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3 or 6dB?

Does combining two identical signals result in a 3dB or a 6dB increase? The answer is “yes”!

In our recent Word for the Day, “In Phase,” we mentioned that combining two identical signals resulted in a 3dB boost. Here’s some clarification on this point — and how 6dB figures into it — courtesy of our own decibel guru, David Stewart:

If you are talking about power (as in wattage) then, yes, the boost would be 3dB. But normally one is not talking about power in this context. Instead we’re concerned with voltage. Voltage is what all of the meters on our gear display.

Try it in your DAW sometime. Take two identical signals and sum them to a bus. The level on the bus will go up by 6dB on the meters.

Power, because it is already a product of voltage and current, is considered to double at 3dB. Go from 100 watts to 200 watts and that’s a 3dB increase. Here’s the formula:

10log (p2/P1) = dB

However, doubling the voltage equates to a 6dB increase. Here’s the formula:

20log (V2/V1).

This 6dB change is also evident from the fact that when you unbalance a balanced signal you lose 6dB (half the differential voltage), or, think about what each bit in digital audio resolution is worth: 6dB of dynamic range, because you have doubled the number of quantization steps, and by doing so have lowered the quantization error level by 6dB.

So in the “In Phase” Word for the Day you could say the signal amplitude doubles and be right on either count (voltage or power). But when you specify a decibel change (which I think is a good idea since that’s what’s displayed on all of our meters) you have to know whether you are talking about voltage, current, power, SPL, or whatever, to know what decibel change to expect or which formula to use if you are making calculations.

To make things even slightly more confusing; let’s say you have a 12-channel mix of tracks in your DAW. You then add an additional 12 tracks to it of various instruments. The overall level is going to increase by more than 3dB (power), but well under 6dB on the meters (voltage). These additional tracks aren’t identical to the first 12, but they are correlated.

Conversely, summing uncorrelated signals, such as noise, will give you a 3dB increase every time you double the number of channels.

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