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 |
14,488 |
12,547 |
7,244 |
13,163 |
257,1 |
327,6 |
276,4 |
19 |
38,87 |
987 |
122,13 |
40,31 |
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20 |
15,276 |
13,229 |
7,638 |
13,504 |
287,7 |
368,6 |
309,9 |
20 |
40,24 |
1022 |
126,41 |
43,52 |
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21 |
16,063 |
13,911 |
8,031 |
13,845 |
320,5 |
412,5 |
345,8 |
21 |
41,60 |
1057 |
130,69 |
46,84 |
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22 |
16,850 |
14,593 |
8,425 |
14,186 |
355,5 |
459,6 |
384,2 |
22 |
42,97 |
1091 |
134,98 |
50,26 |
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23 |
17,638 |
15,275 |
8,819 |
14,527 |
392,8 |
509,9 |
425,1 |
23 |
44,33 |
1126 |
139,26 |
53,80 |
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|
24 |
18,425 |
15,957 |
9,213 |
14,868 |
432,4 |
563,6 |
468,7 |
24 |
45,69 |
1161 |
143,55 |
57,45 |
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|
25 |
19,213 |
16,639 |
9,606 |
15,209 |
474,5 |
620,6 |
514,9 |
25 |
47,06 |
1195 |
147,83 |
61,20 |
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26 |
20,000 |
17,321 |
10,000 |
15,550 |
519,0 |
681,2 |
564,0 |
26 |
48,42 |
1230 |
152,12 |
65,07 |
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|
27 |
20,787 |
18,002 |
10,394 |
15,891 |
566,2 |
745,4 |
615,9 |
27 |
49,78 |
1265 |
156,40 |
69,04 |
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|
28 |
21,575 |
18,684 |
10,787 |
16,232 |
615,9 |
813,4 |
670,7 |
28 |
51,15 |
1299 |
160,69 |
73,12 |
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|
29 |
22,362 |
19,366 |
11,181 |
16,573 |
668,3 |
885,1 |
728,6 |
29 |
52,51 |
1334 |
164,97 |
77,31 |
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|
30 |
23,150 |
20,048 |
11,575 |
16,914 |
723,6 |
960,8 |
789,6 |
30 |
53,88 |
1368 |
169,26 |
81,61 |
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Total length of tubing |
641,9 |
inches @ |
10 |
turns |
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or wire, without ends for
. |
53,5 |
feet |
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connection to tank
circuit. |
16,3 |
m |
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|
length of
tubing / wire, used in resistance calculations |
5,4 |
m |
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Estimating
Primary Copper-Loss: |
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|
DC Resistance = |
0,00441 |
Ohm (for |
1 |
mm wall of Cu) |
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RF Resistance with
skineffect = |
0,018482 |
Ohm (for straight wire) |
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RF Resistance
with skin- + proxyeffect= |
0,024427 |
Ohm (for coiled wire) |
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Primary RF current (RMS), assumed = |
14 |
A ( DC
Cu-Loss = |
1 |
Watt ---> for comparison with RF
Cu-loss only ) |
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RF
Cu-Loss = |
5 |
Watt
( for RRF =
see sheet "Skineffect"+"Proxi-eff." ) |
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Remark: |
Proximityeffect is only
a very raw guess: the primary is taken like a solenoid, even in case of a
flat spiral ! |
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The resistance is taken
for the whole coil, even if the tap is set to fewer turns. |
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Preliminary
calculation of winding supports: |
all dimensions are in [mm] |
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Please fill in the yellow fields, |
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and you will have a proposal for the |
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f total primary = |
681,8 |
|
first winding support and the length |
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|
of the strike-rail. = |
2,126 |
m |
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f strike rail = |
676,8 |
(circumf.= |
2126 |
) |
|
It must be remembered however, |
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that, depending on how many supports |
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you want to use (usually 4,6 or 8),
you |
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Di = |
350 |
|
155,9 |
|
5 |
|
will need to shift the grooves of
the |
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|
No. of |
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8 |
|
following supports by an amount of |
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|
grooves |
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20 |
/ (No
of supports) |
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10 |
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|
toward the outside of the coil
diameter, |
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|
distance |
|
|
in order to have a smooth groove
path |
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|
20 |
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|
to
wind the coil. For |
8 |
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2,0 |
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|
supports this is i.e. |
2,5 |
mm |
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|
94,0 |
|
shift per each
succeeding support. |
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6,0 |
|
Angle a |
|
|
[deg] |
|
152,0 |
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|
30 |
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162,9 |
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5 |
|
The support sketch is for 'saucer'
and |
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flat primaries, while helicals (a = 90deg.) |
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50 |
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anyway need a different
construction. |
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167,9 |
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Calculate capacitor , knowing secondary frequency and primary
value. |
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Calculate L at |
87%[4] |
of primary: |
L = |
61,47 |
uH |
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|
If f in kHz
and L in uH then: C(nF) = 109 / (4p2 x f 2x L) |
C = |
38,26 |
nF |
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Measured C = |
109,40 |
nF @ 1kHz d=0.005 |
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Measured C = |
110,00 |
nF @ 120Hz d=0.003 |
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|
Tip: manipulate XX% of primary by GOAL SEEK, in order to obtain
your goal-value of C ! |
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Calculate F knowing C and L |
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C(nF) |
L(uH) |
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from above: |
38,26 |
61,47 |
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if C in nF, L in uH: |
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F(kHz) = 1000 / (2 x pi sqrt (L x
C/1000)) |
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F (kHz) = |
103,79 |
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( primary at about |
9,00 |
turns ) |
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from fit to measured L = |
8,00054 |
turns |
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best sparks experimental = |
7,5 |
turns |
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Range of
secondary frequencies with |
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various
toroid sizes: Enter your own |
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values for toroid
sizes. (This is added to the |
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self
capacitance of the secondary as calculated above) |
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|
Toroid
Name: |
|
C toroid |
C total |
f |
l |
l/4 |
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|
[pF] |
[pF] |
[kHz] |
[m] |
[m] |
|
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|
Galanis 1600/400 |
|
69,59 |
85,941 |
78 |
3826 |
957 |
|
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|
Galanis 790/220 |
|
34,58 |
50,937 |
102 |
2946 |
736 |
|
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|
Galanis 700/200 |
|
30,66 |
47,013 |
106 |
2830 |
708 |
|
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|
Finn's 600/164 |
|
26,25 |
42,603 |
111 |
2694 |
674 |
|
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|
Langenthal 515/120 |
|
22,25 |
38,606 |
117 |
2565 |
641 |
|
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Langenthal 520/70 |
|
19,83 |
36,182 |
121 |
2483 |
621 |
|
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|
Aluflex-duct 400/110 |
|
17,94 |
34,291 |
124 |
2417 |
604 |
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|
Styropor-Adventskranz 300 |
10,79 |
27,144 |
139 |
2150 |
538 |
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|
Calculate
toroid capacitance: |
Equation courtesy of
Bert Pool |
|
For spheres: |
Csphere |
= er * ( 0.5* Dsphere ) / 9 |
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Toroid: |
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Sphere: |
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|
d1 |
d2 |
s |
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Dsphere |
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|
Enter
values for toroid: > |
750[5] |
200[6] |
0[7] |
mm |
|
0[8] |
mm |
|
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|
29,5 |
7,9 |
0 |
inches |
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|
C toroid = |
32,7720[9] |
pF |
|
C sphere = |
0 |
pF |
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|
Calculations above use C top = |
32,7720[10] |
pF |
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center-center diam.= |
0,55 |
m |
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cord circumference = |
0,628319 |
m |
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|
total outer surface = |
1,085656 |
m2 |
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|
metal volume = |
0 |
ccm |
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|
metal density r
= |
2,6989 |
g/ccm |
|
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|
weight calculated = |
0,0 |
kg |
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|
weight measured = |
13,5 |
kg |
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|
s = thickness of metal sheet |
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|
Alternative
toroids for evaluation (list of my toroids) |
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|
cord |
total outer |
metal |
metal |
weight |
weight |
|
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|
Toroid
Name: |
|
d1 |
d2 |
s |
C toroid |
c-c diam. |
circumf. |
surface |
volume |
density r |
calculated |
measured |
|
|
|
|
[mm] |
[mm] |
[mm] |
[pF] |
[m] |
[m] |
[m] |
[ccm] |
[g/ccm] |
[kg] |
[kg] |
|
|
|
Galanis 1600/400 |
|
|
1600 |
400 |
1 |
69,5865[11] |
1,2 |
1,256637 |
4,73741 |
4725,567 |
2,6989 |
12,75 |
13,5 |
|
|
|
Galanis 790/220 |
|
|
790 |
220 |
1 |
34,5822 |
0,57 |
0,69115 |
1,237648 |
1232,023 |
2,6989 |
3,33 |
3,015 |
|
|
|
Galanis 700/200 |
|
|
700 |
200 |
1 |
30,6584 |
0,5 |
0,628319 |
0,98696 |
982,0256 |
2,6989 |
2,65 |
|
|
|
|
Finn's 600/164 |
|
|
600 |
164 |
1,5 |
26,2482 |
0,436 |
0,515221 |
0,705716 |
1048,892 |
2,6989 |
2,83 |
|
|
|
|
Langenthal 515/120 |
|
|
515 |
121 |
0,5 |
22,2513 |
0,394 |
0,380133 |
0,470524 |
234,2896 |
2,6989 |
0,63 |
|
|
|
|
Langenthal 520/70 |
|
|
520 |
70 |
0,5 |
19,8269 |
0,45 |
0,219911 |
0,310893 |
154,3359 |
2,6989 |
0,42 |
|
|
|
|
Aluflex-duct 400/110 |
|
|
410 |
112 |
0,2 |
17,9358 |
0,298 |
0,351858 |
0,329408 |
65,76394 |
2,6989 |
0,18 |
|
|
|
|
Styropor-Adventskranz 300 |
|
|
247 |
65,5 |
0,2 |
10,7895 |
0,1815 |
0,205774 |
0,117332 |
23,39481 |
2,6989 |
0,06 |
|
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|
.... End of TC calc !
.... |
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