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Re: Flat Coils



Original poster: "Jim Lux by way of Terry Fritz <twftesla-at-qwest-dot-net>" <jimlux-at-earthlink-dot-net>



Tesla list wrote:
> 
> Original poster: "Barton B. Anderson by way of Terry Fritz
<twftesla-at-qwest-dot-net>" <tesla123-at-pacbell-dot-net>
> 
> Hi John T.-
> 
> The inductance is increasing because you are dramatically increasing the
number
> of turns in the helical compared to the flat coil to keep the wire length the
> same. Inductance is a function of the turns.
> 
> A helical or flat coil with the same length of wire must come out to the same
> inductance as long as the length, wire size, spacing between turns, and
number
> of turns remains constant (if your going to do a comparison of inductance).
> When accomodating these constants, you will need to wind a helical coil at a
> diameter twice the inner diameter of the flat coil. You should find that
R and
> L remain the same for the same length of wire.

I don't know that this is true.  The interwinding mutual inductance has a
large effect on the overall inductance, and the mutual inductance will be
very different in a flat spiral compared with a helix.  I, off hand, can't
think how you could keep the interturn distances the same for helix vs
flat.  The coupling between turns is why L varies as Nturns^2 (roughly) for
a closewound coil.  If the distance between turns is different, then the
coupling is different, etc.

Now, it is possible that for some restricted range of sizes, number of
turns, etc, the two might generally work out the same.  It is such
restrictions that lets us use approximations like Medhurst's and Wheeler's,
and the fact that TC's in general, are 5-10% tolerance kinds of devices.

Circular 74 does give (exceedingly long and complex) equations for all
these cases, and, as expected, they all are strongly dependent on N^2 plus
some "geometry factors".  

Wheeler's equations are:
Single layer solenoid
L (uH) = r^2 * n^2 / (9 * r + 10 * l)

where 

r = coil radius in inches
l = coil length in inches
n = number of turns



Flat "pancake" coil
L (uH) = r^2 * n^2 / (8 * r + 11 * w)

where

r = radius to center of windings in inches
w = width of windings (in inches)
n = number of turns


> 
> I like your method of winding the flat coil. That's the route I would go.
> 
> Take care,
> Bart
> 
>