Riassunto decibel

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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, because 10 · log10 ( P1 P2 ) dB = 10 · log10(2) dB = 3 dB. 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). • 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 · log10 ( PT 1 W ) = PT|dBm − 30 dB 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): P1 · G1/L1 = P2 ⇔ 10 · log10 ( P1 · G1/L1 1 W ) = 10 · log10 P2 1 W ⇔ P1|dBW + G1|dB − L1|dB = P2|dBW • Subtracting two powers (dBW or dBm) which is equivalent to computing their ratio (dB): P1 P2 ≜ 10 · log10 ( P1 P2 ) dB = 10 · log10 ( P1 1 W ) − 10 · log10 ( P2 1 W ) = P1|dBW − P2|dBW = 10 · log10 ( P1 1 mW ) − 10 · log10 ( P2 1 mW ) = P1|dBm − P2|dBm 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 1 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 = 10 W · 10 = 100 W ≜ 20 dBW ⇔ PT|dBW + GT|dBi = 10 dBW + 10 dBi = 20 dBW • Never add a bunch of…