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Re: [TCML] tank circuit power



Hi Jim..

Hey, I'm just gonna put something out here.

The main question I gathered from the person inquiring was do you need large copper on the primary? For SG, usually not, but you may need adequate spacing between turns simply because the turn to turn voltage is higher for an SG coil. For a solid state coil (SSTC, DRSSTC, etc), your better to go big on the tubing, but narrow spacing is usually okay (low turn to turn voltage). Heating depends on I^2R losses over time and the heat that will occur on the primary at that inner turn or two if very different for SG compared to SS. We can attempt rms numbers in the primary, but if your gonna do that, don't leave out proximity effects that occur from circulation currents from turn to turn and whatever else. There is much that goes into the heating of a primary coil (time of running is a big factor) and it is not a simple calculation. For most SG coilers, power is low enough to not require a large primary tubing (1/4" to 3/8" suits most everyone). I would bet that most coilers would say "i never realized any heat in my primary". But there are other coilers that have run higher power on SG's and also many SS coilers that would say "damn, primary got real hot". Of course, one of the side affects to solid state coils is that if the primary support doesn't melt, we tend to not pay attention to temperature. Then when it melts, we freak out. This is much less of a concern to SG coilers, but it can and does happen.

Take care,
Bart


 5/15/2012 8:46 PM, Jim Lux wrote:
The question comes up of what is the RMS current in the primary tank. This comes up when looking at losses, and when looking at RF safety calculations for the magnetic field from the primary.

A few basic assumptions:

The loaded Q of a tesla coil is approximately 10.
The equation for Q = 2*pi * Energy stored/(energy lost per cycle)
or, Energy lost = Energy stored * 2 *pi/Q
For Q = 10, that's 6.28/10 or .628...
That is, the tank loses about 62.8% of its stored energy in every cycle. If you look at the voltage, it goes as the square root (so each cycle is about 60% the amplitude of the previous)

Previous analyses have shown that one of the larger losses is in the spark gap (which has a "cathode drop" of around 100V per gap. (why a rotary or blast gap is more efficient than a static multi gap)

From that, we can calculate what the stored energy in the primary capacitor is (1/2 C *V^2) and from the stored energy in the cap, we can calculate the peak current in the primary (= energy in cap, to a first order)

the next question is "how much energy is dissipated in the resistance for a half sine with peak value X". For this, I assume that there's no loss during the actual half cycle, so the current is perfectly symmetrical around the peak:

So what we want is

integral[sin(omega t)^2] for t=[0, pi/omega]

which is

(omega t)/2 - sin(2omega t)/4 +C

This is zero for t=0

(omega pi/omega)/2 - sin(2* omega pi/omega)/4
or
pi/2 - sin (2pi)/4 = pi/2

So the energy dissipated in the primary resistance, R, if the peak current is I, is
R *  pi/2 * I^2 * thalfcycle

Then you build up a little spreadsheet and sum things up..
( stored is how much energy is in the cap at the peak, the loss is the joules lost to the resistance, to sec is the energy transferred to the secondary)

Here's an example:
L    3.70E-05    Q    10
C    6.80E-08    r    0.1
f     1.00E+05
    V    I
t            stored    loss    to sec
0    21000    900    14.99    0.63    7.30
0.5    14406    618    7.06    0.30    3.44
1    9883    424    3.32    0.14    1.62
1.5    6779    291    1.56    0.07    0.76
2    4651    199    0.74    0.03    0.36
2.5    3190    137    0.35    0.01    0.17
3    2189    94    0.16    0.01    0.08
3.5    1501    64    0.08    0.00    0.04
4    1030    44    0.04    0.00    0.02
4.5    707    30    0.02    0.00

    Total joules        1.20    13.78


With twice the Q
L    3.70E-05    Q    20
C    6.80E-08    r    0.1
f     1.00E+05
    V    I
Cycle            stored    loss    to sec
0    21000    900    14.99    0.63    3.70
0.5    17703    759    10.66    0.45    2.63
1    14924    640    7.57    0.32    1.87
1.5    12581    539    5.38    0.23    1.33
2    10605    455    3.82    0.16    0.94
2.5    8940    383    2.72    0.11    0.67
3    7537    323    1.93    0.08    0.48
3.5    6353    272    1.37    0.06    0.34
4    5356    230    0.98    0.04    0.24
4.5    4515    194    0.69    0.03

        Total joules        2.12    12.21

with 0.4 ohms and Q=10
L    3.70E-05    Q    10
C    6.80E-08    r    0.4
f     1.00E+05
    V    I
Cycle            stored    loss    to sec
0    21000    900    14.99    2.54    5.40
0.5    14406    618    7.06    1.19    2.54
1    9883    424    3.32    0.56    1.20
1.5    6779    291    1.56    0.26    0.56
2    4651    199    0.74    0.12    0.26
2.5    3190    137    0.35    0.06    0.12
3    2189    94    0.16    0.03    0.06
3.5    1501    64    0.08    0.01    0.03
4    1030    44    0.04    0.01    0.01
4.5    707    30    0.02    0.00

        Total joules        4.79    10.19
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