Homebrew Crossovers

Making your own crossover inductors

I use three values here, namely 0.3, 0.7 and 1 mH (These are the values used in the Ariel loudspeakers). Here's how to get from inductance value to actual-coil-in-your-hot-grubby-little-paws.

The calculator at Mogami-wire gives the following for 8, 10, 12 and 14 gauge copper wire:

Wire size	Area	Diameter (mil)	Diameter (mm)	Resistance
8 AWG	8.336mm^2	128.5 mil	3.264mm	0.00206 Ohm/m
10 AWG	5.261mm^2	101.9 mil	2.588mm	0.00328 Ohm/m
12 AWG	3.309mm^2	80.8 mil	2.053mm	0.00521 Ohm/m
14 AWG	2.081mm^2	64.1 mil	1.628mm	0.00829 Ohm/m

Lynn Olson recommends North Creek 10 or 12 gauge air-cored inductors for the Ariel crossover. And so do I, if you can easily get hold of them. We on this side of the pond have to deal with ~20% import duties, expensive shipping, and a terrible exchange rate, so I'm going to try and make my own inductors.

The North Creek inductors have the following DC resistances, from which I calculated how much wire they used. (You must agree that this is pretty quick and dirty... :-)

Coil Inductance	10 Gauge R	Equivalent length	12 Gauge R	Equivalent length
0.3 mH	0.04 Ohm	12.195m	0.07 Ohm	13.436m
0.7 mH	0.06 Ohm	18.293m	0.11 Ohm	21.113m
1.0 mH	0.09 Ohm	27.439m	0.14 Ohm	26.871m

Note that the equivalent length will merely give a starting point (About 80 meters of wire per side). You would still need an inductance bridge to check the coils, and more importantly, to balance the left and right channel coils. (North Creek coils are balanced to 1%)

I've sourced the enamelled copper wire locally, from WST (021 511 6287). They gave me the following information:

Wire diameter Length/kg Price/kg Price/100m

2.12mm 31.49m/kg ~R36 R114 (2001)

2.5mm 22.67m/kg ~R36 R159

Wire diameter	Length/kg	Price/kg	Price/100m
2.12mm	31.49m/kg	~R36	R114 (2001)
2.5mm	22.67m/kg	~R36	R159

Calculating coil size for the required inductance:

You can use the calculator at Shavano Music Online, which gives

Inductance	Re	height	radius	turns
1 mH	0.11 ohm	30.83 mm	61.66 mm	75 turns
0.7 mH	0.09 ohm	28.52 mm	57.04 mm	65 turns

for 10 gauge and

Inductance	Re	height	radius	turns
1 mH	0.16 ohm	25.56 mm	51.13 mm	82 turns
0.7 mH	0.13 ohm	23.73 mm	47.46 mm	71 turns
0.3 mH	0.08 ohm	19.8 mm	39.6 mm	51 turns

for 12 gauge wire.

Alternatively, the calculator at Lalena (using Shavano's dimensions) gives

Inductance	Re	height	radius	turns
1 mH	0.1 ohm	30.83 mm	61.66 mm	73 turns
0.7 mH	0.08 ohm	28.52 mm	57.04 mm	63 turns

for 10 gauge and

Inductance	Re	height	radius	turns
1 mH	0.15 ohm	25.56 mm	51.13 mm	79 turns
0.7 mH	0.12 ohm	23.73 mm	47.46 mm	69 turns
0.3 mH	0.07 ohm	19.8 mm	39.6 mm	50 turns

for 12 gauge wire.

The formula they use is
L=((D^2 * T^2)/(1000*(18*D+40*C)))
Where D is the average turn diameter, C is the coil length, and T is the number of turns.

There's also a calculator on Peter Ortner's site which is based on A.N. Thiele's paper Air Cored Inductors for Audio. To summarise the summary :-) Thiele derives a time constant K = (L/R) (with L in uH, R in ohm) which he uses to get the optimum dimensions for an inductor. The inner radius, thickness and width of the coil are all equal, namely C = sqrt( K / 8.66).

Apparently, the length of the wire required is W = 0.1873 * sqrt(L*C)
The number of turns is N = 19.88 * sqrt(L/C)
The wire diameter is D = 0.841*C/sqrt(N)
The mass of the wire is (C^3)/21.4.

For the 1mH 10 gauge coil above, L = 1000, R = 0.11
K = 9090.9, C = 32.4.
W = 33.7 m
N = 110.4 turns (Lalena gives 103 turns for a coil with these dimensions)
D = 2.59 mm
and you will need 1589 grams of wire (which is 36 metres long according to WST, so things seem to check out).

Looking at North Creek's resistance values, and the ones obtained by the calculators and Thiele's formula, I must assume that they have a kick-ass formula that tells them how to wind coils with such a low resistance... (1.0 mH and 0.09 ohm can be achieved using 2.93 mm diameter (about 9 gauge) wire with Thiele's formula)

The classical coil inductance formula is L=(r^2 n^2)/(9r+10l) with the dimensions in inches, or L=(r^2 n^2)/(25.4*(9r+10l)) with r and l in mm, but I doubt if that would be at all relevant here :-)

Zobel Network

The impedance of a woofer will show a peak at resonance, and then a slow rise from the nominal impedance with increasing frequency.

A Zobel network consists of a series network of a capacitor and a resistor (a high wattage unit) connected in parallel with the woofer.

The purpose of the Zobel network is to cancel the rise in impedance, which is caused by the driver's voice coil impedance. In effect, the voice coil impedance is resonanted out using a capacitor.

With R the nominal impedance of the loudspeaker (4 or 8 ohms) and Le the voice coil impedance, C=Le/(R^2). Other sources suggest that the resistor should be 1.25 times larger than the voice coil resistance.

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