For many of us, fundamentals are like Swiss cheese: mostly solid but with intermittent but noticeable holes. This is the second part of a series of articles exploring the principles and properties of audio systems and related fields. (Read Part 1 here.)
We’re going to focus on the properties of analog electronic transmission. Perhaps you know everything on this subject already, but just maybe there are a few holes that can be filled in and make the reading effort worthwhile.
Q: What’s the difference between peak and rms?
At least 3 dB. Maybe a lot more. Peak is easy to define. It’s the waveform’s amplitude value at any given moment in time. View it on an oscilloscope (or Pro Tools) and there it is.
The rms value is the challenging one because it’s strictly a mathematical construct. We don’t listen to rms versions of our favorite songs (it would be worse than an MP3!). The term “rms” stands for root of the mean of the square. It’s functionally the average amplitude, but we must go through the squaring and square rooting because an audio signal has positive and negative values (which would otherwise average to zero).
So what does the rms value give us? For electrical signals, it’s the heat dissipation value and for acoustic signals the perceived loudness. Loudspeakers can be destroyed by too much of either (peak tears them up and rms burns them up).
Peak values are inherently higher than rms values. The differential between peak and rms is termed the “crest factor” and varies with input signal (Figure 1). A sine wave has the lowest crest factor (3 dB), pink noise has around 12 dB and transient impulses can exceed 40 dB.
Bear in mind that dynamic range is limited by peak rather than rms levels. It’s the peak waveform that clips, e.g., a transient impulse (like a snare drum) can clip the system and yet barely move an rms-reading level meter.
A final note: the numerical renderings of digital audio are always peak-to-peak. There is no reason to calculate heat load or loudness of a number.
Q. What’s the difference between 0 dBV and 0 dBu?
2.21 dB (i.e. 0 dBV = +2.21 dBu). The reference point for the dBV scale (that’s dB “voltage”) is 1 volt rms. Seems logical. By contrast, 0 dBu (dB “unloaded”) is referenced to 0.775 volts, which sounds like somebody was loaded when they thought this up.
The dBu standard is the descendent of dBm (dB “milliwatts”), which I guess contrasts to “dB not measured.” The dBm standard was created to monitor power transmission for grandpa’s passive telephone: 0.775 volts across a 600-ohm load = 1 milliwatt. dBu keeps the voltage part of dBm and unloads the impedance part (Figure 2).
Q. What is headroom?
The distance between the top of your head and the doorway you’re walking through. I have about 3 dB more than Shaquille O’Neal.
An audio waveform contains the full extensions of the peak-to-peak amplitude levels. If our signal can be moved along without hitting the upper/lower limits (i.e. clipping) then we have headroom, which can be characterized in dB. Simply put, headroom is the remaining peak capability before overload on a moment to moment basis.
In an analog electronic context this the voltage left before hitting the DC rails. For a loudspeaker, it’s how much distance remains before reaching the excursion limits. In digital world: the remaining bits before full scale.
Q. What is dynamic range?
At the opposite end of headroom is the floor, in this case, the noise floor. Dynamic range is the area between the noise floor (the point where our signal gets swamped by the competition) and the overload point (analog electronic clipping, loudspeaker excursion limits, etc.).
In the digital world, the dynamic range is the difference because the highest number we can count (full scale digital) and the threshold point of the lowest bit.