[TowerTalk] Comments on Array Solutions "dissimilar antennas" phasing application note.

[Jim Lux]

In connection with a post about phasing dissimilar antennas in a stack,
someone posted a link to a way to determine the phases using an oscilloscope

http://www.arraysolutions.com/Products/dissimilarants.htm

Determining the received phase of signals from stacked antennas is something
that I've been spending a lot of time on recently at work, albeit at 7 GHz,
not 14 MHz, but the principals are the same.  So, here are a few comments:

1) First off, we need to think about what accuracy do you need for this
measurement.  This in turn depends on what you're trying to accomplish.  If
all you worry about is some abstract "max gain in some direction", then your
needs aren't very stringent (perhaps 20 degree accuracy is good.. even 30
degrees ).  If you are worried about steering the composite beam with an
accuracy of a few degrees, and the antennas are moderately (more than 1/4
wavelength) far apart, the requirement could be much tighter.  The shift in
the beam is arctangent(phase shift (deg)/spacing (deg)).

You can reverse the equation to get phaseshift(deg) = tan(beam
direction)*spacing(deg).  Since presumably you're going to all this trouble
for DX signals with low angles of arrival, let's say you are worried about a
5 degree change in pattern. That works out to about 15 degrees of phase
shift if the antennas are a half wavelength (180 deg) spacing.

A general guideline is that if you want to measure or control something, you
need to measure it with a technique that has at least 3 times the accuracy.
So, we probably need a phase measurement technique with an accuracy of
around 5 degrees.

This is fairly challenging.


2) The basic idea of using a source that's some moderate distance away is a
good one, assuming that you remember that the pattern of the antenna changes
very rapidly close to the ground, implying that phase shifts change rapidly.
The saving grace is that both antennas you're measuring will probably be
affected similarly.   The measurement should be done at several different
directions and/or distances, and the results compared to see if this effect
is biting you.

3) Now let's look at the oscilloscope technique.  You need a fairly hefty
signal to be able to see it on the scope face.  Say you're on the 50
mV/division (most sensitive on many scopes).  You want an amplitude that's
at least 4 or 5 divisions, so that's around 250mV.  Into 50 ohms (you are
terminating the scope inputs, right?) that's about a milliwatt (0dBm), which
is a fairly strong signal.

Say your buddy is transmitting with 100W from a 6 miles away, and you've
both got 5dBi antennas.  Path Loss between isotropes: 32.44+20log10(10) +
20log10(14) =32.44+20 +22  (http://home.earthlink.net/~w6rmk/pathloss.htm )
About 75 dB.  The antenna gain reduces this to 65 dB.  Your buddy is
radiating +50dBm, so you'll be seeing about -15dBm, which is a pretty small
signal. (about 40mV), barely a division on the scope face.  Tell your buddy
to fire up the linear!.

The scope's also not a narrow band detector, so you'll be looking at a
combination of ALL signals.  However, your buddy with the kilowatt a couple
miles away will dominate.  The frequency selectivity of the antenna will
help.  However, what's the "noise floor" of your scope?  Are you going to be
looking for that 50 mV sine wave in 50 mV of noise?


4) Measuring phase on a scope to an accuracy of a few degrees is quite
challenging.  Spread one cycle out over 10 divisions, and each division is
36 degrees.  By eye, you can probably estimate to a fifth or sixth of a
division on a noisy signal.  On a real clean signal, a tenth of a division
is possible, so you're potentially in the 4-5 degree range, accuracy wise.
With a good scope that has a X10 expansion, and with VERY stable triggering,
you can do better, but you are really depending on the triggering.

Don't forget that you're making a measurement between two signals, so the
overall uncertainty is actually 1.4 times the uncertainty in measuring one
signal.


5) We haven't even begun to address the errors due to mismatches, reflected
power, etc.  All of these can actually add up to a fairly large phase error.
Considered just in terms of phase error, a mismatch of 20dB (1.22:1 VSWR)
can result in a phase error of arctan(0.1), or 5.7 degrees. (that's why
having the scope termination matched to the line is important!) (1.5:1, 14
dB = 11 deg error, 2:1, 10dB = 17.5 deg max error)


Jim, W6RMK