Coil impedence calculation

I was hoping some one could help me with a calculation. I am an engineer in another dicipline who has been trying to stitch together formulas from many sources to try to solve what I would have thought to be a basic problem. That is:

How many turns are required for a single layer air-gap-coil of 4"diameter and 4" length to provide 8 ohms impedence at 80hz.

The length of the coil can be varied 25% either way if that helps.

I kept coming up with approx 1 turn, but thought this must surely be wrong.

Any help would be appreciated.

-Scott Hooper

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in article, scott at wrote on 9/10/03 8:13 PM:

It sure is!

If you can, go to a decent technical library. There are books devoted to inductance calculations. Terman's Radio Engineers' Handbook has a number of such formulae. In addition, look at books on electroacoustics. They will go into how poorly the impedance at speaker terminals represent the true acoustic impedance.

Your other problem is that the impedance is not just a matter of winding inductance and frequency. Ideally, the impedance of a voice coil is really the transduced acoustical impedance of the voiced coil coupled to the speaker cone in turn coupled to the air. Think rms force applied to the cone divided by the rms rate of voice coil displacement as a first estimate. Think of the voice coil as a motor shaking the air.

Life is not that simple. Coupling of most cones to the air that is driven is usually very poor. The result is, that the electrical impedance seen by the amplifier is more a measure of voice coil *resistance* rather acoustic radiation resistance.


Have fun.


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Repeating Decimal

Unless you are using a air coupling transformer called a Klipse horn. Free air I believe has an impedance of about 52 ohms if I remember correctly

I use a Georgian speaker which I built myself. It stands about 5 feet tall and stands out about 3 feet from the corner of the room and uses another 4 feet of wall to couple to the free air. It is about 8 times as power efficient as an ordinary speaker. . . I DO NOT FOLLOW MANY OF THESE NEWS GROUPS To answere me address mail to

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I don't think he mentioned a speaker cone at all. I think all he wants is a simple inductive reactor with 8 ohms reactance at 80 Hz. Any good radio textbook will give you the formulae.


Reply to
Daniel Indyk

Well, I have a bad radio textbook and it gives:

L = ( R^2 * N^2 )/( 9R + 10S )

where R is radius and S is length in inches, N is turns and L is in microHenries

Also inductor impedance is:

X = 2 * PI * F * L

so at 80 Hz, the O.P. needs 15.9 milliHenries, or 15.9*10^3 microHenries

plugging that into the first formula with R = 2 and S = 4, I get 480 turns.

The formula has no factor for conductor size (which wasn't specified anyway) and is from an old radio handbook, so it may make some assumptions that are more appropriate for dimensions used in higher frequency work.

Reply to
Paul Hovnanian P.E.

Thankyou! Thankyou! Thankyou! Thats just what I was looking for.


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Also see

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As an supplement, there is this old technician's trick; Put the coil that you think will work in series with an 8 ohm resistor and apply an 80 Hz signal at twice the voltage that the coil will see in use. Adjust the coil (number of windings, spacing, core) so that an AC voltmeter reads the same across the coil and the resistor. Repeat at 105 and 1% voltage. (If the coil and the resistor no longer have equal voltage drops at the lower voltages, it's a sign of a saturation problem).

This is a variation of the old technician's trick for finding the impedance of an unknown coil; do as above but vary the resistance until they match, then remove the variable resistor and measure with an ohmmeter.

None of this is a substitute for learning how to design coils, but it's a nice sanity check for the person who has never done it before and thinks that his design might be way off.

Reply to
Guy Macon

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