Skineffect
Lit.: Meinke.Gundlach, Taschenbuch der Hochfrequenztechnik, 4.Aufl., Springer-Verlag, 1986
       edited by Klaus Lange and Karl-Heinz Loecherer, pages B13..B17
       ISBN 3-540-15393-4 Springer Berlin... Und ISBN 0-387-15393-4 Springer New York....
Physical constants: mo 1,26E-06 [H/m] = 1,256637 [uH/m] k1 = sqrt (ksilber/kmetall) - k und r -
eo 8,855 [pF/m] Table for some metals
Secondary Skin-Effect:  
Secondary-Coil Data: Metal k1 k [m/mm2W] r [Wmm2/m]
    von bis von bis
length of secondary conductor L = Lsec 722,5663 [m] Silver 1 62,5   0,016  
relative magnetic permeability mr 1 [ - ] Copper 1,03 56   0,01786  
spec.resist.of copper (20C) r =  r  0,01786 [Ohm mm2 / m] Bronce 1,07 55 18 0,018 0,056
conductivity of conductor k 55,99104 [m / (mm2 Ohm)] Gold 1,2 44   0,023  
diameter of secondary conductor (=solid wire) D = Dsec 0,8 [mm] Aluminium 1,35 35   0,02857  
resonant frequency f 103,79 [kHz] Magnesium 1,69 22   0,045  
at resonant frequency w 652127,7 [s-1] Tungsten 1,86 18   0,055  
Zinc 1,95 16   0,063  
Brass 2,2 14 11 0,07 0,09
Nickel 2,19 13 9 0,08 0,11
Iron 2,50 10 7 0,1 0,15
Decisive for the losses by skineffect is the so called skin-depth d, Tin 2,7 9,1   0,11  
The fields will then have declined to 1/e = 37% of the field-strength Platin 2,6 9 7 0,11 0,14
at the surface. In practice: Tantal 2,9 7,43   0,13456  
- for flat conductors of thickness      D > 10d, or Plumb 3,61 4,8   0,21  
- for circular conductors of diameter D > 10d , Nickelin 5,21 2,3   0,43  
an evenly distributed current within a surface-layer of thickness d can Manganin 5,21 2,3   0,43  
be assumed, and the material below considered without current flow. Konstantan 5,6 2   0,5  
Correct resistance values are obtained by applying this assumption. Stainl.Steel 6,7 1,39   0,71824  
Mercury 7,75 1,04   0,96  
Skin-depth  d = SQRT( 2 / (w mo mr k) ) = d 0,208778 [mm] Coal, ca. 50 0,0250   40  
           
 Alternative skin-depth formula (s. table!) Data in part from Moeller Franz, Grundlagen der Elektrotechnik Bd.I,
 d [mm] = 64*k1 / SQRT( f [MHz] ) d 0,204617 [mm] B.G.Teubner Verlagsgesellschaft mbH, Stuttgart 1959, Seite 19
(Data at 20C)
Remark: The result from the first formula is used in the calculations below.
Circular solid wires: ( Length L[m], Diameter D[mm] )
DC resistance Ro = L / ( k D2 p/4 )  25,67375 Ohm
actual D/d  3,831824 R/Ro
If  D/d  <   2 then R = Ro not valid Ohm n.a.
If   2 < D/d  <   4 then R = Ro [ 1 + (D / 5.3d )4 ] 32,68843 Ohm 1,273224
If   4 < D/d  <   10 then R = Ro [ 0.25 + (D / 4d ) ] not valid Ohm n.a.
If  D/d  >   10 then R = Ro  (D / 4d )  not valid Ohm n.a.
Final result for secondary coil (---> TC calc.) =  32,68843
Primary Skin-Effect:  
Copper Tubing / Wire Primary-Coil Data:
length of primary conductor + wiring, used in calculation L = Lprim 5,43 [m]
relative magnetic permeability mr 1 [ - ]
spec.resist.of copper (20C) r =  r  0,01786 [Ohm mm2 / m]
conductivity of conductor k 55,99104 [m / (mm2 Ohm)]
diameter of primary conductor D = Dprim 8 [mm]
Leave empty or set to zero if solid wire ------> tube wall thickness w 1[1] [mm]
resonant frequency f 103,79 [kHz]
at resonant frequency w 652127,7 [s-1]
Skin-depth  d = SQRT( 2 / (w mo mr k) ) = d 0,208778 [mm]
w/d  4,78978
 Alternative skin-depth formula (s. table!)
 d [mm] = 64*k1 / SQRT( f [MHz] ) d 0,204617 [mm]
w/d  4,88719
Remark: The result from the first formula is used in the calculations below.
Circular solid wires: ( Length L[m], Diameter D[mm] )
DC resistance Ro = L / ( k D2 p/4 )  0,001929 Ohm
actual D/d  38,31824 R/Ro
If  D/d  <   2 then R = Ro not valid Ohm n.a.
If   2 < D/d  <   4 then R = Ro [ 1 + (D / 5.3d )4 ] not valid Ohm n.a.
If   4 < D/d  <   10 then R = Ro [ 0.25 + (D / 4d ) ] not valid Ohm n.a.
If  D/d  >   10 then R = Ro  (D / 4d )  0,018482 Ohm 9,58
Circular tubes:  ( Wall thickness w = 1 [mm] )
R/Ro
DC resistance Ro = L / { k [D2-(D-2w)2] p/4  } 0,00441 Ohm
Ro ~= L / { k (D-w) p w  } 0,00441 Ohm 1
actual w/d  4,78978
If  w/d  <=   1 then R = Ro (Error < 10%) not valid Ohm n.a.
If  w/d  >   2.5 then R = L / ( k d D p )  0,018482 Ohm 4,19
If  w/d  =   1.6 then R ~= 0.9 Ro not valid Ohm n.a.
( = ca. 90% of the solid wire resistance with equal cross-section)
(    meaning: in this case, tube is better than solid wire !!           )
Final result for primary coil (---> TC calc.) =  0,018482
Flat conductors: ( Thickness s, Width b, Length L )
Thickness s 0,6 [mm] 
Width b 50 [mm] 
Length L 5,43 [m]
Material Copper
Specific conductivity    k 56 [m / (mm2 Ohm)]
DC resistance Ro = L / ( k s b )  0,003232 Ohm
actual s/d  2,873868
If  s/d  <   0.5 then R = Ro (Error < 10%) 0,003232 Ohm
If  s/d  >   5 then R ~ = L / (2 k d b )  0,004644 Ohm
If  w/d  =   p then R ~ = 0.9 L / (2 k d b )  0,00418 Ohm
( = ca. 90% of "fat-sheet"-resistance: Minimum!)
End of Primary Skin-Effect calculation  
The following graph for circular conductors was taken from
Lit:  Telefunken -Laborbuch, 2.Ausgabe 1958
Herausgeber: Telefunken GmbH, Ulm/Donau
Druck: Brueder Hartmann, Berlin, Germany
Remark: Minor quality of the graph, because the values in the table were
transferred manually, and 'by eye', from a tiny graph in the book.
With f[kHz], w[mm], D[mm], k [m/(mm2 Ohm)]
we have the definition of  x = (1/1000)*sqrt[ k * 1000f * w * (D-w) ]
or vice versa  f = 1000 * x^2 / [ k * w * (D-w) ]
solid wire
f R/Ro R/Ro R/Ro R/Ro R/Ro R/Ro
[kHz] x D/w=0.5 D/w=0.2 D/w=0.1 D/w=0.05 D/w=0.02 D/w=0.01
0,00 0 1 1 1 1 1 1
2,55 1 1,3 1,14 1,04 1,02 1 1
10,21 2 2,2 1,35 1,2 1,03 1,005 1,001
22,96 3 3,2 2,37 1,7 1,2 1,01 1,0015
28,63 3,35 3,5 2,6 1,85 1,3 1,02 1,002
40,82 4 4 3,2 2,28 1,6 1,1 1,003
50,52 4,45 3,5 2,5 1,75 1,15 1,005
63,79 5 2,8 2,06 1,25 1,07
91,85 6 3,5 2,5 1,5 1,18
125,02 7 2,85 1,76 1,25
163,29 8 3,38 2,1 1,45
206,67 9 3,8 2,38 1,62
255,14 10 2,65 1,77
[1]
Leave empty or set to zero, if solid wire primary