| Project: |
"Black&White" TC for 10kVA+
(caps: 3 Maxwell 0.3uF/100kV) |
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| Tesla
Equations |
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| Input value
cells are |
yellow |
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measured values are |
green |
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Results are in |
blue |
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beyond actual situat. |
extrapol. |
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Conversion factors |
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Specific resistance at 20C |
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Density |
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1 inch = |
2,54 |
cm |
Aluminium |
Al
(20C) |
0,02857 |
Ohm mm2/m |
Acryl.Rho 1.18 |
1,18 |
kg/dm3 |
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1 foot = |
0,3048 |
m |
Copper |
Cu (20C) |
0,01786 |
Ohm mm2/m |
PVC Rho |
1,4 |
kg/dm3 |
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Tungsten |
W
(20C) |
0,055 |
Ohm mm2/m |
Al Rho |
2,702 |
kg/dm3 |
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Brass |
0,07 |
0,09 |
Ohm mm2/m |
Cu Rho |
8,93 |
kg/dm3 |
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Bronce |
0,018 |
0,056 |
Ohm mm2/m |
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| Secondary
Design: |
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| Dimensions: D = diameter, B = length of windings, G =
wire gauge, T = turns/inch or cm |
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| AWG |
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diameter |
wdg.length |
AWG |
turns/unit length |
length |
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Approx. Weight of
secondary |
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| G |
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D |
B |
G |
T |
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of tube |
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Dens.Rho |
8,93 |
kg/dm3 |
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| 20 |
inch |
7,87 |
39,39 |
20,1 |
29,2 |
turns/inch |
46,46 |
inch |
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Former D |
1,99 |
dm |
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| enter value
in [cm] |
20,00 |
100,1 |
0,087 |
11,49 |
turns/cm |
118,0 |
cm |
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Former L |
11,8 |
dm |
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diameter of wire, bare copper = |
0,800 |
mm ( |
0,503 |
mm2 cross.sect.) |
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Former x |
8[1] |
mm |
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diameter of wire, with insulation = |
0,860 |
mm |
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Former V |
5,7 |
dm3 |
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wire spacing between turns = |
0,010 |
mm |
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Former W |
50,6 |
kg |
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Disks x |
10[2] |
mm |
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Number of secondary turns
= |
1150,00 |
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Circumference = pi * D |
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Disks No. |
4 |
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Circum = |
24,74 |
inch |
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Disks V |
1,2 |
dm3 |
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Length of wire
needed = |
2371 |
feet |
Radius = |
3,94 |
inch |
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Disks W |
11,1 |
kg |
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722,6 |
m |
Circum = |
62,83 |
cm |
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Copper W |
3,2 |
kg |
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Radius = |
10,00 |
cm |
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PU-Seal |
4,5 |
kg |
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H/D aspect ratio = |
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5,00 |
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Weight = |
3,243 |
kg Cu |
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Weight = |
69,5 |
kg = calculated |
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d/s wire diam./spacing
ratio = |
0,92 |
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DC Resistance = |
25,67 |
Ohm |
Space wound Sec' with Nylon-line |
Weight = |
48,0 |
kg = measured |
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DC Resistance = |
14,50 |
Ohm |
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RF
Resistance of straight wire, with skin-effect = |
32,69 |
Ohm |
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Coil
RF Resistance with skin- and proximity effect = |
101,19 |
Ohm |
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Nylon f = |
0,8715 |
mm |
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Q-factor,
without considering of dielectric loss(=coil-former + sealing) Q = |
309 |
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interturn space s = |
0,8715 |
mm |
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Wheeler Equation: R = radius
", N = no.of turns, B = length of windings " |
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Date |
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L (uH) = (R^2 x N^2) / (9R + 10B) |
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fmeas |
######## |
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Q |
kHz |
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L = |
0,047746 |
H L. = |
47,7 |
mH |
L Meas.= |
54,67 |
mH |
23,2 |
1 |
14,8 |
Rv (Ohm) |
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Error in calculated L = |
-12,7% |
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54,60 |
mH |
2,9 |
0,12 |
14,2 |
Rv (Ohm) |
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An approximation to the Nagaoka inductance, |
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accurate to 5
decimal places, was given by Lundin [1]. |
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a = radius, metres. |
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0,1 |
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b = length, metres. |
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1,0005 |
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N = number of turns |
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1150,00 |
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MU = 4*3.14159*1.0E-7 |
1,26E-06 |
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x = 4 * a*a/(b*b) |
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0,03996 |
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f = (1 + 0.383901*x +
0.017108*x*x)/(1+0.258952*x) |
1,004969 |
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Ldc = MU*N*N*a*a*PI/b *(f - 8*a/(3*PI*b))
Henries. |
0,048016 |
H |
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(Accurate to rather better than 1%.) |
Ldc = |
48,02 |
mH XL= |
31313 |
Ohm |
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Error in calculated Ldc
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-12,2% |
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Counting turns, 30.3.00 |
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Turns |
DL [cm] |
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90 |
18,6 |
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| Medhurst
Formula: |
Self Capacitance: |
C(pf) = K x D |
D = dia. in cm |
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100 |
21,3 |
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100 |
21,3 |
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| K will
automatically be determined by |
K from table |
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K from fit |
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100 |
21,6 |
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| using H/D
from a lookup table at the end |
0,810 |
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0,818 |
*
) |
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100 |
22,5 |
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| of this
spreadsheet |
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100 |
22,0 |
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from table |
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from fit |
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100 |
21,9 |
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| Self
capacitance of secondary: |
C(pf) = |
16,2 |
pF |
16,4 |
pF |
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100 |
22,0 |
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23 |
4,7 |
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| *
) Setting x = H/D (with 1< H/D < 8 ) the fitted
function for K may |
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813 |
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be used in the form: K = a+bx+cx^(1.5)+dlnx/x+e/x^2 |
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or, if H/D < 1 or H/D > 8, by
the fitted function for K, |
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in the form: K = a+bx+cx^2lnx+dx^(2.5)+e/x^(0.5) |
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with the parameters a,b,c,d,e in sheet "Medhurst". |
That's the way it is implemented. |
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Measurements 22.7.00 / Finn+Sk |
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Resonance, coil with Toroid
1.6/0.4m |
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69 |
kHz |
outdoors |
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Self resonant frequency of
secondary: |
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manual trick trimming possibility of |
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total secondary capacitance |
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Measurements 11.4.00 / Sk+Andi |
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f(khz) = 1/2pi(sqrt (L * C)) |
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man.corr. |
0 |
pF (normally 0) |
Resonance, bare coil, indoors |
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fo |
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Scope |
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f = |
180,5 |
kHz |
Unloaded |
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by Toroid or Sphere formula: |
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119,00 |
kHz |
amplitude |
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119,0 |
kHz |
Measured |
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C top = |
32,77 |
pF |
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119,51 |
kHz |
60-70%, f+ |
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Error in f = |
51,6% |
calculated - measured |
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118,67 |
kHz |
60-70%, f- |
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(the addition for C total is approx.
only!) |
0,84 |
kHz |
bandwidth ? |
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f = |
103,8 |
kHz |
Loaded |
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C total = |
48,97 |
pF |
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141,7 |
Q |
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69,0 |
kHz |
Measured |
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288,5 |
Rv (Ohm) |
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Error in f = |
50,4% |
calculated - measured |
In order to have a more realistic C
total |
Higher f peaks |
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run Terry Fritz's great |
E-Tesla |
for |
309,82 |
kHz |
2,603529 |
x fo |
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722,1 |
Lambda/4 [m] |
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C total = |
0,00 |
pF |
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448,00 |
kHz |
3,764706 |
x fo |
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722,6 |
wire length [m] |
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( Fill and run sheet
E-Tesla in order |
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to automatically fill-in the value ! ) |
119,40 |
kHz |
coil moved, ca. 1m |
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Readings on HP counter |
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| Primary
Design: |
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| Di = inner
diameter , S = spacing between turns , n = number of turns, d = wire or
tubing diameter |
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From Jim Lux, mail on 27th August 2000, Pupman |
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| Di, S and d
are in inches |
inn.dia. |
spacing |
wire dia |
angle |
# turns |
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"calculating safe
primary turn-to-turn distance" |
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Di |
S |
d |
a |
n |
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The breakdown strength for air in a uniform field (not the case for |
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| enter
values:> |
inches |
13,78 |
0,472 |
0,315 |
30 |
10 |
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parallel wires) is about 31 kV/cm (70 kV/inch) |
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cm |
35,0 |
1,20 |
0,80 |
30 |
10 |
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D is center to center spacing of
cylinders |
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| w = width
of windings on one side = |
7,4 |
inches = |
18,8 |
cm |
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d is gap between cylinders |
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| W = proj.
of windings on one side = |
6,4 |
inches = |
16,3 |
cm |
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r is radius of cylinders |
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| h = height
of windings = |
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3,7 |
inches = |
9,4 |
cm |
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| R = average
radius = (1/2 * Di) + (1/2 * W) = |
10,1 |
inches = |
25,6 |
cm |
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E = V * SQRT(D^2-4*r^2)/(2 * r * (D
- r)*arccosh(D/2r)) |
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w/(2*R)
used as a replacement for H/D for proxieffect calc. = |
0,366606 |
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d/s for proxyeffect calc.
= |
0,4 |
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Uprim = |
8000 |
V |
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| Total
outside diameter of coil = |
26,6 |
inches = |
67,6 |
cm |
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n used = |
5 |
turns |
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V = |
1600 |
V / turn |
1600 |
V / turn |
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Lh. = |
67,4 |
uH |
Lh(uH) = (R2 * n2) / (8R+11W ) |
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D = |
2,0 |
cm |
2,0 |
cm |
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Lv = |
79,7 |
uH |
Lv(uH) = (R2 * n2) / (9R+10h ) |
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d = |
0,8 |
cm |
0,8 |
cm |
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r = |
0,4 |
cm |
0,4 |
cm |
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L = |
70,7 |
uH |
L (uH) = sqr [ (Lv*sin(a))2 + (Lh*cos(a))2 ] |
D / 2r = |
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2,5 |
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80,6 |
uH |
@ 9.37 Turns |
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E = |
1462 |
V/cm |
1950 |
V/cm |
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Jim Lux's |
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Küpfmüller P.86 |
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(2 parallel cylinders) |
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calc.of trigonometric func's. |
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angle a |
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degrees |
30 |
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arc |
0,523599 |
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sine |
0,5 |
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cosine |
0,866025 |
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tangent |
0,57735 |
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cotangent |
1,732051 |
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Tubing or
wire |
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| Turn # |
w |
W |
h |
R |
Lh |
Lv |
L |
Turn # |
Dia. |
Dia. |
Length |
S Length |
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[inch] |
[inch] |
[inch] |
[inch] |
[uH] |
[uH] |
[uH] |
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[inch] |
[mm] |
[inch] |
[m] |
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| 1[3] |
0,315 |
0,273 |
0,157 |
7,026 |
0,8 |
0,8 |
0,8 |
1 |
14,33 |
364 |
45,00 |
1,14 |
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| 2 |
1,102 |
0,955 |
0,551 |
7,367 |
3,1 |
3,0 |
3,1 |
2 |
15,69 |
398 |
49,29 |
2,40 |
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| 3 |
1,890 |
1,637 |
0,945 |
7,708 |
6,7 |
6,8 |
6,7 |
3 |
17,05 |
433 |
53,57 |
3,76 |
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| 4 |
2,677 |
2,318 |
1,339 |
8,049 |
11,5 |
12,1 |
11,7 |
4 |
18,42 |
468 |
57,86 |
5,23 |
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| 5 |
3,465 |
3,000 |
1,732 |
8,390 |
17,6 |
19,0 |
17,9 |
5 |
19,78 |
502 |
62,14 |
6,80 |
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| 6,45 |
4,606 |
3,989 |
2,303 |
8,884 |
28,6 |
31,9 |
29,4 |
6,45 |
21,76 |
553 |
68,35 |
8,54 |
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| 6,97 |
5,016 |
4,344 |
2,508 |
9,062 |
33,2 |
37,4 |
34,3 |
6,97 |
22,47 |
571 |
70,58 |
10,33 |
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| 8 |
5,827 |
5,046 |
2,913 |
9,413 |
43,3 |
49,8 |
45,1 |
8 |
23,87 |
606 |
75,00 |
12,24 |
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| 9 |
6,614 |
5,728 |
3,307 |
9,754 |
54,6 |
63,8 |
57,1 |
9 |
25,24 |
641 |
79,28 |
14,25 |
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| 9,37 |
6,906 |
5,980 |
3,453 |
9,880 |
59,2 |
69,4 |
61,9 |
9,37 |
25,74 |
654 |
80,87 |
16,31 |
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| 11 |
8,189 |
7,092 |
4,094 |
10,436 |
81,6 |
97,7 |
85,9 |
11 |
27,96 |
710 |
87,85 |
18,54 |
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| 12 |
8,976 |
7,774 |
4,488 |
10,777 |
97,4 |
117,9 |
102,9 |
12 |
29,33 |
745 |
92,13 |
20,88 |
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| 13 |
9,764 |
8,456 |
4,882 |
11,118 |
114,8 |
140,3 |
121,7 |
13 |
30,69 |
780 |
96,42 |
23,33 |
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| 14 |
10,551 |
9,138 |
5,276 |
11,459 |
133,9 |
165,1 |
142,3 |
14 |
32,05 |
814 |
100,70 |
25,88 |
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| 15 |
11,339 |
9,820 |
5,669 |
11,800 |
154,8 |
192,3 |
165,0 |
15 |
33,42 |
849 |
104,99 |
28,55 |
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| 16 |
12,126 |
10,501 |
6,063 |
12,140 |
177,4 |
222,1 |
189,6 |
16 |
34,78 |
883 |
109,27 |
31,33 |
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| 17 |
12,913 |
11,183 |
6,457 |
12,481 |
202,0 |
254,5 |
216,3 |
17 |
36,15 |
918 |
113,56 |
34,21 |
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| 18 |
13,701 |
11,865 |
6,850 |
12,822 |
228,5 |
289,7 |
245,2 |
18 |
37,51 |
953 |
117,84 |
37,20 |
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| 19 |