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# decibels relative to carrier (dBc)

dBc (decibels relative to carrier) is a measure of the strength of an instantaneous signal at radio frequency . The dBc increment is based on the decibel , a logarithm ic measure of relative signal strength. Suppose a signal has an unmodulated-carrier power of P watts and a modulation signal power of P watts at some specified instant in time. Then the instantaneous modulated signal strength in dBc, symbolized S dBc ,is:

S dBc = 10 log 10 P / P

Signal strength in dBc can also be calculated in terms of the effective signal voltage if the impedance remains constant. Suppose a signal has an unmodulated-carrier root-mean-square ( rms ) voltage of V volts and a modulated rms signal voltage of V volts at the same impedance. Then the instantaneous modulated signal strength in dBc is:

S dBc = 20 log 10 V / V

If the dBc figure is positive, then the instantaneous modulated signal strength is greater than the unmodulated-carrier signal strength. If the dBc figure is negative, then the instantaneous modulated signal strength is less than the unmodulated-carrier signal strength.

This was last updated in March 2011

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The two equations above contain V/ V and P/ P which is '1'. Please correct the equations with the correct subscriptions to differentiate between the denominator and the numerator.
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