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## "thickness" of antennas, and length

Jul 27th 2021, 14:09

#### WILS760

Joined: Dec 9th 2009, 13:43
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I have heard since I was a child that a "fatter"antenna has greater bandwidth. But a friend building a loop out of copper tubing raises an interesting question. That loop will be fairly thick. If the distance around the loop (or think of the length of a wire antenna, or an element of a yagi, etc.) is supposed to be X, is that the distance around the outside? The inside? Up the middle? We casually use formulas, without thinking much about what the length even means!

Anything we make an antenna of,even a thin wire, will have a different length if measured down the middle, or from one edge to (at the opposite end) the opposite edge, etc. When we talk about the length of some antenna element, what matters? Of course for a thin wire antenna the difference will be small. But at a theoretical level, and in practice for larger diameters, what are we talking about? (I realize that modern tuners may make this not too important practically, but I'd still like to know!)

Bob Wilson, WA9D
Jul 28th 2021, 05:25

#### W1VT

Super Moderator

Joined: Apr 4th 1998, 00:00
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Antenna modeling programs typically use the center of the conductor to define length.

As for equations, it is very hard to come up with math derived equations that are valid for thick conductors. I have yet to see a valid derivation for the impedance of a thick monopole or dipole. Typically the "K" factor comes from a set of measured data or computer models that use method of moments brute force number crunching.

Zak Lau W1VT
ARRL Senior Lab Engineer
Sep 20th 2021, 23:33

#### KE7CDT

Joined: Nov 16th 2004, 08:30
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The ARRL Antenna Books contain a figure for determining the "k" factor for length vs. diameter, but the graph does not extend far enough for my purpose.

Is there an extended graph available, or even a curve fit formula anywhere?

Also, is it correct to say that this is a capacitive effect? Does that mean there should be two factors, one for end effect and another for the diameter effect? Trying to understand what is going on rather than just relying on cut-and-trim.

John Poland
KE7CDT
Sep 22nd 2021, 05:47

#### W1VT

Super Moderator

Joined: Apr 4th 1998, 00:00
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The 24th edition of the Antenna Book has a formula

K=1-0.2250706/((ln(lamda/(2*d))-0.429451) page 2.3