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VK2ZRG > TECH 14.07.04 11:34l 82 Lines 3714 Bytes #999 (0) @ WW
BID : 19663_VK2AAB
Read: GUEST OE7FMI
Subj: Stripline impedance
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Sent: 040714/0849Z @:VK2AAB.SYD.NSW.AUS.OC #:19663 [SYDNEY] FBB7 $:19663_VK2AAB
From: VK2ZRG@VK2AAB.SYD.NSW.AUS.OC
To : TECH@WW
Hello to all techies,
I was looking at my ARRL Microwave Experimenters Handbook
recently and found a formula that calculates Stripline impedance for various
line widths. Stripline is a structure, usually of printed circuit board, where
you have a conductor sandwiched between two ground planes. This is not as
common as Microstrip which has a single groundplane.
This is the formula. Zo = (60 / ûEr) * LN((4 * B) / (Pi * D));
Where B = groundplane separation. Er = Dielectric constant.
W = Stripline width T = Stripline thickness
D = W/2 * (1 + T/W * (1 + LN(4*Pi*W/T) + (Pi/2 * (T/W)ý)))
The strange thing about this formula (on page 5-36 in Fig 45) is that it
can produce a dramatic change in the calculated Zo for a small change in line
width. If you have this handbook, look at the bottom of tables 11 through to
16 on pages 5-37 to 5-39. I've put this formula into a programme and it
produces identical results as appear in the tables 11-16.
This is most of table 11 (for Er = 4.8 B = 3 mm and T = 0.044 mm)
W in mm Ohms mm ohms mm ohms
W = 0.10 Zo = 88.02 W = 1.10 Zo = 46.45 W = 2.80 Zo = 24.31
W = 0.20 Zo = 78.95 W = 1.20 Zo = 44.49 W = 3.00 Zo = 22.60
W = 0.30 Zo = 72.36 W = 1.40 Zo = 40.96 W = 3.50 Zo = 18.73
W = 0.40 Zo = 67.23 W = 1.50 Zo = 39.36 W = 4.00 Zo = 15.35
W = 0.50 Zo = 62.99 W = 1.60 Zo = 37.85 W = 4.50 Zo = 12.35
W = 0.60 Zo = 59.38 W = 1.80 Zo = 35.06 W = 5.00 Zo = 9.64
W = 0.70 Zo = 56.22 W = 2.00 Zo = 32.54 W = 5.50 Zo = 7.18
W = 0.80 Zo = 53.41 W = 2.20 Zo = 30.23 W = 6.00 Zo = 4.93
W = 0.90 Zo = 50.88 W = 2.40 Zo = 28.11 W = 6.50 Zo = 2.85
W = 1.00 Zo = 48.57 W = 2.60 Zo = 26.15 W = 7.00 Zo = 0.91
You can see that a change in width of 5 to 7 mm is supposed to result in a
10 to 1 impedance change. This of course is impossible! If the range of
W is extended past 7.0 the impedance numbers become negative.
W = 7.10 Zo = 0.54
W = 7.20 Zo = 0.18
W = 7.30 Zo = -0.18 This is even more curious.
W = 7.40 Zo = -0.54
W = 7.50 Zo = -0.89
The formula is obviously rubbish. Just goes to prove that you shouldn't
believe everything that you read, whether it's in a book or on a computer
screen.
Consulting Reference Data for Radio Engineers (4th edition) on page 599
I find a graph that gives Zo for various combinations of T/B and W/B.
For Er = 4.8 B = 3 mm T = 0, I get these numbers.
W = 0.3 mm Zo = 89 ê This is more like it!
W = 0.9 mm Zo = 59 ê
W = 1.05mm Zo = 55 ê
W = 1.5 mm Zo = 46 ê
W = 2.7 mm Zo = 32 ê
W = 4.5 mm Zo = 22 ê
W = 6 mm Zo = 17.5 ê
W = 9 mm Zo = 12.5 ê
W = 12 mm Zo = 9.5 ê
Computers are meant for number crunching. I like writing small utility
programmes that give better numbers than you can get by interpolating a
graph or a table of numbers. Books can easily get misplaced, computers
are harder to loose.
Can anyone give me a formula that either gives strip width for Zo
or Zo for strip width, for a strip thickness of zero up to 1/4 of
the groundplane spacing. The formula should produce numbers that are
comparable with the graph in Reference Data for Radio Engineers
(4th edition) p599. This graph also appears in a number of handbooks.
It comes from a paper by S.B. Cohn "Problems in Strip Transmission Lines"
which was published in IRE Trans., PGMTT-3, 2, pp. 119-126 March 1955
Thanks in advance.
73s from Ralph VK2ZRG@VK2WI.#SYD.NSW.AUS.OC
/ack
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