# Re: 1/4 WAVE SECONDARIES

• To: tesla-at-grendel.objinc-dot-com
• Subject: Re: 1/4 WAVE SECONDARIES
• From: "Malcolm Watts" <MALCOLM-at-directorate.wnp.ac.nz>
• Date: Tue, 24 Oct 1995 08:09:29 +1200
• >Received: from rata.vuw.ac.nz (root-at-rata.vuw.ac.nz [130.195.2.11]) by uucp-1.csn-dot-net (8.6.12/8.6.12) with ESMTP id NAA05003 for <tesla-at-grendel.objinc-dot-com>; Mon, 23 Oct 1995 13:11:21 -0600

```Comments on comments/queries from Ed Harris.....

> forcing each coil to resonate at a frequency such that the wire in each
> coil is 1/4 wavelength long at that frequency.
>
> EH> I just want to make sure I understand: Are you saying that for the
> EH>given length of wire you then compute what frequency corresponds
> EH>to that wavelength (using free-space  speed of light?)
>
Yes.

>      The diameter of all coils is 12". The h/d ratios considered are 2,3
> and 4. For a given h/d ratio and diameter, the self-capacitance of the
>
> EH> By self capacitance, do you mean the interturn winding capacitance?
> EH> There is also the capacitance from each winding to ground which depends
> EH> specifiaclly on the environment near the coil...
>
I'm talking about self-capacitance as measured (using L and fr) and as
defined by Medhurst (who has yet to fail for all the coils I've meas-
ured.) How exactly it is distributed is not totally clear but it
appears to be primarily to ground as a whole. The inter-turn capacit-
ances are effectively connected in series if you look up the coil
which makes them rather small in total.

> coils are pre-determined prior to adding a terminal. Changing the wire
> diameter for a given former size changes the number of turns, inductance
> and therefore resonant frequency of each coil in addition to wirelength.
> The self-capacitance does not change under these conditions.
>
> The procedure for generating the coils is as follows :-
> (1) Choose h/d ratio and Dsec, hence Hsec and self-capacitance follow
> (2) Choose a wire gauge
> (3) From the table Richard Q. supplied, the number of turns for the
>     chosen wire gauge is defined (this table takes wire insulation
>     thickness into account)
> (4) Calculate the coil inductance
>
> EH> If you use one of the standard formulas like Nakaoga's (sp?) it will
> EH> probably be in error since the reduction of inductance due to the skin and
> EH> proximity effects are almost never taken into accout
>
I've never used Nakaoga - in fact I wasn't aware of it's existence
till you mentioned it just now. I use Wheelers standard formula
which once again measures well. Skin and proximity effects only
affect A.C. resistance, not inductance.

> (8) Calculate the thickness of wire in terms of skin depths for this
>     frequency (this determines the suitability of the chosen wire gauge
>     at this frequency)
>
> EH> There is also the proximity effect, could you elaborate?
>
I appreciate that. How severe it is depends on whether the coil is
closewound or not. I think the above statement is self-explanatory.
If you are not happy with a minimum wire gauge of 3x skin depth
make it 4 or 5. I've had very good results with a minimum of 3.

> (9) Calculate Lsec/Ctot ratio (mH/pF)
>
> NOTE : Q is considered incalculable due to factors such as radiation
>        resistance (i.e. I haven't figured out how to do it yet).
>
> EH> I have a couple of papers, one theoretical, and one experimental which
> EH>make a crack at it. Do you really think radiation is a major loss? I

If you can light fluoro lamps some distance away from the coil you
are losing significant amounts of energy by this mechanism. How
high a Q have you managed to score for any coil you've built (without
a terminal - i.e. with best possible L/C ratio) ?  Can skin resistance
account for all the losses you've experienced ?

> EH>haven't seriously esimated it, but since tesla coils dimensions are all a
> EH>small fraction of the working wavelength, they sould be very inefficient
>
The highest Q coils aren't good radiators, but they do radiate. I
appreciate what you're saying re - size vs. wavelength but we are
talking about a large amount of wire, not a whip aerial.

> NOTES :
> - For a chosen h/d ratio, the capacitance required to force ANY
>   coil
>
> EH> Is it true though, that you have based this condition on measurements
> EH> done on coils with a fixed form diameter? For given H/D, but different
> EH> D, I'd have expected a change in the interwinding capacitance.
>
True. I'm sorry, the sentence was incomplete. I think I stated more
succinctly in the following sentence or paragraph. Certainly there
is a change between diameters - the tables clearly show that.

>   identical!! Since self-capacitance is constant for any coil with
>   the same diameter and h/d ratio, the terminal capacitance is
>   always the same as well! It would appear that this constancy has

Malcolm

```