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Author Topic: Dipole Impedance vs length  (Read 2237 times)
AE5EK
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Posts: 53




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« on: June 14, 2012, 08:19:25 AM »

What are the equations for a center fed dipole R and X as a function of its length in wavelengths of the transmit frequency?
What are the equations for an Off Center Fed (1/3, 2/3) dipole R and X as a function of its length in wavelengths of the transmit frequency?

tks

Dennis
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WB6BYU
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Posts: 13018




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« Reply #1 on: June 14, 2012, 08:44:08 AM »

It depends also on the wire diameter, height above ground, and the ground characteristics.

As such, it is easier to model the antenna under the specific circumstances of interest
rather than trying to build a complex equation that includes all the variables.

The free version of EZNEC, or a freeware program such as 4NEC2, can do this for you,
or if you have a specific situation in mind you can ask here and someone may be able
to model it for you.


This article by the late W4RNL gives some data for 40m dipoles at different heights above
ground, both for feedpoint impedance and resonant length, so you can see how much
it can vary:

http://www.cebik.com/content/gup/gup2.html
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W5DXP
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Posts: 3546


WWW

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« Reply #2 on: June 14, 2012, 01:08:12 PM »

What are the equations for a center fed dipole R and X as a function of its length in wavelengths of the transmit frequency?

One can use the telegrapher's equation for such. Of course, one needs to estimate the attenuation factor which, in the case of a dipole antenna, includes normal losses plus radiation "losses".

http://www.vk1od.net/transmissionline/TE/TE.htm

Here's a little brain teaser. Given that a #14 wire 30 feet in the air has a characteristic impedance of 600 ohms and given that a particular 1/2WL dipole has a 50 ohm feedpoint impedance, what is the ratio of forward voltage to reflected voltage on the dipole wire at the antenna feedpoint. Hint: (Vfor-Vref)/(Ifor+Iref) = 50 ohms for the 1/2WL dipole.
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73, Cecil, www.w5dxp.com
The purpose of an antenna tuner is to increase the current through the radiation resistance at the antenna to the maximum available magnitude resulting in a radiated power of I2(RRAD) from the antenna.
K3VAT
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Posts: 701




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« Reply #3 on: June 15, 2012, 05:01:53 AM »

Quote from:  link=topic=83593.msg602741#msg602741 date=1339687165
What are the equations for a center fed dipole R and X as a function of its length in wavelengths of the transmit frequency? ... tks Dennis

In the ARRL Handbook (20th Ed) on pages 2.2 through 2.4 are several instructional graphs that illustrate the above relationship including, as WB6BYU has pointed out, wire size.  73, Rich, K3VAT
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WB6BYU
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Posts: 13018




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« Reply #4 on: June 15, 2012, 11:01:28 AM »

I guess part of the answer depends on what level of detail you want to be able to calculate.
For example, the late W4RNL gives the feedpoint impedance of antennas on various ham bands
in the articles on his web site, such as these:

http://www.cebik.com/content/a10/wire/iocf.pdf
http://www.cebik.com/content/a10/wire/abd.html
http://www.cebik.com/content/gup/gup5.html
http://www.cebik.com/content/gup/gup9.html
http://www.cebik.com/content/gup/gup10.html
http://www.cebik.com/content/gup/gup11.html

This will give you an idea of what impedances to expect when you use a particular antenna
on various bands, but not to the level of detail of changing from, say, 0.5 wavelengths
to 0.55 wavelengths.


The late W2PV's book on Yagi Antenna Design includes formulas for the reactance of an
element near 1/2 wavelengths long.  Several books, including the ARRL Antenna Book,
contain graphs of resistance and reactance vs. length for some specific wire size, though
the detail might not be sufficiently accurate for some purposes.

So if you can give us a better idea of your application, and the sorts of questions you are
trying to answer, we might be able to provide you with information that meets your needs.
Otherwise it is a pretty complex answer that handles all the possible cases.
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