A large part of sound engineering involves adjusting signal level: finding the right level or finding the right blend of levels. The level of a real sound traveling in air can be measured in µN/m2 (or µPa/m2 – micropascals per square meter if you prefer), or more practically dB SPL with reference to 0 dB SPL or 20 µN/m2. The level of a signal in electrical form can be measured in volts, naturally, or it can be measured in dB. The problem is that decibels are always a comparison between two levels. For acoustic sounds, the dB SPL works by comparing a sound level with the reference level 20 µN/m2 (the threshold of hearing).
Therefore we need a reference level that works for voltage.
Going in back in history, early telecommunication engineers were interested in the power that they could transmit over a telephone line.
They decided upon a standard reference level for power, which was 1 mW (1 milliwatt, or one thousandth of a watt). This was subsequently called 0 dBm. The ‘m’ doesn't stand for anything, it just means that any measurement in dBm is referenced to 1 mW. Today in audio circuitry, we are not too concerned about power except at the final end product – the output of the power amplifier into the loudspeaker. For the rest of the time we can happily measure signal level in voltage. Going back into history, standard telephone lines had a characteristic impedance of 600 ohms. (‘Characteristic impedance’ is a term hardly ever used in audio so explanation here will be omitted). The relationship between power, voltage and impedance is: P = V2/R. Working out the math we find that a power of 1 mW delivered via a 600 ohm line develops a voltage of 0.775 V. This became the standard reference level of electrical voltage, and it is still in use today.
There is a slight problem here. Over the years it became customary to refer to a voltage of 0.775 V as 0 dBm. This is not wholly correct. It is only true when the impedance is 600 ohms, which is not necessarily the case in audio circuitry. Despite this, any reference you find to 0 dBm, in practice, means 0.775 V regardless of what the impedance is.
Technical sound engineers abhor inconsistencies like this, so a new unit was invented: dBu, where 0 dBu is 0.775 V, without any reference to impedance. Once again, the ‘u’ doesn't stand for anything. ‘dBu’ is sometimes written ‘dBv’ (note lower case ‘v’). Confusingly there is also another reference: dBV (note upper case ‘V’), where 0 dBV is 1 volt. In summary:
dBr is a measurement in decibels with an arbitrary quoted reference level dBFS is a measurement in decibels where the reference level is the full level possible in a specific item of digital audio equipment. 0 dBFS is the maximum level and any measurement must necessarily be negative, for example –20 dBFS.
All of the above (with the exception of dBFS) refer to electrical levels.
We also need levels for magnetic tape and other media. Analog recording on magnetic media is still commonplace in top level music recording, and outside of the developed countries of the world. Magnetic level is measured in nWb/m (nanowebers per meter). ‘Nano’ is the prefix meaning ‘one thousandth of a millionth’. The weber (Wb) is the unit of magnetic flux. Wb/m is the unit of magnetic flux density, or simply ‘flux density’. Wilhelm Weber the person (pronounced with a ‘v’ sound in Europe, with a ‘w’ sound in North America), by the way, is to magnetism what Alessandro Volta is to electricity.
There are a number of magnetic reference levels in common use. Ampex level, named for the company that developed the tape recorder from German prototypes after World War II, is 185 nWb/m. NAB (National Association of Broadcasters, in the USA) level is 200 nWb/m. DIN (Deutsche Industrie Normen, in Europe) level is 320 nWb/m. In summary:
Ampex level: 185 nWb/m NAB level: 200 nWb/m DIN level: 320 nWb/m
It’s worth noting that none of these reference levels is better than any other, but NAB and DIN are the most used in North America and Europe respectively.
Operating Level
An extension of the concept of level is operating level. This is the level around which you would expect your material to peak. Much of the time the actual level of your signal will be lower, sometimes higher. It’s just a figure to keep in mind as the roughly correct level for your signal. In electrical terms, the standard operating level of professional equipment is 0 dBu. There is also a semi-professional operating level of –10 dBV.
This does cause some difficulty when fully professional and semi-professional equipment is combined within the same system. Either you have to keep a close eye on level and resign yourself to making corrections often, according to what combination of equipment you happen to be using, or buying a converter unit that will bring semi-pro level up to pro level.
Magnetic tape also has a standard ‘operating level’ - several of them in fact. To simplify a little since analog magnetic tape is now a minority medium, albeit an important minority: In a studio where VU meters are used, then it is common to align the VU meters so that 0 VU equals +4 dBu. Tape recorders would be aligned so that a tone at 200 nWb/m gives a reading of 0 VU. In short:
200 nWb/m on tape normally equates to +4 dBu and 0 VU
Most brands of tape can give good clean sound up to 8 dB above 200 nWb/m and even beyond, although distortion increases considerably beyond that.
Digital equipment also has an ‘operating level’, of sorts. In some studios - mainly broadcast - digital recorders such as DAT are aligned so that –18 dBFS (18 dB below maximum level) is equivalent to +4 dBu and 0
VU. This certainly allows plenty of headroom (see later), but it doesn’t fully exploit the dynamic range of DAT. Most people who record digitally record right up to the highest level they think they can get away with without risk of red lights or ‘overs’.
Gain
Gain refers to an increase or decrease in level and is measured in dB.
Since gain refers to both the signal level before gain was applied, and signal level after gain is applied, then the function of the decibel as a comparison between two levels holds good. The signal level from a microphone could be around 1 mV, for instance. Apply a gain of 60 dB and it is multiplied by a thousand giving around 1 V – enough for the mixing console to munch on. Suppose the signal then needed to be made smaller, or attenuated, then a gain of –20 dB would bring it down to around 100 mV. Some engineers find it fun to play around with these numbers. Your degree of fluency in the numbers part of decibels depends on whether you want to be a technical expert, or just concentrate on the audio. There is work available for both types of engineer.
The need to make a signal bigger or smaller is fairly easy to understand, but what about making it stay the same level? What kind of gain is this?
The answer is ‘unity gain’ and it is a surprisingly useful concept. Unity gain implies a change in level of 0 dB. In the analog era it was important to align a recorder so that whatever level you put in on record, you got that same level out on replay. Then, apart from being spared changes in level between record and playback, you could do things like copy tapes, edit bits and pieces together and the level wouldn’t jump. If you hadn't aligned your machines to unity gain then the levels would be all over the place. With digital equipment, it is actually the norm for digital input and output to be of the same level, so unity gain – in the digital domain at least – tends to happen automatically.
RMS and Peak Levels
How do you measure the level of an AC (alternating current) waveform?
Or to put it another way, how do you measure the level of an AC waveform meaningfully? A simple peak-to-peak measurement, or peak measurement, shows the height (or amplitude) of the waveform, but it doesn't necessarily tell you how much subjective loudness potential the waveform contains. A very ‘peaky’ waveform (or a waveform with a high crest factor, as we say) might have strong peaks, but it will not tend to sound very loud. A waveform with lower peaks, but greater area between the line and the x-axis of the graph will tend to sound louder on delivery to the listener. The most meaningful measurement of level is the root-mean-square technique. Cutting out all the math, the RMS measurement tells you the equivalent ‘heating’ capability of a signal. A waveform of level 100 Vrms would bring an electric fire element to the same temperature as a direct (DC) voltage of 100 V. A waveform of level 100 Vpeak-to-peak would be significantly less warm.
Frequency Response
It is generally accepted that the range of human hearing, taking into account a selection of real live humans of various ages, is 20 Hz to 20 kHz, and sound equipment must be able to accommodate this. It is not however sufficient to quote a frequency range. It is necessary to quote a frequency response, which is rather different. In addition, we are not looking for any old frequency response, we are looking for a ‘flat frequency response’ which means that the equipment in question responds to all frequencies, within its limits, equally and any deviations from an equal response are defined. The correct way to describe the frequency response of a piece of equipment is this:
20 Hz to 20 kHz +0 dB/-2 dB or this:
20 Hz to 20 kHz ±1 dB
Of course the actual numbers are just examples, but the concept of defining the allowable bounds of deviation from ruler-flatness is the key.
Q
Q is used in a variety of ways in electronics and audio but probably the most significant is as a measure of the ‘sharpness’ of a filter or equalizer.
For example, an equalizer could be set to boost a range of frequencies around 1 kHz. A high Q would mean that only a narrow band of frequencies around the center frequency is affected. A low Q would mean that a wide range of frequencies is affected. Q is calculated thus:
Q = f0/(f2-f1) where f0 is the center frequency of the band, f2 and f1 are the frequencies where the response has dropped –3 dB with respect to f0.
It may be evident from this that Q is a ratio and has no units. Q doesn't stand for anything either, it’s just a letter. Whether you need to use a low Q setting or a high Q setting depends on the nature of the problem you want to solve. If there is a troublesome frequency, for example acoustic guitars sometimes have an irritating resonance somewhere around 150 Hz to 200 Hz, then a high Q setting of 4 or 5 will allow you to home in on the exact frequency and deal with it without affecting surrounding frequencies too much. If it is more a matter of shaping the spectrum of a sound to improve it or allow it to blend better with other signals, then a low Q of perhaps 0.3 would be more appropriate. The range of Q in common use in audio is from 0.1 up to around 10, although specialist devices such as feedback suppressers can vastly exceed this.
Noise
Noise can be described as unwanted sound, or alternatively as a non-meaningful component of a sound. Noise occurs naturally in acoustics, even in the quietest settings. Air molecules are in constant motion at any temperature above absolute zero and since sound is nothing more than the motion of air molecules, then the random intrinsic motion must produce sound - sound of a very low level, but sound none the less. We are not generally aware of this source of noise, but some microphones are. A microphone with a large diaphragm will have many molecules impinging on its surface, and the random motion of the molecules will tend to average out and be insignificant in comparison with the wanted signal. A microphone with a small diaphragm however (such as a clip-on mic) will only be in contact with comparatively few air molecules so the averaging effect will be less and the noise higher in level in comparison with the wanted signal.
When sound is converted to an electrical signal, the signal is carried by electrons. Once again, electrons are in constant random motion causing what is called Johnson noise. If the signal is carried by a large current (in a low impedance circuit), then Johnson noise can be insignificant. If the signal is carried by only a small current with relatively few electrons (in a high impedance circuit), then the noise level can be much higher. We can extend this concept to any medium that can carry or store a sound signal.
Noise is cause by variations in the consistency of the medium. One more example would be a vinyl record groove. The signal is stored as undulations in the groove, but any irregularities such as dust or scratches translate into noise on playback.
Digital audio systems are not immune to noise. When a signal is converted to digital form, it is analyzed into a certain number of levels, 65,536 in the compact disc format for example. Of course, most of the time the original signal will fall between levels, therefore the analysis is only an approximation. The inaccuracies necessarily produced are termed quantization noise.
Signal to Noise Ratio
Signal to noise ratio is one measure of how noisy a piece of equipment is.
We said earlier that a common operating level is +4 dBu. If all signal were removed and the noise level at the output of the console measured, we might obtain a reading somewhere around –80 dBu. This would mean that the signal to noise ratio is 84 dB. In analog equipment, a signal to noise ratio of 80 dB or more is considered good. The worst piece of equipment as far as noise is concerned is the analog tape recorder, which can only turn in a signal to noise ratio of around 65 dB. The noise is quite audible behind low-level signals. Outside of the professional domain, a compact cassette recorder without noise reduction can only manage around 45 dB. This is only adequate when used for information content only, for instance in a dictation machine, or for music which is loud all the time and therefore masks the noise.
As we said, digital equipment suffers from noise too. Quantization noise is more grainy in comparison to analog noise and therefore subjectively more annoying. Digital equipment requires a better signal to noise ratio.
In basic terms, the signal to noise ratio of any digital system can be calculated by multiplying the number of bits by six. So the compact disc format with a resolution of 16 bits has a signal to noise ratio of 16 x 6 = 96 dB, if all other parts of the system are optimized. Currently the professional standard is moving to 24-bit resolution, therefore the theoretical signal to noise ratio would be 24 x 6 = 144 dB. This is actually greater than the useful dynamic range of the human ear, but in practice this idealized figure is never attained.
Another way of measuring the noise performance of equipment is EIN or Equivalent Input Noise, and this is mainly of relevance to microphone preamplifiers. An example spec might be 'EIN at 70 dB gain: -125 dBu (200 ohm source)'. This means that the gain control was set to 70 dB and the noise measured at the output of the mic preamp - in this case the measurement would be –55 dBu. When the set amount of gain is subtracted from this we get the amount of noise that would have to be present at the input of a noiseless mic amp to give the same result. The '200 ohm source' bit is necessary to make the measurement meaningful.
If the EIN figure does not give the source impedance, then I am afraid the measurement is useless. Perhaps it is giving the game away to say that the reason a gain of 70 dB is quoted is because mic preamps normally give their optimum EIN figures at a fairly high gain. The lower the gain at which a manufacturer dare quote the EIN, the better the mic input circuit.
Modulation Noise
Noise as discussed above is a steady-state phenomenon. It is annoying, but the ear has a way of tuning out sounds that don’t change. However, there is another type of noise that constantly changes in level, and that is modulation noise. One source of modulation noise is that which occurs in analog tape recorders. The effect is that as the signal level changes, the noise level changes. This can be irritating when the signal is such that it doesn't adequately mask the noise. A low frequency signal with few higher harmonics is probably the worst case and will demonstrate modulation noise quite clearly. Noise reduction systems, as mainly used in analog recording, also have the effect of creating modulation noise.
Noise reduction systems work by bringing up the level of low-level signals before they are recorded, and reducing the level again on playback – at the same time reducing the level of tape noise.
Unfortunately, the noise level is now in a state of constant change and thereby drawing attention to itself. Some noise reduction systems have means of minimizing this effect. All of the various Dolby systems, for example, work well when properly aligned.
Quantization noise in digital systems is also a form of modulation noise.
At very low signal levels it is sometimes possible to hear the noise level going up and down with the signal.
Where you are most likely to hear modulation noise is on a so-called Hifi VHS video recorder. The discontinuous nature of the audio track causes a low frequency fluttering noise which requires noise reduction to minimize. On some machines, this noise reduction is not wholly effective and the modulation noise created can be very irritating.
It is worth saying that signal to noise ratio should be measured with any noise reduction switched out, otherwise the comparison between peak or operating level and the artificially lowered noise floor when signal is absent gives an unfairly advantageous figure unrepresentative of the subjective sound quality of the equipment in question.
Distortion
Unfortunately, any item of sound equipment 'bends' or distorts the sound waveform to a greater or lesser extent. This produces, from any given input frequency, additional unwanted frequencies. Usually, distortion is measured as a percentage. For a mixing console or an amplifier, anything less than 0.1% is normally considered quite adequate, although once again it's the analog tape recorder that lets us down with distortion figures of anything up to 1% and above.
Distortion normally comes in two varieties: harmonic distortion and intermodulation distortion. Looking at the harmonic kind first, suppose you input a 1 kHz tone into a system. From the output you will get not only that 1 kHz tone but also a measure of 2 kHz, 3 kHz, 4 kHz etc. In fact, harmonic distortion always comes in integral multiples of the incoming frequency - rather like musical harmonics in fact. This is why
Distortion normally comes in two varieties: harmonic distortion and intermodulation distortion. Looking at the harmonic kind first, suppose you input a 1 kHz tone into a system. From the output you will get not only that 1 kHz tone but also a measure of 2 kHz, 3 kHz, 4 kHz etc. In fact, harmonic distortion always comes in integral multiples of the incoming frequency - rather like musical harmonics in fact. This is why