[TowerTalk] Takeoff Angles and Non-Reciprocal Propagation

[Richard (Rick) Karlquist]

Reciprocity does not mean the takeoff angle of the transmitting
station is the same as the takeoff angle of the receiving station.
It simply means the path loss is the same in either direction.
Suppose there is an asymmetrical hill with station A on the west side
and station B on the east side.  It is not a violation of reciprocity
to say that if station A works DX stations via skywave to the east,
he will experience different propagation than if station B works DX
stations via skywave to the west.  For the purposes of this discussion,
assume that the DX stations are all at sea level on flat terrain,
and that propagation effects of the ionosphere are uniform in all
directions.  What reciprocity says is that if A transmits to B, the
path loss will be the same as if B transmits to A.  Now if there are 
noisy power lines running along the west side of the hill, it is 
possible that A will report that he can't hear B, but B will report that 
he can copy A, even if A and B have identical stations.  This apparent
"one way propagation" is not a failure of reciprocity.

There is an analogy to circuit theory.  It is very common for a 2
port network to be reciprocal but asymmetrical.  Therefore, the
input impedance at the two ports will differ, ie s11 does not
equal s22, but the transmission loss is the same in both
directions, ie s12=s21.

Rick N6RK

David Gilbert wrote:
> I don't mean to be dense (although it is a distinct possibility that I 
> am) and I am most definitely not trying to be contentious, but if signal 
> strengths versus takeoff angle are at least partially a function of 
> terrain diffraction products, and if diffraction is not the same from 
> different directions for asymmetrical terrain, how can there be full 
> reciprocity for signals going both ways (i.e., transmit and receive)?  
> Please explain.
> 
> 73,
> Dave   AB7E
> 
> 
> 
> Richard (Rick) Karlquist wrote:
>> You have disproven the statement:
>>
>> "Diffraction is the same, regardless of asymmetries in the terrain".
>>
>> But I didn't say that.  I only said it was RECIPROCAL.
>> Meaning the same on transmit as receive.  If it wasn't, HFTA would
>> ask you whether you wanted to do a transmit analysis or a receive
>> analysis.
>>
>> Rick N6Rk
>>
>> David Gilbert wrote:
>>   
>>> Richard (Rick) Karlquist wrote:
>>>
>>> "Diffraction is reciprocal, regardless of asymmetries in the terrain."
>>>
>>>
>>>
>>> HFTA would seem to suggest otherwise.
>>>
>>> I generated four arbitrary terrain profile files and fed them into HFTA 
>>> last evening.  Each of the four terrain profiles had a peak 660 feet 
>>> high (I said it was arbitrary) 5,000 feet distant from the antenna.  The 
>>> peak for the first profile was broad and smooth on both the near and far 
>>> side.  The peak for the second profile was sharp and steep on both near 
>>> and far side.  The peak for the third profile was sharp on the near side 
>>> and smoothly broad on the far side, and the peak for the fourth profile 
>>> was smoothly broad on the near side and steep on the far side.  I 
>>> assumed a yagi antenna on 14 MHz (8 elements to get more gain 
>>> visibility) at 70 feet above ground.
>>>
>>> HFTA shows markedly different takeoff angle profiles for the four 
>>> terrains.  In general, HFTA says a peak with a steep near side slope and 
>>> a sharp peak will diffract the signal lower than a more rounded near 
>>> side slope and a broad peak.  A peak that is symmetrically sharp appears 
>>> to bend the signal the most, although not much more than if only the 
>>> near side is steep.  A peak that is broad on the near side and steep on 
>>> the far side is almost identical to a peak that is broad on both sides.  
>>> For the heights, distances, and terrain shapes I arbitrarily chose, 
>>> either of the terrain profiles with a steep near side slope gave at 
>>> least ten db stronger signals than either of the terrain profiles with a 
>>> broad near side slope at all takeoff angles of six degrees or less.  At 
>>> higher angles, the plots tended to be similar with lots of crossing back 
>>> and forth among them.
>>>
>>> I played around a bit with different antenna heights and the decibel 
>>> difference between the plots varied somewhat, but the general 
>>> relationships held.  I haven't tried to change the distance or height of 
>>> the peak to see what combinations might have the most effect ... I 
>>> simply picked some numbers for a first pass comparison.
>>>
>>> Unless I messed up (probable), the two relevant plots from HFTA should 
>>> (might) be available by clicking on the links below:
>>>
>>> http://www.mediamax.com/ab7e/Hosted/Diffraction1.jpg
>>> http://www.mediamax.com/ab7e/Hosted/Diffraction2.jpg
>>>
>>> The links for the four terrain files are:
>>>
>>> http://www.mediamax.com/ab7e/Hosted/rnd_near-shp_far.PRO
>>> http://www.mediamax.com/ab7e/Hosted/round_symmetric.PRO
>>> http://www.mediamax.com/ab7e/Hosted/sharp_symmetric.PRO
>>> http://www.mediamax.com/ab7e/Hosted/shp_near-rnd_far.PRO
>>>
>>> If those files aren't accessible, someone please let me know and I'll 
>>> try to fix the links.  I can also send them as attachments directly to 
>>> anyone who asks.
>>>
>>> I'd appreciate any comments on this quick and maybe questionable 
>>> analysis, but it seems to suggest that signals approaching a 
>>> non-symmetrically shaped terrain feature from different directions could 
>>> skew differently, and therefore that a signal going one way along a 
>>> specific path might have a different strength than a signal going the 
>>> other direction along that exact same path.  It has occurred to me that 
>>> a signal approaching a terrain feature from slightly above the horizon 
>>> might behave differently than a signal approaching that same feature 
>>> from below, but since HFTA won't handle negative takeoff angles I can't 
>>> really check that out, and at six degrees or less I wouldn't think the 
>>> difference would be large anyway.
>>>
>>> Simple diffraction aside, real life terrain contains more than one 
>>> feature that would make full reciprocity even less likely, in my 
>>> opinion.  According to the algorithms built into HFTA,  the net energy 
>>> leaving at any particular angle is the result of multiple combinations 
>>> of reflections and refractions, refractions of reflections, reflections 
>>> of refractions, and so on.   Intuitively, it seems impossible to me that 
>>> a ray arriving from a distance at that same angle can somehow split 
>>> itself into those same components in reverse.  As a minimum, some of the 
>>> reflecting surfaces available to the outgoing ray might be totally 
>>> shadowed to the return signal by secondary terrain features.
>>>
>>> But again, if I'm wrong here I'd appreciate someone correcting me with 
>>> enough explanation that I can understand it.
>>>
>>> 73,
>>> Dave   AB7E
>>>
>>>
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>>>     
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