View source for DBc

{{Short description|Unit used in signals}}
{{lowercase|title=dBc}}
'''dBc''' ('''decibels relative to the [[Carrier wave|carrier]]''') is the power ratio of a signal to a [[Carrier wave|carrier]] signal, expressed in [[decibels]]. For example, [[phase noise]] is expressed in dBc/[[Hertz|Hz]] at a given [[frequency]] offset from the carrier. dBc can also be used as a measurement of Spurious-Free Dynamic Range ([[Spurious-Free Dynamic Range|SFDR]]) between the desired signal and unwanted spurious outputs resulting from the use of signal converters such as a [[digital-to-analog converter]] or a [[frequency mixer]].

If the dBc figure is positive, then the relative signal strength is greater than the carrier signal strength.  If the dBc figure is negative, then the relative signal strength is less than carrier signal strength.

Although the [[decibel]] (dB) is permitted for use alongside [[International System of Units|SI]] units, the dBc is not.<ref>[http://physics.nist.gov/cuu/pdf/sp811.pdf Taylor 1995, Guide for the Use of the International System of Units (SI), NIST Special Publication SP811]</ref>

== Example ==
If a carrier (reference signal) has a power of <math display=inline>\mathrm{C} = 0{.}1\,\mathrm{mW}</math>, and noise signal has power of <math display=inline>\mathrm{S} = 10\,\mathrm{\mu W}</math>.

Power of reference signal expressed in decibel is :

: <math>P_\mathrm{C} = 10\log_{10} \left(\frac{0{.}1\,\mathrm{mW}}{1\,\mathrm{mW}}\right) = -10\,\mathrm{dBm}</math>

Power of noise expressed in decibel is :

: <math>P_\mathrm{S} = 10\log_{10} \left(\frac{10\,\mathrm{\mu W}}{1\,\mathrm{mW}}\right) = -20\,\mathrm{dBm}</math>

The calculation of dBc difference between noise signal and reference signal is then as follows:

: <math>P_\mathrm{S} - P_\mathrm{C} = -20\,\mathrm{dBm} - (-10\,\mathrm{dBm}) = -10\,\mathrm{dBc}</math>

It is also possible to compute the dBc power of noise signal with respect to reference signal directly as logarithm of their ratio as follows:

: <math> P_\mathrm{S} - P_\mathrm{C}  = 10\log_{10} \left(\frac{\mathrm{S}}{\mathrm{C}}\right) = 10\log_{10} \left(\frac{10 \,\mathrm{\mu W}}{0{.}1\,\mathrm{mW}}\right) = -10\,\mathrm{dBc}</math>.

==References==
{{reflist}}

==External links==
*[http://www.rp-photonics.com/decibel.html Encyclopedia of Laser Physics and Technology]

{{Decibel}}

[[Category:Units of measurement]]
[[Category:Radio frequency propagation]]
[[Category:Telecommunications engineering]]
[[Category:Logarithmic scales of measurement]]


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