Transmission Lines

From: 	Malcolm Watts[SMTP:MALCOLM-at-directorate.wnp.ac.nz]
Sent: 	Sunday, August 03, 1997 5:17 PM
To: 	tesla-at-pupman-dot-com
Subject: 	Transmission Lines

Hi all, 
        To do some investigation into transmission line effects I 
have constructed an artificial line consisting of 13 lumped coils
in series (each about 1.6mH) and a C from the junction of each to
ground. During the experiments, I altered the C's to introduce 
grading into the structure. Much work yet to be done to model the TC 
accurately but that is the track I am on. The point is that 
introducing instrumentation to a TC secondary alters its 
characteristics markedly due to the normally low capacitance in the 
resonator. I could make my C's arbitrarily large to minimize the 
effects of scope loading. First goal is to accurately model the real 

    I must state the _limited_ applicability of these tests right 
here:  NO SPARK - all measurements were taken with the end of the 
resonator open circuit
       CW DRIVE ONLY - I cannot stress this one strongly enough as I 
know someone is going to gloss over this and immediately apply these 
results to our normal cap discharge/limited energy situation

Some results:
    I measured the Q of the line as each stage was hooked in using 
the 3dB bandwidth tests. The frequency went down and down as stages
were added but it was clear that coil and cap losses were dominant 
after adding the 7th stage because Q started going back down.
    I then measured Vo/Vin. This showed agreement to within 1% for
Vout being raised by VSWR, that being related to Q by: VSWR=4Q/PI
This result held for different values and capacitive gradings along 
the line.
    Next, I checked lumped circuit L-C resonant values against what I 
actually measured. It was clear that while Wheeler and Medhurst are 
useful tools for predicting resonator frequencies, they are far from
an accurate description of distributed resonator behaviour. To Greg 
Leyh: the tests suggest that the PSPICE model is incorrect. My lumped
calcs always produced a frequency lower than that measured.
    I first used equal L's and equal C's along the line. A mile off.
Next I graded the C's so that I went from largest at the bottom to 
smallest at the top. The comparison was worse.
Next, I graded the C's so that the smallest was at the bottom working 
towards the largest at the top. Comparison much improved. (Hmmm.., 
starting to mimic a radio aerial).
    I haven't yet done it but am next going to grade both L's and C's 
so that largest L is at the bottom and largest C is at the top. I 
suspect this will get the comparison within cooee. This would make 
sense of course because the top turns in a TC have virtually no load 
on them so L at the top of the resonator is almost non-existent.
    Of real interest was the fact that more "topload" didn't 
greatly affect Q (or VSWR). 

More to come. Watch this space. Along with correct grading will come 
constant energy pulse feeds to determine Vo and how this tracks pulse 
energy and whether this agrees with the sqrt(Cp/Cs) scenario.