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Author Topic: Impedance of ladder-line  (Read 932 times)
K5PSO
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Posts: 68




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« on: December 09, 2002, 09:48:54 PM »

Anyone know the formula or how to figure the impedance of home made line? For example, I'm thinking of feeding a quad with balanced line, with an impedance of, around 100 ohms or there abouts. COmments appreciated. 73, Dan K5PSO
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AC5E
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« Reply #1 on: December 10, 2002, 07:24:02 AM »

Hi Dan: Well, the formulas are in most handbooks. And in theory you COULD build 100 ohm twinlead. The mininum is around 80 ohms, the point where the conductors are actually in contact. But if you use reasonably sized wires the spacing between wires becomes so small that the power handling capacity of the resultant cable is virtually nil.

For example, a pair of #12's air spaced 0.1 inch apart, about the same as the thickness of the insulation on house wiring, has an impedance of just under 110 ohms. More practically, a pair of #20's spaced the same tenth of an inch would have an impedance of around 225 ohms. And either way, there are simpler ways to match a quad.

Personally, I use half inch hardline up the tower, a flexible jumper around the rotor and up the mast to the quad boom, a switch between individual loops, and a quarter wave section of RG11 to the outer loop. The inner loops have much lower drive impedances, of course.

Results - the SWR is under 1.5 across 20, under 1.3 on 15 below 21.4, and under 1.3 from 28.0 to 28.8. Where I operate, of course. Excess losses from high VSWR? Absolutely negligible.

73  Pete Allen  AC5E
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AC5UP
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« Reply #2 on: December 10, 2002, 12:23:00 PM »

If you want the mental exercise of designing ladder line that's OK... And here's a web page to start with.

http://www.qsl.net/aa3rl/tlcalc1.html

But, if you want to get it done there's an easier way. Check the ARRL handbook for the nomograph of wire size vs spacing -or- pick a convenient size.

Huh?

Fact is, ladder line is very tolerant of SWR and impedance variations and you're building a non-critical matching section that will be dialed in with a pair of wire cutters. The chances either of us will home brew a section of line that's textbook perfect from end-to-end is next to nil, so I'd pick something easy like a pair of 14 gauge insulated THNN 'house' wires spaced 1" apart and prune it into resonance. Don't worry about the actual impedance, just make sure you start with more than 1/4 wave in length so you can't miss the sweet spot.

1/4" C-PEX tubing in the plumbing section of your local mega-store cuts into dandy spacers with a tubing cutter and cinches on to the lines with a Ty-Rap attached 'dog-bone' style. Figure about $3.00 per 10' length of C-PEX and you have plenty of spacers...

- AC5UP
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WB2WIK
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« Reply #3 on: December 10, 2002, 12:32:43 PM »

Ladder line per se might be awfully difficult to fabricate, since it involves extruding dielectric materials and then cutting windows in the material.

I think what you're really looking for is the formula for open-wire line, which is:

Zo = 276log (2S/d)

Where S= center-to-center spacing of the conductors
and d= the diameter of the wires used.

When you crunch the numbers, you'll see that 100 Ohm open-wire line made of any reasonable conductor size to carry appreciable current would be very difficult to make, because the wires will nearly touch.

Which is probably why you don't see such line sold commercially!

I'd use 50 or 75 Ohm coax and a balun, instead.

WB2WIK/6
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AC5UP
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« Reply #4 on: December 10, 2002, 12:33:34 PM »

The previous comment was made on the assumption the loop will be fed by a 1/4 wave open-wire matching section connected to a 1:1 current or 'choke' Balun with any length of coax back to the rig...

That's how I do Loops, Doublets and EDZ's.

- AC5UP
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AC5UP
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« Reply #5 on: December 10, 2002, 12:54:13 PM »

Looks like most folks prefer 1/4 wave of 75 Ohm coax instead of playing with an open wire matching section. I've gotten handy with open wire feeders and have no problems with them as they're very tolerant of construction variations. But... Here's a thot:

If you're set on a 100 Ohm parallel line, consider paralleling two 50 Ohm coaxial cables into a shielded 100 Ohm balanced feed line.

(?)

- AC5UP
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AD6JN
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Posts: 172




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« Reply #6 on: December 10, 2002, 04:03:14 PM »

The equation cited is for air and the 276 needs to be divided by the square root of the dielectric coefficient if an insulation separates the pair.  For PVC this is near 3 depending on the additives.  I am not sure about the power you are running but 18 awg. black electical wire should work.  Black is more UV resistant.  Tape the wire every few inches to retain the close spacing.

Depending on the frequency and/or length the line will give a different impedance reading if tested.  Plotted over the HF bands (1.8 to 30 Mhz.) you will see the average impedance comes close to the value of the equation.  For PVC it will tail-off toward the higher frequency.  PVC is not as frequency stable as TFE (Teflons).

Bob AD6JN

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WB2WIK
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« Reply #7 on: December 10, 2002, 05:38:07 PM »

I remember from my early days that #18 AWG stranded lamp cord ("zip" cord) with flexible (usually brown colored) insulation used to measure about 75 Ohms or so and was a good substitute for real "transmitting twin lead" or coaxial cable when used below 30 MHz.  But that was 30+ years ago, and I have no idea if the modern construction lamp cord made of today's materials would be as good, or as stable.

It would be interesting to repeat these measurements using off-the-shelf lamp cord today, to see how it fares.

WB2WIK/6
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AC5E
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« Reply #8 on: December 10, 2002, 06:31:25 PM »

"Modern" plastic insulated #16 conductor "small appliance" cord has a measured impedance of 105-115 ohms, and a measured loss of approx. 3.0 dB per 70 feet at 14. mHz. Or 1.0 dB per 100 feet at 3.8 mHz. Power handling capacity is probably 200 watts to a fairly well matched load. And that's a whole lot worse than the old DCC covered rubber insulated stuff I used for feedline over 50 years ago. I suspect the plastic insulation is mostly recycled plastic bags.

However, the question was about feeding quads. The outer loop should have a feedpoint impedance in the 105-110 ohm range at resonance and a few feet of RG11 will make an almost perfect match to 50 ohm coax. The inner loops have a drive impedance in th 50-60 ohm range and need no matching.

Which, unless you like to beat your head against the wall because it feels so good when you stop, coax makes a much cleaner and easier to install feedline.

73 Pete Allen  AC5E
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