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Golden ratio claim funniness

  1. Aug 3, 2014 #1
    Hello all,
    I am in the process of designing a tesla coil for a research paper, and, just when I thought I had seen all the crack science there could possibly be, I came across a claim concerning the golden ratio. (The natural progression of events, I guess...) There is a real problem when choosing a capacitance value for the tank capacitor, because if the capacitive reactance is equal to the inductive reactance of the transformer's secondary coil, resonance can cause voltage rise lethal to the delicate secondary windings.
    This is where the golden ratio reportedly comes to the rescue. If a larger than resonant capacitor is used, one can avoid the out of control voltage gain and help prevent damage to the transformer. Specifically, there seems to be a consensus that one should use a capacitance of 1.618 times the resonant sized capacitance, because when two numbers are in the golden ratio, they have no common integer multiples, eliminating the possibility of resonance, and thus miraculously solving the problem.
    I know that this is because φ is irrational, but why φ? Why not something like the square root of two, which would allow a lower capacitance (and a lower budget in most cases!)? I have never really understood the fascination with the golden ratio, perhaps, then, I am missing something?
  2. jcsd
  3. Aug 3, 2014 #2

    Simon Bridge

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    Welcome to PF;
    You could probably find out the actual ideal value as an aside to your main research... adjusting the capacitor value seems straight forward and you can take steps to protect the secondary. Apart from not being "resonant", what other constraints are there? Where does this "consensus" come from - reputable sources or crackpots?

    There are a lot of things in life that are kinda spirally, and the golden ratio comes from a spiral so people get fixated on it. You get a similar fixation with pi.
  4. Aug 3, 2014 #3
    The only real constraints to get a working coil seem to be that that your capacitor must
    a) have a reactance equal to the primary inductive reactance to achieve tank circuit resonance (NOT the problem area resonance with the transformer) which is responsible for sending energy into the secondary circuit,
    b) be able to cope with the strenuous working conditions,
    c) not be too small, then the capacitor would end up at peak capacity before the ac wave hits an extremum, which really robs the system of energy, as you can imagine, and
    d) be affordable, of course.
    So bigger capacitance is alright, it's just not as efficient a use of resources.
    Apparently, this isn't much of a problem for heavy duty transformers like the pole distribution variety, which, from what I understand, are designed to survive some degree or another of lightning strikes. I am using a neon sign transformer though, and man, those things are temperamental.

    As for the sources, there are some scholarly sources which cite coil building websites, which usually, as you might already have guessed, don't cite a thing. Many websites that have coil design programs for the unmotivated (just kidding, they can actually be pretty handy sometimes) use the 1.6 figure, but without an explanation as to why.
  5. Aug 3, 2014 #4
    I think that in the coil I am designing I will use a capacitor with a capacitance of √2 times the resonant value. It's just as irrational as φ, as far as I can tell, because neither is transcendental, so I don't, at this point, see any particular advantage to using √2 over φ.
  6. Aug 4, 2014 #5

    Simon Bridge

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    (a) it is usually easier to build capacitors to spec than coils - but it looks like you really just want to build your coil to have a different reactance to the transformer right?
    (b) define "strenuous".
    (c) how small is "too small"? Is it not possible for the cap to be too big?
    (d) naturally :)

    which "scholarly sources" cite coil-building websites? Please provide an example.

    Which websites that have coil design programs which use the 1.6 figure
    Please provide an example.

    Note: 1.6 is roughly the cube-root of 4 ... so what?

    Why not just 1.5x or 2x ? Why funny numbers at all?
    If you need a large capacitor, and there is no upper constraint, then why not 100x? 1000x?
    So far what you are doing amounts to numerology.

    Do you have an equation that tells you the "resonant value" you are trying to avoid?

    In a nutshell:
    Given the coils - you want to pick a capacitor which optimizes something.

    What are you trying to optimize?
    That will give you another constraint.

    You could just accept 1.6x as a rule of thumb and leave it at that.
    This is your research project after all.
    I'm trying to get you to think scientifically.

    What level are you doing this project at anyway?
  7. Aug 4, 2014 #6
    well, as far as i can tell, there is no optimum sized capacitor other than that required to match the resonant frequency of the secondary circuit, which hinges on the inductance of the primary circuit (i probably should of mentioned this, but when building primaries, there are always extra turns built in. That way, you can actually use a 'tap' to easily change the length of the primary and thus the inductance, to tune).
    As for capacitors sizes in general, i am not aware of any problems with being too big, other than it being a waste of resources. The capacitor's job is just to build voltage until the dielectric strength of the air in between the spark gap is exceeded. Then, the gap fires, creating the oscillating tank circuit where energy moves between the cap and the primary. So the cap just stores energy until the gap fires, and then the oscillations start at MUCH higher frequencies then those of the step up transformer.
    So, sorry for the rambling by the way, the efficient thing to do would be to get a cap size that is able to be charged in half an AC cycle, but still affect the resonance needed in the tank circuit oscillations. If the capacitance is too small, the cap will be charged early before the AC hits a maximum (or minimum) which can put strain on the dielectric, and cause the loss of otherwise useable energy. Oh, and by strenuous i mean that the cap has to be able to withstand rf frequencies of rapid charge and discharge, as well as currents that can hit many (I've heard of hundreds and more) amperes. It's a little scary to thing about the abuse that a primary circuit can go through.
    In the morning I will provide some of those sources... an a circuit diagram probably
    Thanks for your attention!
  8. Aug 4, 2014 #7
    golden ration claim funniness

    this is for my IB extended essay. We are generally very strongly advised to do one in history or english, but I really love math and physics, and its what I'd rather be doing anyways. I also have had a lot of experience metalworking and making stuff like this just to learn, so I decided to choose this topic. It's a paper mostly on the theory, but I can't just get that close and not build one right?

    I keep realizing that I am forgetting o answer your questions!
    I am not actually sure about how small is too small, but anything lower than resonant charging size would be on the small side. Of course, the effects certainly vary.
    As to the frequencies you want to block out, I mentioned that the resonant frequency of the tank circuit (and matched secondary circuit) is significantly higher than the line frequency (60 hz). For example, static spark gap coils can operate in the range of several hundred kHz, and solid state tesla coils can operate in MHz ranges.
    So, just like standing waves on a string, you can just keep going higher and higher, if you cave the energy to do so. The idea, then, is to make sure that the capacitive and inductive reactances (for our cap and our step-up transformer) cannot share some common multiple, because if they did, then, from what i am trying to extrapolate, you would just end up reinforcing some integer multiple of the fundamental resonant frequency; you would get a harmonic, which is bad.
    I hope I am making a little cohesive sense here, and yeah, it kind of does sound like numerology. yuck. :)
    Last edited: Aug 4, 2014
  9. Aug 5, 2014 #8
    maybe, what this means is that you simply don't want your capacitance to be a multiple of the original capacitance, because (if you look at the equation for the resonant frequency of an LC circuit, f=1/[2*pi*(LC)^(1/2)]) then the new resonant frequency could be a whole number multiple of the fundamental frequency, a harmonic. Besides, the inductance and capacitance can't change, so it really seems like a non-issue now. it really seems like a lot of baloney the more and more I think about it.
  10. Aug 5, 2014 #9


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    You have been asked repeatedly to cite at least some of the "sources" you say exist but continue to fail to do so. That's bad form on this forum.

    Although I know better than to trust my "common sense" when it comes to science, I DO agree w/ you that it seems like baloney.
  11. Aug 5, 2014 #10
    I said that I would provide sources and a circuit diagram in the morning. It is now the morning, and I will deliver.

    This is the scholarly article, written by a student of physics. You can find the golden ratio reference at the top of page 38.


    If you scroll to the bottom of the page the download link is named "The Tesla Coil." He cites the golden ratio claim as coming from Kevin Wilson, at his own website:


    Use the finder to search for "I use a MMC" and it will take you right to the reference to the golden ratio.

    Next, we have this site:


    If you scroll to the heading "Proper Capacitance value for the capacitor" (it's not that far down at all) you will see, interestingly, that for state gaps, the 1.6 (≈golden ratio) is used, and for synchronous rotary gaps, a value in between 2.6 and 3.2 (≈e, ≈π) is recommended. I had never noticed that until now, as synchronous gaps never concerned me!


    This site references the larger than resonant capacitor size, but does not recommend any need to change to it as long a safety gap is introduced to the circuit and your transformer is not horribly weak already. You can find this statement by using the finder to search for "some people say to avoid"


    These two sites present the issues of resonant rise, and something I just learned about, inductive kick. Which can occur in capacitors of larger than resonant values. What is interesting is that he (Richard Burnett) found that a capacitance of 2 times the resonant matched size gave NO resonant voltage rise.

    Finally, there's a circuit diagram I did real quick in the attachments.

    I am going to get out of the house for a little while now. Later I will try to scrape up some more references, but I hope that those helped. Sorry for not getting on this right away, and I hope I haven't angered anyone too much...

    Attached Files:

  12. Aug 5, 2014 #11


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    When we refer to "sources" in the technical PF forums, we mean peer-reviewed journal articles or mainstream textbooks. Can you provide such sources? If not, this thread will be closed as nonsense.
  13. Aug 5, 2014 #12
    golden ration claim funniness

    I really don't think this should be passed off as nonsense... Do you really believe that there is nothing to be learned or expanded upon here, because I sure don't think so. The building of Tesla coils is predominantly something undertaken by hobbyists, and as such, most references and papers are written by, you guessed it, hobbyists. Some of these hobbyists have doctorates, such as Mark Rzeszotarski, some have been building and experimenting for a long time, like decades, some may be trying to come up with better and safer ways to do things, and some, such as myself, are just trying to learn some new things.
    I saw an interesting claim, and when researched, I found very little foundation for it. I instead found quite a bit of acceptance of it, and so I think it's an interesting question. Not nonsense at all, but something that just seems interesting.

    Isn't that what these forums are for anyways? Discussing stuff?

    Not everything worth discussing can be found in a peer-reviewed journal, and furthermore, just because it is not in a peer-reviewed or a mainstream textbook does NOT mean that it is NONSENSE.

    Please, I just was looking for some input as to what others think about the technical viability of the claim, not about whether or not it's rubbish.

    And just remember that at one point in history things we take for granted now were not always found first in a peer-reviewed journal or mainstream textbook. Ideas can start out through discussion too.
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