Re: Inductance Calculations for iron core

Tesla List wrote:

> Original Poster: "Coiler" <mycroft-at-access1-dot-net>
> What I am looking for is a guesstimate, or even the formulas to compute
> the inductance knowing the approximate cross section area. My plan is to use
> a bunch of rebar tie wire I have here, cut to about 20" lengths, to fill
> a 2" PVC pipe. This would give me an open core with about a 1.6 square inch
> cross section.
> Estimated inductance per turn would be best, I'll probably use #10 THNN wire
> for about 6 TPI. (roughly 110 turns end to end)
> The OD of the PVC is actually 2.4" if that helps.
> (and if someone could refresh me on the formula for reactance, I wouldn't
> complain
> either :) )
> Thanks!
> Michael Baumann
> Coiler, Homebrewer, Nerd. mycroft-at-access1-dot-net


I built a few test coils, before building an induction coil of roughly the size
you are suggesting.  I found I could wind a much smaller test coil, and
extrapolate the results.  I didn't know that at the time (or didn't believe the
text books).  The following data is from my full-sized test coil:

My induction coil has a 1.77 square inch, cross-section area, 18" long.  The
wire I used for a core, yielded an Inductance of  about .203 micro henries per
turn (squared) and an impedance of 76.6 micro ohms per turn squared (at 60 HZ).

Inductance (and Impedance) goes up in proportion to the core cross-sectional
area.  Increase the area by a factor of two, you increase the inductance by a
factor of two.

Inductance (and Impedance) goes up in proportion of the SQUARE of the turns.
Double the turns, you quadruple the Inductance.

My test coil had 354 turns of wire around the core bundle and an inductive
reactance of 9.61 ohms at sixty cycles.  That was at 6.23 amps with 60 volts
across the coil, for a total of 1,582 ampere-turns.

In power inductors, with iron cores, the inductance peaks at some flux density.
The impedance with the test coil was 5.5 ohms at .20 amps, 8.3 ohms at 1.34
amps, and 9.61 ohms at 6.23 amps.  At higher currents the impedance begins to
fall slightly.  At 8.45 amps, the impedance was 9.53 ohms.

An inductance bridge won't give accurate results unless it is pumping
current through the inductance under test (that rules out hand-held LCR
multi-testers).  As more current is forced through the coil, the iron begins to
saturate and impedance starts dropping again.

As the coil gets warm, its resistance rises, causing the impedance to rise
(something to watch out for when testing).  When checking current with a
clamp-on ammeter, keep the meter several feet from the coil under test.  Leave
about one diameter of core sticking out of either end of the coil.  Multiple
layers of turns, versus one layer, don't really affect the results of the
calculations (within reason).  For all practical purposes, the resistance
of the
wire will be insignificant compared to the inductive reactance.

It would be better to decrease the wall-thickness of the tubing you wind your
coil around.  If I understand you correctly, you will have an outside diameter
of 2.4 inches and about 1.5 inches inside diameter (for core material).
You can
lower your wire cost by close to 40% by using a thin-wall tube or wrapping the
core bundle with tape.  You will also minimize resistance losses and heating.
US Plastics has some thin walled tubing in a variety of sizes.

Inductive reactance = 2 pi (6.28)* frequency * inductance.

Inductance  = Inductive reactance (in ohms), divided by 6.28 * frequency.

Inductance is in henries, reactance in ohms, frequency in hertz.