|Elliott Sound Products||Noise In Audio Amplifiers|
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. Much of the material here is simplified, and is aimed at audio applications. There are comprehensive texts available on the topic if you need to know more.
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, 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. These topics are not covered here.
Noise is inherent in all electronic circuitry, and comes in five basic flavours:
The final two are not issues with opamps intended for audio applications, and they are not generally considered in any noise analysis. However, avalanche noise (junction reverse breakdown) is useful in dedicated noise generators such as Project 11 - Pink Noise Generator. Burst (or 'popcorn') noise is primarily due to imperfections and/or impurities in the semiconductor material itself. Modern semiconductor techniques have minimised the impact of burst noise.
Shot noise is random, 'white' in character and has constant energy per unit bandwidth. Shot noise is created when current crosses a potential barrier, such as a semiconductor P-N junction. This causes changes in molecular energy levels as a semiconductor device conducts. It is independent of temperature.
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 many data sheets. At the low frequency extremes, the noise level increases more or less linearly (hence 1 / f noise). Flicker noise is current dependent, and is found not only in semiconductors but also in carbon composition resistors (where it is sometimes referred to 'excess' noise).
Thermal noise is the main focus of this article. It has a constant energy per unit bandwidth and is generated by the thermal agitation of electrons in a conductor. It is also known as Johnson noise, named after the man who discovered the phenomenon in 1928. The typical sound is hiss (white noise), hopefully at a low level so that it does not intrude on the programme material. It is calculated using Nyquist's relation:
VR = √ ( 4k × T × B × R )
VR = resistor's noise voltage
k = Boltzmann constant (1.38E-23)
T = Absolute temperature (Kelvin)
B = Noise bandwidth in Hertz
R = Resistance in ohms
Note that the temperature is in Kelvin, so given that zero K is -273°C, at the 'standard' temperature of 25°C that's 298K (use 300K to account for internal heating within the equipment). 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 not undesirable, as are high resistance values. If your calculator doesn't do exponents ('E'), the Boltzmann constant can also be expressed as 1.38×10^-23.
While 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, voice coils and other pickups usually have a fairly low resistance compared to impedance, and only the resistive part generates thermal noise. The impedance is not relevant for noise calculations.
Figure 1 - Resistor Noise Voltage
For anyone who hates the idea of using a formula, the above chart will help. The plot shows the noise at 25°C (298K) for resistances from 10 ohms to 10 megohms. It includes graphs for -50°C and 125°C for reference. As you can see, the noise increases by a factor of 10 (20dB) for each x100 of resistance. It falls by the same amount as resistance is reduced. Each time the resistance is increased by 2 (6dB), the noise increases by 3dB. Note that the graph says 4.1nV/√Hz for 1k at 25°C, but to be exact it's 4.055nV/√Hz. The difference is immaterial.
While temperature obviously plays a part, it's effect is fairly small compared to the very wide range of resistance used in circuitry. Over the normal temperature range of most electronic equipment, the noise change due to temperature can usually be ignored. For example, using a 1k resistor at 29°C vs. 129°C, the noise changes from 4.07nV/√Hz to 4.7nV/√Hz, which isn't something to get too excited about (1.25dB). However, keeping the temperature low has other benefits, in particular longer life and improved stability, so avoiding elevated operating temperatures is still most worthwhile.
Using reasonably typical values we can assume a reference resistance of 200 ohms (this is a standard value for noise tests), an absolute temperature of 300K (27°C which is very common inside enclosures) and 20kHz bandwidth. This gives the noise from the resistance alone as 0.257uV (257nV). At very high impedances, current noise becomes the dominant characteristic.
Our 200 ohm source resistance with its noise voltage of 257nV limits the maximum possible signal to noise ratio to ...
E IN = 20 × log ( 1V / 257nV ) = 131.8dB (V) ... or
E IN = 20 × log ( 775mV / 257nV ) = 129.6dB (u)
This means that a 'perfect' noiseless amplifier cannot be any better than the thermal noise from the source resistance. With a 200 ohm source, this means that equivalent input noise for a microphone preamp (for example) cannot be less than -129.6dBu. If the source resistance is reduced you will get a better figure, but it is likely to be unrealistic because of the resistance of real-life sources. A 100 ohm resistor has a thermal noise of 182nV - 3dB lower than the 200 ohm example.
Amplifying device current noise (I IN) must be considered with high impedance circuits, because the current noise is effectively in parallel with the source. With low impedance sources, current noise is effectively shorted to ground, but as the impedance increases this no longer happens.
I R = √ ( 4k × T × B / R )
I R = resistor's noise current
k = Boltzmann constant (1.38E-23)
T = Absolute temperature (Kelvin)
B = Noise bandwidth in Hertz
R = Resistance in ohms
The total noise contribution of any amplifier circuit is the combination of voltage noise, current noise, circuit noise and gain. At low impedances, noise voltage is the predominant effect, but as source impedance increases noise current becomes dominant. The transition impedance depends on the amplifier input topology. FET inputs are preferred for high impedances and bipolar inputs are more suited to low impedances. The impedance range for best noise performance is usually between 1k and 10k for bipolar and between 10k - 100k for FETs, but there are wide variations in practice. With few exceptions, FET input opamps have a higher noise voltage than bipolar input devices. The noise from most opamps is also higher in the inverting configuration than non-inverting, so you will see very few 'low noise' amplifiers that use the inverting topology. The reason is that although the signal voltage gain is unity (-1 to be precise), the noise gain is two because of the input resistor and feedback resistor.
Many mic preamp circuits (including most of the IC types) are only capable of extremely low E IN figures at or near maximum gain. This is because the second (fixed gain) stage of the circuit contributes noise all the time, and at the same level. It is only when the input preamps are producing a significant signal output level that the contribution of the fixed gain stage becomes less of an influence.
Unless operated with low gain with low level signals, the 'limitations' of most mic preamps are not usually a problem.
Always remember that noise signals do not simply add. Thermal noise is random, so two 1V noise voltages sum to 1.414V (the square root of the sum of the voltages squared). Thus, 3 x 3mV summed noise sources will give a total of ~5.2mV, not 9mV as you might assume.
Before we continue, there are a couple of terms that need explanation.
Firstly, the term 'dBv' (or 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. Note that it is common for these notations to be mixed up or not specified properly.
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' (E IN) 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 a better figure by another 10dB or so. This is actually meaningless, since no-one will (or can) operate equipment at the maximum level at all times, and the average will be considerably less.
Thirdly, it is commonly accepted that the minimum theoretical input noise (E IN) 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 meaningless though, since no real-world signal sources have zero impedance. Some may come close though, so the amplifier under test should always have its input terminated with a resistance 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 first gain 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 "voltage noise is 5nV/√Hz" is not very friendly (and is the same terminology used to determine resistor noise above). 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 (E IN) 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 = -123dBV)
Signal to noise (dB) = 20 x log (1V / 70.7uV) = 20 x log (14144) = 83dB
We can also calculate this using dB alone.
EIN = -123dBV
Gain = 40dB
S/N = 123 - 40 = 83dB (ref 0dBV)
For low level preamps (such as microphone or moving coil phono pre-amplifiers), it is common to specify 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 active and passive components (especially transistors, opamps, resistors, etc.) 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 with a source resistance of 200 ohms. This means that with a gain of 60dB, the best possible signal to noise ratio will be 69dB relative to 775mV (or 71.2dB ref 0dBV).
As an experiment, I built a three opamp precision microphone preamp using 1458 opamps (equivalent to a dual µA741). 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 very limited because of the low speed 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 and 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. NE5532 (or LM833, although I usually do not recommend them) dual opamps are an excellent choice for low noise, but bear in mind that LM833 opamps in particular 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. One of the best is the LM4562, with input noise of 2.7nV/√Hz (~380nV with 20kHz bandwidth). This is an expensive part, but it is exceptionally quiet. The TLE2027 is another low-noise part (also 2.7nV√Hz) but appears only to be available in an SMD package. There are other that are even quieter, such as the AD797B (the 'B' variant is the 'better' version, with 0.9nV/√Hz), but you pay dearly for the low noise!
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. This is hard to recommend when opamps such as the LM4562 are available.
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.
Opamps can also be paralleled to get lower noise. Outputs must be combined using low value resistors to ensure proper current sharing and prevent circulating currents between the opamps. The noise improvement is much the same as with discrete transistors.
Most noise is random, and can be described in a number of ways. The probability of a noise peak being positive, negative, of any particular amplitude or phase displacement is (by definition) completely unpredictable. The most common explanation is to show a 'Gaussian Distribution' along with statistical analysis to examine the long-term behaviour. In the graph below (adapted from Chapter 10 - Op Amp Noise Theory and Applications, Literature Number SLOA082) the symbol 'σ' is the standard deviation of the Gaussian distribution. The probability curve is commonly known as a 'bell curve', due to its shape. Note that this only applies to thermal and shot noise, and other noise sources do not have the same probability (1/f or 'flicker' low frequency noise for example).
Figure 2 - Gaussian Noise Distribution
The peak amplitude (statistically) will be within ±1σ 68% of the time, and this usually (but not always!) equals the RMS value. That does not preclude a noise spike exceeding the ±3σ value, and at least in theory, such a spike can even be infinite. That doesn't usually happen in what's laughingly known as 'real life' ). In any real circuit, the likelihood of a noise signal exceeding the supply rails is infinitesimal, and unless there is a major component failure, noise outside the ±3σ is thankfully rare. In fact, it will happen, but mostly will not be audible unless the duration and amplitude are great enough.
For all resistors in low noise input circuits, you absolutely, positively, must use 1% tolerance resistors, which will be metal film and the lowest practical value for lowest noise. The value must be chosen with reference to the device's specifications - not all opamps (for example) can drive low impedance loads without limiting the output voltage or introducing serious distortion.
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. As noted in that article and elsewhere on the ESP site, I am firmly of the (educated) opinion that A-Weighting should be banned, because it simply lets people get away with making excessive noise (especially low frequency noise which all but disappears with A-Weighting).
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 in telephony - A-Law, used by all European countries, much of South America, Australia and New Zealand etc., and μ-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 dreadful. 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 depths 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 × Log10 65535 = -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.
It's not at all uncommon to see astonishingly high figures claimed for many 'high end' digital systems, but these are nearly always based on the theoretical limits, rather than practical (or 'real world') levels. Given that the resistance of the source sets the minimum possible noise level in most cases, it's unrealistic to expect a digital system to somehow negate simple physics.
You also need to consider your listening level and the minimum background noise level in your listening space. Unless it's exceptionally well insulated, you can expect the background level in a fairly quiet room to be between 25-35dB SPL (A-weighted). With many listening spaces, it will be somewhat worse. Your maximum listening level should be comfortable, and not so loud as to cause hearing damage. An average of around 90dB SPL (unweighted) is the maximum recommended for up to 2 hours. The level should be reduced for longer listening sessions.
A signal to noise ratio of 100dB is quite clearly well in excess of what is actually necessary, but there is no reason not to get the best possible, providing it doesn't involve great expense. Once the system noise is below the room noise level, then it's immaterial in real terms. Note however, that some noises are quite audible even when below the room noise. Buzz is particularly troublesome, because it consists of a series of fixed harmonic frequencies, usually determined by the mains frequency (50Hz or 60Hz).
Noise is inescapable. Adding (often very) expensive 'super' regulators usually won't change a thing, because most of the noise we can hear is due to simple realities in the components we use. To minimise the noise levels, resistor values should be as low as possible, and this is especially important in locations where the signal level is very low. For example, it would be rather foolish to use an AD797 opamp in a moving coil phono preamp, then use 100k feedback resistors to set the gain. Wherever possible, use the lowest value resistances you can, but be mindful of the opamp's ability to drive very low impedances. Most have a definite upper limit to the current they can deliver, and almost without exception, approaching the limit(s) will increase distortion.
You also need to consider the signal level. If the signal is at 1V (RMS), then using an ultra low-noise opamp and low value feedback resistors is pointless, because the typical circuit noise is so far below the operating level. Even if the circuit has a noise output of 100µV (which would require some seriously poor decisions to achieve), the S/N ratio is still 80dB. In reality, this would be difficult to reach using any reasonable parts, so there are few real restrictions with high-level signals.
When signal levels are low (e.g. less than 1mV), then you have to use every trick in the book to keep the noise level low enough to prevent it from intruding on your music. However, by careful selection of the various components, sensibly low resistor values (which may require that the supply voltage be reduced to prevent excessive dissipation), very low noise designs are well within reach. It often takes a bit of thought about what you're trying to achieve, but it can be done.
You also need to ensure that measurements are based on the real world. There's no point measuring noise from 2Hz to 200kHz for an audio preamp that only has to deliver a signal within the 20 to 20kHz band. All you're doing is measuring noise that's inaudible, leading to unrealistically poor results. Once the output is sensibly band-limited, you may well discover that it's perfectly alright (as a measurement at least). Mostly, if you can't hear any noise from the listening position, then aiming for less is unrealistic (and expensive). There is no tangible benefit, but if you happen to believe in so-called 'micro-dynamics' then I suggest that you need to get proof of the theory (plenty of references, but I've never seen actual proof, as determined by a double-blind test).
It's actually quite rare that noise is intrusive with well designed and built systems (whether commercial or home made). The most common complaints are due to poor earthing/ grounding causing hum or (more commonly) buzz. Thermal and shot noise are always present, but usually at levels that don't cause any audible deterioration. For example, it's unrealistic to expect a S/N ratio of 100dB from a vinyl recording, and even a standard CD has a 'real world' S/N ratio of about 95dB (and that doesn't include noise that entered the signal chain during recording and post-processing).
So, while noise is escapable, it's generally at a level that doesn't intrude. Poor design choices can make it worse than it may otherwise be, but mostly it's a non-event with 'normal' signal levels.
|Copyright Notice. This article, including but not limited to all text and diagrams, is the intellectual property of Rod Elliott, and is Copyright © 1999-2006. Reproduction or re-publication by any means whatsoever, whether electronic, mechanical or electro- mechanical, is strictly prohibited under International Copyright laws. The author (Rod Elliott) grants the reader the right to use this information for personal use only, and further allows that one (1) copy may be made for reference while constructing the project. Commercial use is prohibited without express written authorisation from Rod Elliott.|