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VK3ABK > TECH 31.05.06 11:05l 74 Lines 2736 Bytes #999 (0) @ WW
BID : 30968_VK3HEG
Read: DL1LCA GUEST
Subj: Capacitor dielectric (VK2ZRG)
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Sent: 060531/0622Z @:VK3HEG.#WEV.VIC.AUS.OC #:30968 [Ballarat] $:30968_VK3HEG
From: VK3ABK@VK3HEG.#WEV.VIC.AUS.OC
To : TECH@WW
Hello all Cynics.
Ralph, VK2ZRG, has given the ARRL Handbook a hard time recently, and has
also, cast doubt on other vital information. Let's ignore the 'net, as this
not always a source of reliable information.
Ralph wrote....
I don't believe everything in print, or on a computer screen, just because
the it is published by some reputable organisation. My 1990 ARRL UHF/Microwave
Experimenter's Manual has many errors in it. Not only in mathematical formulas
and such like, but also in text. I'll quote from the chapter on transmission
lines, talking about coaxial lines.
"And distributed capacitance should vary directly with the square root of
the permittivity of the dielectric, just as the capacitance of any capacitor
increases by a factor of four if the dielectric constant is doubled."
And comments....
" Well that is plainly wrong. I hope everyone knows that capacitance is
proportional to the dielectric constant. It was when I learnt about it, and
still is, unless the laws of physics have been changed."
Comment....
I haven't seen this quotation, but after thinking about the differences in
capacity formulas for parallel plates and coaxial (or other cylindrical)
formations, I suggest the following.....
Take the usual formula for a parallel plate capacitor....
C = K A (n-1) where K is the dielectric constant
ÄÄÄÄÄ A represents plate area
d and d the plate spacing.
Here, the capacity is directly proportional to the dielectric constant.
Now, the cylindrical or coaxial capacity. Here the electric field is not at
right angles to the plates (forget your differential calculus for now!) but
as I see it, it is the 'resultant of forces' and we are told that....
C = (SQRT K) A Actually, for coax cable Z = 120 pi
ÄÄÄÄÄÄÄÄÄÄ ÄÄÄÄÄÄ
d (SQRT K)
This is a simplified version.
I think you can justify the SQRT function with a diagram....
O Consider this diagram as electric forces in the
/ ³ (sectional) dielectric of a coaxial cable and
/ ³ the dashed line is on the radius. Given that the
/ ³ length of each solid line is '1', then the radius
/ ³ (the radial electric field) would be 'SQRT 2'.
/ ³
0ÄÄÄÄÄÄÄÄÄÄÄÁ 0 is at the coax core, and O is the outer surface.
So, maybe the ARRL HB is correct, as long as you look at the right formula
for the right capacitor formation.
73. Dick. VK3ABK.
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