Quarter Wavelength Frequency Discussion
Edited/Updated: October 28, 2004
First Post
Subject: Re: Quarter Wavelength Frequency. Date: Thu, 01 Jul 2004 08:15:29 -0600
Original poster: Harvey Norris
--- Tesla list <tesla-at-pupman-dot-com> wrote:
> Original poster: "Anthony"
>
>hi guys can anybody tell me how to calculate secondary quarter
wavelength resonant frequency not just the >standard resonant frequency
It might serve you well to read the current idiotic thread entitled Tesla Coil
Construction Question...where a guy has the idea that his secondary will resonate in
mega-Hz instead of kHz.
From:
http://groups.yahoo-dot-com/group/teslafy/message/1130
The standard thinking is that for high h/d ratio secondaries, where yours is
45/6= 7.5, the actual resonant frequency for your secondary may be as high as
50% above the quarter wave calculation. So here we make the quarter wave
calculation. You have 1048 turns -at- 6 inch diameter. Each turn is then
1.57 ft, and the wire length then is 1645 ft.
This then is a quarter of the cycle for resonance or we need to find the time
period for 1645 ft * 4 = 6580 ft which equals 1.24 mile. C is 186,000 miles per
second... 1.24 mile/186,000 miles per sec = 6.7 *10^-6 sec the reciprocal
of this value is a cycle in that time period, or about 149,252 hz. Given the
fact that your secondary has this higher h/d ratio, you may wish to start out
with a value 50% higher then the calculation just made, or about 224,000 hz, or
224 Khz. I noticed
you were using the Mhz term, implying mega hz or millions of hz. This should be
incorrect, the frequency wouldn't be that high given the numbers you have shown...
Again to argue against the Mhz thinking of that individual...
http://groups.yahoo-dot-com/group/teslafy/message/1134
Aha, you are employing radio frequency formulas often quoted in Mhz. My Pocket
Reference manual via Thomas J
Glover shows the following formula for RF in Mhz.
LENGTH OF AN ANTENNA
Quarter Wave Antenna:
Freq in Mhz = (984)/wavelength in feet.
Again the wavelength itself is 4 times the actual quarter wave value of the
antenna, or in this case the distance of
your TC secondary length.
1.57 ft/turn * 1048 turns = 1645.36 ft.
Four times that for wavelength figure gives 6581.44 ft.
Applying the formula gives
MGhz freq = 984/6581.44 = .1495 MGhz = 149.5 Khz
Since the advise is to use a value 50% greater then that for starters,(since the
h/d ratio is so high) to find the closer actual resonant freq for the secondary,
this would then be 224 khz, exactly as before made as a prediction.
Historically there has always been a certain amount of criticism on the tesla
list for those asking about the
quarter wave length figure to calculate a secondaries resonance figure, because
typically it doesn't apply
for larger H/d ratio secondaries.
>From
Answer to the quarterwavelength riddle
http://groups.yahoo-dot-com/group/teslafy/message/250
The 1/4 wave resonant frequency of a wire, when wound into a solenoid, is
typically more than 50% higher
than that of the straight line value.
The extraordinary persistence of the wire-length myth comes from the willingness
of people to accept things
on faith without making even the most basic of cross checks. (Paul Nicholson)
See the comments and graph in
http://www.abelian.demon.co.uk/tssp/misc.html
For the idea of a natural resonant frequency of any typical inductor, formulas
may not apply, and even scope measurements may be in question, since every scope
also has its own stated internal capacity, and different scopes with different
internal capacities show those differences. For spirals containing massive
internal capacity, by employing flattened windings with a plastic dielectric
barrier between windings, scopes with differing internal capacity give different
answers, and even the 1x vs 10x probe settings may also give different answers.
For a double set of Mega Cable Radio Shack speaker wire spirals in four layers,
the differences between obtainable readings can vary between 330,000 hz for
ordinary returned winds vs winding routes enhancing internal capacity where then
the same 25 pf internal capacity scope then records 250,000 hz. Those readings
give values about 5 times below what the the calculations employing
quarterwavelength would provide. Thus on the single layered solenoid the
resonant value may be higher then the quarter wave value, and on coils employing
internal capacity, it may be much lower then the
quarter wave value. For a more comprehensive mathematical proof involving how
internal capacity can be enhanced by winding routes in multilayered coils see;
True Meaning of Bifilar/ 2-d Bifilar Calculations,
http://groups.yahoo-dot-com/group/teslafy/message/582
"Thus by this data then the 1-d bifilar has 31% more internal capacity as
measured by these samplings then
does its adjacent layering method, and further then the 2-d bifilar then has
590% more internal capacity
than its 1-d method!" These URL's can be accessed by signing on to yahoo
group at teslafy at
http://groups.yahoo-dot-com/group/teslafy/ .
Sincerely, HDN.
Subject: Re: Quarter Wavelength Frequency. Date: Mon, 05 Jul 2004 11:28:17 -0600
Original poster: Jared E Dwarshuis
Hello my name is Jared Dwarshuis and my friend?s name is Lawrence Morris. We
have been experimenting with wire length resonance (as well as two part resonant
transformer designs). We have found that matching wire length to L.C. is
critical to the operation of our integer wavelength coils.
We use an inductor that is wrapped around a donut or toroidal form, because this
inductor has no ends. It is the closest possible fit to the derivation of the
classic inductor formulae L = uo Nsqrd Area/length. Because we have formed our
inductor from a single loop of wire we have a boundary constraint, this coil can
now only form integer
wavelengths which it does very nicely, at even multiples of the fundamental wire
length frequency.
It may be the case that cylindrical coils can deviate enough from the ideal
inductance formulae to cause discrepancies between wire length and L.C.
resonance, or perhaps current nodes are not exactly where
people think they are, and this has lead people to believe that wire length has
no significance (an understandable mistake).
When we match the L.C. frequency to the wire length frequency we believe that it
minimizes interference between the two distinct resonant energy storing
mechanisms. Clearly L.C. resonance occurs in systems that ignore wire length
(such as the primary inductor), but when the wire length is also considered in
design, the dynamics change. Our experiments indicated that it was
impossible to find a top end capacitor pair that would kill the wire length
resonance entirely, so we are inclined to believe that when your primary is
tuned to the wire length, the wire length resonance will be the dominant energy
storing mechanism.
Check out
http://people.emich.edu/jdwarshui/ to see our articles describing the above
in greater detail. We would be happy to respond to polite inquiries on
these matters. If you are a serious coiler living near Southeastern Michigan or
just a local kid and would like to see the Levi?s configuration in operation,
send us an e-mail jdwarshuis-at-emich.edu.
Subject: Re: Quarter Wavelength Frequency. Date: Mon, 05 Jul 2004 18:12:13 -0600
Original poster: Paul Nicholson
Jared E Dwarshuis wrote:
> When we match the L.C. frequency to the wire length frequency
> we believe that it minimizes interference between the two distinct
resonant energy storing mechanisms.
This isn't very clear - could you say what you mean by 'two distinct resonant
energy storing mechanisms'?
> Clearly L.C. resonance occurs in systems that ignore wire length
> (such as the primary inductor), but when the wire length is also
considered in design, the dynamics change.
We're getting the impression that you're treating 'wire length resonance' and
'LC resonance' as two different physical resonant behaviours, rather than simply
alternative descriptions of the same phenomena.
I looked on your website for comparisons of measured resonant frequency against
the prediction light_speed/wire_length, but could not find anything. We
would not expect the velocity factor 'along the wire' of the toroidal coil to be
unity, which your web site notes seem to take as an assumption.
Or is it that you are *selecting* coils which happen to have unity velocity
factor, in order to achieve some
special effect? Please clarify.
It would be interesting to know what the measured velocity factor is, for each
resonant mode. Absence of end effects simplifies things but there should
still be a fair amount of dispersion.
Please give us details of the mode spectrum of your test coil. It should
not be qualitatively different from a short-
circuited straight solenoid. Paul Nicholson.
Subject: Re: Quarter Wavelength Frequency. Date: Mon, 05 Jul 2004 18:12:45 -0600
In my experience (obviously limited to what I have done) it is apparent that cylindrical coils *do* deviate in the manner described. I have yet to find a single case where they do not and an investigation I conducted at a time when a multitude of wirelength formulae were being touted as being *the formula* to use were, at best, applicable to a very limited set of circumstances (e.g. a particular coil geometry, H/D ratio etc.). Some appeared not to work for any case. (Well they were all different and couldn't possibly have all been correct could they?).
I find it difficult to reconcile the lack of a single example of a helical coil obeying the case you describe as a mistake. I have yet to observe more than one outstanding resonance in a bare helical resonator and that resonance has always been at a frequency considerably above what you would expect if you considered the wavelength of the wire stretched out. Tesla himself repeatedly ran into the conundrum as detailed in the Notes.
One can of course add topload capacitance to make the coil resonate at its
"1/4 wavelength" and I have done that with several coils. I have not observed
any special properties appearing or significant performance gains when this is
done. That is not to say they don't, just that any that do appear don't seem to
make themselves outstandingly apparent. I am more than happy to have my thinking
corrected by a single, demonstrable, repeatable counterexample as I
am always happy to learn more and correct past errors.
Your toroidal coils I would regard as a quite different configuration as you appear to, yes? Malcolm.
Subject: Re: Quarter Wavelength Frequency. Date: Tue, 06 Jul 2004 16:45:46 -0600
Original poster: biomed-at-miseri.winnipeg.mb.ca
See my comments below. These are mostly theoretical from my college days
and other reading related to tesla coils.
Shaun Epp.
>Original poster: Jared E Dwarshuis
>Hello my name is Jared Dwarshuis and my friend?s name is Lawrence
>Morris. We have been experimenting with wire length resonance (as well
>as two part resonant transformer designs). We have found that matching
>wire length to L.C. is critical to the operation of our integer wavelength coils.
Are you talking about the standard 1/4 wave or 1/2 wave (bipolar) tesla coils,
or are you winding them more than that? Tuning a coil past one voltage
maximum (at the end of the solenoid, or both ends for a bipolar) is a waste and
creates corona problems where you don't want them!
>We use an inductor that is wrapped around a donut or toroidal form,
>because this inductor has no ends. It is the closest possible fit to
>the derivation of the classic inductor formulae L = uo Nsqrd Area/
>length. Because we have formed our inductor from a single loop of wire
>we have a boundary constraint, this coil can now only form integer
>wavelengths which it does very nicely, at even multiples of the
fundamental wire length frequency.
>It may be the case that cylindrical coils can deviate enough from the
>ideal inductance formulae to cause discrepancies between wire length
>and L.C. resonance, or perhaps current nodes are not exactly where
>people think they are, and this has lead people to believe that wire
>length has no significance (an understandable mistake).
Wire lengths only affects the number or turns you can put on a form for a given
diameter of the form! Each turn of a solenoid is magnetically linked to
the adjacent turns of the solenoid, hence inductance occurs within the solenoid.
Capacitance occurs between the adjacent turns of the coil because of there
physical proximity and the fact that there is a voltage difference between them.
These two elements, mutual inductance and self capacitance, set the resonant
frequency of the secondary coil, not the wavelength the wire used to wind the
coil. The wavelength formula is for a
straight wire, not looped like in a coil where inductance comes more into play.
Granted there is a small amount of inductance and capacitance on a piece of
straight wire, which doesn't affect the wavelength formula, or maybe this is
where the propagation velocity comes from. Once you loop the wire like a
coil, you have self inductance and interwinding capacitance!
>When we match the L.C. frequency to the wire length frequency we
>believe that it minimizes interference between the two distinct
>resonant energy storing mechanisms. Clearly L.C. resonance occurs in
>systems that ignore wire length (such as the primary inductor), but
>when the wire length is also considered in design, the dynamics change.
>Our experiments indicated that it was impossible to find a top end
>capacitor pair that would kill the wire length resonance entirely, so
>we are inclined to believe that when your primary is tuned to the wire
>length, the wire length resonance will be the dominant energy storing mechanism.
There is always going to be some energy that is coupled into the secondary coil
from the primary coil. You maybe near enough to resonance that you get
appreciable energy transfer, but this has nothing to do with wavelength, just
that you are close enough in frequency to get energy out of the secondary.
Shaun Epp.
Subject: Re: Quarter Wavelength Frequency. Date: Tue, 06 Jul 2004 16:46:17 -0600
Original poster: robert heidlebaugh
Paul: In communications you can use 1/4 wavelength tuned stub or you can use
tuned coils and tapped connections to match the same performance. I have used
1/4 wave stubs coiled to reduce size with good results and no tapped
connections required for impedance matching with ideal SWR. The thought of
trying that in tesla coils could be a interesting study. I guess the physical
size would be more than most of us would try. Robert H.
Subject: Re: Quarter Wavelength Frequency. Date: Fri, 09 Jul 2004 07:34:18 -0600
Original poster: "Malcolm Watts"
On 5 Jul 2004, at 11:28, Tesla list wrote:
One of Tesla's desired goals was to eliminate capacitance from his extra coil
entirely and in the Notes, one can read of the many schemes he dreamt up to try
and achieve this. Eventually, he resigned himself to the fact that nature was
placing limits on his endeavours. Had he been successful, he would have
ended up without a resonator as it would have had no dynamic energy storage
mechanism. Malcolm. <snip>
Subject: Re: Quarter Wavelength Frequency. Date: Fri, 09 Jul 2004 07:35:16 -0600
Original poster: Jared E Dwarshuis
Mr. Nicholson: Yes we believe that an envelope exists between L.C. resonance and
wire length resonance. When we run our full wave devices we can only get them to
work at the wire length frequency (or multiples). Changes in top end capacitance
do not destroy the resonance; it appears to be fixed by the primary L.C. and the
wire length of the secondary.
Observing and understanding are different animals. We suspect that L.C.
resonance requires an interplay of timed events between both the inductor and
the capacitor, where wire length resonance deals with timed events along just
the inductors length itself.
When we ran up the Levi configuration for the first time we got a slow beat
frequency between the two coils (a slow cycling of spark length). We knew
the wire length difference was very small, so we removed wire a bit at a time
from one of the coils and the beat frequency got slower and slower. When
we had removed about a meter of wire, the beat frequency disappeared entirely.
Now, subtracting a wind or two of wire from an inductor with most of a mile of
wire on it is a negligible change in inductance. And, on the surface it
also seems to be a negligible difference in wire length. But this
difference in wire length was enough to eliminate the beat frequency.
Making two wires nearly a mile long to almost exactly the same length is not too
difficult. But, making two toroidal inductors by hand at different
times and of different gauge core material to exactly the same inductance is
very difficult (read impossible). It is not possible that removing two
winds from one of the coils would match the inductance that closely.
Yes the velocity appears to be very close to, if not exactly, the speed of
light. How close? couldn?t say. We have to base our conclusions mainly on
observations and calculations. Our instruments are only good for two digits, so
we have to look at a body of evidence to draw conclusions. Naturally, all of our
work needs confirmation, re-examination and possible re-working by people with
different skill sets and interpretations than our own.
Mr. Watts I believe my choice of wording may have offended, and I apologize. And
add that we both have an enormous respect for the small minority of coilers (
maybe a dozen or two active theoretical experimenters ) such as yourself who
have shown a keen interest in understanding and developing theory.
I believe you were referring indirectly to our ideal resonance formulae, There's
not much to this formulae, it is merely an extension of already existing
formulae to a general case. ( a convenient accounting tool) It is
Ideal in the same sense that the classic inductance formulae was ideal, it
assumes a uniform magnetic field throughout. Our formula also pre supposes that
periodicity occurs at quarter wave intervals, that inductance for purposes of
establishing
resonance can be found within these intervals. This formulae specifically states
that it is only applicable to wire length
resonators.
We use Wheelers formula for all of our primaries, for short inductors it
cannot be beat, but when we go to make a secondary we use the altered classic
form for inductance. The two formulae differ significantly in the values they
predict, but they are both correct for the applications intended.
Mr. Epp: Suppose we make a hypothetical secondary with 1000 turns of 22
gauge around an 8 inch diameter pipe, Medhurst predicts about 11.7 Pf.
Wheelers formula gives .523 Henry while the classic inductance formula gives
.594 Henry, then the self resonant frequency of this coil would be between
240,000 and 260,000 Hz But the predicted quarter wave wire length frequency is
only 118,000 Hz. The coil operating at 118,000 Hz will have much larger
amplitudes
and be easier to tune.
As to the differences between a quarter wave, a half wave, and a full wave. To
simplify I will only consider the case where they are all wire length dependent.
So I make the coil described above and resonate it at 118,000 Hz. After a
while, I get bored and decide I want to make a half wave. Here is what to
do: make an extra coil exactly the same, remove the old ground and solder the
two coils together. Slap the same primary on as before, centering it between the
two coils. Remove the top end capacitor and replace it with a capacitor that has
? of the capacitance and stick another ? capacitor on the other end of the coil.
Now you have a half wave, but you can run it with one breakout or two. It
looks like a quarter wave with just one breakout as the entire arc will appear
on the end with the breaker (assuming your radius is large enough to suppress an
arc without a breakout). If you put the caps close together you get a nice
clean arc between them. Now mind you we could also make a grounded half wave,
but there would be no advantage.
So I get bored again and I want a ? wave; no problem.
Make another coil, stack it on top, put the quarter wave capacitor back on top.
Put the primary on the bottom and ground it like a quarter wave.
This time I want a full wave. We have some choice here. We could place 4
inductors in line and ground both ends then place the ? capacitors at the ? and
? points. We could also assemble a pair of ? waves, described above, and
drive just one of the pair and get a capacitor coupled anti- symmetric mode
arrangement (Marsha configuration). We
can arrange one breakout or two between the coils. Amazingly, we can even
take two Saskia coils, power just one of the coils, place just one ? capacitor
on each coil and we will have satisfied the capacitance requirements (Levi
configuration). But you can see this is very much like 8 quarter waves ( two
sets of 4 quarter waves driven anti-
symmetric), where we drive just one pair and the rest go along for the ride.
The role of Medhurst is not a cumulative one. We calculated it, once and
only once, for a quarter-wave section, as it also follows the trends of
periodicity.
All of this is like rope resonance. Once you find the driving frequency
and tension to get one anti-node (the bump part) you can simply add more
sections of the same length rope and get more anti-nodes. You don?t change
the frequency, and you don?t change the tension. ( see our
derivation of correspondence)
Good luck and don?t get hurt.
Subject: Re: Quarter Wavelength Frequency. Date: Fri, 09 Jul 2004 07:35:57 -0600
Original poster: "Bob \(R.A.\) Jones" Hi Shaun ----- Original Message ----- Sent: Tuesday, July 06, 2004 3:45 PM Subject: Re: Quarter Wavelength Frequency > Original poster: biomed-at-miseri.winnipeg.mb.ca > >> >length has no significance (an understandable mistake). > > Wire lengths only affects the number or turns you can put on a form for a > given diameter of the form! Each turn of a selenoid is magnetically linked > to the adjacent turns of the selenoid, hence inductance occurs within the > selenoid. Capacitance occurs between the adjacent turns of the coil > because of there physical proximity and the fact that there is a voltage > difference between them. These two elements, mutual inductance and self > capacitance, set the resonant frequency of the secondary coil, not the > wavelength the wire used to wind the coil. The wavelength formula is for a > straight wire, not looped like in a coil where inductance comes more into > play. Granted there is a small amount of inductance and capacitance on a > piece of straight wire, which doesn't affect the wavelength formula, or > maybe this is where the propagation velocity comes from. Once you loop the > wire like a coil, you have self inductance and interwinding capacitance! of the secondary. Shaun Epp. > Yes it is the self C and L that determine the prop velocity of an open wire. Given the the fact that the self inductance and capacitance are of a solenoid are 100s of time different from an open length of it's wire never the less they change in such a way that the length of the wire in a solenoid is very approximately (say with in times two for typical coils) equal to the a 1/4 wave length in free space of the coil's first resonant frequency. Incidentally, the adjacent turn to turn C does not contribute significantly to the self C of coil. Its mostly the C to ground and the C between the top and bottom of the coil particularly so in isolated coils. Check out Paul's TCSP site for details. Bob Jones.
Subject: RE: Quarter Wavelength Frequency. Date: Sat, 10 Jul 2004 11:18:33 -0600
Original poster: "David Thomson"
Original poster: "Malcolm Watts"
On 5 Jul 2004, at 11:28, Tesla list wrote:
> One of Tesla's desired goals was to eliminate capacitance from his
extra coil entirely and in the Notes, one can read of the many
schemes he dreamt up to try and achieve this. Eventually, he resigned
himself to the fact that nature was placing limits on his endeavours.
Had he been successful, he would have ended up without a resonator as
it would have had no dynamic energy storage mechanism.
Hi Malcolm,
Tesla was only trying to dispense with a physical capacitor, not
capacitance. He developed his "coil for electromagnets" hoping to get the
coil to act as both inductor and capacitor.
Capacitors were not as electrically tight in Tesla's day and were cumbersome
to produce. By eliminating the capacitor he would have made the coil, as
well as coil production, more efficient. And we all know how much
efficiency meant to Tesla.
Dave.
Subject: Re: Quarter Wavelength Frequency. Date: Fri, 09 Jul 2004 17:03:20 -0600
Original poster: "Jim Lux"
> One of Tesla's desired goals was to eliminate capacitance from his
> extra coil entirely and in the Notes, one can read of the many
> schemes he dreamt up to try and achieve this. Eventually, he resigned
> himself to the fact that nature was placing limits on his endeavours.
> Had he been successful, he would have ended up without a resonator as
> it would have had no dynamic energy storage mechanism. Malcolm
> <snip>
wouldn't that be "half a dynamic storage mechanism"... the inductance can store
energy as current, but without a capacitor to store energy as charge, it
wouldn't be much of a resonator.
Subject: Re: Quarter Wavelength Frequency. Date: Sat, 10 Jul 2004 21:51:08 -0600
Original poster: Paul Nicholson
Jared E Dwarshuis wrote:
> we believe that an envelope exists between L.C. resonance and wire length resonance.
This seems to be where you're going wrong in your
interpretation of your coil's behaviour. LC resonance
and 'wire length' resonance are two equivalent
descriptions of the coil's resonant modes, and should
not be thought of as two different modes of resonance
capable of being excited simultaneously in order to
produce beating or interference.
A common factor in the two descriptions is the distributed
inductance and distributed capacitance of the wire. To
proceed in one direction, you integrate these to produce
overall equivalent 'lumped' L and C values for use in the
'LC resonance' model. Going the other way, you proceed to
derive a propagation velocity for the coil (from 1/sqrt(LC)
where L and C are the per-unit-length values), and so
deduce the 'wire resonance' modes. They are of course the
same set of physical resonant modes in both descriptions.
The distributed L and C of the wire depends strongly on
how the wire is arranged with respect to itself and
surroundings. Both alter in a more or less complicated
way when the straight wire is wound into a coil. Therefore
you cannot draw upon the reactances (and the corresponding
resonances) of the original straight wire when interpreting
behaviour of the wound structure, since the original straight-wire distributed reactances were completely lost when the coil
was wound.
During winding, the self inductance of a wire element is
greatly increased by the presence of the neighbouring
turns being brought up against it. At the same time, the
self capacitance of the wire element is greatly reduced,
because it is now partially shielded by the adjacent conductors
being at almost the same potential. These two changes occur in
approximately the same ratio, give or take a factor of 2 or so,
resulting in the velocity 1/sqrt(LC) usually being within a factor
of two each way of light speed.
Now the claim that 'wire length' resonance and 'LC resonance'
are occurring simultaneously as physically distinct resonant modes
requires the coil to resonate with its wound resonance, while at
the same time somehow 'remembering' the reactive properties that
the wire once had when straight and resonating in accordance with
those too. If this were the case, it would be possible to observe
the mode spectrum of a coil to be the union of the free-space straight-line original wire mode spectrum, plus the normal spectrum of wound
'LC' resonances.
This is never seen, instead we always see a single mode spectrum
whose mode frequencies can be related (equally correctly) via an
LC model or via a wire resonance model, back to the distributed
reactances of the wound wire.
A typical straight solenoid has a fundamental resonant frequency
a little higher than that which the straight wire used to have.
Using the example offered to Shawn,
> Suppose we make a hypothetical secondary with 1000 turns of
> 22 gauge around an 8 inch diameter pipe, Medhurst predicts about
> 11.7 Pf. Wheelers formula gives .523 Henry while the classic
> inductance formula gives .594 Henry, then the self resonant
> frequency of this coil would be between 240,000 and 260,000 Hz
> But the predicted quarter wave wire length frequency is only 118,000 Hz.
Indeed so (*). Now to be satisfied that only the 200kHz resonance
is present, it is merely necessary to sweep the coil with a
signal generator to see that there is no mode lower than this, and
in particular there will be no change in the coil's dynamics as
you sweep through the frequency that the wire used to resonate at
before it was wound.
(*) For this coil, assuming 28" wound length and mounted 4"
above a ground plane, base grounded, I get 198kHz for the 1/4 wave,
50.8mH for DC inductance, 41.7mH for the lumped equivalent
inductance of the 1/4 wave resonance, 15.5pF for the corresponding
effective lumped capacitance, and irrelevantly, the Medhurst
capacitance would be 12.7pF.
> The coil operating at 118,000 Hz will have much larger amplitudes and be easier to tune.
We're supposing here that you mean pulling the 200kHz resonance
down to 118kHz by end loading with topload capacitance. But there
is no evidence that any special behaviour occurs when this
is done. We know that to do so results in a satisfactory
proportion of stored charge in the topload of the TC, but there is
no reason either experimental or theoretical, to suppose that
the original straight line wire length resonance is the optimal
target to aim for. If you were to study the dynamics of this
hypothetical coil in the region between DC and the resonant
frequency of 198kHz, you would not be able to find any measurement
which does not vary smoothly and indifferently as you pass
through the frequency corresponding to the resonance of the
original straight wire. Likewise if you top-load the resonance
down to lower and lower frequencies - again you will not see
any measurement reach any sort of a peak or optimum as you
load down through the frequency of the original wire resonance.
> When we run our full wave devices we can only get them to work at the wire length frequency (or multiples).
Perhaps so. It is quite feasible that winding into a toroidal
coil just happens to leave a unity velocity factor.
Or do you mean that the coils won't perform unless you apply
additional reactance in order to pull the natural resonant
frequency of the toroidal coil down to or up to the frequency
that its wire used to have before it was wound?
> Changes in top end capacitance do not destroy the resonance;
You mention top-end capacitance, so you have, it seems, added loading.
> ...it appears to be fixed by the primary L.C. and the wire length of the secondary.
Ok, that's fine. It might suggest the resonant modes you are exciting
are not strongly coupled to the top capacitance, i.e., the top-C is
perhaps near a voltage node? Without data we can only do futile
speculation.
> When we ran up the Levi configuration for the first time we got
> a slow beat frequency between the two coils (a slow cycling of spark length).
You must look for a more realistic explanation for this beating, one
which doesn't require radically new physics. I took a look at
the web page
http://people.emich.edu/jdwarshui/groundless.html
which gives a few hints as to what you're doing, but it doesn't give
anything like enough info to go on. Referring to the arrangement
which produced the beats, a circuit diagram would be helpful, and
some indication of how you are driving the coil. It is difficult
to draw any conclusions from the info given so far.
> Yes the velocity appears to be very close to, if not exactly, the speed of light. How close? couldn?t say. We have to
>base our conclusions mainly on observations and calculations.
If so, then you will have measured the wire length, and measured the
resonance frequencies, and then simply calculated velocity (along the wire) = wire_length * resonance_freq.
for the full wave resonance, etc.
The coil configurations that you're working with look to be quite
interesting and complicated and will be difficult to study. The
fact that you're using three coils, at least two of which appear
to be floating, and two of which may be capacitively as
well as inductively coupled, makes things trickier still.
The whole system should be measured and studied carefully before
coming to any conclusions about which resonant modes are being
excited to produce the observed spark behaviour. The explanations
given to us at present seem to be rather vague and partly
based on a familiar myth. Plus they are not supported by any
measurements, circuit diagrams and dimensions, and so on, which
leaves us, temporarily I hope, unable to offer more reasonable
alternatives.
I think we would like to see first some basic studies of the
toroidal coil resonances themselves, i.e., for each coil in isolation
we would want to see what its mode spectrum was: the resonant
frequencies, and for each resonance the locations of voltage and
current nodes. This in itself would be quite a challenge, because
the spectrum and the node locations will be sensitive to symmetry
and balance of the toroid with respect to ground, and so on.
You might be able to observe mode splitting due to asymmetry,
etc. And you might even be able to obtain a slowly rotating
pattern of nodes by careful excitation of one of these coils
at two frequencies.
Let me thoroughly recommend studying to death just one of these
toroidal coils before even considering exploring its coupling to
other coils. If this is not done, then when you observe
interesting behaviour of the coupled system, you will have
no firm basis upon which to offer more than speculative
explanations. I'm sure many list members would, like me, be
interested in a close look at this type of coil.
Paul Nicholson.
Subject: Re: Quarter Wavelength Frequency. Date: Sat, 10 Jul 2004 21:53:29 -0600
Original poster: "Gerry Reynolds"
Hi Jared,
I've been following this thread with much interest. There are a lot of
experience folks on this list that have said that 1/4 wave resonance does
not come into play and the resonance is determined by the effective LC
parameters of the coil (or coil and top load combo). L being a little
strange here because the current profile is not linear. One argument that
I've heard often is that the individual turns of the coil are mutually
coupled to each other and thus a field couples other turns directly and
sorta bypasses the conduction path following the wire (if I may over-simplify this).
There have been other discussions about being out of tune and resulting in
voltage gradients that have caused racing arcs in portions of the coil. To
me this has some sort of wave action feel to it, not totally unlike voltage
rises in a transmission line that is not properly terminated.
If I understand what you have said, would it be the case that if one excited
a coil (assume no top load) at the base to find its resonances, one would
find two resonances - one determined by the wire length and the other
determined by the effective LC parameters of the coil? If this is true
would the same be the case with a typical topload present? Gerry R.
Subject: Re: Quarter Wavelength Frequency. Date: Sat, 10 Jul 2004 21:54:03 -0600
Original poster: Ed Phillips
> One of Tesla's desired goals was to eliminate capacitance from his
extra coil entirely and in the Notes, one can read of the many
schemes he dreamt up to try and achieve this. Eventually, he resigned
himself to the fact that nature was placing limits on his endeavours.
Had he been successful, he would have ended up without a resonator as
it would have had no dynamic energy storage mechanism.
Hi Malcolm,
Tesla was only trying to dispense with a physical capacitor, not capacitance.
He developed his "coil for electromagnets" hoping to get the coil to act as both
inductor and capacitor.
Capacitors were not as electrically tight in Tesla's day and were cumbersome to
produce. By eliminating the capacitor he would have made the coil, as well
as coil production, more efficient. And we all know how much
efficiency meant to Tesla. Dave.
"Apparently he didn't appreciate the effect of dielectric loss in his multilayer
coils. Ed.
Subject: Re: Quarter Wavelength Frequency. Date: Sat, 10 Jul 2004 22:11:25 -0600
Original poster: Terry Fritz
Hi,
To make a very long story short....
Consider how long it takes for current at the base of a coil to reach to top of
the coil...
If it travels the length of the wire (say 1000 feet) then the wire "length idea"
holds.
But here is the catch that changes everything!!!
The coil's turns are all magnetically linked to each other!!
So the current at the top of the coil does not have to wait for the electrons to
travel the length of the wire, but only the length of the coil!! The
effects of primary base current are magnetically linked to the top of the coil
through a distance of only say 3 feet... The coil is not a 1000 foot long
antenna. It is a close wound inductor with the all the turns closely
magnetically linked....
That simply is the "killer" the of wire length/quarter wave stuff...
Listen to Paul here!!! He has studied this stuff to extreme detail!!!!
http://www.abelian.demon.co.uk/tssp/.
Cheers, Terry.
Subject: Re: Quarter Wavelength Frequency. Date: Sat, 10 Jul 2004 22:34:59 -0600
Original poster: Terry Fritz
Tesla was using salt water caps....
His spark gaps and capacitors were chewing up an enormous amount of his
system's power.
Dielectrics losses in his coil forms and such was far down on his list ;-)))
With the discovery of polypropylene in 1951 by Paul Hogan and Robert Banks
of Phillips Petroleum, capacitor losses got low enough for Tesla coils :-)))
The first practical use of poly was wasted on hula hoops ;-)))
http://inventors.about-dot-com/library/inventors/blhogan.htm
Wham-O is the most successful manufacturer of hula hoops in modern times
and the company that trademarked the name Hula Hoop® and start
manufacturing the toy out of Marlex in 1958. Twenty million Wham-O hula
hoops sold for $1.98 in the first six months.
(<http://inventors.about-dot-com/library/inventors/blhogan.htm>Marlex®
is the
tradename for crystalline polypropylene and high-density polyethylene
(HDPE) plastics invented by research chemists Paul Hogan and Robert Banks
of Phillips Petroleum.)
Knerr and Melin began working in a LA garage in 1948 to market a slingshot
that they had originally invented to hurl meat into the air while training
pet falcons and hawks. It was called "Wham-O" because of the sound it made
when it hit the target. It became the name of their company.
http://inventors.about-dot-com/library/inventors/blhulahoop.htm.
:-)))))))).
Cheers, Terry.
Subject: RE: Quarter Wavelength Frequency. Date: Sun, 11 Jul 2004 17:28:43 -0600
Original poster: "David Thomson"
Hi Terry,
You raise an excellent point concerning the magnetic transfer of current through
a coil. So are you saying the current is flowing through the coil as both
electrons AND photons, with the electrons flowing the length of the wire and the
photons flowing the length of the coil?
If this is the case, how do we quantify the split traffic? Are there
equations we can use to determine how much work is being performed by the
electrons and how much is being performed by the photons?
Is there a certain ratio of traffic along each route that is better than other
ratios?
It would appear that a coil is then quantified simultaneously as a radio
frequency and as an AC current, with different quantities of work being
performed by each. The total work would be the total work of the AC plus
the total work of the RF.
Dave.
Date : Wed, 14 Jul 2004 17:29:35 -0600, Subject : Re: Quarter Wavelength Frequency
Gerry wrote:
> There is only one fundamental resonance.
Yes, the currents and the fields are locked together in a manner described by
the Maxwell/Lorentz equations. Given the current and charge distributions you
can calculate the field, and vice versa, so there is no room to independently
vary one without the other following suit.
The helical conductor imposes boundary conditions on the field which lead to a
spectrum of resonances in much the same way as the walls of a chamber impose
boundary conditions on the air within to produce a set of acoustic resonances.
Each resonance can be described in terms of the motion of the field or the
motion of the charges - the two descriptions are equivalent and
interchangeable. From the point of view of the charges, the presence and motion
of charge in one part of the winding affects the motion of charges elsewhere in
the conductor, and the set of 'mechanical' constraints thus imposed forces the
system to obey a differential equation in the charges
and currents. Alternatively, we can set up a differential equation in the
field variables by combining Maxwell's equations with the constraints imposed by
the wire. The two equations lead to the same solutions because they describe
the same set of resonances in equivalent terms.
We can (when certain conditions are satisfied) express the remote coupling
between charges through the 'mechanism' of the field by means of the
abstractions of capacitance and inductance - concepts which neatly encapsulate
all the relevant Maxwellian detail of the remote interactions between the
charges along the wires. This saves us a great deal of work - we can operate
with 1-dimensional arrays of 2-component quantities (current and charge) rather
than 3D volumes or 2D surfaces of 3-component field vectors.
But we mustn't forget that these 'circuit theory' models are no more than a way
to represent the behaviour of the EM field in terms of the behaviour of the
associated charge movements. If we forget this, we might find ourselves
suggesting that the currents can do things independently of the fields.
When we come to apply circuit theory to TC's, we calculate the mutual
capacitance between any two points x and y on the coil. In fact we do that for
*every* possible pair of points x and y. Then we do a similar thing to get the
mutual inductance between every pair of points on the coil. These two 'mutual
reactance distribution functions' tell us all we need to know about how the
charges throughout the coil affect one another. They go into a straightforward
but tedious calculation out of which pops all the resonances, charge and current
distributions, impedances, and so on. Then if we want to know what the the
field is doing, we just calculate that from the currents and charges. Paul
Nicholson.
Date : Mon, 19 Jul 2004 08:03:37 -0600. Subject : Re: Resonance _s_ Re: Quarter Wavelength Frequency
Original poster: Paul Nicholson
I thought I'd just write a few lines to try to clarify some of the notions about
resonance which are in circulation.
Someone wrote:
> Wind the wire up and the stray capacitance and others effects
> will change the fundamental, the harmonics and add a few nearby ones.
No new resonances are added in the winding up process.
> Add a capacitance top hat and another set is _added_.
The existing resonances are shifted a bit, but no new ones are added. Putting
on top capacitance lowers the frequency of each mode by a factor in some inverse
proportion to the number of quarter waves in the resonance. This means the
lowest mode suffers the most reduction, and if the added top capacitance is
large compared to the coil's own capacitance, then this fundamental mode is
pulled down much lower than the first or higher overtones, to the extent that it
can be treated as the only resonance for many practical purposes.
In this regime of the heavily end-loaded quarter wave, the coil current is
almost the same at both terminals, and most of the capacitive reactance is
gathered into one lump. The circuit then behaves most closely to the idealized
abstractions of the 'lumped LC model'. But the idealized model only has one
degree of freedom, ie it can only represent one resonant mode (per LC
pair). The real resonator betrays its physical nature by exhibiting a spectrum
of overtones.
It is perhaps because under these conditions the fundamental mode is pulled down
so much lower than the lowest of the overtones, that many treat it,
unjustifiably, as a physically different type of resonance (sometimes even to
the extent, it seems, of suggesting it can exist simultaneously with the
original unloaded resonance).
A familiar example is the TC primary, which fits into this 'heavily end loaded'
class of resonator. Without the primary
capacitor (ie with the gap open) a typical spiral primary inductor will have its
fundamental (1/4 wave) mode at perhaps a Mhz or so, along with the usual
spectrum of overtones (at distinctly non-integer multiples of the
fundamental). This spectrum is set by the distribution of the primary coil's
inductance and capacitance, (or equivalently, by the velocity factor along the
wire!). When we close the gap, the primary capacitance now takes part in the
resonance, and pulls all the coil mode frequencies down some. (In particular we
hope it pulls the primary quarter wave down to the operating frequency we
want.) The primary capacitor is perhaps around 100 times the size of the
primary coil's self-capacitance,
and so the primary resonator fundamental frequency with the gap closed will be a
tenth that of the unloaded primary, ie it has been pulled down by 90%, say. The
first overtone of the primary (the 3/4 wave) might end up only about 30% lower
than it was when unloaded. The next higher (5/4 wave) may be 10% lower, and so
on.
When the primary resonator is fired, the overtones are excited, not just the
fundamental. An example of this can be seen in
http://www.abelian.demon.co.uk/tssp/md110701/
which show secondary base currents from Marco's Thor system. These show
evidence of the primary overtones appearing in the secondary base current. (The
extent to which primary overtone energy might contribute to onset of racing arcs
is unknown, and would be a good research topic.)
But this illustrates that although we tend to treat primary resonators as 'LC
resonators', what we really mean is that we
can easily model them as an 'ideal LC resonator' with good enough accuracy at
the operating frequency. It doesn't imply that the primary is resonating in any
essentially different way when end loaded, than it was when unloaded.
If any coilers remain unconvinced by this snippet of EE theory, then take any
resonator and sweep it with a signal generator up to a few Mhz and make a note
of first 3 or 4 or so resonances. Then add a little end capacitance and
take another sweep. Keep on doing this until you have enough end capacitance
for you to be happy to call it a lumped resonator. When you plot the resonant
frequencies, you'll see how they're all pulled down in the manner
described. You'll be convinced by this procedure that 'Lumped LC' is just a
model set up to represent the lowest mode of the resonator's spectrum.
Someone wrote:
> A lumped L-C circuit will have only one resonance.
and a reply was:
> An ideal one, perhaps...
> A real one will have another where the coil resonates with self C.
The real one will have lots of resonances (lets try never to call them
harmonics). All the resonances (ie fundamental and all the overtones) involve
both the self C and any end-loading C that is present.
The 'lumped LC model' models only a single resonance (per LC section). The
'lumped LC circuit' doesn't exist in nature, only on paper. But many resonant
circuits look sufficiently lumped (by the means described above, for example)
that they can be easily represented with sufficient accuracy by an LC *model*.
Those resonators which are not so physically lumpy can still be represented by
an LC model - we just have to be careful to calculate the correct equivalent L
and C values.
I've tried to draw a distinction between the 'lumped LC model' which is a
mathematical thing, and what you might call a 'lumped-looking resonator' which
is a real circuit with a spectrum of modes. Failure to appreciate this used to
lead to long debates where individuals argued that a certain resonator is a
lumped or a distributed resonator. One enthusiast would try to settle the
matter with phase measurements. Another would suggest that you modify your coil
to operate in 'distributed mode' rather than 'lumped' mode in order to achieve
some remarkable but non-existent
effect. But this was all futile and a bit silly, because the choice between
'lumped' and 'distributed' is a free choice of which *model* you care to apply
to the resonator, rather than a switch between two different physical modes of
vibration. Real resonators always have many resonances, even the most lumped
looking ones.
I'll post a little more on this topic later. Paul Nicholson.
Date : Mon, 19 Jul 2004 08:03:59 -0600, Subject : Re: Quarter Wavelength Frequency
Ed wrote:
> As L/D gets large the ratio goes to 1/2, just what one would expect with a
straight wire.
The fact that it tends to such a round number with mathematical precision
suggests that the figures you give are simply revealing some mathematical
relationship inherent in the equations you are tabulating.
For us to say more, you would have to describe the steps in the calculation, and
in particular how you are determining lambda. Paul Nicholson Manchester,
UK.
Date : Mon, 19 Jul 2004 16:30:47 -0600. Subject : Re: Resonance _s_ Re: Quarter Wavelength Frequency
Original poster: Mddeming@aol.com
Hi Paul,
Very clear and concise explanation. It should enlighten all, and settle the
matter for all but the most die-hard "True Believers" who, when faced with a
conflict, will reject any science in favor of The Faith. Your insightful
explanations are greatly appreciated by many. Matt D.
In a message dated 7/19/04 10:11:23 AM Eastern Daylight Time,
Original poster: Paul Nicholson
I thought I'd just write a few lines to try to clarify some of the notions about
resonance which are in circulation.
Someone wrote:
> Wind the wire up and the stray capacitance and others effects
> will change the fundamental, the harmonics and add a few nearby ones.
No new resonances are added in the winding up process.
> Add a capacitance top hat and another set is _added_.
The existing resonances are shifted a bit, but no new ones are added. Putting
on top capacitance lowers the frequency of each mode by a factor in some inverse
proportion to the number of quarter waves in the resonance. This means the
lowest mode suffers the most reduction, and if the added top capacitance is
large compared to the coil's own capacitance, then this fundamental mode is
pulled down much lower than the first or higher overtones, to the extent that it
can be treated as the only resonance for many practical purposes.
In this regime of the heavily end-loaded quarter wave, the coil current is
almost the same at both terminals, and most of the capacitive reactance is
gathered into one lump. The circuit then behaves most closely to the idealized
abstractions of the 'lumped LC model'. But the idealized model only has one
degree of freedom, i.e., it can only represent one resonant mode (per LC
pair). The real resonator betrays its physical nature by exhibiting a spectrum
of overtones.
It is perhaps because under these conditions the fundamental mode is pulled down
so much lower than the lowest of the overtones, that many treat it,
unjustifiably, as a physically different type of resonance (sometimes even to
the extent, it seems, of suggesting it can exist simultaneously with the
original unloaded resonance).
A familiar example is the TC primary, which fits into this 'heavily end loaded'
class of resonator. Without the primary
capacitor (i.e. with the gap open) a typical spiral primary inductor will have
its fundamental (1/4 wave) mode at perhaps a MHz or so, along with the usual
spectrum of overtones (at distinctly non-integer multiples of the
fundamental). This spectrum is set by the distribution of the primary coil's
inductance and capacitance, (or equivalently, by the velocity factor along the
wire!). When we close the gap, the primary capacitance now takes part in
the resonance, and pulls all the coil mode frequencies down some. (In
particular we hope it pulls the primary quarter wave down to the operating
frequency we want.) The primary capacitor is perhaps around 100 times the size
of the primary coil's self-capacitance, and so the primary resonator fundamental
frequency with the gap closed will be a tenth that of the unloaded primary, ie
it has been pulled down by 90%, say. The first overtone of the primary
(the 3/4 wave) might end up only about 30% lower than it was when unloaded. The
next higher (5/4 wave) may be 10% lower, and so on.
When the primary resonator is fired, the overtones are excited, not just the
fundamental. An example of this can be seen in
http://www.abelian.demon.co.uk/tssp/md110701/
which show secondary base currents from Marco's Thor system. These show
evidence of the primary overtones appearing in the secondary base current. (The
extent to which primary overtone energy might contribute to onset of racing arcs
is unknown, and would be a good research topic.)
But this illustrates that although we tend to treat primary resonators as 'LC
resonators', what we really mean is that we
can easily model them as an 'ideal LC resonator' with good enough accuracy at
the operating frequency. It doesn't imply that the primary is resonating in any
essentially different way when end loaded, than it was when unloaded.
If any coilers remain unconvinced by this snippet of EE theory, then take any
resonator and sweep it with a signal generator up to a few MHz and make a note
of first 3 or 4 or so resonances. Then add a little end capacitance and
take another sweep. Keep on doing this until you have enough end capacitance
for you to be happy to call it a lumped resonator. When you plot the resonant
frequencies, you'll see how they're all pulled down in the manner
described. You'll be convinced by this procedure that 'Lumped LC' is just a
model set up to represent the lowest mode of the resonator's spectrum.
Someone wrote:
> A lumped L-C circuit will have only one resonance.
and a reply was:
> An ideal one, perhaps...
> A real one will have another where the coil resonates with self C.
The real one will have lots of resonances (lets try never to call them
harmonics). All the resonances (ie fundamental and all the overtones) involve
both the self C and any end-loading C that is present.
The 'lumped LC model' models only a single resonance (per LC section). The
'lumped LC circuit' doesn't exist in nature, only on paper. But many resonant
circuits look sufficiently lumped (by the means described above, for example)
that they can be easily represented with sufficient accuracy by an LC *model*.
Those resonators which are not so physically lumpy can still be represented by
an LC model - we just have to be careful to calculate the correct equivalent L
and C values.
I've tried to draw a distinction between the 'lumped LC model' which is a
mathematical thing, and what you might call a 'lumped-looking resonator' which
is a real circuit with a spectrum of modes. Failure to appreciate this used to
lead to long debates where individuals argued that a certain resonator is a
lumped or a distributed resonator. One enthusiast would try to settle the
matter with phase measurements. Another would suggest that you modify your coil
to operate in 'distributed mode' rather than 'lumped' mode in order to achieve
some remarkable but non-existent
effect. But this was all futile and a bit silly, because the choice between
'lumped' and 'distributed' is a free choice of which *model* you care to apply
to the resonator, rather than a switch between two different physical modes of
vibration. Real resonators always have many resonances, even the most lumped
looking ones.
I'll post a little more on this topic later. Paul Nicholson.
Date : Mon, 19 Jul 2004 18:38:28 -0600. Subject : Re: Resonance _s_ Re: Quarter Wavelength Frequency
Original poster: Ed Phillips
" Real resonators
always have many resonances, even the most lumped looking ones.
I'll post a little more on this topic later.
--
Paul Nicholson
I agree with your use of "higher-order resonances" rather than "harmonic
resonances", and I guess the term "most lumped looking ones" is pretty
descriptive too. I question how many of those harmonic resonances would be
observed at the input terminals of a long coil with any significant parallel
tuning capacitance.
I'll have to think more on where there is a (single?) factor to describe the
frequencies of the higher-order resonances, as your statement seems to
say. Certainly the response will get less and less as the number goes up.
Ed.
Date : Mon, 19 Jul 2004 18:39:44 -0600, Subject : Re: Quarter Wavelength Frequency
Ed Wrote:
>As L/D gets large the ratio goes to 1/2, just what one would expect with a
straight wire.
>
> The fact that it tends to such a round number with mathematical precision
suggests that the figures you give are simply revealing some mathematical
relationship inherent in the equations you are tabulating.
>
> For us to say more, you would have to describe the steps in the calculation,
and in particular how you are determining lambda. Paul Nicholson
Manchester, UK.
> --
Answer to last question first; it's a very simple program. For lambda I use
c/Fr, where Fr is the self-resonant frequency calculated using Lundin's
approximate expression for inductance and a power series approximation to
Medhurst's data as given in an old handbook I have. In other words, the program
calculates L, calculates (estimates?) C, and computes the parallel resonant
frequency of the combination. I'm sure the accuracy of the calculations doesn't
justify three significant figures or maybe even two!!!!! However, I have made
the calculation for several different coils and compared the calculated
frequencies and was quite surprised to find agreement within a couple of
percent. I attempt to measure Fr by feeding the bottom of a coil, isolated as
far as possible from nearby objects, with a low-impedance source and observing
the "top voltage" with a small plate remotely located and again "as far as
possible" from the coil. Crude but works OK. Of course, it should
also be possible to observe the voltage at generator port and looking for the
frequency giving a dip, but that seemed a little artificial to me. The signal
generator I'm using is a standard "Hewlett Packard" circuit, since it's the only
one I have putting out significant voltage in the region above 100 kHz. It
doesn't go high enough in frequency to observe any overtone responses. Ed.
Date : Mon, 19 Jul 2004 18:39:56 -0600, Subject : Re: Quarter Wavelength Frequency
> Ed wrote:
> > As L/D gets large the ratio goes to 1/2, just what one would expect with a straight wire.
>
> The fact that it tends to such a round number with mathematical
> precision suggests that the figures you give are simply
> revealing some mathematical relationship inherent in the equations you are tabulating.
>
> For us to say more, you would have to describe the steps in
> the calculation, and in particular how you are determining lambda.
> --
> Paul Nicholson Manchester, UK.
Forgot to say that "the mathematical precision" was used with tongue in cheek to
say the least and I agree that the value quoted does "simply reveal some
mathematical relation". Two figure accuracy maybe, under the
right conditions. Ed.
Date : Mon, 19 Jul 2004 18:40:10 -0600, Subject : Re: Quarter Wavelength Frequency
"Hi Ed, Is L/D like H/D or is L the length of the coiled wire uncoiled and
straightened out? Is D is the diameter of the coil? Could you define the
geometry for lambda (I believe it is the wavelength but not sure if it is the
wavelength of the coiled wire or the straightened out wire)? Gerry R.
Should have explained that. L is the length of the coil and D is the mean
diameter, including wire diameter. As I noted in another message, I calculated
the ratio of the wire length wavelength corresponding to the parallel resonant
frequency. Two many lengths mixed up in one statement. Hope this is
clear. This is a simple program running in Quick Basic, originally developed on
a Mac. I have a PC version I could send to you if you're interested - it's only
a few lines. Ed.
Date : Mon, 19 Jul 2004 21:04:57 -0600, Subject : Re: Quarter Wavelength Frequency
Original poster: "Antonio Carlos M. de Queiroz"
Tesla list wrote:
>
> Original poster: Ed Phillips
>...
> I attempt to measure Fr by feeding the bottom of a coil, isolated as far as
possible from nearby objects, with a low-impedance source and observing the "top
voltage" with a small plate remotely located and again "as far
as possible" from the coil. Crude but works OK. Of course, it should also be
possible to observe the voltage at generator port and looking for the frequency
giving a dip, but that seemed a little artificial to me. The signal generator
I'm using is a standard "Hewlett Packard" circuit, since it's the only one I
have putting out significant voltage in the region above 100 kHz. It doesn't go
high enough in frequency to observe any overtone responses.
A very sensitive method to observe the resonances of a coil is to drive it
through a tuned primary circuit, as in a Tesla coil. In place of the gap
place a low-impedance square-wave generator, generating a frequency of about
1/100 of the expected resonance frequencies, and tune the primary circuit to
find the resonances. At each of them you will see full beats in the
voltage over the primary inductor. The observed oscillation frequency is the
resonance frequency of the secondary too. There is no need then to observe
what is happening in the secondary. The setup may be this, with a square
wave generator made with a 555 and a buffer:
http://www.coe.ufrj.br/~acmq/tesla/tuner.gif . Change C1 (easier) or a
tap in L1 for tuning. I use a few capacitors and a large variable capacitor, all
in parallel connection, as C1. When you find one of the resonances, slide
a finger along the secondary coil, and you will see clearly where are the
voltage nodes (zeros) along it, places where the presence of the finger causes
less perturbation in the waveform. It's a funny experiment. It's easy to
see many resonances in this way. Antonio Carlos M. de Queiroz.
Date : Tue, 20 Jul 2004 08:13:40 -0600. Subject : Re: Resonance _s_ Re: Quarter Wavelength Frequency
Original poster: Paul Nicholson
Ed wrote:
> I question how many of those harmonic resonances would be
> observed at the input terminals of a long coil with any significant parallel tuning capacitance.
You might be able to count more overtones when the coil is
loaded than when unloaded! Some that were beyond the range
of the generator will be pulled down into view by the added C.
But others may be harder to see because Q factors and
impedances reduce.
> Certainly the response will get less and less as the number goes up.
Yes, eventually the overtones peter out as the 'axial' mode
of the coil becomes more and more lossy with rising frequency.
A wave decays away before it can meet its reflection and so
fails to achieve interference and form a standing wave.
Thus the input impedance response stays flat above some cut-off
frequency. It's like using an open length of some old/lossy
coax as a dummy load for microwaves.
This would be a good point for someone to bring in some
measurements of the spectrum of a primary resonator, say
in the range 0-5Mhz or so. The secondary would have to be
removed from the scene so that we can be sure we're seeing
primary overtones. Some readings with and without the primary
capacitor connection would show what's happening to the coil
resonances as terminal reactance is added. A low-Z generator
in series with the primary ground terminal is required, and
something (scope probe, neon, etc) connected to the hot end of
the coil to pick out the coil activity.
There are already plenty of secondary spectra on various
websites, including tssp - Terry has done lots of those.
So let's focus on the lumpy primary resonator instead.
Hey, an OLTC running with the volts turned down and no
secondary would make a great platform for recording a 'ping'
of the primary into a digital scope. With its small inductance
and large external C, that very lumpy resonator should make a
tough test of these claims.
I've no doubt that the overtones will be visible. The issue
is probably one of 'Does any of this matter to the coiler?'
Matt wrote:
> It should enlighten all, and settle the matter for all but the most die-hard ...
Thanks for your comments. You know that I don't have any
time or patience for the True Believer and luckily we're not
faced with anything like that. I see that here and there,
some of the list community's common understanding of coil
resonance is a bit off the mark (although often adequate) in
the technical detail. Individuals develop a personal
understanding of the physics that they're comfortable with
and which works, apparently. So it can't be too far wrong
and they're not going to relinquish that just on somebody else's
say-so. I would expect no one on this list to change their
views without making sure that what is being suggested actually
makes better sense than they already have! To do that, each
coiler must arrive at a new understanding themselves, not just
take anything on faith.
And of course, any replacement ideas must work as advertised!
I hope that people will go and look for the overtones in
'lumped resonators' and decide the matter on the basis of
what they find. As often the case, the laws of physics
are not at stake here, it's just a matter of learning how to
apply them correctly to TCs. Here we're debating which laws
to apply and how. Experiment can often decide that in cases
where it's not too clear by thought alone.
Paul Nicholson
Date : Tue, 20 Jul 2004 21:13:49 -0600, Subject
: Re: Quarter Wavelength Frequency
"Hi Ed,
Your explanation helps. Since lambda asymptotically approaches .5 could I
conclude that the coil is not base grounded and would be like a bipolar coil?
Gerry R."
No, the "Medhurst" self-capacitance data I quoted is for "single-ended solenoids
with one end EARTHED [=grounded in Australia]". The values came from TABLE 1,
Chapter 11, Section 2.ii. of the Radiotron Designer's Handbook, Fourth edition,
1953. This particular part deals with calculation of self-capacitance, and is on
pp 451 and 452. If anyone is sufficiently interested I suppose I could scan
these pages and sent them to hotstreamer. Ed.
Date : Tue, 20 Jul 2004 21:14:36 -0600, Subject : Re: Quarter Wavelength Frequency
I don't see any problem with the calculations or measurements, that all looks
great, but the answers are a little unexpected.
The method of Fres measurement should excite 1/4 wave resonance so your
frequency calculations must be for the 1/4 wave, I guess you are simply using
1/(2*pi*sqrt(Lundin*Cmed)), which should be fine.
But why I wonder, does your table tend to 0.5000 rather than 0.2500? Is the
turn count doing something here, perhaps?
(There's some doubt about the mode, because you mention a parallel resonance,
but your generator would see a series resonance at the base terminals when
driving the 1/4 wave.)"
You're correct about how I defined "wavelength". I don't know why the
wavelength ratio approaches 1/2, but I've seen that mentioned in the literature
somewhere. Is that really 1/2, or ~1/2? I don't have any idea. While the
inductance calculation was run for a fixed winding pitch (winding factor and
wire size), but Medhurst data is stated to be independent of the winding factor
in one of the earlier references I have read and to which I no longer have
access. I'll trying to find the measurements for the four coils I
measured. Three of them had an inside diameter of about 3.17" and were about
15" long, with wire size from #26 to #30 (I have a lot of the latter and it
seems to wrok fine). The fourth coil has an ID of 5.25" and a length of 18",
and is wound with
litz wire and turns spaced with cotton string. All seemed to check quite
closely, somewhat to my original surprise. I don't begin to have the ambition
to make a bunch of coils of different geometries and winding pitches, but just
to suggest that the calculations are a useful guide for coil tuning.
I'm not sure what mode is being excited when a self-resonant coil with no
external capacitance loading is fed from one end, but the frequency observed
corresponds to the measured frequency of the same secondaries
excited with a normal primary and loosely (spelling?) coupled.
All of this was done many years ago and I'll have to dig for the data.
"Let's tabulate the velocity factor (along the wire) as calculated by
velocity = 4 * wire_length * Fres
= 4 * wire_length * c/lambda
velocity_factor = v/c = 4 * wire_length/lambda.
(the 4 because we're supposed to be measuring the 1/4 wave).
Then your table becomes:-
L/D length of wire/lambda velocity_factor
0.5 0.228 0.912
1.0 0.298 1.192
1.5 0.343 1.372
2.0 0.374 1.496
3.0 0.413 1.652
4.0 0.435 1.740
5.0 0.449 1.796
7.0 0.466 1.864
10 0.478 1.912
100 0.49998 1.99992
1000 0.50000 2.00000
I would expect the factor to be a greater than unity for typical TC L/D ratios,
which they are, but it should tend
down to unity, not up to 2."
Hadn't thought about this at all so no useful comments. When I have a chance
I'll go over stuff on helical antennas. "REFERENCE DATA FOR RADIO ENGINEERS" by
FT&T has quite a bit on them but I've never paid much attention. I have always
thought of an unloaded TC as being equivalent to an extremely short helical
antenna and tried to calculate the radiation resistance once. It turns out to
be nil which probably
explains why our coils don't create more of a ruckus than they do.
The program is a few lines of QuickBasic code and I'll send the text listing
later. In order to call it forth I have to shut down this Mac and restart it in
a different mode, something I don't want to bother to do right now. Here is the
listing for the inductance calculation:
"Calculation of inductance by Lundin's approximation to Nagaoka's constant.
[Letter to Proceedings of the IEEE, Volume 75, Number 9, September 1985 pp 1428
=1429]
FOR A SOLENOID OF DIMENSIONS:
DIAMETER (INCHES) = D
LENGTH (INCHES) = LE
NUMBER OF TURNS = N
CALCULATE
X=D/LE
X2=X^2
A(X)=(1+.383901*X+.017108*X^2)/(1+.258952*X)
B(X)=(.093842*X+.002029*X^2-.000801*X^3)
IF X = > 1
K = (.6366198#/X)*((LOG(4*X)-.5)*FNA(1/X2)+FNB(1/X2))
INDUCTANCE =.0250688*D*X*N^2*K MICROHENRIES
IF X < = 1
K=FNA(X2)-.42441318#*X
IND=.0250688*D*X*N^2*K MICROHENRIES
I can't find the original letter, so the stuff above is a rewrite of the
expressions in the Basic program I wrote at the time; hope I didn't make any
mistakes. "Just in case" here are the original Basic statements:
INPUT "DIAMETER, LENGTH, (INCHES) AND NUMBER OF TURNS"; D,L,N
DEF FNA(X)=(1+.383901*X+.017108*X^2)/(1+.258952*X)
DEF FNB(X)=(.093842*X+.002029*X^2-.000801*X^3)
X=D/L
X2=X^2
IF X<1 THEN LT1
K=(.6366198#/X)*((LOG(4*X)-.5)*FNA(1/X2)+FNB(1/X2))
LT1:
K=FNA(X2)-.42441318#*X
IND=.0250688*D*X*N^2*K ' INDUCTANCE IN MICROHENRIES"
Wow but this is long but may of interest to someone besides Paul or I'd try to
send it direct. Criticisms and corrections and rebuttals welcome. Ed.
Date : Wed, 21 Jul 2004 17:50:38 -0600. Subject : Re: Quarter Wavelength Frequency
Original poster: Ed Phillips
"Hi Ed,
Could you give a quick qualitative definition of velocity factor. I'm thinking
a factor of 2.0 does not mean 2x the speed of light. Yet the formula below
suggest just that. How does one get faster than "c". Maybe you don't have
1/4 wave or... could the velocity factor be comparing the uncoiled propagation
time (with velocity of c) to the coiled propagation time (expected to be
smaller)?? Gerry R."
I haven't thought about "velocity factor" in this sense and haven't figured out
what to think yet. Ed.
Date : Sat, 24 Jul 2004 11:34:56 -0600, Subject : Re: Quarter Wavelength Frequency
Original poster: "Paul Nicholson"
Ed Phillips recently posted a table relating wire length to free space
wavelength for unloaded coils. I added a column for velocity factor = 4 *
wire_length/lambda, and we got:-
> L/D length of wire/lambda velocity_factor
> 0.5 0.228 0.912
> 1.0 0.298 1.192
> 1.5 0.343 1.372
> 2.0 0.374 1.496
> 3.0 0.413 1.652
> 4.0 0.435 1.740
> 5.0 0.449 1.796
> 7.0 0.466 1.864
> 10 0.478 1.912
> 100 0.49998 1.99992
> 1000 0.50000 2.00000
where L/D = axial_length/diameter = h/d, lambda is an abbreviation for 'free
space wavelength'.
Ed's figures are based on Ldc (via Lundin) and Medhurst C from a series.
The observations are that:-
a) Ed's calculations tend to velocity factor 2.0 as h/d tends to infinity. We
might have expected unity here on the basis that the coil's becoming more
stretched out like a straight wire.
b) The actual figure that Ed's calcs tend to is an exact 2.0000...which probably indicates a mathematical limiting value.
In order to see where these observations stand, I ran through my database of
about a dozen accurately measured coils. The following table reports the
measured frequencies and wire lengths, and the
velocity factor calculated from them:-
System Fres c/fres/4 wire h/d vfactor
sk38b50 221.3kHz 338.9m 417.4m 1.15 1.23
pn1 150.7kHz 497.7m 659.9m 1.36 1.33
pn2 92.0kHz 815.2m 1321.0m 2.84 1.62
tfltr 148.4kHz 505.4m 818.7m 2.92 1.62
sk20b49 217.2kHz 345.3m 607.9m 3.26 1.76
mwa1-4hd0 224.0kHz 334.8m 582.5m 4.00 1.74
mm3 61.9kHz 1211.6m 2077.9m 4.65 1.71
sk12b49 405.1kHz 185.1m 340.4m 4.83 1.84
tfsm1 358.8kHz 209.0m 398.8m 6.15 1.91
mm4 237.0kHz 316.5m 572.0m 6.78 1.81
sk5b503 979.7kHz 76.6m 149.9m 8.04 1.96
sk16b50 152.3kHz 492.4m 999.5m 8.71 2.03
mm1 455.5kHz 164.7m 347.3m 8.92 2.11
mm2 276.9kHz 270.9m 577.1m 9.97 2.13
(The above are all bare coils, i.e., no toploads or top probes or anything to
perturb the frequency. c = 300e6).
Bearing in mind that these are measured values, we do seem to have the real
coils tending to a high velocity factor as h/d increases.
Is there anybody out there with a coil with h/d > 10 ??? If so, we want your
measurements!
The interesting thing is that these coils all have a variety of turns and
pitches, yet they all land within a narrow range of one another when h/d is
plotted against velocity factor.
This implies that we can get a good estimate for Fres by simply taking the free
space quarterwave frequency for the straight wire and then multiplying by the
corresponding velocity factor for the given h/d.
In other words,
Fres = Phillips(h/d) * 75e3/wire_length (kHz)
where Phillips(A) is a function interpolated from the right hand two columns of
the above table and the wire_length is in metres.
I think this is a very interesting observation by Ed and, along with the fact
that the velocity factor increases well beyond unity, ought to be telling us
something quite general about coil resonance.
Thanks, Ed, for bringing up this neat little observation. It hints at a fairly
simply stated mathematical relation between the overall coil geometry and the
Fres. A very nice result.
I'll now go away and test the this 'Phillips function' against a large database
of a few thousand simulated coils to try to pin down a semi-empirical formula
for it. Paul Nicholson.
Date : Sat, 24 Jul 2004 18:20:33 -0600. Subject : Re: Quarter Wavelength Frequency
Original poster: "Ed Phillips"
> L/D length of wire/lambda velocity_factor
> 0.5 0.228 0.912
> 1.0 0.298 1.192
> 1.5 0.343 1.372
> 2.0 0.374 1.496
> 3.0 0.413 1.652
> 4.0 0.435 1.740
> 5.0 0.449 1.796
> 7.0 0.466 1.864
> 10 0.478 1.912
> 100 0.49998 1.99992
> 1000 0.50000 2.00000
where L/D = axial_length/diameter = h/d, lambda is an abbreviation for 'free
space wavelength'.
Ed's figures are based on Ldc (via Lundin) and Medhurst C from a series."
The last sentence turns out to be wrong. On reading a listing I realized I had
used Wheeler's simplest approximation instead of Lundin's much more exact
method, but for the range of L/D above the difference is
less than a percent so makes no significant difference in the results.
The main error is in estimating Cd anyway. Of course the velocity factor
approaching 2.000000000 is an artifact of the program, not a
fundamental law of nature. Ed.
Date : Sun, 25 Jul 2004 11:50:01 -0600. Subject : Re: Quarter Wavelength Frequency
Original poster: "Paul Nicholson"
Dr. Resonance wrote:
> 11,058 ft.
> 1/4 lambda freq = 23 kHz w/o large toroid topload
This seems to assume a velocity factor of unity for the wound wire,
whereas we know it will be faster than that for anything in the
normal TC range of length/diameter ratios.
Ed wrote:
> Wire length 11058 feet
> Wire weight 56.07 pounds
> DC resistance 70.6 ohms
> Fr 16.779 kHz
Is that Fres for the loaded coil Ed? If for unloaded then you'd
expect something 20% to 100% over 23kHz instead.
Malcolm wrote:
> I have a coil which I will measure tonight and post on tomorrow which has a totally outlandish H/D ratio
One problem with longer, thinner coils, is that the dielectric
properties of the coil former material begin to affect the
frequencies. Where the thickness of the tube wall is more than a
negligible fraction of the tube radius we get a noticeable portion
of the internal capacitance E-field passing through the dielectric
instead of the air. The mutual capacitances along the coil are
increased above the values we would calculate by any of our methods
and the actual resonant frequencies can be 5% or 10% lower than
predictions. This problem also appears to show up at small h/d
as well as small radius.
Short of immersing the coil in a large tank of liquid dielectric
chosen to have the same permittivity as the tube material, I'm not
sure how to allow for this!
Phil LaBudde wrote:
> So as the pitch increases, you are "stretching out" the coil back
> into a straight wire. But doesn't space winding decrease the "Q"
> of a coil, and therefore make it less efficient as an inductor,
> which is what you would expect from effectively unwinding one?
We're not opening out the pitch in our models which must be why the
velocity factor is heading up to some number above 2 instead of to
around 1. But yes, the Q would deteriorate beyond some optimum
pitch, as inductance goes down and radiation resistance increases.
If radiation resistance is suppressed by enclosing the resonator
in a cavity then the high Q factors are restored - so the low
inductance, by itself, isn't the problem.
Interesting suggestion for the use of spiral core spark plug
wire. The unknown dielectric properties would exclude it for
quantitative measurements, but it would be fun to play with a
piece to see how it behaved at RF. It could be looped into a
toroid and so on. You never know, it might be a handy material for
use in radio circuits where a long-ish, perhaps tapped, resonator
is required. It might be a worthwhile exercise to try to measure
its reactances per unit length, Q factors, etc. I guess the
wire's pretty thin, though.
Ed wrote:
> On reading a listing I realized I had used Wheeler's simplest
> approximation instead of Lundin's much more exact method, but for
> the range of L/D above the difference is less than a percent so makes no significant difference in the results.
Oh well, no matter, it doesn't affect the conclusions: By comparing
things against measured results and against calculations drawn from
a more detailed model, we no longer need to rely on the original
calcs you used to arrive at this discovery.
> The main error is in estimating Cd anyway.
Agreed. Anyway, nice work Ed. You've shed some much needed light
on the relationship between wire length and resonant frequency.
Until now all we've been able to say is that the frequency changes
in some complicated way as the wire is wound up. You've shown that
it actually varies quite smoothly with the overall geometry (as
opposed to being some complicated chaotic function involving turns,
pitch, etc). As a result, coilers can now get an estimate of Fres
directly from h, d and wire length - an estimate which is probably
at least as good as using Wheeler times Medhurst.
There is one big puzzle though. I'll write about that in another
thread.
Paul Nicholson.
Date : Sun, 25 Jul 2004 16:20:10 -0600. Subject : RE: Quarter Wavelength Frequency
Original poster: "Robert Heidlebaugh"
Garry. R : A number of reactant effects change the velocity. The distributed
capacitance has the greatest effect, but not the only effect. 12% lower velocity
is quite common around a wire. Robert H.
Date : Sun, 25 Jul 2004 16:21:19 -0600. Subject : Re: Quarter Wavelength Frequency
Original poster: "Ed Phillips"
Ed wrote:
> Wire length 11058 feet
> Wire weight 56.07 pounds
> DC resistance 70.6 ohms
> Fr 16.779 kHz
Is that Fres for the loaded coil Ed? If for unloaded then you'd expect
something 20% to 100% over 23kHz instead."
Yes, that was for the parameters for "Big Bruiser" and includes the effect of
136 uufd of externinal terminal capacitance. That note should have been more
explicit for those who hadn't followed the conversations
about BB. Ed.
Date : Tue, 27 Jul 2004 08:33:45 -0600. Subject : Re: Quarter Wavelength Frequency
I note that every attempt (successful or otherwise) to formulate Fr for a
single-layer resonator incorporates the h/d ratio in one form or another
(Medhurst does for example) so this cannot be an accident. All past
attempts to do this using wirelength and h/d range from relatively simple
formulations to some that can only be described as arcane. I suspect some of
these types of formulae were concocted to fit particular cases.
Malcolm.
Date : Tue, 27 Jul 2004 12:52:33 -0600.
Subject : Re: Quarter Wavelength Frequency
Original poster: "Ed Phillips"
"I note that every attempt (successful or otherwise) to formulate Fr for a
single-layer resonator incorporates the h/d ratio in one form or another
(Medhurst does for example) so this cannot be an accident. All past
attempts to do this using wirelength and h/d range from relatively simple
formulations to some that can only be described as arcane. I suspect some of
these types of formulae were concocted to fit particular cases.
Malcolm"
I'm not sure what you mean by "concocted" but Medhurst took the measured Cd
values for a number of different coils WITH ONE END GROUNDED and found that the
parameter which best characterized it was h/d, the aspect ratio. He started
from empirical data. More recently there has been some theoretical work done in
Italy on the subject but I've lost the reference to the publications. Maybe
someone here remembers them. Ed.
Date : Wed, 28 Jul 2004 07:11:52 -0600. Subject : Re: Quarter Wavelength Frequency
Original poster: "Gerry Reynolds"
Hi Paul,
I think it has been hypothesized that as H/d go to infinity the velocity factor
goes to 1.0 and the end effects for shorter H/D coils bring the velocity factor
to greater than one. I'm wondering if an opposite hypothesis might be
true. That is, an infinitely large H/d would have a velocity factor of
something around 2 and the end effects for shorter coils would reduce the
velocity factor. Gerry R.
