Signal Levels

This article is a quick summary about audio signal levels, and why it's important to know what they are.

AD/DA Conversion

We won't go into great detail into this process in this article, but thought it was important to call out the importance. To get our analog audio into our DAWs, we need to use an Analog-to-Digital converter - typically incorporated in our audio interface. The Voltage-over-Time signal is sampled at some frequency, and quantized to a digital reproduction; or the opposite Digital-to-Analog on the way back out from our computer to some external piece of music gear. The main takeaway here is the capabilities of your converter are the crux of the quality of your audio your every time it passes to/from your computer, and it relates to voltages.

For a very thorough overview, check Chapter 3: ADC and DAC of The Scientist and Engineer's Guide to Digital Signal Processing By Steven W. Smith, Ph.D. The entire book is free to read/download online!

Decibel

Get ready for the math-y part!

A bel correlates to a change of power (think Watts) by a factor of 10. 2 bel of amplification is 10x10, or a signal that is 100 times more than the original. That's an awful lot for the signal levels we typically work with, so we usually use decibel (dB), which is a tenth of a bel. -10 dB, 0dB, 10 dB have the power ratios of 0.1, 1, 10, and so on.

For a $P_{in}$ and $P_{out}$, we can write that as

$$dB = 10 \times log_{10} \frac{P_{out}}{P_{in}}$$

We are usually more interested in a signals amplitude A than its power, so we can use their relationship to also write it this way

$$dB = 20 \times log_{10} \frac{A_{out}}{A_{in}}$$

These equations show us that the decibel are a convenient way to think of a ratio between signals (a great example is gain). Some useful things drop out of this, like every +3dB correlates to a doubling of the power (or halving, in the negative direction). If we compare the ratio of a signal against some standard, then we have something that allows us to speak to each other in a common understanding.

But, in typical human fashion, we take common understanding and make it complicated. When something is given in dBV, it's references to a 1 volt rms signal. dBm is a signal that produces 1mW of power into a $600\Omega$ load, but dBu is referenced to an unloaded rms voltage of 0.775V.

$$dBm = 10 \times log_{10} \frac{P_{out}} {1mW}$$

$$dBu = 20 \times log_{10} \frac{P_{out}}{0.775V}$$

We'll talk about dBVU (Volume Unit - think of an analog audio meter) in the Line Level section.

Mic Level

Microphones typically output in the mV to tens of mV range, depending if they have a small amplifier already built in. Using our equations above, that correlates to roughly -60 to -40 dBV. We can see from these numbers that we could end up needing quite a bit of gain for a low-output mic. We can use this knowledge to make sure we have an appropriate mic preamp to pair with the microphone intended to be used.

Line Level

There are two line-levels to be aware of: Pro Audio, and Consumer Audio.

In Pro Audio, 0 dBVU is defined as +4 dBu or 1.228 V rms (roughly 2 dBV). In Consumer Audio, 0 dBVU is defined as -10 dBV or 0.316 V rms. So if we try to use a lint out on our personal CD player into our pro mixer, we would find the signal is about 12 dB too low (or 12 dB too high the other way around!).

Knowing all these operating voltage levels/ranges is important for different devices to work well with each other, so that the output of one is in the sweet spot on the input of another. Nobody wants an unexpected +12 dB blast to their headphones. This is the cornerstone of gain staging.

Digital Level

dBFS (dB Full Scale), which is used in digital systems like DAWS, where 0 dBFS is the hard limit, and harsh clipping will occur with no wiggle room. There isn't an exact conversion from dBFS to dBVU, but it is typically calibrated somewhere around -16 to -20 dBFS to equal 0 dbVU - which will probably depend on what your AD/DA converters are capable of!

If you don't have a VU meter handy, you can use a trusty multimeter to measure the AC voltage across pins 2 and 3 (hot and cold respectively, with pin 1 being ground) of an XLR output from your converters. You can use a tool such Room EQ Wizard to send a 1 kHz sine wave at a particular dBFS level, and figure out which level gives you 1.228 V. Knowing this level will get you in a great spot to know what volumes to target for sending from your DAW to outboard analog audio gear, and how much headroom you have at your disposal.

Gain Staging

The key takeaway so far has been that it's important to know what signal levels different pieces of gear expect as input, and produce as output, so that we can effectively chain them together while they operate in there designed sweet spot. This is especially true for analog gear, which is usually made to operate nominally around 0 dBVU, and can be musically driven with slightly more gain. It is just as important in the digital-only world, as plugins can clip - or may even be made to emulate driving analog hardware. By keeping our audio levels in check between each piece of gear, or VST, (aka gain staging) we can avoid unwanted distortion and noise.