What makes Tesla coils better than conventional transformers at generating high voltages?

Question

The voltage gain of a Tesla coil can be determined from the primary and secondary inductances \$L_1\$ and \$L_2\$ using the following formula (Wikipedia has a simple derivation): $$ \frac{V_2}{V_1} = \sqrt{\frac{L_2}{L_1}} $$

I've seen several websites show this formula and claim that it is the reason for Tesla coils' high gain. But the same formula also applies to an ordinary transformer built from coils of the same inductance - as @user287001 said, \$ \sqrt{\frac{L_2}{L_1}} \$ is the turns ratio \$ \frac{N_2}{N_1} \$.

My question is:

1. Why would I want to build a Tesla coil rather than a simpler transformer of equal gain?
2. In particular, do Tesla coils really have higher gain than an ordinary transformer with the same ratio of turns? I keep hearing this, but it contradicts what I said above about voltage gains.

The only explanation I can think of is that having a capacitor in the primary circuit allows us to first slowly charge it, and then transfer the energy without drawing extreme currents from voltage supply. Either that, or my reasoning about voltage gains is wrong.

Answer 1

A Tesla coil supports a high secondary voltage by having a large spacing between the primary and the secondary, at least the high voltage end of the secondary. If the secondary has single high voltage end, it's single layer, so will be low inductance.

The large spacing means low coupling, which then requires the primary and secondary to be resonant to achieve any sort of efficiency.

You can build a high voltage transformer without using the Tesla construction, but then you need a lot of oil or other good insulation round the secondary, as well as a core to get good coupling and decent inductances.

It's a great construction for amateurs. The use of air for insulation and no core means a cheap construction. The interrupted air-spark switched primary drive means you can run fairly low power (one domestic outlet), and still get high voltage sparks.

Answer 2

Why would I want to build a Tesla coil rather than a simpler transformer of equal gain [for high voltage]?

Primarily, because of two things:

• Tesla coils operate in resonance, so produce a much higher voltage output.
• The close proximity of cored-transformer coils limits the upper working voltage.

For high voltages (greater than about 4kV or so) most typical insulative materials begin to weaken against arcing, especially over time. So more radical insulative measures are taken, such as potting and encapsulation. But even these have limits.

Consider a 10kVAC neon sign transformer. These often have the secondary mid-point grounded, so that only 5kV potential exists between either end and the core material. If it were instead end-grounded, then 10kV would exist between the opposite end of the winding and the core, which would likely fail much sooner. These are also potted under a vacuum.

Tesla coils, being air-core, are not limited by any of this. They also do not suffer from core saturation and remanence effects, meaning they can be used at very high-frequencies (MHz) and powers (MW, pulsed) while cored transformers cannot.

• Laminated-core transformers are typically rated for 50/60Hz and 400Hz for marine/aerospace.
• Ferrite-core transformers are typically rated for 20-200kHz.
• The higher the transformer operating frequency, the physically smaller it can be to deliver the same power.

Answer 3

Term "better" should be considered as "more volts with less turns"

Tesla coil is a resonant system where the voltage is built higher by resonance. If you load it the voltage drops radically. Normal iron core transformers are not based on resonance. They change voltage by the winding ratio. They are designed to keep the output voltage drop reasonably small at the specified max output power.

Modern Tesla coil derivations such as Slayer Exciter have also another voltage rising mechanism: the inductive kickback phenomena. Finally there's the old familiar winding ratio. The kickback together with resonance and winding ratio can generate easily tens of thousands of volts with surprisingly small windings as you can see from their drawings.

BTW your formula $$ \frac{V_2}{V_1} = \sqrt{\frac{L_2}{L_1}} $$

is the winding ratio N2/N1. Inductance is proportional to the square of the number of the turns if the dimensions are not changed.