That secondary harmonic voltage distribution stuff...

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 
>turned :-O 
>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!