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Re: Spice simulation pictures
Tesla List wrote:
>
> |> Subject: Re: Spice simulation pictures
> |Subject: Re: Spice simulation pictures
> |> Subject: Re: Spice simulation pictures
>
> >From Benson_Barry%PAX5-at-mr.nawcad.navy.milMon Oct 21 21:25:34 1996
> Date: Mon, 21 Oct 1996 06:43:00 -0400 (EDT)
> From: Benson_Barry%PAX5-at-mr.nawcad.navy.mil
> To: tesla-at-poodle.pupman-dot-com
> Subject: Re: Spice simulation pictures
>
> What formulas do you use for the skin and proximity
> affect on your spreadsheet. Bessel functions?
> I am working on a spread sheet in Excel but
> haven't figured out how to do summations
> in spreadsheeteese for calculating the
> bessel function expansions for solving for
> Rac/Rdc from the formula I got in Reddick's
> book.
> Barry
<Big SNIP>
Barry,
I use a wire table, and a couple of calculations combined with a series
of tables from the "Radio Engineers' Handbook", 1943, by Frederick
Terman, McGraw-Hill. Terman provides an in depth, excellent discussion
of both skin and proximity effects. More importantly for coilers, he
provides a number of formulas and tables to permit practical estimation
of both effects. Unfortunately, these tools are not presented as simple
formulas which can be dropped into a spreadsheet. I don't have access to
the Reddick book mentioned in your post (which book is it??)
For a straight round wire, the AC current density is greatest at the
outer surface, decreasing exponentially as we go toward the center. This
"skin effect" reduces the usable cross-sectional area of the conductor,
causing an increase in AC resistance. Furthermore, if we wind the same
wire into a multi-turn coil, the presence of the nearby conductors
causes additional, non-uniform, current-bunching, called proximity
effect, further increasing the AC resistance. These two effects combine
to make total Rac higher than Rdc.
A. Skin Effect:
===============
Terman handles the calculation of Rac/Rdc due to skin effect by first
calculating a parameter (X), and then using a lookup table to compute
Rac/Rdc.
For round copper wire:
X = 0.271*d*sqrt(f)
where: d is the copper diameter (mils)
f is in MHz.
Once X is calculated, the matching Rac/Rdc value is looked up (Terman,
Table 4., p. 31). For those without access to Terman's book, this table
is duplicated below.
TABLE 1.
X Rac/Rdc X Rac/Rdc X Rac/Rdc
0.0 1.0000 5.2 2.114 14.0 5.209
0.5 1.0003 5.4 2.184 14.5 5.386
0.6 1.0007 5.6 2.254 15.0 5.562
0.7 1.0012 5.8 2.324 16.0 5.915
0.8 1.0021 6.0 2.394 17.0 6.268
0.9 1.0034 6.2 2.463 18.0 6.621
1.0 1.005 6.4 2.533 19.0 6.974
1.1 1.008 6.6 2.603 20.0 7.328
1.2 1.011 6.8 2.673 21.0 7.681
1.3 1.015 7.0 2.743 22.0 8.034
1.4 1.020 7.2 2.813 23.0 8.387
1.5 1.026 7.4 2.884 24.0 8.741
1.6 1.033 7.6 2.954 25.0 9.094
1.7 1.042 7.8 3.024 26.0 9.447
1.8 1.052 8.0 3.094 28.0 10.15
1.9 1.064 8.2 3.165 30.0 10.86
2.0 1.078 8.4 3.235 32.0 11.57
2.2 1.111 8.6 3.306 34.0 12.27
2.4 1.152 8.8 3.376 36.0 12.98
2.6 1.201 9.0 3.446 38.0 13.69
2.8 1.256 9.2 3.517 40.0 14.40
3.0 1.318 9.4 3.587 42.0 15.10
3.2 1.385 9.6 3.658 44.0 15.81
3.4 1.456 9.8 3.728 46.0 16.52
3.6 1.529 10.0 3.799 48.0 17.22
3.8 1.603 10.5 3.975 50.0 17.93
4.0 1.678 11.0 4.151 60.0 21.47
4.2 1.752 11.5 4.327 70.0 25.00
4.4 1.826 12.0 4.504 80.0 28.54
4.6 1.899 12.5 4.680 90.0 32.07
4.8 1.971 13.0 4.856 100.0 35.61
5.0 2.043 13.5 5.033 Inf Inf
Example 1: For 22 AWG straight wire at 90 kHz:
X = 0.271*25.3*sqrt(0.090) = 2.057
RAC/RDC = 1.086 (interpolating from above table)
Example 2: For 14 AWG at 150 kHz:
X = .271*64.1*sqrt(0.150) = 6.728
Rac/Rdc = 2.648 (interpolating from above table)
B. Proximity Effect:
===================
Proximity effect is a complex function of wire material, wire diameter,
turn-to-turn spacing, coil diameter, and coil height. Of interest to
coilers, Terman provides methods for calculating the effect in
single-layer solenoids employing solid wire with not-too-close turn
spacing and for close-wound coils, and coils wound from Litz wire (pp.
77 - 80). Unfortunately, the combination of formulas and tables is much
too involved to show here. Suffice it to say, the added AC resistance
attributable to proximity effect is often equal to, or greater than,
straight-wire skin effect. Proximity effect is increased by
close-winding, and by using larger coil length/diameter ratios. Terman
provides one of the better overall descriptions and tools to actually
estimate the effect. Most other texts discuss proximity effect in
passing, but do not attempt to provide any ways of estimating it.
However.....
>From a very _practical_ standpoint, most coilers find it considerably
simpler to wind the coil, measure the Q, then back-figure the effective
Rac. In fact, the problem posed by Robert Stephens was the _first_ time
I actually had any need to compute the impact of proximity effect...
Safe and not-too-theoretical coilin' to ya!
-- Bert --