[TowerTalk] Method of calculating phase delay variation

[Jim Brown]

On 9/3/2013 8:28 AM, K7LXC at 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