Secondary Resonant Circuit Size

[benet]

I'm trying to build a mini Tesla coil, but I have run into a problem in the design phase. Throughout anywhere I looked I haven't been able to find the proper size for the secondary resonant circuit. I understand that it needs to have the same resonant frequency as the primary resonant circuit but that only has bearing on the ratio between the capacitor and inductor. The only lead so to speak that I have is that the secondary in primary coils work as a transformer but again nothing I've found says to what degree. I have to imagine that there is a point where the secondary coil is too big to work with the rest of the circuit, but I have not been able to figure out what that size is. This seems like a relatively basic question but for the life of me I have not been able to figure it out. So is anyone else knows what I'm missing here that would be greatly appreciated, as this is the last thing I need to finish my design. Thank you.

[davekni]

Play with JaveTC:
http://classictesla.com/java/javatc/javatc.html

It is aimed at classic spark-gap coils, but is great information for solid-state versions too.  Start with their built-in demo coil.  Do be careful of units (cm or inches selectable) and radius vs diameter (some parameters are diameters and others are radii - all listed, but pay attention).

[Mads Barnkob]

I'm trying to build a mini Tesla coil, but I have run into a problem in the design phase. Throughout anywhere I looked I haven't been able to find the proper size for the secondary resonant circuit. I understand that it needs to have the same resonant frequency as the primary resonant circuit but that only has bearing on the ratio between the capacitor and inductor. The only lead so to speak that I have is that the secondary in primary coils work as a transformer but again nothing I've found says to what degree. I have to imagine that there is a point where the secondary coil is too big to work with the rest of the circuit, but I have not been able to figure out what that size is. This seems like a relatively basic question but for the life of me I have not been able to figure it out. So is anyone else knows what I'm missing here that would be greatly appreciated, as this is the last thing I need to finish my design. Thank you.

I tried to cover a lot of these topics, about how to size things to a given power, budget or expected spark length. I wrote a very large DRSSTC design guide, that for most parts are principles that work for all types of Tesla coils.

For the secondary coil size, I also made a data table with many different design choices to different wire gauges, forms and ratios, lots to choose from in the tesla coil secondary design guide

[benet]

Your website is very helpful and the material the charts we're on are exactly what I'm looking for. But despite that I couldn't actually find what calculations you used to come to your conclusions. at least four the optimal coupling ratio of the primary and secondary coils, as well as the recommended resident frequency. If you could either link to those equations or point out if I missed it on the original website that would be greatly appreciated. thank you.

[Uspring]

Is that a spark gap TC you want to build or a DRSSTC or SSTC? The design choices differ somewhat for each type. Wrt to coupling: Usually more is better. It's an engineering challenge to avoid racing sparks or flashovers that often accompany large coupling values. Davekni e.g. has mapped out some extremes: https://highvoltageforum.net/index.php?topic=1268.msg9305#msg9305
But that requires a lot of work and knowhow.

[benet]

Is that a spark gap TC you want to build or a DRSSTC or SSTC? The design choices differ somewhat for each type. Wrt to coupling: Usually more is better. It's an engineering challenge to avoid racing sparks or flashovers that often accompany large coupling values. Davekni e.g. has mapped out some extremes: https://highvoltageforum.net/index.php?topic=1268.msg9305#msg9305
But that requires a lot of work and knowhow.

I'm just starting out so I'm making a mini spark gap Tesla coil

[Uspring]

Initially, when the spark gap fires, all of the energy of the TC is stored in the primary tank capacitor. After a number of cycles, all of this energy will be transferred to the secondary tank, if the tanks are tuned to the same frequency. The same number of cycles later, the energy will have returned to the primary tank. In a TC made to produce big sparks, we don't want the energy to go back to the primary tank. It should be used to feed the spark.
Think about 2 extreme cases:

1) Very little or no secondary loading by the arc. Then the energy will mostly return to the primary before a significant amount of it is dissipated by the arc.
2) Extreme arc loading, i.e. practically a short cut of the secondary. In this case no or little energy will arrive in the secondary tank.

So there is a kind of impedance matching condition between secondary impedance and arc resistance. A close to optimum condition would be, that there is a strong enough arc loading, so that most of the energy in the secondary tank is dissipated, before it returns to the primary. And also that arc loading should not be too strong to prevent energy arriving in the secondary at all.
This boils down to a secondary impedance recommendation of about 50k ohms. Arcs, though, start out small and then grow during a burst. That means, that arc loading is by far not constant during a discharge. So all of these estimates are a compromise between differing arc sizes.

A certain secondary impedance determines a L/C ratio, but that still allows for either a large L and C or a small L and C. There are 2 constraints on secondary C:

One is, that enough voltage is produced. Energy conservation requires, that

1/2 * Cpri *Vpri^2 = 1/2 * Csec * Vsec^2, so that Vsec = Vpri * sqrt(Cpri/Csec)

If the top load is too large, then you might not generate a high enough voltage.

The other one is, that if you make the top load too small, then the capacitance of the arc will bring the coil out of tune too much, since you will be adding a large arc capacitance to a small top load capacitance. It's probably a good advice to follow John Freaus remark here:

https://www.pupman.com/listarchives/2020/Apr/msg00009.php

He states, that it's difficult to obtain large arcs from small toroids. I believe the reason for this to be arc detuning effects.
In sum a rough prescription for a SGTC secondary would be:

1. Choose an arc length you want to achieve.
2. Divide that by 2 or three to get a toroid diameter
3. Calculate its capacitance
4. Calculate the secondary inductance by the 50k impedance recommendation

I should add, that my practical experience with SGTCs is limited and the above is more about a line of reasoning than about particular values.

[benet]

Thank you for your response. I am still a bit confused about two things.

 First what you mean by “After a number of cycles, all of this energy will be transferred to the secondary tank.” The way that I currently understand resonant circuits, the capacitor is entirely discharged within one cycle and then recharged at the beginning of the next. Is there a different cycle that you're referring to then the resident frequency?

2nd how is the energy returning from the secondary tank back to the primary tank. I know that the energy can go from the secondary tank to the secondary coil via the ground. But how is the energy traveling backwards into the previous capacity?

[Uspring]

Right, the cap is discharged after half a cycle and the energy is then stored in the primary inductor. Then it goes back into the primary cap. That's the usual operation of a single tank. But, in addition to this, the primary tank is coupled to the secondary. After a few cycles, depending on the coupling strength, the energy will be transferred to the secondary tank and back again. This happens as a result of the coupling. The ground does not play any role here. This is much better explained e.g. here: http://www.richieburnett.co.uk/operation.html#operation

I should add a comment ot my statement:

1. Choose an arc length you want to achieve.

The length depends on the amount of power you supply. You can estimate the length from Freaus equation
 
length = 1.7 * sqrt(P)

with length in inches and P in watts.