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VK2ZRG > TECH 01.06.06 12:10l 159 Lines 7629 Bytes #999 (0) @ WW
BID : 2367_VK2ZRG
Read: DL1LCA GUEST
Subj: Re: Capacitor dielectric (VK2ZRG)
Path: DB0FHN<DB0MRW<DK0WUE<DB0RES<ON0BEL<VK7AX<VK2TGB<VK2IO<VK2WI
Sent: 060531/0250Z @:VK2WI.#SYD.NSW.AUS.OC #:16019 [SYDNEY] FBB7 $:2367_VK2ZRG
From: VK2ZRG@VK2WI.#SYD.NSW.AUS.OC
To : TECH@WW
VK2ZRG/TPK 1.83d Msg #:2367 Date:01-06-06 Time:6:45Z
Hello Dick VK3ABK, Cynics and all.
Dick wrote :-
>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.
Well Dick, I did title my bulletin re resistance of chromium as
"Possible error in ARRL Handbook" , That's not being too hard on them is it?
No one can say where the error came from originally. It's likely the ARRL
took the numbers from some "reliable" reference source and assumed the
numbers must be correct. This sort of thing happens often.
In your bulletin of 24th May titled "Resistivity again (VK3ZRG)" , there
were resistivity figures of 2.6 Ohm cm x 10^-6 for chromium. Maybe the number
is missing a 1 and should be 12.6 instead. 12.6 is close to the numbers from
the CRC handbook that Pete, G6KUI posted on packet, and close to other numbers
I've found since my original bulletin. If chromium really did have a low
resistivity, could you imagine some advertising agency passing up the
opportunity of saying "Our xyz RF product is chromium plated for good looks
and low surface resistivity." I've never heard such a claim, have you?
In the list that Paul M0CNL posted on packet, (not Paul's list, it was a
list that Paul found on the web, so let's be clear about that) tin was shown
as having 1.15 * 10-5 ohm-metres compared to copper at 1.673 * 10-8. I've
never heard or read any dire warnings about avoiding tin plated things at RF
because of the high surface resistivity.
That's the good thing about experience, you know when you see some number
or other that looks very odd, that it just must be wrong. Take the formula
for galactic noise that Andy G0FTD posted on packet recently. (Not Andy's
formula I must hasten to add). On the 8th March (gee was it that long ago!)
a bulletin from Andy had
>The median galactic noise is represented by:-
>
>Ng = 52.0 + 23 log10 (f) - 204 dBW (4.1)
Later in the same bulletin Andy wrote :-
>OK lets plug some numbers into this expression for 14MHz
>
>Ng = 52 + (23log10) x 14 - 204 gives
> 52 + (13.6100) x 14 - 204 = 714.6db over 1 watt/hz
>
>Eh!
>
>I don't think so.
>
>Have I been fed any stupid pills by accident or what ?
I replied to Andy's bulletin on 8th March mentioning BODMAS. In part I said:-
>I read the formula from your bull as 52 + 23*Log(F) - 204 dBW
>
>I think you will find that it should be 52 - 23*Log(F) - 204 dBw
>as Galactic noise decreases with frequency. That's what my reference
>books say.
> At 14 MHz the answer is -178.36 dBw
There were quite a number of bulletins on the subject at the time. In one
from Andy on 17th March, Andy said re the formula:-
>But it's NOT my formula - it comes from research of the US Military,
>the Voice of America, the Radio Propagation laboratory, National Bureau of
>Standards, the CCIR and a whole host of other interesting parties.
I interpreted this as "Well it comes from some very authoritative sources so
it must be right." This view point is perfectly reasonable, why should any
one doubt it you may ask. Well, you just do the calculation and think whether
the answers are reasonable.
At 1 MHz 52 + 23*Log10(F) -204 = 52 + 23*0 - 204 = -152 dBW per Hz
At 100 MHz 52 + 23*Log10(F) -204 = 52 + 23*2 - 204 = -106 dBW per Hz
At 1000 MHz 52 + 23*Log10(F) -204 = 52 + 23*3 - 204 = - 83 dBW per Hz
At 50 GHz 52 + 23*Log10(F) -204 = 52 + 108 - 204 = - 43 dBW per Hz
Taking the 50 GHz (50000 MHz) figure and multiplying by a bandwidth that
might be used for, say, a receiver in a radio telescope of maybe 5 MHz, you
have an extraordinary figure of +24 dBw power from a dipole antenna. +24 dBw
is 250 watts! It should take no more than 2 micro seconds for anyone to
decide that there is something seriously wrong with the formula!
Now onto capacitors and dielectrics. The quote didn't come from the ARRL
Handbook, Dick. It came from the ARRL UHF/Microwave Experimenter's Manual,
1990 edition.
I don't think there is any difference whether the capacitor has flat plates
or is in a co-axial form Dick. There are formulas, one of which is in your
bulletin, that have a SQRT(K) factor in them. So one can be forgiven for
getting it wrong about co-axial lines, but to add to the statement that in ALL
capacitors, the capacitance varies by the square of the dielectric constant
is just plain silly. (Just think what the definition of dielectric constant
is!) Here are some formulas for capacitance in co-axial lines from a Suhner
and Huber catalog of co-axial cables.
1) C pf/metre = 3.336 * 10^3 * (SQRT(Er)/Zo)
2) C pf/metre = Er / (18 * 10^-3 * LN(D/d))
My comment...10^3 is 1000 and 10^-3 is 0.001 or 1E-3. D is outside diameter
and d is inside diameter. Er is dielectric constant or K in other formulas.
For a 50 ohm co-ax with Er = 2.6 and D/d = 3.833
1) 3.336 * 1000 * (1.612/50) = 107.58 pF/m
2) 2.6 / (18*0.001 * 1.3437) = 107.49 pF/m
In formula 2) it is plain that if Er is doubled, so is the capacitance.
In formula 1) this is not so clear.
While on the subject of transmission lines, here is another example of
getting things wrong. In figure 45 on page 5-36 of the ARRL UHF/Microwave
Experimenter's Manual, there is a formula (Eq 56 and 57) for the Zo of a
stripline transmission line. Stripline is usually a flat strip conductor,
centrally placed between two ground planes. (This is not the same as microstrip
which has one ground plane.) There are six tables of dimensions versus Zo
for different types and thickness of printed circuit board material that
one might use to construct a stripline. The startling thing that I noticed
in these tables is, that at the low Zo end of the tables, a smallish change
in strip width was supposed to have a very major change in Zo.
E.g. in table 11, a 5 mm strip width had a Zo of 9.64 ohms and a 7 mm
width had 0.91 ohms. In table 15, a 3 mm strip was listed as 12.52 ohms
and a 6 mm width as 0.27 ohms.
How could that be true? Well it can't be and isn't. It turns out that there
are two formulas for striplines, one for narrow strip widths and the other
for wide widths. The change over between formulas occurs at a certain ratio
of width to ground plane separation where both formulas give the same answer.
The tables in the ARRL book used the formula for narrow widths, for the whole
range of widths in the tables. (The ARRL book formula had significant
differences from the narrow width formula, of the pair of formulas, that
were found on the web.) You might wonder if the formula in the ARRL book
said the Zo was 0.27 ohms for a 6 mm width, what was the answer for 7 mm?
Not surprisingly, it gave a negative Zo answer! I would have thought that
the alarm bells would have rung when the formula gave a negative number.
But no, they just terminated the tables to exclude negative Zo numbers.
Subsequent to getting the "right" formulas and putting them in a little
programme to do the number crunching, I found other formulas that gave very
similar results to the pair of formulas from the web. I have made stripline
using the right formula that when measured, had the calculated Zo. The
stripline was designed for a series of 416 MHz directional couplers which
all measured to the design coupling within a small fraction of a dB and had
an excellent directivity of >40 dB.
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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