Inductance (fwd) [correction]

From:  Malcolm Watts [SMTP:MALCOLM-at-directorate.wnp.ac.nz]
Sent:  Sunday, April 05, 1998 5:32 PM
To:  Tesla List
Subject:  Re: Inductance (fwd) [correction]

Hi Mike,
             Apart from my very own measurements, I would be happy to 
supply as many references as you want:

> From:  Hollmike [SMTP:Hollmike-at-aol-dot-com]
> Sent:  Thursday, April 02, 1998 6:54 AM
> To:  tesla-at-pupman-dot-com
> Subject:  Re: Inductance (fwd) [correction]
> Malcolm,
>    I would be interested in seeing the reference source that gave you the H/D
> at one for max Q.  I have an old electrical engineering/radio communications
> handbook that gives the D/H ratio of 2.45 for the mas inductance which is in
> fair agreement with 2.222 which Erik worked out.  I also worked this out a
> couple of years ago and got the same result as Erik(gave me something to do on
> a long boring road trip).  
>      Perhaps this 1:1 ratio is better at certain frequencies or some other
> conditions that I am unaware of.  The real goal is to get maximum Q.  Whether
> or not this corresponds to max inductance(and apparantly it doesn't by what
> you are saying) is interesting.  I tried to figure out all the variables that
> affected the Q and thought that maximizing the inductance was the best way to
> improve the Q.  I would appreciate it if you could elaborate on this.
> Mike Hollingsworth

The problem is that maximum inductance does not correspond with 
minimum self-capacitance for a given coil diameter. Q = SQRT(L/C)/Rac

 #1: RF CIRCUIT DESIGN   Chris Bowick  ISBN 0-672-
21868- 2     pub. Howard W. Sams & Co.
P.17 Heading: Single-Layer Air-Core Inductor Design

The author first gives a variation on Wheeler's Inductance Formula 
then goes on to say: "Keep in mind that even though optimum Q is 
attained when the length of the coil (l) is equal to its diameter 
(2r), this sometimes not practical and, in many cases, the length is 
much greater than the diameter". (He is dealing with ideals vs 
shape practicalities in building coils for radio circuits.)

#2: Electronic and Radio Engineering 4th Ed.  F.E. Terman  
    pub. McGraw-Hill
p.32: second paragraph

"In designing a single-layer coil, the highest Q in proportion to 
size is obtained when the length of the winding is somewhat less than 
the diameter of the coil".  Here, the author lists two references at 
the bottom of the page. Immediately below this piece, the author 
shows a graph for a coil with h/d = 0.96  The rest of what he says in 
this paragraph is well worth quoting and agrees with measurements I 
have conducted.
     " The number of turns required is then determined by the exact 
ratio of length to diameter that is selected, by the diameter, and by 
the inductance desired; when these factors are all settled, the 
optimum wire size corresponds to a conductor diameter that is between 
0.5 and 0.75 times the distance between the centres of adjacent 
turns. If one compares the Q of two coils having the same inductance 
and the same ratio of length to diameter but different physical size,
then the coil that is larger will have the highest Q provided it is 
wound with wire of optimum size."

When discussing single layer solenoids in the context of Tesla Coils, 
it should always be borne in mind that we are dealing with a 
*particular* case of connecting these inductors. They are connected 
to and worked against ground. For example, while Medhurst's Cself 
formula works brilliantly in this context, it would utterly fail for 
a coil in outer space unless that coil had a ground plane connected 
to it and sited below it.