Re: 8-9 RFI noise thoughts.

Hi Terry, Alwyn,
                           Some comments:

> Original Poster: Terry Fritz <twftesla-at-uswest-dot-net>
> Hi Alwyn,
> At 12:10 AM 8/23/99 +0100, you wrote:
> >Hi Terry,
> >

<snip - points noted.> 
> >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.

Been there, done that.  It is quite fun to power a long secondary with 
a mistuned primary and see the range of "arcs" which appear like 
solar prominences along the length of the coil.
> 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.

Of course one might argue, as does the 1/4 wave school of thought 
that the structure determines the propagation velocity along the wire 
which also invalidates the notion of a simple relationship between
frequency and wirelength. I actually think that the differences are 
moot for a resonator operating at its fundamental.

> 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.

That is a key problem for the 1/4 wave school to reconcile IMHO. 
Nothing speaks louder than a good measurement.
> 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!

It surprises me that the 1/4 wave school haven't found a way of 
calculating resonator frequency without using arcane formulae 
incorporating fifth powers and suchlike. However, it is also notable 
that Medhurst's formula incorporates either a tabulate factor or
a function which is also complex in order to generate the factor vs 
H/D curve from whence the factor values may be derived.  So 
perhaps it's not that surprising after all ;)
> >A particularly surreal effect that I discovered was this. I wound a 10in
> >long coil  on an 18in piece of 1.5in diameter plastic water pipe using 0.5mm
> >wire. I mounted the coil above a sheet of aluminium to act as a ground
> >plain. I connected the base of the coil and ground plain to a signal
> >generator that had a maximum output of 20v pk to pk. When the frequency of
> >the generator was at one of the resonant frequencies of the coil there was
> >sufficient voltage strength to light a small florescent tube if it was put
> >close to the coil. At the higher resonate frequencies it was possible to
> >observe the standing waves along the coil as a series of nodes at which the
> >tube would light brightly. The Q was about 150 so tuning is tricky.
> >Presumable the lumped view can not explain this effect.
> I am not surprised by your fluorescent lamp experiment.  If you put 20 Vp-p
> into the base of a coil with a Q of 150, then the top of the coil should
> have 3000 Vp-p present (20*150).
> >The same coil could have been used to demonstrate the relatively slow
> >propagation down the coil directly by applying a square wave to one end and
> >observing
> >the delay to the signal at the other. Despite the fact that one end of the
> >coil is only 4ns away from the other the propagation of the wave along the
> >coil axis is never the less hundreds of times slow than its free space
> >velocity. The now old fashioned analogue TVs contained a delay line that was
> >inserted in the luminance signal path to compensate for the delay in the
> >colour signal path. It consisted of a long helical wound coil. An other
> >example is many oscilloscopes contain a delay line in the signal path to
> >allow observation of the trigger event. In some cases the delay line is a
> >piece of coax the centre conductor of which is helical wound.
> Delay lines differ from Tesla coils in two important respects.  Delay lines
> are very long thin coils.  This allows the bottom end to easily become
> de-coupled magnetically from the other end.  The coils in delay lines are
> also capacitively coupled along their length by the outer shield or by many
> small capacitors where Tesla coils are coupled to ground through a large
> space charge region roughly in the shape of a sphere.  Thus, the delay line
> can truly delay the signal since its construction is very close to a
> classic transmission line with its parameters adjusted to emphasize delay.

I really have to say something here. Coupling (as we all know?) is a 
function of the geometrical attributes of a structure. By that I mean 
that absolute size is not a dependency, only the shape, proximity
and *relative sizes* of the components. I have used this to argue 
against the notion that the secondary behaves differently when 
coupled to the primary than when it is free standing (i.e. when the 
gap goes out or in a three coil system) as the Corums claim. Here is 
the argument I once alluded to but didn't expand on:

Consider k between the bottom turn of a resonator and its top turn. 
For all intents and purposes it is near zero. Well below 0.01 at any 
rate. Far less significant that overall k (ksys). I have measured this.
Suppose one designs a primary consisting of a single turn and 
places it *right next to and directly below* the bottom turn of the 
secondary. Any argument about coupling that applies to the bottom 
turn of the secondary wrt to the top or any other piece of it also 
applies to the single turn primary. The currents and voltages in the 
primary will be near identical to those in the bottom turn of the 
secondary as k between these two turns is as near 1 as it can get. 
Hence, secondary behaviour cannot change whether the primary is 
present or not. Any other primary couples less well to the bottom 
turn and more or less to the rest of the coil depending on where it is 
positioned and its relative geometry.

QED in at least the single turn primary case. 

Back to relative sizes: build any 2-coil system you like and you will 
find that if the primary and secondary dimensions and placement 
are exactly scaled, k doesn't change. I cannot buy the difference 
between the delay line and secondary based on size argument.
> >It has been suggested that because the phase of the current flowing in the
> >base of the coil is in phase with the current in to the top C this
> >invalidates the above argument. At resonance the voltage at the top of the
> >coil will lag the bottom by about 90deg, the current in to the top C will
> >lead the voltage at the top by 90deg, hence no phase shift of current from
> >bottom to top. If the coil is resonating in its times three mode the voltage
> >at the top will lag the bottom by 270deg, hence the current into the top C
> >will lag by 180deg. This can be easily verified.
> I have probed along coils at resonance driven by a signal generator.  One
> has to be sure to use a properly terminated antenna or the capacitance and
> coax loading will mess up the phase of the measurement.  I use a short 50
> ohm antenna (cell phone or scanner type), a length of coax, and a 50ohm
> terminating resistor at the scope end.  Although the amplitude of the
> signal along the secondary definitely rises and falls along the length, the
> phase of that signal stays in phase.

That measurement is extremely important. I have seen no 
measurement like this from any other quarter.

> >Perhaps somebody with a big coil would like to modify it so that the primary
> >operates at approximately three or five time the resonate frequency of the
> >secondary. It should be possible in a darkened room to observe the rings of
> >corona round the secondary coil. Or alternatively the hot end can be
> >connected to the ground plain in which case the frequency need only be
> >approximately doubled. And it would avoid the effect being swamped by corona
> >from the top. You can than take a pic and post it.
> Such and experiment should be possible.  But I don't think it will prove or
> disprove anything.  There are voltage nodes and anti-nodes created but both
> theories support that...

Do they?  I would be interested to hear how a lumped parameter 
argument explains it happening in a structure whose only 
discontinuities are at the ends..

> Many thanks for your thoughtful and interesting comments on all this.
> Personally, I think the lumped parameter theory is rock solid.  If there
> are holes or disagreements, I want to be sure to get them solved.  Nothing
> is worse than to have a great theory with only a few exceptions... :-))
> Cheers,
> 	Terry
> >Regards  Alwyn
> >
> >
> >snip..............