# Re: The very basics

```Reinier (and other newer coilers),

I'll take a shot at doing a high-level summary for you. Veteran coilers
can delete this now to save time! :^)

1. Why do we use high primary circuit voltages? And why the spark gap in
the primary circuit?
Capacitor-discharge Tesla Coils use a high voltage transformer to charge
up (temporarily store energy in) the primary (tank) capacitor (Cp). Once
the voltage on the capacitor rises to a sufficient level to ionize the
main spark gap (Vgap), the gap "fires", and acting as a switch,
electrically closes the loop between the primary winding (Lp) and
charged tank capacitor.

The gap's firing causes the primary LC circuit to oscillate, or "ring",
much like a bell getting struck by a hammer, creating an oscillating
electromagnetic field around the primary. The amount of energy available
to "ring" the primary system is a function of the tank capacitance and
voltage at the time the gap fired, and is typically called the "bang"
size. Bang size represents the maximum amount of primary tank cap energy
that's available for transfer to the secondary each time the gap
initially fires. Mathematically, the bang size will be Ep =
0.5*Cp*(Vgap*Vgap) in Joules. Doubling the tank cap size doubles the
bang size... BUT, doubling the main gap breakdown voltage QUADRUPLES the
bang size. This is one reason why higher power systems tend to use
higher operating/gap breakdown voltages and larger value tank caps.

Now, only a relatively small portion of the primary's electromagnetic
field, typically 10-25%, interacts with the secondary. This fraction,
called the coupling coefficient (k), is purely a function of the
geometries and relative placement of the primary and secondary windings.
The secondary and top terminal also form an LC circuit, made up of the
secondary inductance (Ls), the self-capacitance of the secondary to
ground (Cs), plus the effective capacitance of any top terminal we've
added (Ct). The magnetic coupling betwwen the primary and secondary
permit us to transfer energy between the two LC systems. A 2-coil Tesla
Coil is properly tuned when the primary's ringing frequency is made
equal to that of the secondary, forming a dual-tuned resonant
transformer. This condition can be expressed mathematically as Lp*Cp =
Ls*(Cs+Ct), and the natural ringing frequency Fo of each is
approximately 1/(2*Pi*Sqrt(LpCp)).

2. Where does the high voltage output come from??
Here's where it gets a bit more complex...
When the main gap fires, the energy initially stored in the ringing
primary LC circuit begins to electromagnetically couple into the
secondary LC circuit, causing it to "ring". However, any energy which
transfers to the secondary MUST reduce the amount of energy that remains
in the primary, since Tesla Coils do NOT violate Conservation of Energy,
and all we've got to play with is the initial "bang" energy stored in
the primary tank cap at the instant the gap fired.

Because of the relatively loose coupling between the primary and
secondary, it takes time for the primary's energy to fully transfer to
the secondary. Called the secondary "ring-up" time, it is typically 2-4
cycles at Fo - the greater the coupling corefficient (k), the less time
it takes. During this transfer time, we're also losing energy to gap
resistance, skin effect, and other losses in the system, and the maximum
energy that we can practically transfer to the secondary is typically no
more than 60-85% of the initial bang size. At some point near the
completion of the secondary's "ring-up", we'll ideally get "breakout" of
the top terminal, forming one or more streamer discharges. Once this
occurs, we'll typically begin losing significant energy to the streamers
(a very desirable loss!).

Once we've transferred all the available energy from the primary to the
secondary, ALL the system's energy resides in the secondary's LC system.
If we now "open up" the primary gap (called first notch quenching), we
will prevent any of this energy from coming back into the primary LC
circuit, and the secondary's remaining energy will hopefully dissipate
into the streamers as it "rings down". However, if we are not successful
in quenching the main gap, it reignites, and much of the secondary's
energy then transfers back to the primary until all the remaining system
energy again resides in the primary LC circuit.

This energy interchange process can repeat (often many times) until the
gap finally does quench. Irrespective of when we quench, ALL the
original bang energy will eventually be be dissipated, and the gap
extinguished. The HV source then begins recharging the tank cap for the
next bang. One important thing to remember: In a disruptive system,
there is never any energy "carried over" from one bang to the next;
secondary energy does NOT build up from one bang to the next.

The high output voltage that you see is actually due to the
comparatively small capacitance in the secondary LC circuit compared to
the primary and the Conservation of Energy. If there were no system
losses, ALL of the bang energy would be transferred to the secondary. In
practice, a well-constructed coil may deliver over 85% of this energy to
the secondary. For now, let's call this fraction the energy transfer
efficiency, or X.

Let's assume that we transfer X% of the primary bang energy to the
secondary. The maximum energy in the secondary, and thus the maximum
output voltage, will be directly limited to X*Ep. And we can thus find
Vout as a function of the othter variables:

Let Ep = Initial Primary Bang Energy = .5Cp*Vgap^2)
Let Es = Energy transferred to the Secondary = 0.5*(Cp+Ct)*(Vout^2)
And, let's assume Es = X*Ep.

Solving for  Vout:
Vout = Vgap*SQRT(X*Cp/(Cs+Ct))

In typical 2-coil systems, Vout will be in the range of 10-30 times
Vgap. Your mileage may vary! Notice that the turns ratio between the
primary and secondary windings has no direct bearing on Vout! However,
it CAN be shown that there is a relationship between the relative
primary and secondary coil inductances:

Vout = Vgap*SQRT(X*Ls/Lp)

And that's the BASIC theory behind a 2-coil system!

Reality-Check Time:
==================
In practice, the actual interrelationships that govern coil operation
are considerably more complex thant implied above. Simply aiming for
higher Vout will NOT generally deliver better performance! The actual
efficiency of "incinerating the air" (that is, getting the LONGEST
sparks for the MINIMAL input power or coil size) is a very complex, and
still rather poorly understood, combination of bang-size, primary and
secondary impedances, coupling coefficient, gap quenching, streamer
circuit,... well, you get the picture!

The process of predetermining these interrelationships and tradeoffs to
arrive at an optimal coil design is not yet fully understood. As an
example, John Couture's recent post about sparklength INCREASING with
reduced Vout (when we increase topload Capacitance) is one of those
seemingly paradoxical relationships that classical coiling theory alone
will not predict. A similar quandary is created by Terry Fritz's recent
tests which imply that, under some conditions, 2nd-notch quenching may
actually deliver longer sparklength than the more theoretically optimal
1st-Notch quench. Most experienced coilers end up developing a "feel"
for what's optimal through hard-won experience...

In the final analysis, coiling is like peeling an onion... there's
always another layer underneath! But isn't that part of what makes this
hobby so interesting!  :^)

Safe coiling to you, Reinier!

-- Bert --

Tesla List wrote:
>
> Original Poster: Reinier Heeres <rwh-at-worldonline.nl>
>
> Hi all coilers!
>
> I'm looking for the very basics of the tesla coil theories... I hope you
> can help me.
> This is what I know: The first coil induces a current in the second
> coil. Somehow the current in the second coil gets amplified, until the
> voltage is so high that the coil discharges in the air, showing the cool
> light effect... My questions are:
> -Why do you need NST's?
> -Why is the spark gap before the first coil?
> -How is the current in the second coil amplified?
> Could anybody tell me answers to this question or is there a paper about
> it somewhere on the net?
>
> Thanks, Reinier
>
> BTW: I do know about inductance and some other basic electronic/magnetic
> things...

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