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VK2ZRG > PUZZLE 28.09.08 08:37l 55 Lines 2264 Bytes #999 (0) @ WW
BID : 2677_VK2ZRG
Read: GUEST DH9GZ
Subj: A technical puzzle
Path: DB0FHN<DB0MRW<DB0ERF<DB0FBB<DB0IUZ<DB0OVN<DB0GOS<ON0AR<HS1LMV<7M3TJZ<
XE1FH<ON0BEL<VK7AX<VK2TGB<VK2IO<VK2WI
Sent: 080928/0503Z @:VK2WI.#SYD.NSW.AUS.OC #:2748 [Sydney] $:2677_VK2ZRG
From: VK2ZRG@VK2WI.#SYD.NSW.AUS.OC
To : PUZZLE@WW
VK2ZRG/TPK 1.83d Msg #:2677 Date:28-09-08 Time:5:04Z
Hello all,
Here is a puzzle for you, but first some explanation is required.
The inductance formula found in most handbooks like the ARRL is known as
Wheeler's approximation. It's an approximation mainly because it doesn't
use a correction factor as does the "Current sheet" formula. Wheeler's
formula may be easily transposed if you want to find the turns for a given
inductance. The formula needs length, diameter and inductance to give turns.
But if you've never designed a coil before, how do you know how big it should
be? A better method is to start from a wire diameter, length/diameter ratio
and winding pitch to find coil length, diameter and turns. It's easy enough to
derive a formula to calculate values, that will satisfy Wheeler's formula.
The "Current sheet" formula has a correction factor based on number of
turns and winding pitch. This is deducted from the raw inductance number
to give the final value. To get an accurate number of turns and length
(and hence diameter) for a given inductance, starting from a wire diameter
etc, for the "Current sheet" formula, the correction factor must be added to
the inductance first. However to get the correction factor you need to know
the number of turns! This sounds like a classic catch 22 situation.
So here is the puzzle. How do you calculate the correction factor in this
case?
Some technical stuff.
The correction factor can be applied to Wheeler's formula to improve its
accuracy. Then there will be <0.6% difference between the inductance from
the two formulae, for coils with length/diameter ratio >0.4
The "Current sheet" formula is said to be accurate to one part in a 1000.
This is the correction factor formula for coil dimensions in millimetres
Cf = ((6.2795E-4*Coil_Diameter*Turns)*(A+B))
A = LN(1/Pitch)+0.57 (LN is natural logs).
B for three or more turns (N = turns)
B = ((((-0.83/N - 2.5)/N + 3.8)/N - 2.5)/N+1)*0.336 + 0.004
My formula for B, for one or more turns(N)
C = (2.04-N)/40
IF N < 9 THEN R = 1.56 ELSE R = (4-N/3.75)-0.15
B = 0.338*(1-(2.35/(N + R)))
IF N <= 2 THEN B = B-C
73's de Ralph VK2ZRG @ VK2WI
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