Conversions of power levels between W, dBW and dBm

dBm as a function of mW

Decibels (dB) are used to express power ratios in a logarithmic way, so that very large and very small powers can be compared using comfortable numbers. A decibel is a dimensionless pseudo-unit because it's defined on the ratio of two powers. But since decibels are so handy, there is also a way to express power (and not just a ratio) with them: with decibel-milliwatts (dBm) and decibel-watts (dBW). The most common unit is the dBm which is the power ratio relative to one milliwatt. Sometimes also dBW are used and they express the power ratio relative to one Watt. To convert dBm into dBW simply subtract 30.

P = 10 log_10 (p/p_0)    ;     p_0, dBW = 1 W ; p_0, dBm = 1 mW

Power :   P = dBW
P = dBm
p = W

Enter one value (either in dBW, dBm or W) and click the "Convert" button next to it to compute the two other values.


Conversions of amplitude levels between V, dBV and dBμV

dBuV as a function of uV

Especially when dealing with receiving antenna, it's common in some domains (like analog TV antennas) to measure the voltage instead of the power. Absolute voltages can also take advantage of the decibel logarithmic scale by using decibel-microvolt (dBμV) and decibel-volts (V). The most common is the dBμV which express the voltage ratio relative to one microvolt. Sometimes dBV are also used and they express the voltage ratio relative to one Volt. Beware that voltages, because do not express power directly, use a "20" instead of a "10" in their dB formula. To convert dBμV into dBV simply subtract 120.

U = 20 log_10 (u/u_0)    ;     u_0, dBV = 1 V ; u_0, dBuV = 1 uV

Amplitude :   U =  dBV
U =  dBμV
u =  V

Enter one value (either in dBV, dBuV or V) and click the "Convert" button next to it to compute the two other values.


Conversions between dBuV and dBm

dBm and dBuV as a function of W on 50 Ohms

To convert between dBm and dBμV or, in other words, between power and voltage, the impedance must be known, but the conversion is straightforward. If the impedance is 50 Ω, simply add 107.

P = 10 log_10 (p/p_0)    ;     p_0 = 1 mW    ;     U = 20 log_10 (u/u_0)    ;     u_0 = 1 uV    ;     p = u^2 / Z_c

Impedance :   Zc =  Ω  
Power :   P =  dBm
Amplitude :   U =  dBμV

Enter the impedance in Ohm and one value (either the power in dBm or the amplitude in dBuV) and click the "Convert" button next to it to compute the other value.

This conversion is only valid when the impedance Zc is real and the load is matched to the transmission line.


Bibliography:

P.-G. Fontolliet, Traité d'Électricité, Vol. XVIII: Systèmes de télécommunications Presses Polytechniques et Universitaires Romandes, 1996, Chapter 2.


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