dBc (decibels relative to the carrier) is the power ratio of a signal to a carrier signal, expressed in

decibels The decibel (symbol: dB) is a relative unit of measurement equal to one tenth of a bel (B). It expresses the ratio of two values of a Power, root-power, and field quantities, power or root-power quantity on a logarithmic scale. Two signals whose ...

. For example,

phase noise In signal processing, phase noise is the frequency-domain representation of random fluctuations in the phase of a waveform, corresponding to time-domain deviations from perfect periodicity (jitter). Generally speaking, radio-frequency engineers ...

is expressed in dBc/ Hz at a given

frequency Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...

offset from the carrier. dBc can also be used as a measurement of 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 In electronics, a digital-to-analog converter (DAC, D/A, D2A, or D-to-A) is a system that converts a digital signal into an analog signal. An analog-to-digital converter (ADC) performs the reverse function. There are several DAC archit ...

or a

frequency mixer In electronics, a mixer, or frequency mixer, is an electrical circuit that creates new frequencies from two signals applied to it. In its most common application, two signals are applied to a mixer, and it produces new signals at the sum and di ...

. 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 The decibel (symbol: dB) is a relative unit of measurement equal to one tenth of a bel (B). It expresses the ratio of two values of a power or root-power quantity on a logarithmic scale. Two signals whose levels differ by one decibel have a po ...

(dB) is permitted for use alongside SI units, the dBc is not.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

\mathrm = 01\,\mathrm

, and noise signal has power of

\mathrm = 10\,\mathrm

. Power of reference signal expressed in decibel is : :

P_\mathrm = 10\log \left(\frac\right) = -10\,\mathrm

Power of noise expressed in decibel is : :

P_\mathrm = 10\log \left(\frac\right) = -20\,\mathrm

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

P_\mathrm - P_\mathrm = -20\,\mathrm - (-10\,\mathrm) = -10\,\mathrm

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: :

P_\mathrm - P_\mathrm  = 10\log \left(\frac\right) = 10\log \left(\frac\right) = -10\,\mathrm

References

External links

Units of measurement Radio frequency propagation Telecommunications engineering Logarithmic scales of measurement {{Tech-stub