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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
> > Subject: Re: Spice simulation pictures
>
> >From bert.hickman-at-aquila-dot-comWed Oct 23 21:19:14 1996
> Date: Tue, 22 Oct 1996 22:09:40 -0700
> From: Bert Hickman <bert.hickman-at-aquila-dot-com>
> To: tesla-at-pupman-dot-com
> Subject: 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 --
Very nice post Bert!
The proximity effect is indeed much, much worse on us than the already
bad skin effect. At high frequencies the current will always follow the
path of least inductance! For Tesla coils which are always wound single
layer, and virtually always tight wound, this means that the current in
our resonator coils is concentrated (about 85%) into a tiny little region
underneath the circular wire right next to the form (least inductive
path). I have verified this in exploding wire coils by observing the
Ampere tension forces gouge out a rivulet in 12 gauge copper wire just on
the inner circumferential portion of the round wire leaving shattered
work hardened pieces of bananna like pieces of wire.
The Tesla coil would always be best wound with thin flat copper banding
in order to make these bad effects work to our advantage. The entire
inner portion of our big 4 guage primary wire leads are wasted! Ultra
thin walled copper tubing would be better and waste far less copper.
Unfortunately, wire is actually cheaper than equivalent diameter tubing
due to manufacturing costs. Also, sometimes the insulation around wire
is very desireable and copper tubing is a bear to insulate with anything
other than air.
Richard Hull, TCBOR