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Registered Member #1107
Joined: Thu Nov 08 2007, 10:09PM
Location:
Posts: 792
This question has been bugging me for a while and as the title says, in a LC tuned circuit such as a tesla coil is it better to use a larger primary cap and have less primary inductance or is it better to use a smaller primary cap and have more primary inductance? This is something that i could never really figure out and i just want to know what is better.
Registered Member #56
Joined: Thu Feb 09 2006, 05:02AM
Location: Southern Califorina, USA
Posts: 2445
It depends on how much energy you want stored in your tank circuit. Size the cap to have the right amount of 'bang' energy, then design the primary from there. Is SGTCs it is easy, you just make the cap slightly larger than resonant for your transformer. for DRSSTCs it is trickier but the same general idea applies.
Registered Member #30
Joined: Fri Feb 03 2006, 10:52AM
Location: Glasgow, Scotland
Posts: 6706
As you figured out, you can make an infinite number of resonant circuits that all have the same resonant frequency (F0) since it just depends on the product L*C. 2L and C/2 will resonate at the same frequency as L and C did.
This degree of freedom that you found is called the characteristic impedance, Z0. A LC circuit with a large L and small C will have high Z0, and one with small L and large C will have low Z0. Different values of Z0 are used in different applications: there's no "best".
However there are guidelines, if you upgraded your Tesla coil from a 15/60 NST to a pole pig, you'd need to lower the Z0 of the tank circuit to make use of the extra power, while keeping F0 constant. So you might make your tank cap four times bigger and cut your primary turns in half, which cuts the inductance by about a factor of 4.
For reference, F0=1/(2*pi*sqrt(LC)) Z0=sqrt(L/C)
Hence if you know any two of F0, Z0, L, C, you can calculate the other two with some high school algebra.
Registered Member #1232
Joined: Wed Jan 16 2008, 10:53PM
Location: Doon tha Toon!
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This is a tradeoff in the conventional coil design which has always interested me.
When I used to play about with conventional coils I used to try to arrive at a primary circuit that had a large Lp and small Cp. Obviously whilst still being in tune with the secondary's resonant frequency.
I then compensated for the energy deficiency of the small Cp by getting the primary voltage as high as possible through optimised resonant charging.
My thinking is this:
1. Energy in the primary capacitor is 0.5CV² So it is proportional to capacitance but proportional to the square of the voltage.
2. Increasing Lp and decreasing Cp increases the surge impedance and therefore reduces the peak current in the primary circuit.
3. Capacitor losses, and resistive losses in primary connections are proportional to I² (and gap losses roughly proportional to I) so keeping the primary current down to a sane level seems like a good idea.
The secondary coil only sees the alternating magnetic field generated by the primary coil. All it cares about is ampere-turns. It doesn't distinguish whether they are achieved by lots of amps or lots of primary turns.
A quick thought exercise shows that if you take a given TC system and half Cp and double Lp then the surge impedance (Z0) of the primary will double from Steve's equation. Since you've halved Cp you need to increase the voltage by sqrt(2) to keep the energy in the capacitor the same. Calculating peak primary current shows that it's fallen to 71% of its previous value reducing losses in the spark gap, capacitor and skin losses in the copper conductors. (Since the inductance of the primary is roughly proportional to the number of turns squared, we can assume 41% more turns are required to double the inductance. Multiplying the turns by sqrt(2) compensates for the current being divided by sqrt(2) and the ampere-turns seen by the secondary stay the same!)
I haven't done exhaustive testing in this area by any means. However several practical experiences showed that the same power into a coil with higher Lp and lower Cp gave better spark output from the toroid, and a noticeably less bright and quieter RSG.
...Then there's the whole other question of what ratio should Ls and Cs be in! A high Z0 for the secondary results in lots of open-circuit voltage on the toroid, (voltage is good!) ...but a large toroid stores more charge that is instantaneously available to feed streamers.
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more cap or more inductance?
