>S_i</math> 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:

:<math>S_i = k(T_a+T_{rx})B \; \cdot \; \frac{S_o}{N_o}</math>

where 
:<math>S_i</math> = sensitivity [W]
:<math>k</math> = [[Boltzmann constant]]
:<math>T_a</math> = [[equivalent noise temperature]] in [K] of the source (e.g. antenna) at the input of the receiver
:<math>T_{rx}</math> = equivalent noise temperature in [K] of the receiver referred to the input of the receiver
:<math>B</math> = bandwidth [Hz]
:<math>\frac{S_o}{N_o}</math> = Required SNR at output [-]

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

:<math> S_i = N_i \;\cdot\; F \;\cdot\; SNR_o = k T_a B \;\cdot\; F \;\cdot\; SNR_o </math>

where 
:<math>F</math> = [[noise factor]] 
:<math>N_i</math> = input noise power
:<math>SNR_o</math> = 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 input signal power for a given S/N ratio means better sensitivity since the receiver's contribution to the noise 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&nbsp;[[dBm]] is better than a receive sensitivity of −95&nbsp;dBm by 3&nbsp;dB, or a factor of two. In other words, at a specified data rate, a receiver with a −98&nbsp;dBm sensitivity can hear (or extract useable audio, video or data from) signals that are half the power of those heard by a receiver with a −95&nbsp;dBm receiver sensitivity.{{Citation needed|date=March 2013}}. 
== Electronic sensors ==
For electronic sensors the input signal <math display="inline">S_i</math> can be of many types, like position, force, acceleration, pressure, or magnetic field. The output signal for an electronic [[analog signal|analog]] sensor is usually a voltage or a current signal <math display="inline">S_o</math>. The [[responsivity]] of an ideal linear sensor in the absence of noise is defined as <math display="inline">R=S_o/S_i</math>, whereas for nonlinear sensors it is defined as the local slope <math>\mathrm{d} S_o/\mathrm{d} S_i
</math>. In the absence of noise and signals at the input, the sensor is assumed to generate a constant intrinsic output noise <math display="inline">N_{oi}</math>. To reach a specified signal to noise ratio at the output <math>SNR_o=S_o/N_{oi}</math>, one combines these equations and obtains the following idealized equation for its sensitivity<ref name=":1" /> <math>S</math>, which is equal to the value of the input signal <math display="inline">S_{i,SNR_o}</math> that results in the specified signal-to-noise ratio <math>SNR_o</math> at the output:

<math>S= S_{i,SNR_o} = \frac{N_{oi}}{R} SNR_o</math>

This equation shows that sensor sensitivity can be decreased (=improved) by either reducing the intrinsic noise of the sensor <math display="inline">N_{oi}</math> or by increasing its responsivity <math display="inline">R</math>. 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.<ref name=":0" /> This definition has the advantage that the sensitivity is closely related to the [[detection limit]] of a sensor if the minimum detectable ''SNR<sub>o</sub>'' is specified ([[Signal-to-noise ratio|SNR]]). The choice for the ''SNR<sub>o</sub>'' 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 (signal processing)|bandwidth]] ''BW'' or integration time ''τ=1/(2BW)'' (as explained here: [[Noise-equivalent power|NEP]]), because noise level can be reduced by [[signal averaging]], usually resulting in a reduction of the noise amplitude as <math>N_{oi} \propto 1/\sqrt{\tau}</math> where <math>\tau</math> is the integration time over which the signal is averaged. A measure of sensitivity independent of bandwidth can be provided by using the amplitude or power [[spectral density]] of the noise and or signals (<math>S_i, S_o, N_{oi}</math>) in the definition, with units like m/Hz<sup>1/2</sup>, N/Hz<sup>1/2</sup>, W/Hz or V/Hz<sup>1/2</sup>. For a [[white noise]] signal over the sensor bandwidth, its power spectral density can be determined from the total noise power <math>N_{oi,\mathrm{tot}}</math> (over the full bandwidth) using the equation <math>N_{oi,\mathrm{PSD}}=N_{oi,\mathrm{tot}}/BW</math>.  Its amplitude spectral density is the square-root of this value <math>N_{oi,\mathrm{ASD}}=\sqrt{N_{oi,\mathrm{PSD}}}</math>. Note that in signal processing the words energy and power are also used for quantities that do not have the unit Watt ([[Energy (signal processing)]]).

In some instruments, like [[spectrum analyzer]]s, a ''SNR<sub>o</sub>'' of 1 at a specified bandwidth of 1 Hz is assumed by default when defining their sensitivity.<ref name=":0" /> 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<ref name=":2">{{Cite journal |last=Jones |first=R. |date=1959 |title=Phenomenological Description of the Response and Detecting Ability of Radiation Detectors |journal=Proceedings of the IRE |volume=47 |issue=9 |pages=1495–1502 |doi=10.1109/JRPROC.1959.287047 |issn=0096-8390}}</ref> <math>NEI=N_{oi,ASD}/R</math>.  A lower value of the sensitivity corresponds to better performance (smaller signals can be detected), which seems contrary to the common use of the word sensitivity where higher sensitivity corresponds to better performance.<ref name=":3" /><ref>{{Citation |title=sensitivity |date=2024-08-19 |work=Wiktionary, the free dictionary |url=https://en.wiktionary.org/wiki/sensitivity |access-date=2024-08-21 |language=en}}</ref> It has therefore been argued that it is preferable to use [[detectivity]], which is the reciprocal of the noise-equivalent input, as a metric for the performance of detectors<ref name=":2" /><ref>{{Cite journal |last=Clark Jones |first=R. |date=1952 |title='Detectivity': the Reciprocal of Noise Equivalent Input of Radiation |url=https://www.nature.com/articles/170937b0 |journal=Nature |language=en |volume=170 |issue=4335 |pages=937–938 |doi=10.1038/170937b0 |bibcode=1952Natur.170..937C |issn=1476-4687|url-access=subscription }}</ref> <math>D=R/N_{oi}</math>.

As an example, consider a [[Piezoresistive effect|piezoresistive]] force sensor through which a constant current runs, such that it has a responsivity <math>R=1.0~\mathrm{V}/\mathrm{N}</math>. The [[Johnson noise]] of the resistor generates a noise amplitude spectral density of <math>N_{oi,\textrm{ASD}}=10~\mathrm{nV}/\sqrt{\mathrm{Hz}}</math>. For a specified ''SNR<sub>o</sub>'' of 1, this results in a sensitivity and noise-equivalent input of <math>S_{i,ASD}=NEI=10~\mathrm{nN}/\sqrt{\mathrm{Hz}}</math> and a detectivity of <math>(10~\mathrm{nN}/\sqrt{\mathrm{Hz}})^{-1}</math>, such that an input signal of 10 nN generates the same output voltage as the noise does over a bandwidth of 1 Hz.

== References ==
{{Reflist}}

{{FS1037C MS188}}

==External links==
*[https://www.sengpielaudio.com/calculator-transferfactor.htm Microphone sensitivity conversion from dB at 1 V/Pa to transfer factor in mV/Pa]

[[Category:Electrical parameters]]
[[Category:Microphone technology]]