# Decibels Maths, Query.

#### jvsib

Joined May 23, 2021
5
Good day, everyone!

I am wondering why we cannot add dBm to dBm? But we can add dB to dB and dB to dBm? Thank you!

#### BobTPH

Joined Jun 5, 2013
4,030
dBm is a measure of voltage. Db is a ratio.

Bob

#### Papabravo

Joined Feb 24, 2006
17,240
You can add (and subtract) dBm and dBm since both are referenced to the the same value, which is 0.001 of something. It may usually be 0.001 volts or 1 mV, but this is not a requirement. It could be 0.001 watts, or it could be \$0.001, and you could measure your net worth in dBm if you were so inclined. Things measured in dB still represent a ratio but the reference level is not fixed or even constant. That is why it makes no sense to add or subtract dBm and dB, in the same way it would make no sense to multiply the underlying ratios.

#### Ramussons

Joined May 3, 2013
1,098
Good day, everyone!

I am wondering why we cannot add dBm to dBm? But we can add dB to dB and dB to dBm? Thank you!
dBm is generally used as a measurement of Power in milli Watts. 0 dBm = 1 milliWatt.
You can add / subtract Power

dB is a Ratio - either Gain or Attenuation. This can also be Added or Subtracted.

You can add / Subtract dBm and dB which gives you Power Gain or Power Loss.

#### bertus

Joined Apr 5, 2008
21,667
Hello,

Perhaps the attached PDF's might help.

Bertus

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#### BobTPH

Joined Jun 5, 2013
4,030
dBm has the units of Watts (I got this wrong on my first post.)

dB and dBm are on a logarithmic scale. When you add two logarithms, you are doing a multiplication.

So, if you add two dBm values the result would be in square Watts! Not a meaningful value.

dB is pure number. When you add two dB values you are multiplying the numbers, and the result is still a number expressed in dB.

When you add a dB to a dBm, you are multiplying Watts by a number, which is still Watts, so it is valid.

Bob

#### ZCochran98

Joined Jul 24, 2018
179
dBm has the units of Watts (I got this wrong on my first post.)

dB and dBm are on a logarithmic scale. When you add two logarithms, you are doing a multiplication.

So, if you add two dBm values the result would be in square Watts! Not a meaningful value.

dB is pure number. When you add two dB values you are multiplying the numbers, and the result is still a number expressed in dB.

When you add a dB to a dBm, you are multiplying Watts by a number, which is still Watts, so it is valid.

Bob
Technically, dBm is a measure of power ratio, but not of power level - its units are not Watts. The unit of dBm is a measure of relative ratio of power to 1 mW (the ratio itself is unitless - P/1 mW) - somewhat similarly to how radians can be described as a measure of a unitless ratio of lengths (pi/4 rad = arctan(1/1), for instance). Adding and subtracting dBm is equivalent to scaling the corresponding power. So adding 3 dBm would double (roughly) the power. So adding/subtracting dBm isn't so much "adding/subtracting power" as it is "scaling 1 mW up and down." It doesn't result in W^2 units, as the manipulation is done on dBm, which relies on unitless ratios relative to 1 mW.
Hopefully I didn't just muddy the waters further.