Understanding the Tesla Coil: Science & Math Explained in Detail

[I_am_learning]

Could Someone explain exactly how Tesla coil works with necessary Mathematics and Science. The Wikipedia Article simply states facts but doesn't explain much anything.
Well I can't understand this,

In the secondary of the 115V/15KV transformer the transformed voltage is 15KV at 50Hz.

Then how come the Tank Circuit Resonate at Kilos of Herz. And Also what's the use of the spark gap. Why can't it work without the spark cap.

I well understand the working of regular power transformer. If some one could explain this as an extension to it, it would be good.

 

[vk6kro]

In the circuit shown, a peak value of 21213 volts is produced from the neon mains transformer as a sinewave.
The primary of the second transformer has relatively little inductance, so this voltage is used to charge up the capacitors.

At some point in this charging, the spark gap breaks down and an arc is formed.

This rapidly discharges the capacitors and the ionization continues until the capacitors are almost completely discharged.

The point of the spark gap is to get this rapid discharge current flowing in the primary of the right hand side transformer. Even though this transformer has a relatively low inductance primary, the very large and rapid change in primary current causes rapidly changing flux and a very large voltage spike to be generated across the secondary of this transformer.

This transformer secondary has stray capacitance and behaves like a parallel tuned circuit, typically at about 200 KHz. So, maximum energy is delivered at this frequency.

This occurs twice for each mains cycle.

You could make a mains transformer to generate 100000 volts or more, but because it would have to have a lot of iron in it, (because of the low mains frequency), it would be very expensive. The transformer in this circuit is tedious to make, but relatively inexpensive.

 

[Fish4Fun]

A Tesla coil is a resonant circuit,

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/serres.html

Essentially what happens is current travels through the capacitor bank and the second primary for some period of time determined by the inductance, resistance and capacitance. As the capacitor charge builds, the current slows down causing the second transformer primary inductance to produce a voltage spike which, if everything is tuned properly, exceeds the permeability of the air in the air gap and causes the capacitor bank to fully discharge through the second transformer primary in a very short period of time. Because V = L di/dt, the voltage induced in the second transformer's secondary is quite large.

If no current flows across the air gap then when the capacitor bank becomes fully charged, the current stops and there is a voltage spike in both the first transformer's secondary and the second transformer's primary that "ratchet's" up the capacitor voltage until the air gap does spark, or the first transformer's secondary voltage increases from excitation from its primary.

The circuit in general has a fairly high fault tolerance and will accept a fairly wide range of primary transformer, secondary transformer, air gap and capacitor values and still remain "functional". Maximizing the output voltage/frequency/efficiency and the requisite math I will leave to you and others, I am a bit sleepy this morning.

Fish

 

[I_am_learning]

What I don't understand is the charging of Caps. Since we are dealing with AC, current flows both ways, So how could you keep charging the Caps cycle after cycle to eventually accumulate enough voltage to produce spark in the gap?

As far as my knowledge with power transformer is concerned, I would replace all coils with its R + jXl and then if I solve, all I would get is two cascade Transformers with a load 1/jXc in between. There seems to be no phenomenum of charging.

 

[vk6kro]

The capacitors charge in one half cycle of input voltage. They do not accumulate charge over many cycles. They can't, because there is no rectifier.

You have a sinewave being applied to a capacitor and if there were no spark gap, the voltage would rise to the peak voltage. However, at some lower voltage, say 18000 volts, the spark gap conducts, so the peak voltage is not reached.

Then on the next half cycle, the capacitors get charged in the opposite polarity and the spark gap still conducts and an output pulse of the opposite polarity is produced.

 

[I_am_learning]

The capacitors charge in one half cycle of input voltage. They do not accumulate charge over many cycles. They can't, because there is no rectifier.

You have a sinewave being applied to a capacitor and if there were no spark gap, the voltage would rise to the peak voltage. However, at some lower voltage, say 18000 volts, the spark gap conducts, so the peak voltage is not reached.

But secondary of the first transformer keeps rising to peak voltage, (although it (along with the caps) now sends current through the spark gap. The caps don't get charged to peak.

Due to ultra quick discharging through the gap, large emf is generated in Second transformer ( less in primary and lot more in secondary.)

I hope upto this all is fine, fine.

Now where does the Capacitance and Inductance value come into play, I mean where is the resonance? Where those all interesting Winding Geometry come into play?

Thanks for your help.

 

[vk6kro]

But secondary of the first transformer keeps rising to peak voltage, (although it (along with the caps) now sends current through the spark gap. The caps don't get charged to peak.

Yes, that is partly right. The adjustment of the spark gap would be set so that the capacitors are nearly fully charged, but not quite.

The transformer has internal resistance in the secondary and a special magnetic core, so as soon as the spark gap starts to break down, the voltage from the transformer does not rise any higher. This is a brutal thing to do to a normal transformer, but these transformers are built to tolerate a short circuit.
Read this article which explains how the neon sign transformer can be operated into a short circuit or left open circuited:
http://en.wikipedia.org/wiki/Neon_sign_transformer

Note the safety warning.Now where does the Capacitance and Inductance value come into play, I mean where is the resonance? Where those all interesting Winding Geometry come into play?

You can see where the inductance comes from. It is that huge coil of wire.
In between the turns of wire, there is capacitance. You have two conductors with an insulator between them so it behaves like a lot of capacitors distributed across the winding.

So this inductance and this capacitance adds up to one big tuned circuit.
You can measure this resonance. If you connected an audio generator to the primary of the transformer, and varied the input frequency, at one frequency there will be a big increase in the output voltage. This is the resonant frequency of the transformer.

There are tricks used like adding a metal hat to the top of the coil to increase the capacitance.

At this stage, it becomes a bit of a black art and tuning for maximum spark is the main object.

 

[regisz90]

"This occurs twice for each mains cycle."

So if we have a spark gap and if the input frequency is 50Hz, it must create an arc 100 times per second?

 

[vk6kro]

Yes, there would be one arc per half cycle, but the output would consist of many cycles at the resonant frequency of the transformer secondary.

These would be in bursts of 120 per second if the mains frequency was 60 Hz.

 

[the_emi_guy]

At some point in this charging, the spark gap breaks down and an arc is formed.

This rapidly discharges the capacitors and the ionization continues until the capacitors are almost completely discharged.

When the spark gap discharges it does more than simply drain the caps.

The primary circuit (primary coil and capacitors) resonates. The secondary is designed to match the resonant frequency of the primary.

Current in the primary is a damped resonance in the KHz range and when its envelope drops below a threshold, we get "quench" and the spark gap stops conducting. Then we wait for the next peak of the mains waveform to kick it off again.

 

[sophiecentaur]

All this spark gap does is to produce a high frequency oscillation with a fair amount of power. It is the way the original Tesla coil was made. You can get a much more efficient system, involving less radiated interference, if a transmitting valve is used instead. If he'd had valves available, Tesla would surely have used them. The valve functions as a power oscillator and produces much more power at the wanted frequency, giving you some really impressive sparks.