Signals, Noise, and Signal-to-Noise Ratio

Signals, Noise, and Signal-to-Noise Ratio

By Paul Joppa – Version 1.0 March 29, 2007

Introduction

Every audio device has a range of signal levels that it is designed to handle. This range is limited at the high end by overload distortion and at the low end by noise. The device will operate most satisfactorily when the musical signal is kept between these extremes, so that neither overload distortion nor noise are audible. The purpose of this article is to help set up a system so that all the elements operate in this ideal range.

This article includes a good deal of background information which some may find helpful. Those in a hurry to solve a problem are encouraged to skip ahead to the section called “Adjusting the amplifier/speaker sensitivity”as this is the most common problem.

Decibels

Signal levels are usually expressed in decibels. The decibel scale is a logarithmic way of describing a ratio; specifically it is 10 times the base-10 logarithm of a power ratio. Since power into a given resistance is proportional to voltage squared, it is often calculated as 20 times the base-10 logarithm of a voltage ratio. Here are some examples:

  1. The gain of a preamp is usually expressed as a voltage gain, that is the ratio of output voltage to input voltage.
  2. The power of a power amp is sometimes calculated as the output power ratio to 1.0 watt; in dB this would be called dB(w), that is dB in watts.
  3. The voltage level in a cable may be expressed as the voltage ratio to 1.0 volt, called dB(v). It is also expressed relative to some other reference voltage or power. A very old tradition uses dBm to identify the level relative to 1.0 milliwatt. This can only be translated into a voltage if the impedance is specified. The most common, though certainly not universal, reference is the old telephone standard of 600 ohms. The voltage which would produce 1 milliwatt into 600 ohms is 0.775 volts. Today this is called dB(u) (dB relative to 0.775 volts).
  4. The sound level output of a loudspeaker is usually expressed as the sound pressure relative to 0.00002 Pascal, which is the approximate threshold of hearing at 1kHz.
  5. The ratio of a signal to the background noise floor is called the signal-to-noise ratio. Abbreviated S/N, and usually expressed in decibels. Sometimes the S/N is evaluated at the maximum signal before overload distortion, which produces the largest number, but is only relevant when the signal level is actually at its maximum.

Nominal and peak signal levels

The maximum signal level for audio signals can be measured in different ways, which give very different results. There are two very common measures which must be understood in order to make sense of S/N and operating signal levels.

Nominal signal level

The nominal signal level is that which is measured by a typical, simple AC meter. Such meters measure the short-term average of the signal magnitude, and are usually calibrated to read the correct rms value is presented with a sine wave. There are many different standards for the averaging time and the frequency range, so this is not defined very precisely. For setting signal levels in audio systems, the most common measure is the VU meter, which has an averaging time of around 200mS and is a good measure of the perceived loudness of a signal. It has been traditional practice for decades in studios to operate at a signal level of zero VU for the musical peaks; tape recorders and phonograph disc cutters are usually set up so that if this standard is adhered to, they will not overload audibly on instantaneous voltage peaks. Phonograph cartridges are calibrated at a stylus velocity of 5cm/second rms, which corresponds to this level for typical cutters.

Peak signal level

The instantaneous voltage as seen on an oscilloscope will be much higher than the nominal or short-term average level described above. Normally on well-recorded material this difference, called the peak-to-average ratio, is in the range of 12dB to 20dB. Studio tape recorders would run about 14dB, a high-quality FM radio station might compress the music to achieve a 12dB ratio, good CDs might raise it to 16dB, and the THX standard for movie theaters is 20dB to allow for car crashes louder than the music or dialog. Real, live classical music has been measured at as much as 30dB peak-to-average; it is usually compressed either by the nature of the tape recorder or with an electronic compressor to achieve a ratio of 14dB or so. Pop music and talk radio stations will often compress to a ratio of 2dB or even less.

This becomes important when signals are identified by their peak level, which is also called the full-scale (FS) level. All digital devices have a full-scale level, and are usually specified by that level, for example the red-book standard for CD players is 2.0vrms(FS). Radios are also described in terms of their peak output level.

Note that, for example, this means phono cartridge output (specified at the nominal level) cannot be directly compared with CD player output (specified at the FS level). The differences between them may well depend on the kind of music you listen to, or the company that puts out the recording. Nevertheless, for the purposes of this article the value of 14dB will be assumed for the peak-to-average ratio.

Line level

The line level is the signal voltage level in the interconnects, ignoring speaker cables and phono cartridges. This is the place where S/N problems most often arise in home audio systems, usually because some device produces an exceptionally high line output or because some device requires an exceptionally low input.

There are two standards. In professional studios the standard is fairly consistent – zero VU is +4dBu, or 1.228 volts rms. Peak levels of +18dBu (6.15 volts) would correspond to a peak-to-average ratio of 14dB, though signal not yet compressed might require studio gear to operate at even higher levels. Studio signal are almost always carried on balanced lines.

Consumer gear is much less standardized. The most commonly quoted line level is -10dB(v) or 0.316 volt rms for nominal, which would be 1.58 volt peak at 14dB peak-to-average. This is very close to the CD standard of 2.0vFS, though of course many CD players do not follow that standard. Consumer gear signals are almost always carried on coaxial cable with RCA connectors.

Listening level

The final piece of the puzzle is the listening level. People have different preferences for how loud they like to listen. But surprisingly, there is a broad consensus among professionals. Within a very small margin, studio engineers listen to recordings through their monitor systems at nominal peaks (zero VU) of 82dB per channel, measured at the listening position. This is also the standard for movie dialog in THX movie theaters.

Some audiophiles like to listen louder, some quieter. Rock fans who want to re-create the sound level of a rock concert may need 20dB or more greater levels. Fans of baroque chamber music, or late-night listeners, may be satisfied with 20dB less. But for the purposes of this paper, the 82dB number will be taken as representative.

Noise level

The noise of a device should be low enough to not interfere with the music. While the human ear is capable of an enormous range, neither our environment nor our recording media are capable of exploiting that range fully. Few recordings are able to provide a noise floor more than 60dB below nominal, even though modern CDs are in theory capable of 95dB below FS. Lower noise is always better, but as long as device noises (hiss, rush, hum, buzz, etc) are more than 60dB below nominal most systems will be satisfactory.

In this connection it should be mentioned that the human ear is less sensitive to low-level noise at low frequencies. For this reason noise is often measured with a filter to discount the lower frequencies; the so-called “A-weighting” scale is used almost universally when this is done. Mostly, thus reduces the effects of hum.


Setting levels in the ideal world

In the ideal world, line level would be standard, at -10dB(v) nominal. Devices would be able to handle +4dB(v) or higher peaks without overload, and device noise would be low relative to nominal – i.e. less than -70dB(v), or 0.316mVrms.

Clearly in this ideal world, a preamp would have unity gain in normal use. It might have a maximum gain a bit greater, for listening to quiet passages or under-recorded material, but another 6-10dB should be plenty. A downward adjustment of 20dB would be plenty for late night or background listening.

Sources should adhere to the -10dB(v) nominal standard, which can be accomplished in the source device, or at the input of the target device (preamp, usually). This is relatively easy.

Amplifier/speaker combinations should produce 82dB sound level at the listener’s ear when the input level is -10dB(v). Unfortunately, it is extremely common to find there is too much gain in this part of the chain.

Adjusting the amplifier/speaker sensitivity

Before adjusting the sensitivity of the amplifier to achieve the desired sensitivity, it is useful to determine how much attenuation is necessary. This will help to chose the most appropriate method. To determine the attenuation, you must first determine the existing sensitivity. You can do this by measurement, or with less accuracy by calculation.

Determining sensitivity by measurement

You will need a source of pink noise, a voltmeter, and a sound level meter. Many CDs are available that have pink noise on them, or you can download a .wav file and burn it to CD. You can get a perfectly adequate sound level meter at Radio Shack.

Play the pink noise through one channel, and adjust the level until you read 82dB on the meter. Then remove the interconnect from the amplifier input, and measure the voltage. This is your nominal sensitivity.Alternatively, play a stereo version through both speakers and adjust for 85dB sound level.

The voltage going into the amp is the amp/speaker sensitivity, volts for 82dB per channel. Calculate 20 times the base-10 logarithm of this number to get the sensitivity in dB(v).

Determining sensitivity by calculation

For this you must know the amp’s sensitivity plus the speaker sensitivity, and then make some reasonable guesses about your listening room’s acoustics.

First, find the power required to deliver 82dB. The speaker is usually rated for anechoic dB at 1 meter, for either 1 watt or 2.8 volts input. If it’s an 8 ohm speaker, 2.8 volts is 1 watt. However, a 4 ohm speaker may be rated at 2.8 volts which is 2 watts, so you must subtract 3dB to get the dB per watt at 1 meter anechoic. Then subtract the dB/w/m number from 82 to get the dB(w) needed to produce 82dB sound level.

In typical listening rooms with wide-dispersion speakers the speaker’s output at 1 meter anechoic is approximately the same as the reverberant field level, so no adjustment is needed. You can add or subtract up to 3dB if the room is very “dead” or very “live” Add or subtract another 3dB for very large or very small rooms. Add up to 3dB for very directional speakers. Now you have a good estimate for the dB(w) needed to generate 82dB sound level.

Second, find the voltage required to generate this much power. The amp will be specified either for the voltage to generate full power, or the voltage to generate 1 watt. Convert that voltage to dB(v) by calculating 20 times the base-10 logarithm of the voltage. If it was for full power, subtract the full power rating in dB(w) (which is 10 times the base-10 logarithm of the power rating). Add the dB(w) needed to get 82dB; the result is the dB(v) input needed to generate 82dB sound level.

Calculate the attenuation needed

Now you can compare the input required with the target nominal of -10dB(v). The required input will probably be much less than -10dB(v), and the difference is the amount of attenuation required.

Implement the attenuation

If you can get within +/-6dB of the target attenuation, you will probably be OK. Here are some ways to attenuate the amplifier’s input:

  1. Adjust the amplifier’s gain control, if it has one.
  2. Add an adjustable level control, such as a “passive preamp” between the actual preamp and the power amplifier. Usually this should be placed near the power amp, since such passive level controls cannot drive long lines well.
  3. If it’s a DIY amp, you can build in an L-pad or level control at the amplifier’s input.
  4. You can buy in-line attenuators which plug into the amp’s input jack, and accept RCA plugs at the other end. Harrison makes some, available at Parts Express, and Rothwell in the UK also makes some. Usually attenuations of 12dB or less are available, and many of these have too low an input impedance to use with tube preamps, so check first.
  5. Transformers can be used. Jensen makes some boxes under the “IsoMax” name that do a 12dB reduction, and there are similar items available called a “direct box” with typically a 40dB attenuation. Many of these items have balanced XLR or large phone plug interfaces instead of RCA jacks, and some do not operate properly with long cables on the high-impedance end, so check first.

Last resort

As a last resort, you can reduce the line level between the preamp and power amp. The smaller signal level makes this interface more prone to picking up noise, and deviates from the normal standard voltages, but sometimes it is the most efficient approach. Here are some ways:

  1. Turn down the preamp volume. Some preamps have input attenuation on some or all the inputs which can be adjusted. This does not reduce the preamp’s noise floor, which will still be amplified by the amp and speaker, so it is often a noisy solution.
  2. Attenuate the preamp’s output with a transformer. This produces a lower line impedance so even a modest tube preamp can drive a long line. See item 5) above for comments on transformers.
  3. Install an L-pad or resistive attenuator at the preamp’s output. Usually this will increase the output impedance substantially, reducing the noise immunity and making long interconnects impractical. It can work if a large amount of attenuation is needed, typically 30dB or more.
  4. Replace the preamp with one that has less than unity gain in normal operation. Examples are passive preamps (buffered or not) and most transformer volume controls (TVCs). Beware – some TVCs have gain, which also means those will have low input impedance and usually cannot be driven with tube-based equipment.

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