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I have just started studying Audio Engineering and I have come across a section where I need to add decibel levels together.

I am aware that adding two decibel levels together will always give you the answer of +3dB (e.g, 90dB + 90dB = 93dB)

However, the equation I am using to do this is;

log(10)x(10^(90/10))+(10^(90/10))

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The answer that this gives me is "2,000,000,000"

Is there a step that I am missing here?

Thanks!

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Oops. Careful here.

Let us start with the fact that dB as a measurement is ALWAYS a relation between two things. If the things are equal the relation is 0dB.

It becomes slightly more complicated when we get to 10dB in electrical circuits. The reason is that in electrical circuits, this is where the measurement comes from originally, you may want to talk either about power or about amplitude. For power, 10dB is 10 times the power, for amplitude 20dB is 10 times the amplitude.

When using dB we should always define what the measurement base is. Examples of bases are dBV (1V being the reference), dBW (1W beeing the reference), dBFS (full scale, whatever that is beeing the reference), dBA (sound level, A-weighted) and so on.

In electronics we often talk about amplitude amplification (see as example the gain control on a preamp). An example might be 20dB amplification. In amplitude terms, if we send in a signal at 1 mV, after 20dB amplification it will be 10mV. If we add two amplifiers after each other, each with 20dB amplification, the sum will be 40dB amplification or 100mV.

Assume now that we wish to add together two electrical signals, say both att 0dBV. If we add together two identical signals, the output will be double. Double in dBV is around 6dB. So 0dBV + 0dBV is about 6dBV. And 90dBV + 90dBV is 96dBV.

Assume that instead we wish to add together two electrical signals, say both att 0dBW. The result will now be 3dBW which is double power. Remember that dB can never stand by itself.

Assume that we want to add 0dBV to 0dBW? The result is not possible to answer unless we get more information. We need to know how the reference is created in order to "transform" between the two measurements.

Most often you will work with amplitude. The main formula is that if you add two identical signals, you will add 6dB. If the signals are 180 degrees out of phase the result will be 0 (the two signals cancel). If you add two unrelated signals with the same input level, the benchmark value is around 3dB.

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you're getting confused between signals and levels.

If you mix two identical signals together, in phase, each indicating a level of -X dbFS, then the resulting signal will be 6dB higher.

If the two signals are not identical, then mixing them together will result in a signal level increase of approximately 3dB.

Adding two "decibel" levels together is simply additional 4dB + 5dB = 9dB.

Don't confuse the "decibel level" with the signal.

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You are just using the wrong formula. You'd want $10dB\log_10 (10^{90/10}+10^{90/10})$

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