Microphones: Noise 2
In the seventh installment of his on-going series about microphones, Greg Simmons continues his exploration of noise and how it affects your choice of microphones and preamplifiers…
We began our exploration of noise in the previous installment by looking at the different types of noise found in microphones and preamplifiers, where they exist in the signal path, and how they’re measured and defined. In the process, we looked at Brownian Noise and Thermal Noise, A-waiting and CCIR-weighting, Self-Noise and Impedance. We’ll continue our exploration in this installment by starting with a specification that aims to show us the significance of the noise relative to the signal level. After all, noise is only a problem if it’s loud enough to be a problem…
SIGNAL TO NOISE RATIO
As stated in the previous installment, if you’re capturing a sound with a microphone there is going to be noise. Whether that noise is a problem ultimately depends on the difference between the level of the signal and the level of the noise. This difference is represented in the specification called ‘Signal To Noise Ratio’, also known as ‘S/N Ratio’ or simply ‘S/N’. A microphone’s S/N Ratio represents the difference between its noise and its output signal level when there is a 1kHz sine wave creating 94dB SPL (1Pa) at the diaphragm. The S/N Ratio is expressed in decibels. For a condenser microphone it can be simply derived as follows:
S/N Ratio = 94dB – Self Noise
The simple formula for condenser microphones can be confirmed by looking at the table below, which shows the S/N Ratio values of the condenser mics featured in the previous installment.
Note that in every case where the manufacturer has provided an S/N Ratio (shown in black), it is equal to 94dB minus the Self Noise figure. Some condenser microphone manufacturers don’t include the S/N Ratio in the specification, probably because it can be easily derived from the Self Noise figure (it’s really just another way of specifying Self Noise, using 94dB SPL as the reference instead of 0dBA). Knowing this, we can calculate the missing S/N Ratios of the microphones in the tables above (see the figures shown in blue). The S/N Ratio of Røde’s NT1A is 94 – 5 = 89dB; the same formula has been used to calculate the S/N Ratios for all the listed microphones that do not have a specified S/N Ratio.
It is important for any S/N Ratio specification to include which Self Noise weighting measurement they’re using for the calculation: dBA or CCIR. Neumann’s U87Ai (in cardioid polar response) has a Self Noise that is specified as 12dBA and 23dB CCIR. Its S/N Ratio is 82dB for the dBA specification (because 94 – 12 = 82), and 71dB for the CCIR specification (because 94 – 23 = 71). Similarly, Audio-Technica’s 4022 has a specified ‘Noise’ level (they don’t use the terms ‘Self Noise’ or ‘Equivalent Noise Level’) of 13dB and a specified S/N Ratio of 81dB, because 94 – 13 = 81. Sennheiser specify the Self Noise of their MKH8040 small single diaphragm cardioid as 13dBA and 22dB CCIR. They don’t specify the S/N Ratio but we can calculate it as follows:
S/N Ratio = 94 – 13 = 81dBA
S/N Ratio = 94 – 22 = 72dB CCIR
All of the S/N Ratio information above is related to condenser microphones, where a Self Noise figure is usually given and specified in decibels. Passive microphones (ribbons and dynamics) rarely have an S/N Ratio figure given, partly because their Thermal Noise is so low that it hardly matters in the applications those microphones would be used for – the preamplifier is the dominant noise source due to the microphone’s low Sensitivity. Nonetheless, for the sake of the exercise we can estimate a passive microphone’s S/N Ratio if we know its Sensitivity and Impedance (which allows us to calculate the Thermal Noise). Let’s compare the S/N Ratio for a passive dynamic microphone (Shure’s SM57) with a passive ribbon microphone (Royer’s R121).
Using the calculations in ‘Noise Maths’ (at the end of this installment) we find that the SM57 has an S/N Ratio of 74dB, which is marginally less than some of the small diaphragm condenser microphones listed in the previous installment. In comparison, the R121’s S/N Ratio is 83.1dB, which is actually better than the SM57 – assuming the stated Sensitivity and Impedance specifications from both manufacturers are comparable, and assuming the same testing and measurement conditions. The R121’s higher S/N Ratio of 83.1dB implies it will be quieter than the SM57 on the same signal, and also quieter than some of the small diaphragm condenser microphones listed above, but in practice the S/N Ratio of the signal coming out of the preamplifier will also depend on the amounts of gain in use and the preamplifier’s input impedance, as we’re about to see…
EQUIVALENT INPUT NOISE (EIN)
The EIN specification is a simplified way to represent the noise contributed by the preamplifier in the process of amplifying the signal from the microphone to a useful level. It’s really a ‘crowd pleaser’ specification because it produces a low value that looks impressive on a specification sheet, but requires knowledge of the measurement conditions and a simple bit of maths before it becomes meaningful, comparable… and inevitably worse than it looks.
Although the noise at the output of a preamplifier is measured as a voltage, it’s a very small value and is usually represented in dBu rather than volts. The idea of measuring a preamplifier’s noise seems simple at first: turn it on, measure the voltage level of the noise at its output, and convert that voltage to dBu. How hard can it be? Let’s see…
At this point it’s important to remember that a microphone preamplifier has one fundamental job: to accept the very small signal from a microphone and amplify it to a useful level for the rest of the equipment in the signal path. There are many different circuit designs that can do this, each with different outcomes related to price, gain, noise, distortion, tonality and bandwidth – and each with preferred methods of measuring noise that would deliver very accurate results. The EIN specification favours more of a general approach that allows comparisons to be made – but the comparisons are only relevant if the same measurement conditions are used, which is often not the case.
Imagine the preamplifier as a conceptual model with two parts, or ‘stages’. The first is the microphone input stage, which is designed to accept the very small signal from the microphone. The second is the gain stage, which is designed to amplify the very small signal from the microphone. So far, so good…
Like any electronic circuit, the microphone input stage will have a certain amount of Thermal Noise, and that Thermal Noise will be amplified by the preamplifier’s gain stage. The Thermal Noise from the microphone input stage is dependent on its input impedance, and that, in turn, is dependent on the terminating impedance – in other words, the output impedance of the microphone connected to it. That means the EIN measurement must be made with a microphone connected.
Why should a microphone be connected? Because the microphone input stage has a high input impedance so it can accept the very small signal from the microphone. As we saw when discussing Impedance in the previous installment, the preamplifier’s input impedance needs to be at least 5x higher than the microphone’s output impedance. If that high input impedance is left unterminated (i.e. no microphone connected), it will result in an unrealistically high Thermal Noise that will then be amplified by the gain stage, creating an unrealistically high noise level. When a microphone is connected, however, it creates a ‘real world’ scenario where the high input impedance of the microphone input stage appears in parallel with the low output impedance of the microphone, reducing the total input impedance (to a value lower than the microphone’s specified Impedance, in fact) and thereby reducing the Thermal Noise at the input to a more realistic level.
You might be asking, “Won’t connecting a microphone introduce more noise?” Yes it will, but it’s a known quantity of noise that can be allowed for when assessing the noise from the preamplifier. We’ll see how that works shortly…
You might also be asking, “Won’t connecting a microphone introduce the possibility of capturing external sounds and noises that could interfere with the preamplifier’s noise measurement?” Yes it does, and for that reason a microphone is not actually used. Instead, an electronic component called a resistor is used. It’s chosen to have the same Impedance, and therefore the same Thermal Noise, as a typical passive microphone. It’s called a ‘terminating impedance’ because it terminates the preamplifier’s inputs with an impedance that is equivalent to the output impedance of a typical microphone. As far as the preamplifier is concerned the resistor is a passive microphone in a completely silent and sound-proofed room, providing nothing but an Impedance and its accompanying Thermal Noise.
As mentioned above, in this conceptual model the Thermal Noise created by the preamplifier’s microphone input stage is amplified by the preamplifier’s gain stage as part of the process of amplifying the input signal to a useful level – therefore, more gain means more noise.
From the above we can see that the amount of noise coming out of the preamplifier is dependent on two variables: the value of the terminating impedance, and the amount of gain used when making the measurement. Knowing this we can proceed with how the EIN measurement is made and how to interpret it.
Most EIN measurements are made with a terminating impedance of 150 ohms and a gain of +60dB.
With the 150 ohm terminating impedance connected between pin two and pin three of the preamplifier’s microphone input XLR (just like the signal output of a microphone), the preamplifier’s gain is set to +60dB – introducing and/or amplifying the noise to a level that can be accurately measured at the preamplifier’s output. The measured noise voltage is then mathematically reduced by -60dB to arrive at a value that is equivalent to what the noise voltage would be at the input before the +60dB of gain was applied.
In other words, if the preamplifier created no noise of its own, the EIN represents the level of the noise voltage that would have to be fed into the preamplifier’s inputs to create the noise measured at its output when 60dB of gain was applied. Hence, it is the Equivalent Input Noise, or EIN. This noise voltage is then converted to a dBu value and becomes the preamplifier’s specified EIN.
EIN values in dBu should always be negative numbers, and larger negative numbers mean less noise than smaller negative numbers. So a preamplifier with an EIN of -130dBu is quieter than a preamplifier with an EIN of -128dBu, but that’s only true if all the same measurement conditions (terminating impedance, temperature, gain and weighting) are used to measure both preamplifiers.
Noise is only a problem if it’s loud enough to be a problem…
Because the EIN calculation is based on a certain amount of gain and a certain terminating impedance, and because all audio circuits contain a certain amount of Thermal Noise that will be boosted by gain, it should come as no surprise that a preamplifier’s EIN figure changes with gain.
The graph below is based on a presentation given by THAT Corporation at the 129th AES Convention in November, 2010. You’ve probably never heard of THAT Corporation, but it’s highly likely that you’ve heard their products. Among other things, they manufacture the high-quality low-noise microphone preamplifier chips that are used in many of the interfaces and preamplifiers on the market.
The red curve shows the relationship between EIN and gain for what was described as a ‘simple microphone preamplifier’ (brand and model unnamed), measured with a 150 ohm terminating impedance. The use of a 150 ohm terminating impedance means the theoretical minimum EIN for this test will be -130.9dBu (which is the Thermal Noise of a 150 ohm resistance at 20°C and 20kHz bandwidth), so all EIN values can be compared against that minimum value to ultimately determine how much noise has been added by the preamplifier.
It’s worth noting that the lowest EIN figure on the curve occurs at +60dB of gain, which is the gain that most preamplifier manufacturers use when specifying EIN. You could be forgiven for thinking the preamplifier measured here is quietest at +60dB of gain, but that isn’t the case – it’s just the gain where the EIN is lowest. To determine the actual amount of noise coming out of the preamplifier, we need to multiply the EIN by the amount of gain used. Fortunately the graph is using decibels to represent noise levels and gain, so we can simply add the gain value (in dB) to the corresponding EIN value (in dBu) to determine the resulting output noise in dBu.
At +20dB of gain (blue) we see that the EIN is approximately -113dBu. That’s the equivalent level of noise at the input of the preamplifier. To determine the noise at the output of the preamplifier we need to add the preamplifier’s +20dB of gain to that EIN figure, which means the total noise coming out of the preamplifier is -113 + 20 = -93dBu. At +40dB of gain the EIN is approximately -124dBu (green); adding +40dB of gain brings the noise at the preamplifier’s output up to -84dBu. Likewise, at +60dB of gain (black) we see that although the EIN is very low at -129dBu, adding +60dB of gain brings the output noise of the preamplifier up to -69dBu. So while the EIN figure gets lower with gain, the actual output noise of the preamplifier in this example increases with gain as expected.
As with all specifications, we can see that EIN is a helpful figure if you know how to interpret it, and if the same measurement conditions are used and stated – which is rarely the case. Here are some real-world examples: the preamps on Mackie’s 1604VLZ4 mixing console offer an EIN of -128.5dBu at ‘maximum gain’ (the actual gain value is unstated) when terminated with a 150 ohm resistance, while Millennia’s HV3-C rack-mounting preamp offers an EIN of -133dB (no reference after ‘dB’ to indicate whether it’s dBu, dBV, dBA or whatever) at 60dB of gain with “inputs common” (assumedly meaning they’re using zero ohms termination, hence bettering the theoretical limit of -130.9dBu for 150 ohms), and Focusrite’s Scarlett 2i2 interface offers an EIN of -128dBu (gain unstated) but it’s an A-weighted measurement (therefore looks quieter) and provides no indication of the terminating impedance. Unfortunately, none of these EIN figures can be compared confidently or directly due to insufficient details and/or different measurement standards. That’s the great thing about standards, of course…
…if you’re capturing a sound with a microphone there is going to be noise
NOISE & MICROPHONE CHOICE
If you’ve made it through this installment and the previous one, give yourself a pat on the back – you’ve navigated your way through the primary noise sources at the front end of the signal path, from where the sound arrives on the microphone’s diaphragm to where the signal leaves the preamplifier and is ready for additional processing, AD conversion, recording and/or mixing. We’ve explored the noise-related specifications for Self Noise, Impedance, S/N Ratio and EIN, and seen how they’re inter-related and also how they’re related to microphone Sensitivity and preamplifier gain. We’ve also seen how difficult it is to compare these specifications in any meaningful way due to either enormous complexity, a willful defiance of industry standards, or both. So what can we deduce from all of this information?
Noise adds up!
It’s everywhere. It’s in the air that our sounds pass through, and it’s in the electronics that our signals pass through. The further your signal travels from capture to playback, the more noise its going to collect. The noise you really need to avoid is the noise that occurs before or during preamplification – as explored in these two installments – because that’s where the signal level is at its lowest (making the noise more significant) and it’s also where the most amplification occurs (making the noise more apparent). If you need to make a very low noise recording or capture a very quiet sound, you’ll need a microphone with low Self Noise and high Sensitivity (it will almost certainly be a large diaphragm condenser microphone), and you’ll need to combine it with a preamplifier that has a low EIN figure based on your microphone’s output impedance and the levels of gain you anticipate using.
In the best of all possible worlds, microphone manufacturers would provide impedance graphs of their passive microphones (active microphones tend to be more stable in that respect), and preamplifier manufacturers would provide EIN curves for their products using a range of different terminating impedances (say, 50 ohms, 150 ohms and 300 ohms) and gains so you could get a better idea of a preamplifier’s suitability for use with a certain microphone for a certain application.
CLOSING THE LID…
We started our exploration of microphone specifications with Sensitivity in the fifth installment [add link?], which included the following phrase: “Nobody cares about the lovely warm tonality of your ribbon microphone if the signal is buried in noise…” The opening of our exploration of noise (see previous installment) described noise as “the biggest can of worms in audio electronics”, and promised to briefly lift the lid on it. As we’ve seen over the last two installments, noise truly is a can of worms and it’s time to lower the lid and back away slowly – for now. A microphone’s Self Noise or Thermal Noise is part of the signal the microphone delivers, and using a quieter preamplifier isn’t going to change that. A preamplifier with an appropriate EIN figure will result in less noise from the preamplifier itself, but it won’t change the inherent noise from the microphone – other than amplify it with the signal.
It’s just physics. In a can. Filled with worms and agitated by heat…
When capturing very quiet audio, we have to move the emphasis away from microphone and preamplifier combinations that deliver the most tonally pleasing result and towards those that deliver the quietest result. There are numerous apps and plugins that can minimise noise after its been captured, and the carefully-selected demonstrations of these products would have you believe in magic. Sometimes they are magic (in the Arthur C. Clarke sense of the word), but we soon learn to be grateful for any reduction in noise beyond a couple of dB that does not introduce unwanted artifacts or adversely affect the tonality of the signal itself. Sometimes a couple of dB is all the noise reduction we need to get the message: “if you don’t want noise, don’t capture it.”
In the next installment we’re going to explore the other end of the signal level spectrum by looking at clipping distortion and the microphone specifications related to it: Maximum SPL and Dynamic Range. In the installment after that, we’re going to see if there’s a way to make sense of all of these level-related specifications to help us choose the right microphone and preamplifier for the job, landing the microphone’s signal in the preamplifier’s Goldilocks Zone to minimise noise and avoid distortion.
Special thanks to Steve Dove and Terry Demol for their invaluable insights, clarifications and patience when putting together this and the previous installment related to noise in microphones and preamplifiers.
EIN is a helpful figure as long as you know how to interpret it
The following mathematics were used to calculate the values seen in this and the previous installment.
THERMAL NOISE MATHS
In the previous installment of this series we saw that Thermal Noise is, as its name suggests, due to heat. If we know a circuit or component’s impedance, along with the operating temperature and the required bandwidth, we can calculate its Thermal Noise voltage with the following formula:
Thermal Noise = √(4 x kB x Impedance x Bandwidth x Temperature)
Where kB is Boltzmann’s constant (1.38064852 × 10-23), Impedance is in Ohms, Bandwidth is in Hertz and Temperature is in Kelvin.
For most calculations we assume a bandwidth of 20kHz because we’re not interested in noise above the range of human hearing, and a temperature of 20°C (a comfortable room temperature that becomes 293.15 when converted to Kelvin). Knowing this, we can calculate the Thermal Noise for an impedance of 150 Ohms – a value that’s commonly used for microphone and preamplifier noise calculations:
Thermal Noise voltage = √(4 x 1.38064852 × 10-23 x 150 x 20,000 x 293.15)
Thermal Noise voltage = 0.00000022 volts
CONVERTING TO dBu
As we saw in the installment about Sensitivity, in audio we use decibels to represent very large and very small values. Noise voltages are often very small values, as seen in the calculation above, that require a lot of zeroes after the decimal point. They are usually quoted as dBu values rather than voltages (where 0dBu = 0.775Vrms), which makes them easier to read and easier to use alongside other audio levels that are quoted as dBu values.
We can convert volts to dBu with the following formula:
dBu = 20 x log(volts / 0.775)
And we can convert dBu back to volts with the following formula:
Volts = 10(dBu/20) x 0.775
Let’s convert the noise voltage for the 150 ohm resistance calculated in Thermal Noise (above) into dBu:
dBu = 20 x log(0.00000022 / 0.775)
dBu = 20 x log(0.0000002839)
dBu = -130.9
That’s a much easier value to read, understand and compare. Noise values given in dBu should (hopefully!) always be negative values (which indicates that the noise is less than 1.0 volt), and larger negative numbers mean less noise than smaller negative numbers. A noise level of -130dBu has 10dB less noise than a noise level of -120dBu.
To check the dBu maths, let’s convert the -130.9dBu we calculated above back to volts:
Volts = 10(-130.9/20) x 0.775
Volts = 0.00000022
Bingo! So, at a temperature of 20°C and restricting the bandwidth to 20kHz, the theoretical noise voltage for an impedance of 150 ohms is 0.00000022 volts or -130.9dBu (which is often rounded to -131dBu).
SHURE SM57 THERMAL NOISE
The SM57 has an Impedance of 310 ohms at 1kHz. Assuming a room temperature of 20°C (293.15 K) and a bandwidth of 20kHz, we can calculate its Thermal Noise and convert it to a dBu figure as follows:
Thermal Noise = √(4 x 1.38064852 × 10-23 x 310 x 20,000 x 293.15)
Thermal Noise voltage = 0.00000031682 volts
dBu = 20 x log(0.00000031682 / 0.775)
dBu = 20 x log(0.0000004088)
dBu = -127.8
ELECTRO-VOICE RE20 THERMAL NOISE
The RE20 has an Impedance of 150 ohms. Assuming a room temperature of 20°C (293.15 K) and a bandwidth of 20kHz, we can calculate its Thermal Noise and convert it to a dBu figure as follows:
Thermal Noise = √(4 x 1.38064852 × 10-23 x 150 x 20,000 x 293.15)
Thermal Noise = 0.00000022 volts
dBu = 20 x log(0.000000220 / 0.775)
dBu = 20 x log(0.0000002839)
dBu = -130.9
ROYER LABS R121 THERMAL NOISE
The R121 has an Impedance of 300 ohms. Assuming a room temperature of 20°C (293.15 K) and a bandwidth of 20kHz, we can calculate its Thermal Noise and convert it to a dBu figure as follows:
Thermal Noise = √(4 x 1.38064852 × 10-23 x 300 x 20,000 x 293.15)
Thermal Noise = 0.0000003116 volts
dBu = 20 x log(0.0000003116 / 0.775)
dBu = 20 x log(0.0000004021)
dBu = -127.9
AEA R44C THERMAL NOISE
The R44C has an Impedance of 270 ohms. Assuming a room temperature of 20°C (293.15 K) and a bandwidth of 20kHz, we can calculate its Thermal Noise and convert it to a dBu figure as follows:
Thermal Noise = √(4 x 1.38064852 × 10-23 x 270 x 20,000 x 293.15)
Thermal Noise = 0.0000002957 volts
dBu = 20 x log(0.0000002957 / 0.775)
dBu = 20 x log(0.0000003815)
dBu = -128.37
SHURE SM57 S/N RATIO
Here’s the formula used to calculate the S/N Ratio (in dB) when using Sensitivity and Noise voltages:
S/N Ratio (dB) = 20 x log(Sensitivity / Noise)
Where the Sensitivity is measured in volts/Pascal, and the Noise value is measured in volts.
Shure’s SM57 has a stated Sensitivity of 1.6mV/Pa, which is 0.0016 volts. Earlier we calculated the SM57’s Thermal Noise to be 0.00000031682 volts (at 20°C with the bandwidth restricted to 20kHz). Putting those values into the formula we get:
S/N Ratio = 20 x log(0.0016 / 0.00000031682)
S/N Ratio = 20 x log(5051.186)
S/N Ratio = 74dB
ROYER LABS R121 S/N RATIO
According to Royer’s website, the R121 has a stated Sensitivity of -47dBV which equates to 4.46mV/Pa, or 0.00446 volts. Earlier we calculated its Thermal Noise to be 0.00000032 volts. Putting those Sensitivity and noise voltages into the S/N Ratio formula we get:
S/N Ratio = 20 x log(0.00446 / 0.00000031167)
S/N Ratio = 20 x log(14310)
S/N Ratio = 83.1dB
NEVE-LEVEL NOISE HACKS
The previous installment of this series referred to a column that Rupert Neve wrote for AudioTechnology magazine in which he made some seemingly impossible ‘apples vs oranges’ comparisons between the calculated Thermal Noise of a dynamic microphone and the specified Self Noise of a condenser microphone. Using his knowledge of microphone specifications, he did some clever hacks to convert dBA into dBu, and emulated an A-weighting filter by using a bandwidth of 12kHz rather than 20kHz in his Thermal Noise calculations. He qualified his results by saying, “Any equipment designer will point out that I’ve cut a few corners and made a few assumptions that are not strictly accurate. But it’s all within about 1dB and gives you an idea of the relative significance of the various noise sources.” It’s interesting reading…