Subs and Infrasonic Mics (a duffer's guide)
If anyone has been following the discussion @pygmalion and I have been having on the official USB C Mic forum, you'll know we've really got into the weeds of how JFET mic pre-amps work, and in particular the frequency response at the low end.
This stuff also bleeds over into other areas like improving the active filtering used in the Ultimate PC Sound system which has questionable crossover filtering. We'll look at that later - this is not a criticism of Matt, we're ALL learning, especially me.
Pygmalion wants a system to record and analyse the infrasound on some small DC motors and control the levels using a Raspberry Pi. This requires the use of a digital volume control and a mic/amplifier capable of operating down to very low frequencies.
This raises some interesting questions, but mostly in the transducer. Infrasound transducers *(mics) are a very specific area of design ( https://www.grasacoustics.com/products/special-microphone/infra-sound-microphones )
But you can make them like this with a large sub-woofer like this:
An Jim Hannon has made a very *very* large diaphragm condenser mic https://jimhannon.wordpress.com/2013/04/05/infrasonic-microphone-part-i/
Such transducers are used for things like detecting underground nuclear tests with the results analysed by a Fast Fourier Transform - Derek Muller has a very well-produced video that doesn't dig into the polynomials
You can think of sine (and cosine) waves as the atoms of sound. Everything we hear is made up of large numbers of pressure waves, represented by undulating sine/cosine waves of varying amplitudes and frequencies. While it's relatively easy to remove a single sine wave from a signal using a tuned circuit - that's how radio receivers pick a radio station from all the background mush - getting all the frequencies and amplitudes is a much larger task. FFTs take complex signals and reduce them to just a series of sine waves.
Even a simple square wave can be decomposed by an FFT into a single "fundamental" and a (theoretically) infinite number of harmonics.
As you can see this is one of those fractal-like problems that the closer you look, the harder it gets. True infrasound (below 1Hz) requires super-accurate devices like matched microphone arrays that can pick up the pressure at a particular point across a baffle and when combined with multiple other measurements from similar devices can be used to extrapolate the huge wavelengths.
How big? Well, for sound travelling at 343 m/S in air at 20 degrees (68 f for our friends across the pond) for 1Hz that means a peak-to-peak wavelength of 343 meters or about 375 yards. Even at the limit of human hearing, 20 Hz that wavelength is a staggering 17 meters / 18.5 yards
It it's entirely possible to have a multi-microphone array covering that distance if you're trying to listen for earthquakes, underground nuclear tests and so on but it's a bit impractical for us humble experimenters and home builders.
Referencing examples like Jim Hannon's above, @pygmalion and I discussed using large diaphragm condenser (LDC) mics like the ones Matt used in his glorious USB C mic. But there's a problem, which is this, even fairly high-quality capsules are designed with audio frequencies in mind so they aren't optimised for the low end and seem to start "rolling off" (that's the point where efficiency falls away) at frequencies sometimes as high as 80Hz. That might sound daft (if we can hear down to 20Hz) but human voices very rarely get down that low, although Tim Storms, the world record holder can apparently get down below 1Hz
even with fairly cheap 2.1 speakers this guy makes my desk rumble!
So, after all of that, what's the option for people who don't have access to the $multi-1000 mics that can record voices like Tim?
As unimaginable as it is, good quality (say £15-50) SMALL diaphragm (SDCs) condenser mics seem to perform better at low frequencies than their larger cousins. I'll let you in on a little secret, the industry now produces low-pressure transducers for use in disposable vapes which are essentially electret microphones, albeit highly specialised ones.
This suggests that it should be possible to detect relatively low-frequency sub-sonics well below 20Hz.
We usually talk in terms of octaves - the word derives from octa meaning eight and is the difference in frequency (note) between eight keys on a piano. So 10Hz is one octave LOWER than 20Hz, 5Hz is two octaves lower and so on. And when we look at filters and response curves you'll see the designers mention dB (decibels) per octave. That's the relative energy produced as each time the frequency doubles or halves.
dB is one of those mysteries so here's how you work it out in Google (no less) although us old guys had to use calculators or even books of pre-calculated tables. You young people have it so easy. 🙂
The calculation is just this:
dB = 10*log(Value 1/ Value 2)
So measure the power, that's the amplitude of two waves A1 and A2 like this. *
A1 = 20
A2 = 10
10 * log(20/10)
This comes out (in round figures) to 3dB which is twice as much power (not volume, our ears don't work that way sadly)
If we have a volume CUT we might see it like this:
10 * log(10/20)
= 10 * log(0.5)
= -3 dB
Given the decibel cut or gain, you do the calculation in reverse.
Gain = 10^ dB/10
This is how you do antilog right inside Google which saves you digging out your old college calculator.
For 3 dB gain, you'd write - brackets included for clarity:
Gain = 10^ (3/10) = 2
or, for example, a -6 dB cut:
Gain = 10^(-6/10) = -0.25
Which means power has been reduced to one-quarter of its previous value.
If you skipped ahead here you probably already know all this math and can picture dBs although it's worth noting that when you see response graphs of audio equipment they are often extrapolated or even exaggerated. As I've said elsewhere unless you're doing audio measurements for scientific purposes, a perfectly flat frequency response is about as interesting as eating a piece of dry, white bread. Real microphones (and yes, that means the classics from Neuman, AKG, Rode etc. all have little peaks designed to help out where they are going to be used. **
When I've finished a couple of improved pre-amp designs for Matt's mic, I'll put this little bit of "whizz" into that.
The point of this (very) long post is to examine, with Pygmalion's help, is to assess just how low down we can measure with mass-produced SDCs.
The response charts of these devices tend to stop sharply at the low end of interest - they simply don't seem to measure it. Let's look at the Primo EL200
Primo mics claim the mic has a sensitivity of 1V per pascal at 5V with a 5.6 K resistor as the drain load delivers a 600-ohm impedance. Self noise is quite decent at -78 dB (even the lower-cost mics in this range offer -72 dB) both of which beat the FETless LDC from JLI as specified for Matt's build. And this is delivered via a single resistor and 5V supply.
You'll also note that chart "only" goes down to 80 Hz, but we can reasonably infer that it does capture sound well below that and it won't just fall off a cliff, even if it does drop off sharply, we can take a guess by extrapolating from what we have (guessing really), but that gives us a guess as to what sort of compensation might be necessary to bring those frequencies back into useful levels.
So it seems reasonable to construct a low-pass filter that rolls off reasonably sharply after (say) 80 Hz followed by an amplifier. That will leave a little dip in the chart but these things are never as accurate as the design books suggest because we have to deal with real components that have real values. Once we get a design we should really sweep it with a function generator to see how it behaves "but no one got time for dat!"
A simple single-pole filter consists of a resistor and capacitor which forms a voltage divider. The 3dB point is reached when the impedance of the resistor is matched by the reactance (AC impedance) of the capacitor. This works regardless of which way round you arrange it - but since capacitors block DC, it's easy to see that if the capacitor sits "on top" of the resistor you have a high-pass filter. If the resistor comes first, you have a low pass.
The problem is when you put another "pole" that's another voltage divider in line with this, the impedance of that divider (which, remember changes with frequency) it changes alters the impedance of the lower half of the preceding pole. If you managed to follow that, you'll be able to see how this gets really quite tricky and if you're mathematically inclined, I'm not, you'll realise we're into complex polynomials - a word that makes my eyes glaze over.
While I go dust off my design books and look for something (a) suitable (b) practical (c) cheap and (d) simple: pick any four, I'll leave it to Pygmalion to think about where we go from here...
* This is usually peak voltage, but dBs themselves don't rely on a particular measurement so long as both values are the same. You could say Alice has 3dB as many apples as Bob... but that's not useful unless you want to confuse your friends with your awesome math skills.
** Moving coil (dynamic) microphones are horrible in this regard because a little plastic diaphragm has to move a coil of wire which has a considerable mass when compared to the microns thin one found in a condenser. All that extra mass reduces sensitivity dramatically and affects the mic's ability to accurately respond to subtle details (low amplitude sine waves) sound is comprised of. This is why condenser mics are used across most instruments and dynamic mics (like the rock classic Sure SM58) tend to be used where people might scream into the device - higher SPLs (sound pressure level).
Take everything I say with a pinch of salt, I might be wrong!
I think I broke something trying to add this. It's late and the cat is getting fractious.
Here's a two-pole Butterworth Besel (Butterworth needs small amount of feedback to give it a damping factor) with a -3 dB point at 80Hz followed by another one of the same design following right after it. You can see from the plots that the -3bB point slips back to 65 Hz which might (or might not be useful). Modern computer sims make testing this stuff a whole lot easier. This one was simulated here https://www.falstad.com/circuit/
Take everything I say with a pinch of salt, I might be wrong!