dB and dBm in a Signal Chain: Adding Gains and Losses
A gain or loss in dB is added to a level in dBm to give the new level in dBm. A -10 dBm signal through a 20 dB amplifier and a cable with 3 dB loss ends at +7 dBm, about 5 mW.
For practitioners
Why decibels make signal chains easy
Power ratios in an RF chain span many orders of magnitude. An amplifier may multiply power by 100, and a cable may remove half of it. Multiplying these ratios works, but the numbers get awkward. Decibels turn multiplication into addition, so you can follow a level through a chain with a pencil.
A ratio of two powers in decibels is:
A positive result is gain. A negative result is loss. The value is a pure ratio and has no reference level. That is why a gain is written "dB" and not "dBm".
What dBm adds
dBm is power relative to 1 mW:
So 0 dBm is 1 mW and 30 dBm is 1 W. The inverse is:
Because dBm is an absolute level, it names a real power. Because the dB gain is a ratio, the two combine cleanly. This is the rule the whole article rests on:
New level (dBm) = old level (dBm) + gain (dB), where a loss counts as negative gain.
Three anchor values let you estimate most levels without a calculator:
- +10 dB multiplies power by 10.
- +3 dB multiplies power by about 2.
- -3 dB is about half the power.
Other values follow by combining these. For example, +13 dB is +10 dB plus +3 dB, so about 20 times the power.
Following a level through a chain
Write the chain as a list. Start with the input level, then apply each block in order. Gains are positive, and losses (cables, attenuators, filters, connectors) are negative.
Worked example. A signal of -10 dBm goes into a 20 dB amplifier, then through a cable with 3 dB loss.
- Input: -10 dBm.
- After the amplifier: -10 + 20 = +10 dBm.
- After the cable: +10 - 3 = +7 dBm.
The final level is +7 dBm. To check it in linear units: -10 dBm is 0.1 mW. A 20 dB gain multiplies by 100, giving 10 mW. A loss of 3 dB roughly halves that, leaving about 5 mW. Exactly, 10^(7/10) mW is 5.01 mW, so the two routes agree.
Order does not change the final result in this simple case, since addition is commutative. It does change the level at each point. Put the 3 dB cable before the amplifier and the final level is still +7 dBm, but the amplifier now sees -13 dBm instead of -10 dBm. That matters for noise and for compression, covered below.
Add an attenuator and the same method applies. A 10 dB attenuator after the +7 dBm point gives 7 - 10 = -3 dBm, which is about 0.5 mW. If you need the resistor values for a pad, the attenuator calculator gives them.
Keep a table with one row per block: name, gain or loss in dB, and the running level in dBm. Most chain errors show up as a row that does not follow from the one above it.
Where this goes wrong
Adding two dBm values. The sum -10 dBm + 20 dBm has no meaning, because dBm is a logarithm. Powers add, not their logarithms. To combine two signals, convert each to milliwatts, add, and convert back. Two equal incoherent signals of 0 dBm are 1 mW + 1 mW = 2 mW, which is about +3 dBm. If the signals are unequal, the larger one dominates. A 0 dBm signal plus a -10 dBm signal is 1 + 0.1 = 1.1 mW, about 0.4 dBm.
Mixing up dB and dBm in the result. The difference of two dBm levels is a ratio in dB. For example, +7 dBm minus -10 dBm is 17 dB. A dB value plus a dBm value is dBm. A dB value plus a dB value is dB. Keeping track of the unit prevents most slips.
Forgetting dBW. dBW is dBm minus 30. So 30 dBm is 0 dBW. A level quoted in dBW looks 30 units smaller than the same level in dBm.
Treating an amplifier as ideal. The arithmetic adds the small-signal gain. A real amplifier cannot deliver unlimited output. If the computed level exceeds what the amplifier can output, the real level will be lower and the signal will be distorted. Check the output level at each stage against that stage's limit, not only the final number.
Ignoring small losses. Connectors, adapters and short cables each remove a little. Over several blocks, small losses add up. Put each one in the table.
Assuming a perfect match. The method assumes each block passes power as specified. A mismatch between blocks changes how much power is delivered, and that is a separate calculation from adding gains.
To convert any level to watts, volts or dBµV, use the dBm to watts converter.
In plain words · for students and beginners
Signal levels in plain words
An everyday picture
Think of water pressure in a long pipe. The water starts at some pressure. A pump raises it, and a leaky stretch lowers it. You can follow the pressure by adding what each part does: plus for the pump, minus for the leak.
A signal chain works the same way. The signal has a level, measured in dBm. An amplifier adds to it, and a cable or attenuator takes some away. (An attenuator is a part that lowers the signal on purpose.) You just add and subtract.
The picture breaks down in one place. Two signals at the same point do not add as simple numbers. If you pour two cups of water into a jug, you add the amounts. With dBm you must first turn each level back into plain power, add those, and then convert back.
The same example in simple steps
- Start with -10 dBm.
- The amplifier gives 20 dB of gain. Add it: -10 + 20 = +10 dBm.
- The cable loses 3 dB. Subtract it: +10 - 3 = +7 dBm.
The answer is +7 dBm. In plain power, that is about 5 mW. You can check it. +10 dBm is 10 mW, and losing 3 dB cuts the power about in half, so 10 mW becomes about 5 mW.
Mistakes beginners make
- Adding two dBm numbers. If two 0 dBm signals meet, the total is not 0 + 0. Each is 1 mW, so together they are 2 mW, which is about +3 dBm.
- Mixing up the units. dB is a change, like "plus 20". dBm is a real level, like "10 mW". A change added to a level gives a level.
- Forgetting the small losses. Every cable, adapter and connector takes a little. Write each one down.
- Trusting the amplifier too much. An amplifier cannot give unlimited power. If your sum says the output is very large, check what the amplifier can really deliver.
- Mixing up dBm and dBW. dBW is dBm minus 30. So 30 dBm equals 0 dBW.
Remember
- Add gains in dB and subtract losses in dB; the level stays in dBm.
- +10 dB is ten times the power, +3 dB is about double, and -3 dB is about half.
- Never add two dBm values; convert to milliwatts, add, then convert back.
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Frequently asked questions
Can I add two dBm values together?
No. dBm is a logarithm of power, so you must convert to milliwatts, add the powers, and convert back. Two equal incoherent signals of 0 dBm make about +3 dBm, not 0 dBm.
What is the difference between dB and dBm?
dB is a ratio between two powers, so it describes gain or loss. dBm is an absolute level referenced to 1 mW. You add a dB value to a dBm value and the result is dBm.
How do I convert dBm to dBW?
Subtract 30. A level of 30 dBm is 1 W, which is 0 dBW.
How much power is +7 dBm?
P = 10^(7/10) mW, which is about 5 mW. It is roughly half of the 10 mW at +10 dBm, because 3 dB less means about half the power.