# Re: Vf,Zo,R,G,L,C.....

```Hi Jim,

At 08:10 AM 12/29/98 -0800, you wrote:
>Tesla List wrote:
>>
>> Original Poster: Terry Fritz <twf-at-verinet-dot-com>
>>
>> Hi All,
>>
>>         I was doing a little modeling of Tesla coils today and I tried
to use the
>> formula for the parameters of a transmission line from the Corum's papers.
>
>What sort of transmission line is this: balanced pair in free space,
>balanced pair above a ground, single wire above ground? etc....

A single lossy line model.  The corums like the balanced pair but that does
not seem realistic to me...  But perhaps they have a good reason to use the
two lines that I don't understand...??

>
>Here are some equations (exact (assuming lossless conductors (!) (you
>are using lots of liquid He, right?)):

Too cold here to use LHe! :-))

My line is very lossy.  I add the DC resistance as the series R and
adjusted the shunt conductance until the Q of the line matches what my coil
measures.  I have seen a number of equations for the lossless cases but
haven't seen any for the lossy case.  I assume they are not easy...

>
>For parallel conductors in air, well away from ground (many wavelengths,
>unlikely for coiling, but here for reference):
>
>Z0 = 120 inv cosh( D/d) where D is center to center spacing, d is
>diameter of conductor
>   = approx 120 ln (2D/d)
>
>For balanced pair near ground
>
>Z0 = (276/sqrt(epsilon))*log10((2D/d)*(1+(D/2h)^2)^-.5)
>
>h is height of centers above ground, assumes wire diameter very much
>smaller than D or h.
>
>For parallel strip line:
>
>Z0 = approx 377 * w/l
>where w = spacing between strips (not center to center)
>      l = width of strips
>valid for w/l < 0.1
>
>
>Velocity factor is, in general, proportional to 1/sqrt(epsilon), so, for
>air insulated velocity factor is typically > .99
>
>

The Corums suggest a velocity factor in the range of 0.01 to 0.001 !!!
That's a pretty darn low velocity but the equations and models seem to
still give somewhat reasonable numbers.
If there were easy equations they would be best.  However, if not it,
seems easiest just to do a little trial and error work and let the computer
figure the constants out.  I simply hook virtual test devices to the models
(sine gernerators) and run the same tests I do in real life and get the
models to give the same results.

My secondary coil has the following constants assuming the length of the
coil is used as the per distance scale factor along the line.

R = 68.87 ohms
L = 0.0754 H
G = 240e-9 mho
C = 41.24 pF
I have an 11.6pF top load capacitor too.

The Corums equations gave:

Zo = 57119
Velocity Factor = 0.001534

They didn't dwell on losses too much... or I just din't understand.  Their
The numbers were close but realy not close enough (or I'm too picky).

Assuming lossless constants which may or may not work here:

Zo = sqrt(L/C) = 42821 ohms

Time Delay = sqrt(L x C) = 1.7608 uS
The lossy model shows the same number so maybe it works in this lossy case
too.

My coil is 30 inches long and works at 111.7kHz so I think that gives a
velocity of:

1.7608E-6 * 4 = 7.0432E-6 for a full wave to travel 120 inches.

light goes 120 inches in 10.167E-9 seconds

So the velocity factor Vf = 10.167E-9 / 7.0432E-6 = 0.0014435

At least, I think that is how it is done... :-)

Of course, When the Corum's papers where writen in the late 80s they didn't
have all the neat computer models and such.  They used to best they had
then...

BTW - the lumped models give pretty much the same waveforms and results
just like I always said :-))  However, with the transmision lines you can
see the impulse effects of the coil's 3/2, 5/2, 7/2... wavelengths
reflecting back which is sorta neat...  but for most uses, the lumped
parameters ar vastly easier to deal with and give perfectly good results.

Terry
terryf-at-verinet-dot-com

BTW - If anyone knows how to model real transformers with simulated B-H
curves in MicroSim (the demo version) please send an example to Marco or
myself.  We were trying to figure out how to model a saturable reactor
(MOT) but could not see how to do it.  The demo version my not allow this
to be modeled...  The real version is looking cheaper all the time :-))

>
>--
>Jim Lux                               Jet Propulsion Laboratory
>ofc: 818/354-2075     114-B16         Mail Stop 161-213
>lab: 818/354-2954     161-110         4800 Oak Grove Drive