Signal-to-Noise Ratio, Headroom and Dynamic Range

There are a couple of related concepts we need to consider here. Dynamic range is the total range of amplitudes a system can handle. For our ears, that dynamic range is 120 dB from threshold of hearing to threshold of discomfort. For audio systems dynamic range can be defined as the range of amplitudes between the noise floor of the system and its onset of clipping (the level at which the power supply is no longer adequate to provide larger waveforms). For acoustic spaces, the dynamic range can be defined as the range of sound pressure levels between the acoustical noise floor of the space and the onset of non-linearity in the air (around 130 dB SPL).

For convenience, we often divide dynamic range into two more specific ranges: signal-to-noise ratio and headroom. Signal-to-noise ratio is the range between some nominal maximum signal, which we usually call 0 VU or –14 dBFS, and the noise floor of the system. Headroom is the range above that nominal maximum signal to the onset of clipping (er, distortion). So, headroom plus signal-to-noise ratio equals dynamic range.

While this is obvious, it has some important ramifications that are easy to forget. If we increase headroom, we decrease signal-to-noise ratio. If we improve signal-to-noise, we decrease headroom. The two are related and always limited by the overall dynamic range of the system.

Take a look at some relevant dynamic ranges that we have to work with in audio: the range of our hearing, the range of a “good” acoustic environment and the range of a “good” analog audio signal prior to recording.

	Dynamic range of our hearing, a typical “quiet” acoustic environment, and an audio signal. Note that the audio signal’s noise floor may vary widely, depending on the signal processing, the type of recorder, etc. The absolute minimum noise floor (the thermal noise of a wire) is around -130 dBV.

Note that the limiting factor here turns out to be the acoustic environment. Interesting, eh? In fact, the dynamic range of a digital audio recorder, which we are not discussing here, has about the same range as the acoustic environment, ca. 90 dB. Another observation is that the actual range of the acoustic noise floor to the loudest acoustic sound is probably going to be substantially less than 90 dB SPL. Hardly anybody plays at 130 dB SPL!

Another good point to keep in mind is that the overall, final dynamic range of our recording will usually be determined by the smallest headroom range and the smallest signal-to-noise ratio the signal encounters on its odyssey from air to electricity to ear. So in Figure 1 above, the dynamic range of the signal will be 90 dB in spite of the fact that the audio signal and our hearing both have ranges greater than that.