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I understand that certain antenna designs (particularly phased arrays) require feeding each radiating element with a certain number of degrees of phase separation in order to achieve a desired radiation pattern or beamwidth.

I found this 2-meter phased array [pdf] article which goes fairly in-depth into the design and theory but glances over the exact details involved in computing the coax lengths for the phasing harness:

phasing harness diagram from article

The antenna design in the article proposes using a T-connector with a 22" length of coax going to one antenna and a 16" length of coax going to the other antenna to (supposedly) achieve 135-degrees of phase separation.

So my question is... is there a general method or formula for computing these phasing line lengths? (Are the values shown in the article even correct?)

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There is, but it depends on the characteristics of the cable and the frequency of interest. There are online calculators that can do the work for you. For instance the two lengths of your cable have the following attenuation (almost none for RG-58) and phase delay. The phase delay is noticeably different, but as I haven't evaluated the antenna design I don't know if it's correct.

The calculator: http://www.mogami.com/e/cad/coax-freq.html

Phase delay and attenuation for the 16" section:

http://www.mogami.com/cgi-bin/uncgi.cgi/cad/coax-freq.cgi?Opt1=Linear&Opt2=yes&Start=144&Stop=148&Len=.4064&Rs=0&Cs=0&Rr=0&Cr=0&Name=RG-58%2FU

Phase delay and attenuation for the 22" section:

http://www.mogami.com/cgi-bin/uncgi.cgi/cad/coax-freq.cgi?Opt1=Linear&Opt2=yes&Start=144&Stop=148&Len=.5588&Rs=0&Cs=0&Rr=0&Cr=0&Name=RG-58%2FU

There is a reasonably comprehensive document that covers the calculations necessary for this here:

http://ve2azx.net/technical/CoaxialCableDelay.pdf

This should give you more exact numbers if you need a particular solution.

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    $\begingroup$ I'd love to see this answer explain the math in the article some more. $\endgroup$ – Dan Oct 28 '13 at 20:26
  • $\begingroup$ "The Simplest Phased Array Feed System ...That Works", Roy Lewallen, W7EL, The ARRL Antenna Compendium, Vol 2, includes the equations and BASIC source code. $\endgroup$ – Cecil - W5DXP Jan 12 at 22:08
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The easiest and most forgiving phase system for 2 element arrays is the Christman method. Based on 1/4wl spacing, the phase lines are cut to 84 degrees and the lag line is cut to 71 degrees. This system will work from 160 to 2 meters. And easy to make reversible.

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