This last week has been consumed by my efforts to gather the electronic components needed to make the 4th order filter. It has not been easy, Starting with the fact that when I wrote the post above, I was under the misguided notion that I needed inductors in the order of micro Henrys (μH) and in reality I needed those values in MILLI Henrys (mH) *facepalm*.
I began the week by looking for capacitors at the one electronic supply shop that I know in Austin. After a good 20 minute walk from the nearest bus stop, I went in only to find out that the supplier for the shop had gone out of business. I could find very few things in the shop, giving me the impression that COVID 19 is ending just about every other business on sight. Images of Cuba, with people driving 1940's cars, and mechanics winding their own alternators flashed in my mind. When I was a kid, I saw an alternator be re-wound by a mechanic at a shop when we had our RV break down in the town of Taxco in Mexico in 1980. It was a fascinating process.
I managed to scrounge up a few capacitors to wire in parallel to make the 500 μF and 100 μF values I need, but if I need capacitors for a second woofer. I'll be out of luck. With no magnet wire to be found anywhere in town, I realized I could only make my own solenoids for inductors.
But the jump from μH to mH is a difficult one. It's the difference from making your own coil out of less than 50 turns of wire on a plastic tube, to needing a ferrite or iron core, and needing to wind at least a few hundred turns. And 10 mH is a value large enough to need something akin to a small electric transformer with an iron core. Given that this is a 4th order low pass filter for a very low cutoff frequency (100 Hz or lower) means that the inductor will be relatively big and heavy, not something you usually see for speaker crossovers. Some crossovers used by the industry will have values in the order of 1mH and are made by very large numbers of turns of copper wire (literally a golf ball size roll of copper wire). And I need ten times larger than that. This means an iron or ferrite core is mandatory to concentrate the magnetic flux in the solenoid (multiply its efficiency).
Without going much into the science of it, how effective their ability to store energy as a magnetic field depends on the material inside the coil; you're looking at increasing the magnetic field line density inside of the coils so you can keep the amount of wire and the overall size to a minimum, and substances like iron can multiply the flux density value of a solenoid anywhere from a few hundred times (most ferrous metals, ferrite) to 100000 times (pure iron with no oxygen around it). In general terms, in equations (see below) μ is the permeability, that is the resistance to forming a magnetic field which is proportional to the ability to store energy inside the coil, depending on the nature of the material in the core of the coil. Often you will see this term,
μ = μoμr,
where μ
o is the permeability of vacuum, and μ
r is the "relative permeability," a multiplying factor over vacuum depending on the material in the core. Air has a relative permeability of μ
r~1, so it's about the same as vacuum. Metals have a relative permeability ('multiplying factor") between 100 and 100000 which (unfortunately) depends on the strength of the magnetic field, making it difficult to design inductors without good test data on metals.
Relative permeability μ
r for mild steel as a function of flux density, B
The kind of inductor sizes I'm looking for, from 1/10th H to 1 H and beyond, really are values you see in power transformer winding for tabletop electronic appliances, so it gives you an idea of the volume and weight you're looking at when making one of these inductors. This is about 10 times bigger than the values you see in speaker crossover components - not too different in value, but a 10 mH coil made of copper with only an air core is something I haven't seen inside a speaker, as it would require thousands of loops of wire. The only way to reduce it to a more manageable size is to use a ferrite or iron core.
The general formulas to calculate the induction L of a solenoid are:
Linear inductor
Toroid inductor
This is where the Steampunk gene helps you the most. I found a steel ring bearing on the road once , which I kept because it looked interesting. "The ring would be good for a torus inductor," I thought, so I used all my heavy gauge magnet wire good for about 150 turns, but I ran out of magnet wire. I needed about 175 turns - so I couldn't even make something better than 9 mH - I needed 11 mH. You can see my initial mistake in the picture below
About 150 turns of Gauge 22 magnet wire over a torus of hard bearing steel I found on the ground once (right side)
It's about 9 mH. Compare to a 11.2 μH air-core solenoid I made previously (left side)
Not satisfied with the situation, yesterday, I decided to scrounge parts at the hardware store, hoping to find something I could make into inductors - a big chink of steel like a rod should be easy to find, either raw or in the form of a big fence bolt. Maybe I can find magnet wire? If not standard wire? A transformer to adapt?
*I can hear cuban music, smell cigars and feel the dirt and cobble stones under my feet. A 1940 Packard passes me by*
You can make solenoids out of steel door springs
I found several types of steel rods I could use, but nothing as large as 2 cm diameter, which I was looking for to limit the number of coil turns to 75 (I was still thinking of using some left over magnet wire in a thinner gauge), but the though had occurred to me that maybe springs could be used as coils. I didn't take the spring as coil -thing seriously, because I could not remember if would find springs that were thin and long enough. But I did! A few punches in the calculator revealed that less than 200 turns with a 1 cm core of steel would get me close to the values I needed. The core I used is a rod of 3/8 inch zinc plated steel - cold rolled mild steel. The springs are just wide enough to fit over the rod plus insulation (masking tape - electrical tape is too thick).
Making the solenoids was a bit harder than I expected. I had envisioned that I could stretch the springs and then use epoxy or enamel to insulate the wire before releasing the spring. I bought a large 20 cm long spring and a smaller 10 cm spring which I thought would be able to be used with minimal stretch - they were almost the perfect size according to my calculations. That was a big error. I ended up ruining the large spring using that approach. The spring kept getting stuck on the insulation I used for the core - it was a mess, and to pull it off the iron rod, I had to destroy the spring - I managed to save a little piece which I used (see below). Good word of advice, stay away from very stiff springs, only use the softest you can find. Also buy the longest springs you can get, and plan to cut them to size later.
Destroying the large spring reminded me of a trick I learned for my Steampunk business years ago, which was to stretch the springs far enough that they deform plastically, that is, far enough they hold their stretched shape. It's a very tricky thing to do, because you don't know how far each spring will stretch. Too far and the spring will be too "open." Quality control in those type of retail supplies is poor. Each spring will have a different stiffness, so every time you do the stretching the spring will look a bit different at the end - which means that I can't make two identical solenoids. Each is a "one-of." To make matters worse, the more open the spaces between the turns, the weaker the inductance becomes, so you need an extra length of coil if you stretch too far. In other words, make a length in excess and then plan to cut, with calculator at hand to cut at the right place.
Three very fancy inductors. Chromed high carbon steel coils over a core of zinc-plated mild cold rolled steel,
served over a bed of masking tape with vinaigrette
From top top bottom, 1.6 mH / 0.8 Ω, 5.4 mH / 1.2 Ω, 8.9 mH / 1.4 Ω, assuming μ
r = 300
It is possible μ
r may be half as large, but then I'll need test, and double the number of inductors
Unfortunately, as I explained above, it is difficult to know the permeability of the core without testing. And that means I don't really know the inductance values of the solenoids. In the absence of magnetic data sheets, it's very possible the value of the relative permeability μ
r, may only be half as large (cold rolled steel goes down below μ
r=150). If I just build my 4th order circuit as is, and μ
r=150, the cutoff frequency will be a bit over 300 Hz, instead of the 100 Hz I want. I am currently trying to device a method to test the inductance, but because the resistance values are low, I can't use my phone as the signal generator, and I'm having a hard time using the old trick of wiring a potentiometer (variable resistor) to a mains to 12 V transformer (60 Hz), in series and dividing the voltage between the solenoid and the potentiometer evenly to find the equivalent impedance. I may try again tonight without starting a fire or something like that. But in any case, if the relative permeability turns out to be one half than I need, I can always make more solenoids until I complete the required specs.
Normally you don't use high carbon chromed coils to make solenoids, because speaker designers are looking for pure values of inductance with as little resistance as possible. But in my case, since I am connecting a 4 Ω speaker to an amplifier that expects 8 Ω, i need to add resistance anyway. According to my measurements if I add the resistance of the three coils I made, I would be adding 3.4 Ω to the 4.4 Ω of the speaker, so the total (resistive) impedance would be 7.8 Ω, pretty darn close to 8 Ω, seems to me. Just what I need.
Oh well. Time to stop writing!
Cheers!
J. Wilhelm
