dB/dBW/dBm cheat sheet
• dB is a logarithmic ratio of powers. So saying P1 = 2 · P2 is equivalent to saying P1/P2 3 dB,
10·log10P1 dB=10·log10(2)dB=3dB. P2
The unit dBi can be treated just like dB, because it measures the gain of an antenna relative to an isotropic antenna which has the gain of 1 (0 dB).
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• dBm and dBW is a (logarithmic) unit to measure powers. Since dB is a ratio of powers, dBm and dBW are defined by forming the ratio of the power you want to express relative to a reference power, which is 1 W for dBW and 1 mW for dBm. Formally speaking,
PT|dBm=10·log10 PT 1 mW
PT|dBW=10·log10PT =PT|dBm−30dB 1W
Consequently, two things are okay:
• Starting with a power (dBW or dBm) you can add and subtract ratios (dB or dBi) as often as you like
and you still have a power (dBW or dBm):
P ·G/L =P ⇔ 10·log P1·G1/L1=10·log P2 1112 101W 101W
⇔ P1|dBW + G1|dB − L1|dB = P2|dBW
• Subtracting two powers (dBW or dBm) which is equivalent to computing their ratio (dB):
P1 10·log10P1dB=10·log10P1 −10·log10P2 =P1|dBW−P2|dBW P2 P2 1W 1W
=10·log10 P1 −10·log10 P2 =P1|dBm−P2|dBm 1 mW 1 mW
Both powers must have the same unit, do not mix dBW and dBm. Short hand notation for things that are okay:
dBW±dB =dBW dBm±dB =dBm
dBW−dBW =dB dBm−dBm =dB
On the other hand, the following things are not okay:
• Never ever multiply dBW with dB! I have seen students claiming that a power of PT =10 W with an antenna gain of GT =10 gives an effective radiated power of 100 dBW. No! 100 dBW is 10 Gigawatts! Multiply in linear scale, that becomes addition in logarithmic scale:
PT ·GT =10W·10=100W20dBW
⇔ PT|dBW + GT|dBi = 10 dBW + 10 dBi = 20 dBW
• Never add a bunch of quantities in dBW or dBm! Adding powers in log scale means multiplying them in linear scale. If you add 10 dBW with 3 dBW and 6 dBW then you have
10 dBW + 3 dBW + 6 dBW 10 W · 2 W · 4 W = 80 W3 What unit is Watt cubed? I don’t know, you tell me…
• A power cannot be measured in dB. A gain/loss cannot be measured in dBm or dBW.
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