Determining the HV Output of a TC Discussion
Question: What determines the high voltage output of a Tesla coil? If not the step-up ratio of the coil itself, then how about: Firing rate of spark gap -Size of tank capacitor -Operating frequency of coil -All of the above?
Responses:
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Essentially, the ratio of the primary capacitance to the secondary (distributed) capacitance. A classical Tesla coil is a pair of coupled LC tanks tuned to the same frequency, one, the primary, with low impedance, and another, the secondary, with high impedance. When some energy is put in the primary, causing it to oscillate, the oscillations gradually transfer the energy to the secondary, and after some cycles all (or almost, allowing for losses) of it can be transferred. Considering that the initial energy is in the primary capacitor C1 and the maximum output voltage occurs if all the initial energy ends in the secondary capacitance C2, the ideal voltage gain is sqrt(C1/C2).
The energy transfer tends to revert direction after it is complete, returning the energy to the primary tank in the same number of cycles, and the sequence repeats. It happens, however, that eventually the primary gap ceases to conduct at one of the times when all the energy is in the secondary system ("quenches"), and after this the remaining energy is trapped in the secondary system until complete dissipation.
Curiously, as both tanks are tuned to the same frequency, and so L1*C1=L2*C2, the gain is also equal to sqrt(L2/L1). If both coils could be wound with the same geometry, this would be precisely the turns ratio between the coils. -Antonio Carlos M. de Queiroz -
In a Tesla coil, the pri-sec turns ratio is only indirectly related to the step-up ratio. The THEORETICAL ratio is governed by the ratio of sec to pri inductance. Notice the all-caps qualifier though. The theoretical voltage gain would only be realized if no losses occurred in the spark gap, conductor resistance, skin effect losses, and if sparks and corona did not occur. None of this applies to actual coils however.
The firing rate of the gap and cap size affect only the power, not the voltage produced. Some losses may be somewhat lower when the frequency is lower, so frequency may marginally affect the voltage.
The actual voltage produced by an operating coil is something that I'm not sure has ever been accurately measured by anyone on this List. It's easy to estimate the theoretical maximum and apply some derating factor that's been pulled out of a hat to account for losses, but it's just slightly better than a WAG.
The actual voltage is something of academic interest, but little practical use beyond bragging rights. Ebay sellers generally claim nice round numbers like 500kV, no doubt just pulled from the air. Relative performance of coils is generally quantified by citing straight line point-to-point streamer length, and this correlates with input power, not output voltage. Regards, Gary L. -
One thing to keep in mind, when trying to understand why the Tesla Coil Top Voltage is not determined by turns ratio is this: The primary and secondary circuits are resonant at the same frequency. If you drive the primary with a constant input of power, like in an oscillator driven coil, the top of the secondary will reach a voltage higher than the turns ratio, determined by the Q of the coil/topload combo. But the disruptive tesla coil is fed with small bursts of charge from the primary capacitor: as soon as the gap fires, the energy in the primary cap is decreasing rapidly. So in that case the top voltage is determined by the ratio between. the primary cap and the secondary cap, multiplied by primary firing voltage. Either way, the tesla coil top voltage never follows the turns ratio. Cheers, Finn H.
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As well as the excellent answers already provided you might like to have a look at Rich Burnett's web site http://www.richieburnett.co.uk/tesla.shtml, it has an excellent explanation of TC operation. Tom.
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Voltage sec = Voltage pri * SQR (n * L sec / L pri). Essentially it's the square root of the sec. coil's inductance divided by the pri coil's inductance x the pri potential in peak kV (1.414 * Erms). n is an efficiency factor that is determined for each coil setup. Spark length doesn't apply directly to voltage because the high current in the spark can produce a long plasma (spark) that isn't necessarily proportional. It does not depend at all on any of the 3 factors you listed. Dr. R.
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Overall, it can get complex, but here goes with the simple explanation: The TC transfers energy from the primary to the secondary. The energy available to transfer is determined by the primary voltage and the primary capacitor = 1/2 *Cp * Vp^2 That is the absolute maximum energy that can be transferred to the secondary capacitor (the top load + parasitic C from the secondary winding). In reality, there are losses. If you know the secondary capacitance, then you can calculate the voltage from the same equation: = 1/2 * Cs * Vs^2. Hence the usual equation you'll see: Vsec = Vpri * sqrt( Cpri/Csec).
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Since the primary and secondary are part of an LC resonant circuit, and resonate at the same frequency, we know that Lpri*Cpri = Lsec * Csec... That is: Lsec/Lpri = Cpri/Csec
We can substitute that in and get another familiar equation: Vsec = Vpri * sqrt( Lsec/Lpri)
In reality, the max voltage is limited by two effects:
1) Loss... A fair amount of the energy in the primary capacitor is lost in the spark gap (hence the interest in low loss switching with solid state devices) and in such mundane things as the resistance of the wires in primary and secondary.
2) As soon as a spark starts to form on the secondary top load, the voltage tends not to rise any more, and the energy flowing into the secondary goes to making the spark bigger (both in terms of heating up the air, and in terms of charging the increased capacitance of the secondary.. the spark itself has some significant capacitance to ground). The breakout voltage is primarily determined by the radius of curvature of the topload and the surface roughness. At the highest, it's probably 30 kV/cm or 70 kV/inch of radius, so a 4" diameter dryer vent pipe toroid isn't going to get a whole lot higher than say, 280 kV, and probably a whole lot less.
You'll note that turns ratio doesn't enter into this anywhere!
If what you're interested in is big sparks, that's determined more by the energy available to grow the spark, and since sparks have a limited life time, you need high average power too. I have seen several meter long sparks drawn from only 60 kV (but there was several hundred amps in the arc). Likewise, my Van de Graaff, which on a good day might get to 300 kV, can only make sparks 30-40 cm long, and they're pretty thin and wispy. A good rule of thumb for spark gap tesla coils is spark length (in inches) = 1.7 * Sqrt(average input power in watts). Jim L. -
-Firing rate of spark gap
No.
-Size of tank capacitor
Partly
-Operating frequency of coil
No
For a disruptive (i.e. capacitive discharge) coil, the fundamental relationship based on the principle of conservation of energy is Vout = Vgap * SQRT(Cp/Cs) where Vgap is the voltage the gap fires at, Cp is the primary capacitor value and Cs is the total secondary capacitance. A rider has to be added to this by saying that the voltage only gets there if the secondary is not allowed to break out (i.e. emit sparks) which is true for all types of coils.
For a CW coil, the output can be much higher if the coil is not allowed to break out and is governed by the effective shunt resistance of the secondary such that full output voltage is reached when the energy fed into the primary per cycle is equal to the secondary shunt losses per cycle. For this reason, most CW coil designs limit the number of cycles that can be fed to the primary and encourage the secondary to break out at a voltage that does not compromise the secondary insulation and/or allow pri-sec flashovers. Malcolm. -
5-17-11