That secondary harmonic voltage distribution stuff...
Subject: That secondary harmonic voltage distribution stuff...
From: Terry Fritz <twftesla-at-uswest-dot-net>
Date: Tue, 24 Aug 1999 20:31:09 -0600
Hi Alwyn and All,
Tonight I have been playing with E-Tesla3 (soon to be E-Tesla4) and my
coil along with antennas and all the test equipment I have. I have seen
wonderful things and I think I will be able to predict and graph the
voltage distribution harmonics of the fundamental and add a better
understanding to all that.
It appears that the harmonics are not 1, 3, 5 as I, and others, originally
thought but occur at 1, 2, 4, 6 instead. Because of the effects these
harmonic field distributions have on the tuning frequencies (a 1/2 sine
wave has far less field capacitance and thus much higher frequency than a
1/4 harmonic), the harmonics "may appear" to be at 1, 3, 5 but are really
not! The top load terminal and even the top of a bare coil appear to be
fairly good zero potential nodes.
Fortunately, the lumped parameter models seems to still hold true through
all this (whew! :-)) but it is getting rather messy... E-Tesla seems to
have a factor of 2 error but I think it is one of those area under a sine
curve things in the capacitance calculation.... Hopefully, I can get that
figured out in a defendable way...
All this is still very early (many grains of salt can be taken now) but I
felt I had to babble about it after spending all day....... Much FUN!!!
>>I never did respond to your last comment about the 1/4 wave theory. I
>>misunderstood the statement "the secondary can be modelled as a helical
>>antenna" to mean it was finally agreed to be a 1/4 wave effect.
>>You may be convinced by the following experiment. If you connect a sweep
>>generator to the base of a Tesla coil vie a piece of terminated coax and
>>monitor the amplitude you will notice a series of resonance spikes having
>>the approximate relationship in frequency of 1, 3, 5. etc.. Possibly the
>>relationship is not accurately 1,3,5 because the propagation velocity is
>>slower near the grounded end due to the higher self-capacitance and or
>>because the propagation velocity varies with frequency.
>There is no doubt that standing waves can be set up in Tesla coils at a
>number of harmonics. What I would dispute is that there are significant
>propagation and phase shift effects along the length of the coil. If the
>length of wire were a factor, and the current had to travel the length of
>wire in the secondary, then the current would be delayed 90 degrees along
>the coil's length. However, it is easy to make Tesla coils with wire
>lengths other than what the 1/4 wave propagation / wire length theory would
>suggest. In fact, a given coil can operate over a very wide frequency range
>with ease given different top loads. I suggest that the current at the base
>of the coil and the current at the top of the coil are magnetically linked.
>This linkage simply overwhelms the effects of pure wire length propagation.
>If the wire were unwound and in a long straight line, then it would act as a
>simple 1/4 wave antenna. However, by winding it up in a close wound coil,
>the currents in the wire are locked together magnetically. In a fairly
>similar fashion, the self-capacitance of the coil is also locked. Thus, the
>secondary system acts much more like a simple lumped LC network rather than
>a 1/4 wave transmission line.
>I used to have a long coil that had LEDs in series with the winding at every
>inch. It was fun to hit the various harmonics and setup up node and
>anti-node patterns on it. However, that device could not detect the phase
>along the coil.
> There are computer programs now that can predict a coil's resonant
>frequency with top load based on physical dimensions. They do not depend on
>wire length at all. The programs calculate the self-capacitance of the coil
>and the capacitance of the top load as a physical structure in space (with a
>ground plane). This capacitance is then combined with the measured
>inductance to arrive at a resonant frequency. The programs can get within
>5%. These programs are based on the voltage distribution along the coil's
>length as an in-phase sine wave. The current is a cosine wave that is
>delayed in amplitude but not in actual phase (I need to find a better way to
>explain that...). Basically the current is maximum at the base of the coil
>and is some lesser value (like 40%) at the top of the coil but still in phase.
>One fun thing I have never thought of, till you mentioned all this, is to
>change the computer program to use harmonics instead of the fundamental
>frequency in the calculations. It is a simple addition of a 3x, 5x,... in
>the secondary voltage distribution that would do this. Then the program
>should be able to find the harmonic frequencies too! Even more interesting,
>is that E-Tesla3 can plot voltage and field stress plots (with Excel). It
>will be very interesting to see what the voltage distribution is with a top
>terminal in place!! I will run these and post the results. I will also
>check the results against my coil. I'll do the bare coil and then with top
>load. I may not be able to do all this till the weekend. My little nieces
>have turned my Tesla coil lab into a Barbie horsy farm while my back was
>A bare coil's resonant frequency can be very accurately predicted by
>calculating the inductance with wheeler's formula and the self-capacitance
>with Medhurst's formula and calculating the frequency from
>Fo=1/(2piSQRT(LC)). I have never known anyone to be able to repeatedly
>calculate and predict a range of coil's resonance frequency based on wire
>length with any accuracy. Propagation delay and other "things" are always
>blamed for the errors that occur. However, the Wheeler and Medhurst method
>has no exceptions!