Re: quarter wave

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "Gerry Reynolds" <gerryreynolds-at-earthlink-dot-net> 

Hi Paul,

More comments interspersed.

Gerry R.

 > Original poster: "Paul Nicholson" <paul-at-abelian.demon.co.uk>
 >
 >
 > One can certainly begin to picture the energy flow as spiraling
 > around the coil following the path of the current -  to a first
 > approximation.  Two main components of the field are a B field
 > parallel to the axis (due to the circular current motion)

from the circular current motion in both the primary and secondary

 > and a
 > radial E field.  Picture the cross product of these two as a
 > field of arrows which would join to make circles around the
 > solenoid.

ExH (Poynting Vector - rate of energy flow per unit area).  Important thing
here is this is a vector and has direction tangental to the solenoid coil
surface.

Is this with no up or down component or does it follow the wire path since
the current follows the wire path?  There is also a H field created by the
primary that is truely vertical (assuming flat spiral primary).  The net
result is probably in between and negligable difference for close wound
coils.

 >
 > At the same time, we can cross product the radial E field with the
 > circular B field due to the net flow of charge up and down the coil.
 > The result is energy flow arrows pointing parallel to the axis.

ExH  direction up or down.

 >
 > These up and down flow arrows added to the circling arrows give
 > an overall spiral with similar or perhaps the same pitch as the
 > turns of wire.
 >
 > To complete the picture, we must also look at the remaining field
 > components.  We have a vertical E-field, ie potential differences
 > along the coil, whose cross product with the circling B field
 > component points radially inwards and outwards from the coil,
 > representing the stored energy flowing to and fro into the
 > near field.

Interesting.

 >
 > Putting all this together, we might try to visualise the overall
 > effect as a spiralling energy flow, swelling outwards and collapsing
 > twice each RF cycle.  We know that for low frequencies at least,
 > the effective pitch of this spiral must be greater than the winding
 > pitch because signals from one end of the coil arrive at the other
 > end well before they would if confined to the same pitch as the
 > wire.  In terms of inductance and capacitance, we might say that
 > mutual coupling is allowing the signals to leapfrog the turns to
 > some extent (equivalently, those axial-pointing Poynting vectors).
 >
 > It is interesting to look at the velocity factor (with respect to
 > the wire) for a set of resonances.  With figures from one of
 > Marc Metlicka's coils (h/d=4.66, 2898 turns) with 2080 metres of
 > wire, we find
 >
 > Mode    Freq       Free space length    Velocity factor of wire
 > 1/4     61.9 kHz   4847m * 1/4 = 1212m    2080/1212 = 1.72 [+]
 > 3/4    157.9 kHz   1900m * 3/4 = 1425m    2080/1425 = 1.46
 > 5/4    229.7 kHz   1306m * 5/4 = 1633m    2080/1633 = 1.27
 > 7/4    294.4 kHz   1019m * 7/4 = 1783m    2080/1783 = 1.17
 > 9/4    355.6 kHz    844m * 9/4 = 1899m    2080/1899 = 1.10

Interesting, the modes are only odd number of 1/4 (probably a boundary
condition).  Thankyou for definition of velocity factor.

vf = wire length / effective free space length (based on resonant freq and
mode)

 >
 > For shorter and shorter wavelengths in the coil, we find the wire
 > velocity factor coming down towards unity, as if the pitch of the
 > 'field spiral' was becoming more closely aligned with that of the
 > wire spiral.  Terry Fritz also provided some figures for a coil
 > (h/d=2.92, 1000 turns), this one with 819 metres of wire,
 >
 > Mode     Freq       Free space length    Velocity factor of wire
 > 1/4     148.4kHz     2022m * 1/4 = 506m      819/506 = 1.59 [+]
 > 3/4     353.4kHz      849m * 3/4 = 637m      819/637 = 1.29
 > 5/4     513.8kHz      584m * 5/4 = 730m      819/730 = 1.12
 > 7/4     666.4kHz      450m * 7/4 = 788m      819/788 = 1.04
 > 9/4     819.8kHz      366m * 9/4 = 824m      819/824 = 0.99
 > 11/4    977.4kHz      307m * 11/4 = 844m     819/844 = 0.97
 > 13/4   1133.1kHz      265m * 13/4 = 861m     819/861 = 0.95
 >
 > We see with this coil the along-wire velocity is pulled right
 > down to a value 0.95 which would be a typical factor for a
 > straight wire.  The coil is behaving at these higher frequencies as
 > if it were not wound at all.
 >
 > Now there are a few speculative matters worth listing:-
 >
 > a) As the in-coil wavelength becomes shorter, the total mutual
 > coupling affecting a given point on the coil becomes an average
 > over more and more wavelengths of the signal and therefore might
 > be expected to tend to zero. If so, the propagating wave is
 > not able to 'leapfrog' so much, and the velocity comes down to
 > that of the wire itself.
 >
 > b) It may turn out that for an infinite solenoid, the velocity
 > factor is unity (or some other constant near unity) for all
 > frequencies, perhaps for reason (a).
 >
 > c) If (b) is so, then we might legitimately interpret the trend
 > towards effectively higher velocity factors for low frequencies as
 > simply an end effect, ie brought on by the finite length of the
 > coil interrupting long-range cancellation of mutual coupling when
 > below some frequency.

This sorta reminds me of the end effect on a propagating light wave causing
defraction.

 >
 > Another way to present the 'end-effects are the cause' view is to
 > picture the waves travelling at 'c' following the wire spiral, but
 > allowing that they don't have to complete a full traverse of the
 > coil.  The impedance changes as you approach the ends and so a
 > travelling wave would see a gradual rather than a sudden sharp
 > discontinuity, especially at low frequencies.

Could this be the reason that some in the group recommend that the top turns
of the secondary be space wound to provide an impedance transformation?

Every time I reread this, I pick up more nuances.  Again, thankyou for all
the energy you put into this.

Gerry R.