rochester (belated) transmission line...
Belated Rochester NH. Made it Friday, late. Did not make Sattiday, account
r**n. Only itme i saw (beyond the usual acres of meters) was a Pickering
(Picker?) XRray PSU and control set up. roughly one 6 foot 19" rack fulla
goodies. I guess the consensus is that these are TOO high voltage to be readily
useful, since there is a vasty amount of experience and hard won knowledge
in the 15-30KV area... Still....
>I have a gut feeling that the characteristic impedance formula the
>Corums use is not valid (they do admit it doesn't work for all coils).
>Up to now, I have done the simple SQRT(L/C) thing effectively
>averaging the distributed L and C.
I have not reread any of my Corum lately. If sqrt (l/c) is based
on the usual formula for a transmission line, there is a gotcha.
sqrt(L/C) is a SIMPLIFIED VERSION. some references do not point
this out. The full form (from memory) is more like SQRT ((L+R)/(C+g)).
R is the series reistance (per unit length in tx line work).
g is a 'conductance' related to resistive leakage thru the insulation.
For the USUAL range of RF intrest (say 500KHz to 500GHz) the R is so
small relative to the Xl and the g is so 'small' realtive to XC that
the simplified form works out. (Yeah. I switched for L to XL. Bear
with me...). AS THE FREQS GO DOWN, THE SIMPLIFIED FORM BECOMES
PROGRESSIVELY LESS ACCURATE. (I had cause some years ago, to
xperimentally verify this. got paid for it. NOT new knowledge,
tho. First recognized at the turn of the century....)
This is (another) case where a transmission line is not flat. the
impedance RISES as frequency falls into the KHz region. Nothing
mysterious, but not coverd in a lot of books. Does this apply to
'coiling? Dunno. But if i was using that approximation, i'd see
how including the R (and g) affected the match between predicted &
As i recall it:
(SQRT(L/R) is a simplifed form of (This gonna be hard to do in ascii)
Sqrt((Xl+R)/(Xc+g)) (See above for R and g)
This is a lumped model of a transmission line: Inductance per length+
Loss per length and Capacitive effect/length + conductive leakage per
length. Simplification starts by chucking the 'per lengths' as they are
all for the same length at any one time. The the '2 pi' part of the
conversion from 'L' to Xl and 'C' to Xc drops out (divide top and
bottom by the same thing....). result is SQRT((L+R)/(C+g)). as noted
above, the simpification works in the usual ranges. As freqs go down
the simplification breaks down. (Xl gets smaller relative to R).
(This is a 'handwaving' type explanation, a proper text will get to
the same place with more rigour)).
(is the R the 'ac reistance at freq' or the 'DC R'???
>I am going to do some experiments this weekend using resistive terminations to
>determine where the truth lies on this. I have previously seen scoped evidence
>that SQRT(L/C) is the one, but I think this needs to be proved one way or the
>other. The formula the Corums use (Schelkunoff) gives values MUCH lower than
> One thing I realized yesterday : we are dealing with structures
>that have a VERY low radiation resistance
Yep. At least in antenna eng'g sense. (Not meaning to ignite the
'coils do not radiate wars'.)
>whereas helical antenna are designed to have a high radiation resistance
>(effective radiation) and this might well make the difference (what say you
'lectrically short antennas will have low radiation resistance.
Helical antennas come in two sets of types: the ones a wavelength
or so across, commonly seen in olde missile tracking movies. These
have one set of characteristics. The OTHER species, closest, imo,
to a tesla coil (secondary, or secondary plus tertiary) is the
'rubber duckie' class, which tries to 'look like' a 1/4 wave
_at_ _frequency_. My understanding (possibly flawed) is that this
sort of 'helical antenna' is real close in concept to the helical
resonator. In short, i should _expect_ a resonant Tesla secondary to
have a vae impedance approaching 50-75 ohms ON FREQUENCY, dropping
rapidly off resonance. But i could be wrong...
(Semi private to Chip:
Sense resistor usually is a resistor insertedto measure the
current, as you speculate. If you have a current probe, (insulated
for the voltage... 8)>>), i shoudl use it. But i could be worng