Index / Units
Decibel Converter
Power in watts, dBm or dBW; antenna gain in dBi, dBd or a plain ratio; and the EIRP the two of them add up to. Decibels are not one unit but two kinds of thing, and this keeps them apart.
Transmitter
Subtracted from the power before the antenna.
A loss is a positive number here.
Only used for the dBµV row. Everything else is
independent of impedance.
Antenna
EIRP
--
At the antenna
--
Gain
--
The same values, written every way
The two kinds of decibel, and the constants used
dBm and dBW measure a power. dBi, dBd and dB measure a ratio.
They are not interchangeable and this tool will not pretend they are:
there is no answer to “what is 12 dBi in dBm”. A ratio has no
size until you apply it to something, which is what the EIRP line does.
dBm = dBW + 30, exactly. One watt is 1,000 milliwatts, and 10 log10(1000) is exactly 30.
dBi = dBd + 2.15. A half-wave dipole has a directivity of about 1.64 over isotropic, and 10 log10(1.64) is 2.1484 dB. 2.15 is the figure every datasheet and regulator uses, so it is the one used here; the 0.0016 dB difference is far below anything measurable.
Power uses 10 log10, voltage and field strength use 20 log10. This is the mistake that costs people a factor of two. Both ratios are shown below so it is visible which is which: the voltage ratio is always the square root of the power ratio.
dBµV = dBm + 10 log10(R) + 90. At 50 Ω that is +106.99, which is where the +107 in receiver datasheets comes from. At 75 Ω it is +108.75. This is the one figure here that depends on impedance.
EIRP = power − loss + gain, all in dB. ERP is the same thing referred to a dipole rather than an isotropic radiator, so it is 2.15 dB lower. Regulators specify one or the other and rarely say which.
Very large and very small powers are written with SI prefixes (pW, µW, kW) rather than scientific notation, because 0.000000000001 W is not a number anyone can read and 1e-12 is not one anyone can screenshot.
dBm = dBW + 30, exactly. One watt is 1,000 milliwatts, and 10 log10(1000) is exactly 30.
dBi = dBd + 2.15. A half-wave dipole has a directivity of about 1.64 over isotropic, and 10 log10(1.64) is 2.1484 dB. 2.15 is the figure every datasheet and regulator uses, so it is the one used here; the 0.0016 dB difference is far below anything measurable.
Power uses 10 log10, voltage and field strength use 20 log10. This is the mistake that costs people a factor of two. Both ratios are shown below so it is visible which is which: the voltage ratio is always the square root of the power ratio.
dBµV = dBm + 10 log10(R) + 90. At 50 Ω that is +106.99, which is where the +107 in receiver datasheets comes from. At 75 Ω it is +108.75. This is the one figure here that depends on impedance.
EIRP = power − loss + gain, all in dB. ERP is the same thing referred to a dipole rather than an isotropic radiator, so it is 2.15 dB lower. Regulators specify one or the other and rarely say which.
Very large and very small powers are written with SI prefixes (pW, µW, kW) rather than scientific notation, because 0.000000000001 W is not a number anyone can read and 1e-12 is not one anyone can screenshot.