# Re: H/D Ratios

```Subject:       Re: H/D Ratios
Date:   Thu, 22 May 1997 08:46:30 +1200
From:   "Malcolm Watts" <MALCOLM-at-directorate.wnp.ac.nz>
Organization:  Wellington Polytechnic, NZ
To:   tesla-at-pupman-dot-com

Dear List,
Please indulge me once again :)

> I have seen several references to a physical 1/4 wavelength of wire
> being used to wind a secondary. What is the 1/4 wave length based on?
> Is it free space or based on some velocity factor? Is there some magic
> to be had by striving for this.
>
> Based on no facts at all my next secondary will have a H/D ratio of PI.
> It just seems right.

Love it :)
The quarter wavelength thing: In the distributed resonator, no
matter what the length of wire, the profile is 1/4 wavelength at
resonance. Well, that is _strictly_ true for no top load (or nearly
so because like a standard antenna, there is an end capacitance
effect that requires the physical length of the straight wire to be
somewhat shorter than the free-space length). As soon as one adds a
topload, the antenna/coil will resonate at a lower frequency because
of the additional capacitance. That makes the structure shorter than
90 degrees electrically at its resonant frequency. The lower the L/C
ratio, the more the electrical length trends towards zero degrees.
Explanation of physical length: for a straightened out wire, the
wire length is 1/4 wavelength physically as well as electrically. For
the TC resonator, the physical and electrical lengths are entirely
different (we are not talking about wirelength anymore). The
electrical 1/4 wavelength of the resonator is that associated with
its resonant frequency which is dictated by its distributed L and C.
The _physical_ 1/4 wavelength is the _height/length_ of the coil
(former).

There is a historical element to all this. Tesla always thought
of the wirelength alone as being 1/4 wavelength long and tried his
best to reconcile that view with what the coil actually did resonate
at. This is made very clear in both the Colorado Springs Notes and his
1897 lectures. In those lecture notes, he shows an "ideal" primary
profile as having the free space 1/4 wavelength as well as the
secondary. In physical terms, this means the length of wire in both
primary and secondary were ideally the same!!  Of course, he never
did it in practice as far as I can tell.
There is a constant emphasis in his notes that the wire must be
1/4 wavelength long at the resonant frequency. In fact what really
happens is that the coil resonates according to its L and C
components. If that happens so that the actual wirelength is the 1/4
wave free space length at _that_ frequency, then that is lucky. In
fact, I have never found a coil design where this is so. The act of
coiling the wire up and winding it single-layer modifies its L and C
components dramatically, but more importantly, the drop in
distributed C is not compensated for by the increase in L (due to
mutual inductance) so that in practice, one always has to add extra C
by using a terminal if the wirelength really does equal its free
space 1/4 wavelength. I posted a recipe a while back which you can
use to always make the wire 1/4 wavelength long a la its free-space
length. The essence of the method is to work out how much additional
Ctop you need to add to lower Fr to achieve this.
NB - this alone shows that Fr and physical wirelength ore only
loosely related in the resonator.
Is there any advantage to doing this? Skip Greiner thinks there
is and has achieved some excellent results at quite modest power
levels. I am personally unsure at this stage. I wish to experiment
with this myself to see. The good news is we now have some excellent
design tools and equations which makes arranging things (and
investigating various secondary profiles) an absolute breeze. I will
look at some different H/D's at some stage and see which come closest
to making the wire 1/4 wave long without the addition of a terminal.
I am going to make an educated guess here:
h/d = 1 may come closest.  We know that this profile has the
highest Q of all (no terminal) and this Q is degraded with the
extra coil had this profile. Note that it is always true that the
height of the coil is its physical 1/4 wavelength regardless of the
wire length.

Finally, it seems from the charting exercise (I haven't yet
finished) that many coils come close to achieving this 1/4 wavelength
long wire through pure serendipity - the choice of terminals in many
cases appears to be entirely arbitrary as far as their capacitances
go. However, some of the best coils (Richard Hull's Nemesis is a
shining example) have such enormous toploads that the wire ends up
being considerably shorter than the free-space 1/4 wavelength (and
yet they still perform superbly).

I'd better stop there. I think I may have started writing a book.