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Re: [TowerTalk] Method of calculating phase delay variation

To: towertalk@contesting.com
Subject: Re: [TowerTalk] Method of calculating phase delay variation
From: Jim Brown <jim@audiosystemsgroup.com>
Reply-to: jim@audiosystemsgroup.com
Date: Tue, 03 Sep 2013 10:54:50 -0700
List-post: <towertalk@contesting.com">mailto:towertalk@contesting.com>
On 9/3/2013 8:28 AM, K7LXC@aol.com wrote:
OTOH the potential problems with out-of-phase  antennas can be
disastrous. Bob Heil's , K9EID, dramatic demonstration  of out-of-phase speakers
(another propagation device) will give you  pause to maybe pursue  more precise
phasing. (The sound disappears  when they are out of phase. Imagine your
antennas canceling each other  out.)

While the principle at play in Bob's demonstration is important, he used the wrong word to describe it. The correct word to describe the reversal of a pair of wires carrying signal, and the inversion a a signal in a gain stage is "polarity," not "phase." Polarity is a two-valued function -- either positive or reversed -- and it is independent of frequency. Phase is a continuously valued function and has the units of degrees or radians.

Phase can be described only as the difference between two signals of the same frequency, and for any method that we use to shift the phase, increases linearly with frequency. For example, the signal from two ideal sources that are at different points in space will have a different phase relationship with each other at every frequency, and at every point in space (because the travel time to every point in space is different). When we shift the phase between two signals by means of a network, or by adding a length of transmission line to one of them, the phase shift will be different at every frequency. But when we reverse the polarity of the feed to one of the radiators, the phase does not change, but their fields are opposite at all frequencies.

The difference is critically important in understanding how things work. In the field of pro audio, we learned to appreciate and understand this principle more than 30 years ago, and to use the right words to describe what we're talking about. It's long past time for RF engineers to learn them.

Now, getting to the original question -- how to calculate the needed length of delay lines for stacked antennas when those antennas are different from each other. If I were faced with this problem, I would build an NEC model of both antennas, with the geometric relationship between them as close as I could get to how I could mount them, add the feedlines to the model, and tweak the line lengths until I got the far field patterns I wanted. Why? Two very important reasons. First, the amplitude and phase of the field from the two antennas will be different at every vertical and horizontal angle, and the far field pattern will be the result of the complex addition (magnitude and phase) at every angle. Second, the phase shift in the delay lines will be dependent upon the complex impedance at the feedpoint of the antenna. There's a discussion of this second effect in the ON4UN book -- look for Christman feed in the index. It's in the chapter on phased vertical antennas.

73, Jim K9YC
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