Once Again, Signal-to-Noise Ratio, Headroom and Dynamic Range

To briefly reiterate what I said in last month’s article, signal-to-noise ratio is the range between the nominal maximum signal level (typically 0 VU) and the noise floor of the system. Headroom is the range between the nominal maximum signal (0 VU) and the onset of distortion (or pain, in humans). Dynamic range is the sum of these two, the range between noise floor and the onset of distortion/pain. Remember, for a given signal, if you increase headroom, you sacrifice signal-to-noise ratio, and vice versa. Less noise means more likelihood of distortion, etc. Further, remember that the overall dynamic range is limited by the stage(s) with the least headroom and the worst signal-to-noise ratio.

Take a look at the following graphic showing a bunch of dynamic ranges:

	Dynamic range of our hearing, of a good control room, an audio signal that has been through typical signal processing, and a signal coming off a cassette tape.

Notice that the typical control room environment is pretty shabby. All that machine noise, as well as air-conditioning and computer fans, conspire to destroy any semblance of a quiet environment. Meanwhile, most nearfield monitors run out of steam at around 100 dB SPL and 110 dB SPL is about as loud as you can get under normal conditions. It is surprising and a little discouraging to notice that our control room does about as well as a cassette deck!

With that in mind, let’s take a closer look at what happens in the control room. There are a number of issues which we have already alluded to: the noise floor of the room and the level of the monitor speakers. Aside from defining these a little more thoroughly, we also have to discuss the relationship between 0 VU (the nominal maximum signal level) and the level of the monitors, plus a look at reverberant level.

Speaker sensitivity and amp power

All speakers have a given sensitivity. This is usually expressed as the Sound Pressure Level they generate at 1 meter (3 feet) on-axis when fed by a 2.8 Volt signal (which is 1 Watt for a speaker with an impedance of 8 ohms). Small speakers typically have sensitivities in the 83-89 dB SPL range, while larger, more efficient systems have sensitivities in the 89-95 dB SPL range. Sound reinforcement speakers often have sensitivities of over 100 dB SPL for a 2.8 volt input.

What this means is that when you sit on-axis to two loudspeakers each with a given sensitivity of, say 89 dB, each 3 feet away, and each being driven by a 2.8 Volt signal, the sound pressure level at your ears is going to be, in theory, 3 dB (twice the power) above 89 dB SPL, or 92 dB SPL. If your amp will put out 100 Watts per channel, then the peak undistorted output level you can obtain will be 109 dB SPL at each speaker, or 112 dB SPL total. In fact, it may be a little louder, due to phase coherence at low frequencies.

Now it’s wise to leave some headroom here. Just to prevent your monitors from turning to toast, 20 dB of headroom isn’t a bad thing to shoot for. This brings us right back to 92 dB SPL as a reasonable nominal maximum signal level for this quite efficient bookshelf system.

Note that if your speakers are less efficient, say 83 dB for 2.8 Volts input, then approximately 1 Watt/channel will give you 86 dB and you’ll run out of gas 6 dB sooner. My experience has been that you really notice this!

The inverse square law

The above levels are only true when you are sitting three feet from the speakers – and such distances and levels are reasonable when you are working with In-Yer-Face® monitors. Nominal power is around 1 Watt, and 92 dB SPL is plenty loud!

If the monitors are more than 3 feet away, then you have to take into account the loss in level that occurs. The inverse square law states that the loss will be 6 dB for every doubling of the distance that occurs. So, if you sit 6 feet from your monitors, the levels will be 83 dB SPL from each speaker, 86 dB SPL overall, and overload will occur at 106 dB SPL. At 12 feet, the speakers will generate 80 dB SPL overall and clipping will occur at 100 dB SPL.

Another issue that also comes in to play here is reverberance. The levels I have just presented are, I have assumed, direct sound only. A control room is reverberant, and the reverberant level is reasonably constant throughout the room. What this means is that as you move away from the speakers the direct sound will attenuate while the reverberance will remain roughly constant, so that the reverberance will play an increasingly important role in the overall sound. When the reverberance is as loud as the direct sound, by definition you are at the so-called Critical Distance of the room. In the above example, if the Critical Distance for the room was 12 feet, the speakers’ direct sound would be 80 dB SPL at 12 feet, the reverberant sound would also be 80 dB SPL and the overall level would be 83 dB SPL. As you move even farther away, the direct sound will become softer than the reverberant sound, which presents some interesting but serious problems for mixing.

This speaks to one of the other qualities of monitors used in your face – they tend to de-emphasize relative reverberance. However, keep in mind that reverberance is neither (a) all bad, or (b) unnecessary. It is worth noting that mixes sound quite different on In-Yer-Face® monitors at three feet than they do on monitors that are situated more conventionally. Beware!