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VK2ZRG > TECH 03.06.06 07:37l 75 Lines 2563 Bytes #999 (0) @ WW
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Subj: Co-axial capacitance
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Sent: 060603/0346Z @:VK2WI.#SYD.NSW.AUS.OC #:16150 [SYDNEY] FBB7 $:16150_VK2WI
From: VK2ZRG@VK2WI.#SYD.NSW.AUS.OC
To : TECH@WW
VK2ZRG/TPK 1.83d Msg #:2375 Date:03-06-06 Time:4:42Z
Hello Dick VK3ABK and readers,
Here is another way of looking at what happens to the capacitance of a
co-axial capacitor. First of all here are some formulas for L and C in
a co-axial cable, a very common form of a co-axial capacitor.
1) pF per metre = Square Root(Er) / (3 * Zo) * 10000
2) nH per metre = Square Root(Er) * Zo / 0.3
3) pF per metre = 24.154 * Er / Log10(D/d);
D = outer diameter, d = inner diameter, Er = dielectric constant.
Putting some numbers into these equations, Er = 1 Zo = 50 D/d = 2.301
For 1) (1 / 150) * 10000 = 66.667 pF per metre
For 2) (1 * 50) * 0.300 = 166.667 nH per metre
For 3) 24.154*(1/0.36192) = 66.667 pF per metre
Zo of a co-axial cable comes from the well known formula of
4) Zo = (60/SQRT(Er)) * LN(D/d)
For D/d = 2.301 and Er = 1.0, we get 60 * 0.833344 = 50.000 ohms
Now if Er is increased to 2.0, the Zo will be 35.356 ohms, and we get
For 1) (1.4142 / (3*35.356) * 10000 = 133.33 pF per metre
For 2) (1.4142 * 35.356) * 0.300 .. = 166.667 nH per metre
For 3) 24.154*(2/0.36192) .......... = 133.33 pF per metre
Here we see that capacitance per metre is doubled when Er is doubled.
i.e. capacitance is proportional to Er, just as what the definition of
dielectric constant states. Notice that the inductance per metre does
not change when Er changes, just as one would expect.
Using another formula for co-axial cable capacitance per metre of
5) C pF = 3.336 * 1E3 * (SQRT(Er) / Zo)
For Er = 1.0, D/d = 2.301 and Zo = 50 ohms we get
3336 * (1/50) = 66.72 pF per metre
For Er = 2.0, D/d = 2.301 and Zo = 35.356 ohms we get
3336 * (1.4142/35.356) = 133.43 pF per metre
Using yet another formula for co-axial cable capacitance per foot
(In the ARRL Antenna book the 7.354 number is 7.26 and in another book I
have it's 7.36, not that it matters much for this topic.)
6) C pF = (7.354 * Er) / Log10(D/d)
For Er = 1.0, D/d = 2.301 we get
7.354 / 0.36192 = 20.32 pF per foot
For Er = 2.0, D/d = 2.301 we get
14.708 / 0.36192 = 40.64 pF per metre
If the capacitance formula includes Zo, as in 1) and 5), then the Er term
becomes SQRT(Er) but the result still is, that capacitance is proportional
to Er, the dielectric constant!
What say you now Dick?
73s from Ralph VK2ZRG@VK2WI.#SYD.NSW.AUS.OC
Taglines by Colin Coker G4FCN
C Program run, C Program Crash...ReWrite in Pascal!
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