The defining equation for decibels is
A = 10*log10(P2/P1) (dB)where P1 is the power being measured, and P1 is the reference to which P2 is being compared.
To convert from decibel measure back to power ratio:
P2/P1 = 10^(A/10)
Voltage is more easily measured than power, making it generally more convenient to use:
A = 20*log10(V2/V1) (Z2 == Z1)The equation for obtaining voltage ratio from dB is
V2/V1 = 10^(A/20)Decibels are defined in terms of Power ratios. Note well that the voltage-ratio equations are valid only if the two voltages appear across equal impedances.
However, in audio systems where Z0 is essentially zero and Zin is essentially infinite, it is common to use the voltage equation without regard to impedances. If this is done, the decibel values obtaind must in no case be applied to power or power-gain calculations.
Zero-dB standards: Audio industory: 0 dB = 1 mW in 600 Ohm resistance (Measurements to this standards use the unit symbol dBm) Relevision industory: 0 dB = 1 mV rms across 75 Ohm Radio frequency engineering: 0 dB = 1 mW in 50 Ohm resistance or 0 dB = 1 uV/m for electro-magnetic field strength
Radio engineers use absolute dBm of which zero-dB standard is 1 mW or absolute dBu of which zero-dB standard is 1uV.
Nepers by definition are a logarithmic measure of the ratio of two voltage magnitudes ow two current magnitudes, the logarithm being to the base e.