The A‑weighting curve is shown here in red, alongside other weighting curves that are used in some applications.
We conclude our four-part series with a look at how specifications can accommodate the foibles of human hearing.
As mentioned in the first three instalments of this series, audio‑equipment specifications can facilitate useful point‑by‑point paper comparisons, but these evaluations are often more informative when made in the context of your particular use cases, interests and preferences. Measurement systems, however, don’t natively respond to audio signals the way human hearing perceives them.
The Weighting Game
Unless set to do otherwise, audio‑measurement systems observe signals with equal sensitivity across the audio spectrum. This is appropriate for making good objective measurements but ignores the fact that a key element in most audio systems is one or more human ears, which do not exhibit such a flat frequency response. Human hearing is more sensitive to midrange frequencies — roughly 1 to 4 kHz — than to those at either the lower or upper ends of the audio spectrum. As a result, sounds at low frequencies and, to a somewhat lesser degree, high frequencies require greater intensity — sound pressure — to be perceived at the same loudness as a midrange reference tone such as the typical 1kHz.
To approximate the human hearing response at modest volumes, test systems use an A‑weighting filter which rolls off both ends of the audio spectrum, thus approximating the frequency‑dependent sensitivity of the human ear. The A‑weighting filter resulted from data collected and published in 1933 by Fletcher and Munson that showed the non‑linearly variable sensitivity of human hearing over both frequency and loudness. Their seminal work was refined in 1956 by Robinson and Dadson, which formed the basis of the ISO 226 standard equal loudness contours to which you may see references. The most recent revision of this was published in 2003.
A‑weighted measurements are used primarily and extensively for measuring environmental noise and noise in audio equipment. For example, you’ll find an A‑weighting filter (or an otherwise‑named functional equivalent) as an option on most all loudness meters, such as those used in environmental studies and in specific industries where sound exposure is regulated.
One might be tempted to criticise A‑weighted measurements as putting marketing spin on the spec sheet to gain unearned advantage. But that misses the point of the measurement.
In both loudness‑metering and audio signal‑processing applications, A‑weighted measurements report numerically lower amplitudes (with units denoted dBA) than corresponding unweighted measurements in dB made with the same equipment under the same operating conditions. One might be tempted to criticise A‑weighted measurements as putting marketing spin on the spec sheet to gain unearned advantage. But that misses the point of the measurement, which is to express a parameter quantitatively in a way that corresponds well with the qualitative experience of typical human hearing. Just be certain that, when you are comparing specifications for competing pieces of equipment, if one reports an A‑weighted measurement for a specific parameter, ensure the other does as well.
How Noisy Is My Mic?
Note to those disinclined toward mathematics: You’ll never need to do any of the calculations shown below. They are given for spec‑sheet insights and for the physics‑curious. Read through and glean what you can if you like, but don’t panic — there’s no test and, in real‑world practice, the maths are all done by equipment manufacturers’ engineers to prepare their various spec sheets.
Among the common uses for A‑weighted noise measurements are microphone specifications. Microphones come in two basic types: dynamic and capacitor. Assessing the so‑called self‑noise of a dynamic microphone is easy: for all intents and purposes, there is none. To be more precise, the self‑noise of a dynamic microphone is the thermal noise (also called the Johnson noise) of the microphone’s output impedance, R, typically 150Ω. As with all noise measurements, the measurement bandwidth, ∆f, is a factor — we’ll call that 20kHz in round numbers. As the name ‘thermal noise’ suggests, temperature, T, is another factor, so let’s use 20°C as typical, but expressed in Kelvin as the maths require, so 293K. Put it all together and you get the noise voltage:
Vn = √4kTRΔf
where k is the Boltzmann constant. For our example, the self‑noise of a dynamic microphone with 150Ω output impedance is 220nV, which is about ‑133dBV or ‑131dBu. (Recall, dBV is dB relative to a 1 Volt reference; dBu is dB relative to 0.775V — a historically common reference level derived from 1mW into 600Ω.) This is at least a few decibels below the best modern preamplifiers’ own electronic noise floors.
Capacitor microphones, by contrast, have integral powered electronics to convert the signals from their capacitive transducers into a useful voltage signal. They exhibit excellent sensitivity (output voltage for a given acoustic loudness) but the transducer’s associated electronics necessarily include noise sources.
A convention common with electronic signal processors, particularly those with noise outputs that vary with settings, is to lump all noise sources that are distributed throughout the circuitry together and model them as a single noise source that appears at the input of a theoretical, functionally equivalent, noiseless apparatus. The quantity attributed to this modelled noise source is called the Equivalent Input Noise (EIN). This convention is often followed in specifying the self‑noise of capacitor microphones, but due to microphone’s key function, transduction from the acoustic to voltage domains, that puts the EIN in the acoustic realm as if it were a small acoustic noise‑making device at the capsule location with a noise amplitude measured in dBA.
Recall that all measurements expressed in dB are relative to some reference quantity. In this case, it is the threshold of human hearing at 1kHz that defines 0dBA (equivalent to an acoustic pressure of 20 µPascal). Obviously, we can’t measure that virtual noise source directly, but we can measure the physical noise output voltage of the capacitor microphone’s electronics. So, let’s say we effectively mute the capsule, measure the microphone’s resulting output noise voltage (with A‑weighting), and get a noise figure of ‑114dBV (A‑wtd). We can then convert that into a raw rms voltage:
Vnoise = 10(‑114/20) x 1* = 0.002mVrms
(*The x 1 is because of the 1V reference in dBV. If the measurement had been dBu the multiplier would have been 0.775)
Let’s say the microphone’s sensitivity is a typical 20mV/Pa. We can then calculate the noise voltage as a decibel ratio with that 20mV reference:
dB = 20 Log (0.002/20) = ‑80dB
The sensitivity reference is 1 Pascal, which equates to 94dB SPL, so the microphone’s self‑noise is 80dB lower than that:
94‑80 = 14dB SPL
Therefore, the microphone’s EIN figure is calculated to be 14dB SPL.
Like most analogue equipment, the signal‑to‑noise ratio (SNR) of microphones is calculated relative to a standard reference level — in this case, an acoustic input of 1 Pascal = 94dB SPL. Here the maths is trivial if the microphone’s EIN is given in the spec sheet: SNR = 94dB — EIN. So, our previous example with an EIN of 14dBA results in an SNR of 80dB, which a pretty good spec. Similarly, if a microphone’s spec sheet provides the SNR, you can calculate the EIN, if you have use for it, just by flipping the equation around: EIN = 94dB — SNR.
At some elevated acoustic pressure the microphone’s electronics will eventually overload, so microphones’ dynamic range is commonly larger than the SNR. For example, if our microphone has a maximum acoustic input of, say, 115dB SPL, the dynamic range will be 115‑14 = 101dB, which is 21dB greater than its SNR spec suggests.
...a directional microphone’s pattern often is a function of frequency, but how that affects the sonic quality for off‑axis sound sources is difficult to read from pattern maps.
Lastly, remember that some of microphones’ most important characteristics either don’t appear or are only hinted at on microphone spec sheets. For example, frequency response curves can suggest that a certain microphone design is biased for vocal and midrange instrument applications. But two such microphones from different manufacturers may offer very different sonic nuances in how they replicate an instrument or voice. Similarly, a directional microphone’s pattern often is a function of frequency, but how that affects the sonic quality for off‑axis sound sources is difficult to read from pattern maps. So, while specs provide a useful way to narrow down options when comparing audio equipment, there are additional qualities, which are sometimes more subjective, that are worthy of your consideration.
How Much Do Specs Matter?
Comparing spec‑sheet performance is one way to evaluate competing pieces of audio equipment but, as previously mentioned, it needs to be done in the context of your particular audio applications, needs and interests. For example, low‑noise microphones, mic preamps and audio interfaces are great if you’re recording ambient microphones as part of your miking design to pick up the natural acoustic qualities of a performance space. But if you’re a sax player in a funk band looking to put together an on‑instrument rig, chances are noise performance isn’t as high a priority as, say, build quality and physical robustness. Only your specific use cases can inform which equipment specifications are most important for a given equipment purchase.
General recordists, especially independents in the early stages of their career, may benefit from taking a note from the soundless world of still photography, where it is oft said, “The best camera in the world is the one you can put in your hands right now.” The same notion applies to purchasing audio gear: You’ll always have to work within a set of equipment constraints, but optimising your equipment selection process to get the most from your budget is more productive than holding out for the numerically best specified model you can’t afford. Consider your understanding of spec sheets as one tool in your kit to help you do just that and get the best gear your money can buy.
This series was produced in association with Audio Precision, Inc.