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Introduction
It is the purpose of this article to give the reader an introduction to understanding noise in electronic circuits, why it happens, and how to read noise specifications. The latter are not usually explained in a way that makes sense to the uninitiated, so it is hoped that this article will assist those trying to make some sense of it all.
Noise has enormous nuisance value with sensitive (i.e. high gain) circuits, but the information provided by most IC and transistor makers does not always make the choice of the most suitable device easy. Certainly, there is copious information, but explanations of what it means and how to apply it are few and far between.
This short article will hopefully clear up some of the confusion. By nature, it is rather more technical than I generally prefer, but this is unavoidable for a passably thorough understanding of the subject.
In this context, noise refers only to circuit noise, and not hum, buzz or other extraneous outside influences. These are usually the result of bad (or misguided) earthing practices, or signal wiring running close to magnetic field or harmonic generating items such as transformers and bridge rectifiers. Also to blame can be radio frequency interference, which will often cause problems if adequate (and appropriate) precautionary measures are ignored.
Noise is inherent in all electronic circuitry, and comes in three basic flavours:
- Thermal noise
- Shot noise
- Flicker (l/f) noise
Thermal noise is "white" in character (has a constant energy per unit bandwidth) and is generated by the thermal agitation of electrons in a conductor. The typical sound is hiss, hopefully at a low level so that it does not intrude on the programme material. It is calculated using Nyquist's relation:
V²R = 4k * T * R * f
Where ...
V²R = mean square noise voltage
k = Boltzmann constant (1.38 x 10-23)
T = Absolute temperature (Kelvin)
R = Resistance in ohms
f = Noise bandwidth in Hertz
Without even performing any calculations, we can see that the noise from a resistor is proportional to its resistance and temperature. Operating resistors at elevated temperatures in input stages is obviously undesirable, as are high resistance values. This also applies to any other resistive device, such as the voice coil of a dynamic (magnetic) microphone, the coils of a guitar pickup, or a vinyl disc pickup cartridge.
Shot noise is also white, and is inherent in semiconductor devices. It is primarily caused by the changes in molecular energy levels as a semiconductor device conducts.
Flicker noise is a low frequency effect, and as such is not so much of a problem with audio circuits. It becomes worse as frequency is reduced, and this can be seen in some data sheets. At the lower frequency extremes, the noise level increases.
Explanations
Before we continue, there are a couple of terms that need explanation.
Firstly, the term 'dBv' refers to decibels relative to 1V RMS, and 'dBu' means decibels relative to 775mV. This is also known as dBm, and relates to the old convention of 1mW into a 600 Ohm load. This was common in telephony (and still is in some cases), but is of little relevance to audio applications. However, we are stuck with it. 0dBv is equivalent to +2.2dBu.
Secondly, noise is commonly referred to the input of an amplifier circuit. This allows the instant calculation of output noise by simply subtracting the dB figures. So an amplifier with an 'Equivalent Input Noise' (EIN) of -120dBu having a gain of 40dB will have an output noise of -80dBu (120 - 40). This is the equivalent of 80dB Signal to Noise ratio (S/N) relative to 0dBu. Many equipment manufacturers will state S/N relative to maximum output, thereby gaining perhaps 10dB better figures. This is actually meaningless, since no-one will operate equipment at the maximum level, and the average will be considerably less.
Thirdly, it is commonly accepted that the minimum theoretical input noise (EIN) for any amplifier is -129dBu. Although not explicitly stated, this implies that the input will be terminated with a resistance. Typically, a 200 ohm source resistor will give this figure at 25°C. Sometimes, a short circuit is used instead, and this gives better apparent noise performance. A short circuit is actually meaningless though, since no real-world signal sources have zero impedance. Some do come close though, so the amplifier should always be terminated with an impedance that matches (as closely as possible) the output impedance of the signal source. This should be stated in any specification.
This means that a perfect (as noiseless as it is possible to be) amplifier with a gain of 40dB and a 600 ohm source impedance will have an output noise level of -89dBu, and if the gain were to be increased to 60dB, then output noise will be -69dBu.
It is the nature of noise that it does not add in the same way as two equal frequencies. Because of its random nature, two equal noise voltages will increase the output by only 3dB, not 6dB as might be expected. As a result, we can be reasonably sure that it is the input noise of the most sensitive section of a preamp that will set the final limit to the signal to noise ratio of the entire unit.
The way the noise figure of an opamp is commonly described is something else that needs a little explanation, since it is hardly specified in terms that most constructors will be able to relate to. The data sheet telling you that the "noise figure is 5nV/√Hz" is not very friendly. To get this into something we can understand, first we need to take the 'square root of Hz' and make some sense of it. The audio bandwidth is taken as 20Hz to 20kHz, so the square root of this is ...
√20,000 = 141 (it is not worth the effort of subtracting the 20Hz, so 141 is close enough)
With a noise figure of 5nV / √Hz, the equivalent input noise (EIN) is therefore ...
5nV x 141 = 707nV
If we assume a typical gain of a sensitive microphone stage (for example) as 100 (40dB) and an output level of 1V (0dBv), this means that the output noise equals the input noise, multiplied by gain. Signal to noise ratio can then be calculated ...
707nV x 100 = 70.7uV (EIN = -120.8dBu)
Signal to noise (dB) = 20 x log (1V / 70.7uV) = 20 x log (14144) = 83dB
We can also calculate this using dB alone.
EIN = -120.8dBu
Gain = 40dB
S/N = 120.8 - 40 = 80.8 (ref 0dBu), or 80.8 + 2.2 = 83dB (ref 0dBv)
For low level preamps (such as microphone or moving coil phono pre-amplifiers), it is common to specify the EIN only, allowing the user to calculate the noise for any gain setting, since it changes as the gain is varied. The same amplifier as above with unity gain will have a theoretical signal to noise ratio of 123dB (relative to 1V). All of this assumes that the passive components (especially resistors) do not contribute any noise. This is false, as any device operating at a temperature above 0K (zero Kelvin, absolute zero, or about -273° Celsius) generates noise, however the contributions of passive components are relatively small with quality devices provided resistance is kept as low as possible, and voltages minimised.
Remember that a 'perfect' amplifier (contributing noise at the theoretical minimum possible), will have an equivalent input noise of -129dBu. This means that with a gain of 60dB, the best possible signal to noise ratio will be 69dB relative to 775mV (or 71.2 ref 0dBv).
As an experiment, I built a three opamp precision microphone preamp using 1458 opamps (equivalent to a dual uA741). These have a noise input figure of about 4uV - this translates to about 30 to 35nV / √Hz, or nearly 20dB worse than the NE5534A. With a gain of 46dB (200), the circuit managed a signal to noise ratio of 65dB, referred to 0dBv (1 Volt RMS). The apparently better than expected S/N ratio is because the bandwidth was so limited because of the opamps I used for this test.
I measured a S/N ratio of better than 80dB (about 82dB) again at a gain of 46dB using LM833 opamps (National Semiconductor "equivalent" to the NE5532). When I say that I measured this, it was with extreme difficulty. Because of the low noise, my test instruments were at their limits, so I had to guess a bit. The theoretical 'best possible' at this gain is 85.2dB referred to 0dBv, or -83dB ref. 0dBu.
Search carefully for devices with low noise for sensitive circuitry, and make sure they also have the bandwidth needed to achieve high gains. LM833 or NE5532 dual opamps are an excellent choice for low noise, but they also have wide bandwidth and can be troublesome to keep stable. Do not be tempted to use lesser devices, since their bandwidth is too limited - the 1458 was 3dB down at only 8kHz, and died rapidly after that.
In some cases, it will be found that better noise performance can be obtained using discrete opamps - built using individual components. A common technique for low noise is to select transistors based on their noise data, which will indicate the optimum collector current for a given source impedance.
Then, by using multiple devices in parallel, the noise is reduced further. Two transistors in parallel will have a noise level 3dB better than a single device. Using four will reduce this by another 3dB, and eight will give a further 3dB reduction. This is the theory behind it, but of course it will never be as good as ideal theory might indicate. It is generally considered (based on the many such designs I have seen) that between 2 and a maximum of six devices in parallel will achieve the best overall compromise. Project 25 shows a couple of designs using this method, and has some descriptive text explaining the two (very different) techniques. Project 66 gives the circuit diagram for a microphone preamplifier that uses a discrete front end to obtain low noise. No devices are paralleled as such, although the two sections appear in parallel to the following opamp.
Other Stuff
For all resistors in low noise input circuits, you absolutely, positively, must use 1% tolerance resistors, which will be metal film for lowest noise.
Many noise tests are performed using A-weighting, which introduces a filter prior to measurement. The theory of this is that it compensates for the ear's natural rolloff at low and high frequencies, and makes the measurement 'meaningful'. While the idea is quite sound in principle, I do not believe that this should be done, as not everyone is scrupulous about stating that this technique has been used, so results can be very misleading. An A-weighting filter is described in the ESP Project Pages (Project 17), along with an extensive description of the theory behind this practice.
Noise In Digital Equipment
For each digital bit, the relative noise floor is lowered by 6dB. A 1 bit system is of little use, and it is necessary to go to a minimum of 8 bits before even ordinary speech is intelligible - not acceptable, but intelligible. This gives a noise floor of 48dB - about what you would expect from the modern telephone system. Even there, speech is digitised at 16 bits (using an 8kHz sampling rate), and then compressed digitally to 8 bits.
(BTW, Worldwide, there are two different digital compression systems used - A-Law, used by all European countries, much of South America, Australia and New Zealand etc. u-Law (as in mu, the Greek letter) is used in the US, Canada and Japan. Prior to digital to analogue conversion, the signal is returned to the 16 bit format. This has nothing to do with noise, I just thought I'd mention it.)
Some early digital answering machines used 8 bit digitisation, which explains why they sounded so disgusting. Even though the noise floor is (barely) low enough, there is an insufficient number of discrete levels to faithfully reproduce speech. 8 bits only provides 256 discrete levels, and it has been generally accepted that anything less than 12 bits is unacceptable (4096 discrete levels). This is easily verified by recording something on your PC at the various available bit rates and making a comparison.
Minimum Digital Noise = 20 * Log10(number of discrete levels)
When professional digital recording systems were first introduced they were 16 bit. Although this gives a theoretical noise floor 96dB below the maximum level, in reality 90dB was more likely. If maximum level corresponds to +4dBu, this indicates a noise level for each digital channel output of -86dBu.
Noise = 20 * Log1065535 = -96.33dB
In the sound recording industry, the relative differences between analogue tape and digital recording must be considered. In an analogue machine, it is the tape that clips, which it does in a 'soft' manner, introducing predominantly low order harmonics. These are relatively inaudible, provided the duration is kept short (1ms or so), such as on transients.
A digital system by comparison clips suddenly and with great clarity, and it is essential to leave sufficient headroom to prevent this. If 10dB of headroom is left below maximum average level to allow for transients (I would suggest this as a workable minimum), then this implies that the noise level actually present at the output of the digital playback system is -80dBu, relative to nominal (average) playback level.
Many digital systems now have 20 bit or greater resolution, although generally only 20 bits is achieved in practice. This reduces the theoretical noise floor by a further 4 bits, or 24dB. Therefore the noise level at the output of such a machine should be -110dB. Allowing the same 10dB headroom rule as above, this gives a final output noise figure of about -100dB. It is possible in many cases that the associated analogue circuitry within the digital system will be worse than this figure, so the final noise figure is somewhat unpredictable.
