This is the "MAXNR.DOC" file distributed with Z-Track. No attempt has been made to beautify it for presentation on the web... it is almost exactly in its original form, which was intended for viewing on an 80x25 text screen or printing on one of the old "text only" printers that some of us were still using at the time. See also Polarization of EME Signals: How To Succeed More Often
A BRIEF TUTORIAL ON Z-TRACK's "MAX NR" INDICATOR
---------------------------------------------------
MM Software Systems
April, 1993
I've been asked about the "Max NR" figure generated in Z-TRACK by
several users of the program. Most of the questions were just plain
old "Huh ???" , indicating that I really goofed. Max NR, as far as
I know, had never been used in any moon-tracking software prior to
the first release of Z-TRACK. I developed it as a new indicator to
supplement the "Spatial Polarization Offset" so often seen in such
software. I firmly believe it is a much more meaningful and easily
interpreted indicator of polarization conditions. So, here goes my
best shot at removing the shroud of mystery from the Max NR index !!
I've had a go (or two, or...) at explaining this verbally, without
the kind of success I was hoping for. MAYBE I can do better writing
it down (???).
THE PRE-BASICS
----------------
I suspect few people will argue these days that the polarization
of an incoming signal with respect to the polarization of the
receiving antenna makes a tremendous difference in how well the
signal can be heard. A signal perfectly aligned in polarization
with the receiving antenna system will suffer no loss of strength
due to polarization mis-alignment. A signal arriving perpendicular
to the polarization plane of the antenna (90 degrees to it) will
suffer the greatest loss - How much depends on many factors, but
for a typical modern yagi it is generally taken as between 20 and
30 dB. In between these extremes the loss varies logarithmically
with the cosine of the angle (by angle I mean the difference in
degrees between the polarization plane of the incoming signal and
that of the antenna). A formula for this is:
Loss (dB) = 20 log(cos é)
where é = the angle in degrees.
This formula assumes a perfect yagi with no unwanted response to
signals of the opposite polarization. It is VERY close up to about
the 18 or 20 dB point, but beyond that needs a correction factor
to keep the result down to a realistic level.
That's all well and good for two antennas of like polarization
pointing toward each other along the Earth's surface. But what of
two antennas of like polarization pointing off into space? The
situation becomes a little more complicated. In my own crude way
let me try to help you visualize what I mean. Suppose you had a
large round ball sitting in front of you. If you took two samll
model yagis and planted one on the very top of the ball (be sure
to align the elements so they are parallel to the surface of the
ball directly below the antenna) so that it is pointing straight
away from you toward a distant wall, and the other on the left
side of the ball (elements parallel to the surface of the ball)
pointing to the same distant wall, You will have the basis of this
visualization. Both antennas are horizontally polarized with
respect to the surface of the ball (simulated Earth), right? But
stand back and sight along the boom of each yagi, toward that wall.
If you can visualize a signal leaving each antenna and travelling
to the the wall (simulated moon),you will see that the polarization
planes of the two signals hitting the wall are actually 90 degrees
out of sync with each other. This difference is what we call
"Spatial" Polarization Offset! Gee Whiz!
The geometry involved on an EME path is a little more complex,
what with elevation angles and so on. The point of reference used
for such calculations is generally the Earth's polar axis, but a
complete discussion of the mechanics involved is beyond the intent
of this discourse (and is a fantastic way to get a headache). Here
is the basic formula used to calculate a spatial polarizatoion for
an antenna with respect to the Earth's polar axis:
(sin L * cos E - cos L * cos A * sin E)
P = ATN ---------------------------------------
(cos L * sin A)
where L = Latitude of station {footnote 1}
A = Azimuth of antenna
E = Elavation of antenna
P = Polarization angle
The spatial polarization offset (read 'difference') between any two
stations is simply P1 - P2, but keeping it within a range of -90 to
+90 takes additional steps.
MOVING ON TO THE REAL WORLD
-----------------------------
For some time we have been accustomed to seeing a "Polarization"
or "Spatial Polarization Offset" figure in moon-tracking programs
that track the moon for two stations. This figure is in degrees,
with some programs keeping it within a range of -90 to +90 degrees
while others allow it to approach 180. Along with this, many of the
programs have also tried to include a "Polarization Loss" figure in
dB, with 0 dB indicating a polarization offset of 0 (or 180) degrees
and 25 dB or more indicating a polarization offset of 90 derees.
It doesn't take a rocket scientist to figure out that this just
cannot be the case. We've all made some fine EME QSOs when software
told us to expect 20+ dB loss of signal based on polarization! So
what's the deal here? The problem is that programs like that don't
consider the affects of Faraday rotation. The fact is that due to
Faraday rotation in the ionosphere signals can arrive at the receive
antenna at ANY polarization, reguardless of the spatial polarization
relationship between the two stations. Given that consideration,
the next thing we're confronted with is the argument that ALL of
this spatial polarization business should be disreguarded since the
unpredictable Faraday is going to modify the polarization anyway.
In other words we "make our skeds blindly and take our chances".
BUT - and this is a B-I-G but - the ionosphere has another unique
little property that should make us re-think the situation. Simply
put, a signal polarization which rotates in a given direction when
passing through the ionosphere on its way to the moon will rotate
the same amount in the same direction (from the observer's viewpoint)
on the return trip. You can visualize it this way: Suppose you
were standing behind the reflector on your EME antenna and sighting
down the boom to the moon. Further suppose for a moment that you
could see the polarization plane of the signal leaving your antenna
and traveling to the moon and back again to the antenna. If you
sent out a burst of RF and observed that the polarization plane
shifted 45 degrees to the right (clockwise) on the way out to the
moon, your first assumption would probably be that the signal will
rotate in the opposite direction (from your perspective) on its way
back, thus "un-twisting" itself and arriving perfectly in line with
the elements on your antenna. But the ionosphere doesn't see it in
that way. In fact the polarization plane will rotate by the same
amount in the same direction (clockwise) from your vantage point on
the return trip - thus making it now 90 degrees out of alignment
with your antenna.
So what? Consider this: If you add a second station whose QTH
is far enough away from yours so that the spatial polarization
offset between the two of you is 45 degrees, something interesting
begins to take shape. Suppose you transmit and the Faraday causes
the polarization plane of your signal to rotate 45 degrees clockwise
by the time it reaches the other station. It started out at
0 degrees (the spatial polarization of your antenna) and was twisted
45 degrees clockwise, so it arrives at his antenna perfectly aligned
with it (his spatial polarization is 45 degrees greater than yours,
don't forget). Sounds like the Faraday is doing us a big favor,
right? WRONG! Now suppose the other station transmits a string
of O's back to you (having heard your signal very well by virtue of
the perfect polarization alignment). The polarization plane of the
signal starts out at 45 degrees (his spatial polarization) and then
gets rotated 45 degrees clockwise on its way to you, making the
polarization of the signal 90 degrees in "spatial" terms. Yikes!
Your antenna is still at 0 degrees "spatial" polarization, and his
signal is coming in at 90 degrees! Unless you're a BIG GUN, you
just won't be able to hear him. Good grief, one-way propagation!
WHEREAS THE ABOVE SITUATION IS AVOIDABLE...
---------------------------------------------
Fortunately, there is a way to figure out what times are most
likely to yield frustrating one-way conditions in advance. Going
back to the example above... If the spatial offset between the two
stations were 0 deegrees, then Station A transmitting to station
B would result in a clockwise twisting of 45 degrees, arriving 45
degrees out of alignment with his antenna. On the return trip, the
exact same relationship holds. If the Spatial offset were 90
degrees, then station A transmitting to station B would result in
a signal at 45 degrees "spatial polarization" being received by an
antenna with a polarization of 90 degrees, for a difference of 45
degrees. On the return trip, 90 degrees starting from his antenna
gets twisted clockwise to 135 degrees (135 degrees is equivalent
to -45 degrees. It should always be kept in a range of +/- 90
degrees by adding or subtracting 180 degrees as necessary. 180
degrees is physically the same as 0 degrees), which is an offset of
45 degrees with reguard to your antenna. In either of these cases
the signal will be mis-aligned by the same amount (45 degrees) at
both stations. There will be a resulting loss of 3 dB, but at least
it's reciprocal (and 3 dB isn't as bad as 20+ dB).
I could (and probably should) sit here and go through various
possible combiantions of "spatial offset" and Faraday rotation for
a L-O-N-G time. I'm not going to, but I would like to bring up one
other point before going on. If one works away at this problem long
enough (I've been fretting away at it for 5 years now), one then
begins to think in terms of "windows of opportunity". Considering
the original 45 degree spatial offset again... The absolute best
that can be achieved (under normal circumstances) in this case is a
Faraday of 0 degrees or 90 degrees. This would indeed result in a
reciprocal path with 3 dB loss of signal at both ends. BUT, if the
Faraday changes by only 15 degrees in either direction, the signal
misalingment at one station will become 30 degrees (1.24 dB loss)
and at the other station 60 degrees (6 dB). Notice how quickly
the signal falls off at one end of the path for very small changes
in prevailing Faraday - thus a small "window of opportunity" for
reciprocal conditions, what with Faraday being such a changeable
entity. On the other hand, consider either of the perfect cases -
that is either spatial 0, Faraday 0 or spatial 90, Faraday 90.
Under these circumstances the path is reciprocal with 0 dB loss at
either end. If the Faraday changes 15 degrees in either direction
the reciprocity will remain, and the signal will drop by only 0.3 dB
at both stations. Indeed, the Faraday must shift 45 degrees
one way or the other before the signal drops to -3 dB and even
then it is still reciprocal. Hence a greater "window of opportun-
ity".
The bottom line is that one-way conditions are much more likely
to occur when the spatial offset is in the vicinity of 45 degrees
and drops to nearly 0 when the offset is 0 or 90 degrees. Data
collected over the past few years clearly shows that statistically
the chances of completing an EME QSO drop off sharply when the
spatial offset approaches 45 degrees, especially for the smaller
stations who just don't have the signal to spare. Many have clearly
benefitted in the past few years by careful consideration of these
polarization issues.
A BETTER WAY ???
------------------
Considering the spatial offset in degrees is all right up to a
point, but it can become a nuiscance. I couldn't help thinking that
what we really wanted to know was how non-reciprocal a given path
could get at a particular time. The spatial offset information was
nice, but I would find myself wanting to know more. When working up
sked times, I often wondered about the actual non-reciprocity that
might come into play. Hmm, the offset is 38.2 degrees, the cosine of
38.2 is ahhh... and the log of that is ummm..... Blast and drat!
After a few false starts (not to mention sleepless nights) I came up
with the "Max NR" figure. This gives a good approximation of the
non-reciprocity that is likely to be encountered based on a given
spatial offset. The name is somewhat of a misnomer, since Max NR
does not always give the absolute maximum non-reciprocity that is
possible for a given time. It gives a precise maximum only for
offsets of 0, 45, or 90 degrees. At other offsets it gives a very
good approximation of typical non-reciprocity values that are
actually observed on EME. Spatial offsets near 45 degrees will show
the highest Max NR figures, as offsets in that range are the most
likely to cause severe one-way conditions.
One must bear in mind that this is neither a worst-case nor a
best-case indication. However, it is a very good indicator of the
typical non-reciprocities seen on EME and correlates quite well with
EME logs analyzed to date. What the Max NR does is provide a
convenient and user-friendly way of weeding out times that have been
statistically proven to have the lowest chance for success.
A VERY GOOD "FIT"
------------------
When I devised the new Max NR index, I needed to see how well it
would fit with observed EME results, compared to other methods.
I analyzed several EME logs for percentage of QSOs vs spatial offset
and Max NR. The graphs of QSOs vs. spatial offset showed the
anticipated dip around 45 degrees (+/- a fair bit), but it was less
than dramatic, all things considered. I next plotted the QSOs vs.
Max NR and found an amazing correlation. I was not prepared for
the results. All of the logs checked showed 90 percent or more of
the QSOs occurred when the Max NR was less than 3 dB! It was a
smooth curve with a very sharp drop for low but increasing values
of Max NR, leveling out as it approached 25 dB. There was usually
a small "anomaly" at 25 dB, caused by the method used to round off
(or limit) Max NR indices that soar above that point. Remember
my previous comment about the equation for dB loss needing a
correction factor above 18 or 20 dB? I am very pleased with the
results obtained.
Here is an attempt at reproducing the graphs in text form (for a
typical log): [These are lacking in resolution - it's tough to
reproduce graphics on an 80x25 text screen!!!].
EME QSOs VS SPATIAL OFFSET
# 100-|*
90-|** *
O 80-|*****
F 70-|******* **
60-|************* ** * * * **
E 50-|******************** * ****************
M 40-|********************** ************************
E 30-|*********************** ** **************************
20-|**************************** ** ****************************
Q 10-|***************************************************************
S 0-|***************************************************************
O -------------------------------------------------------------------
s 0 10 20 30 40 50 60 70 80 90
SPATIAL OFFSET (DEGREES)
EME QSOs VS MAX NR
# 1000-|*
900-|*
O 800-|**
F 700-|**
600-|***
E 500-|****
M 400-|***** round-off anomaly
E 300-|******** ³
200-|**********
Q 100-|************** **
S 0-|**************************************************************
O -------------------------------------------------------------------
s 0 2 4 6 8 10 12 14 16 18 20 22 24
Max NR (dB)
RECOMMENDATIONS FOR USE
-------------------------
Having introduced the concept of "Max NR" , here is a brief
comment on what I have used it for. When making skeds I start with
the smallest stations I want to run with, scheduling them when the
Max NR is at its lowest (typically less than 1 dB). Then I move up
to progressively larger stations, accepting somewhat poorer times
as the size of the station increases. If you make many skeds you
will find that it is not possible to schedule them all at "ideal"
times! Generally speaking, I try to keep the Max NR on all skeds
under 3 dB. I rarely suffer the "one-way blues" any more, although
it does happen on rare occasions. (For every rule, there is an
exception).
Spatial Offset (and hence Max NR) varies drastically from day to
day as the declination of the moon changes. Hint: if you can't
find a time with low Max NR on a given day, try a few days later or
earlier. Sometimes, you have to give up... During the recent EME
expedition to KC6, I ran a statistical analysis of the path from my
QTH to KC6 and found that the lowest Max NR for the entire common
moon window during that month was 12.6 dB! Arghhh!!!
EXCEPTIONS - QSOs NEAR 25 dB MAX NR
-------------------------------------
Any discussion on the subject of one-way EME conditions would
not be complete (or fair) without some comments about why some good
QSOs are indeed possible at 45 degrees spatial offset (or 25 dB Max
NR). You will have noticed that while the graphs above show a dip
in the number of EME QSOs in this region, it certainly does not
drop to zero. There are at least 3 reasons for this.
Perhaps the most obvious exception is when the two stations have
enough power and combined antenna gain to overcome very substantial
losses. It's certainly possible to give up many dB and still work
some of the super-stations.
As mentioned before, a situation exists when the spatial offset
is 45 degrees and the Faraday is 0 or 90 degrees (and very stable)
causing reciprocal conditions but 3 dB loss of signal at both ends
of the QSO. Sometimes the Faraday is indeed stable enough to
permit complete QSOs in this case (assuming both stations can deal
with the 3 dB loss).
The third exception is that it is possible for the polarization
of a signal passing through the ionosphere to become diffused or
elliptical. In this case weak signals may be heard at a variety of
receive-antenna polarizations, but not without some sacrifice in
signal strength. Depending on the size of the two stations and the
exact nature of the polarization diffusion, some QSOs are indeed
possible in this case reguardless of the spatial polarization
offset. From observations made over a period of time it seems that
such conditions occur more frequently at times of high solar
activity.
Again, the whole point is that it is less likely to complete EME
QSOs when the spatial offset is near 45 degrees (and Max NR is
high) than when the offset is closer to 0 or 90 degrees (in which
case Max NR is low). Therefore, a careful consideration of the
polarization issue when scheduling EME activities can significantly
improve the chances for success (by weeding out times that have the
lowest chance for success), but will never offer an absolute
guarantee of anything. While working on the Max NR concept for use
in Z-TRACK, many controlled tests were run with stations at various
spatial polarization offsets. It was found that QSOs could be made
more frequently and with less effort when the offset was near
either end of the scale than when it was approaching 45 degrees.
Some QSOs were made in the worst-case 45 degree condition, but in
almost every case involved significantly weaker signals at one or
both ends of the QSO than when the offset was more favorable.
-------------------------------------------------------------------
1. This equation was developed by C.H Hustig and was taken from an
article "Spatial Polarization and Faraday Rotation" by Tim
Pettis, KL7WE. This article appeared in PROCEEDINGS of the
22nd CONFERENCE of the CSVHF SOCIETY (Lincoln, NE 1988).
![[....just a fancy line....]](../images/line22.gif){kind=small}