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#1
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Free space pathloss calcs and factor K
Hi all.
No doubt I could get this reading lots and lots of text books. It might however be interesting to air a discussion on it.. Have been reading the free space pathloss formula from the ARRL antenna handbook; Loss in dB = K + 20logf + 20logD Where f is the freq in GHz and D is the distance in miles K is a constant of around 96.6dB I have known about a "fixed K" loss in an antenna system for ages. It even made mention I think in this NG recently when talking about a passive repeater system. From my own exposure to path modelling (EDX/Pathloss etc) I noted a very high dB loss per distance rate in the first (say) 100 wavelengths when looking at graphs of same. (I wasnt doing the actual job, just providing data to the engineer to compare measured with predicted. Fascinating stuff!) What I wonder is where roughly does the 96dB odd "come from". More interestingly can it be reduced by any appreciable amount. Is it maybe a antenna to "air" coupling loss, maybe even that a RX antenna cant possibly extract all of the energy from the wave as it goes past. I would appreciate any input on this. My initial forays (as a young ham) into LOS paths went through the isotropic/point source radiators and looking at the surface area of the covered "sphere" containing all of the radiated power idea. Then the RX antenna "aperture" area was used to calculate the actual received power. Needless to say it never met the actual measured values! Cheers Bob VK2YQA (in W5) |
#2
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"Bob Bob" wrote in message ... Hi all. No doubt I could get this reading lots and lots of text books. It might however be interesting to air a discussion on it.. Have been reading the free space pathloss formula from the ARRL antenna handbook; Loss in dB = K + 20logf + 20logD Where f is the freq in GHz and D is the distance in miles K is a constant of around 96.6dB I have known about a "fixed K" loss in an antenna system for ages. It even made mention I think in this NG recently when talking about a passive repeater system. From my own exposure to path modelling (EDX/Pathloss etc) I noted a very high dB loss per distance rate in the first (say) 100 wavelengths when looking at graphs of same. (I wasnt doing the actual job, just providing data to the engineer to compare measured with predicted. Fascinating stuff!) What I wonder is where roughly does the 96dB odd "come from". More interestingly can it be reduced by any appreciable amount. Is it maybe a antenna to "air" coupling loss, maybe even that a RX antenna cant possibly extract all of the energy from the wave as it goes past. I would appreciate any input on this. My initial forays (as a young ham) into LOS paths went through the isotropic/point source radiators and looking at the surface area of the covered "sphere" containing all of the radiated power idea. Then the RX antenna "aperture" area was used to calculate the actual received power. Needless to say it never met the actual measured values! Cheers Bob VK2YQA (in W5) For interest the K is 36 if the frequency is in MHz and the distance in miles, or 32.5 if the distance is in Km. Used it for years and it's never far out. -- Woody harrogate2 at ntlworld dot com |
#3
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Hi,
Loss in dB = K + 20logf + 20logD Where f is the freq in GHz and D is the distance in miles K is a constant of around 96.6dB What I wonder is where roughly does the 96dB odd "come from". More interestingly can it be reduced by any appreciable amount. Is it maybe a antenna to "air" coupling loss, maybe even that a RX antenna cant possibly extract all of the energy from the wave as it goes past. I would appreciate any input on this. Don't know that particular expression but plug in very low values for 'f' and 'D' and you come up with something like Loss(dB) = K(dB) -(~100dB) since the log of numbers less than 1 is negative. The formula then is simply of the form - y = 20log(f) + 20log(D) + C So when 'f' and 'D' are both equal to 1, the path loss = 96dB and, when much less than that, it approaches zero. Cheers - Joe |
#4
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Also, for frequencies above 5 to 6 GHz the effects of atmospheric
absorption become much higher and non linear with frequency. It has to do with molecular resonance and atomic cross sections of the molecules. Bob Bob wrote: Hi all. No doubt I could get this reading lots and lots of text books. It might however be interesting to air a discussion on it.. Have been reading the free space pathloss formula from the ARRL antenna handbook; Loss in dB = K + 20logf + 20logD Where f is the freq in GHz and D is the distance in miles K is a constant of around 96.6dB I have known about a "fixed K" loss in an antenna system for ages. It even made mention I think in this NG recently when talking about a passive repeater system. From my own exposure to path modelling (EDX/Pathloss etc) I noted a very high dB loss per distance rate in the first (say) 100 wavelengths when looking at graphs of same. (I wasnt doing the actual job, just providing data to the engineer to compare measured with predicted. Fascinating stuff!) What I wonder is where roughly does the 96dB odd "come from". More interestingly can it be reduced by any appreciable amount. Is it maybe a antenna to "air" coupling loss, maybe even that a RX antenna cant possibly extract all of the energy from the wave as it goes past. I would appreciate any input on this. My initial forays (as a young ham) into LOS paths went through the isotropic/point source radiators and looking at the surface area of the covered "sphere" containing all of the radiated power idea. Then the RX antenna "aperture" area was used to calculate the actual received power. Needless to say it never met the actual measured values! Cheers Bob VK2YQA (in W5) |
#5
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"Bob Bob" wrote in message
... Hi all. No doubt I could get this reading lots and lots of text books. It might however be interesting to air a discussion on it.. Have been reading the free space pathloss formula from the ARRL antenna handbook; Loss in dB = K + 20logf + 20logD Where f is the freq in GHz and D is the distance in miles K is a constant of around 96.6dB I have known about a "fixed K" loss in an antenna system for ages. It even made mention I think in this NG recently when talking about a passive repeater system. From my own exposure to path modelling (EDX/Pathloss etc) I noted a very high dB loss per distance rate in the first (say) 100 wavelengths when looking at graphs of same. (I wasnt doing the actual job, just providing data to the engineer to compare measured with predicted. Fascinating stuff!) What I wonder is where roughly does the 96dB odd "come from". More interestingly can it be reduced by any appreciable amount. Is it maybe a antenna to "air" coupling loss, maybe even that a RX antenna cant possibly extract all of the energy from the wave as it goes past. I would appreciate any input on this. My initial forays (as a young ham) into LOS paths went through the isotropic/point source radiators and looking at the surface area of the covered "sphere" containing all of the radiated power idea. Then the RX antenna "aperture" area was used to calculate the actual received power. Needless to say it never met the actual measured values! Cheers Bob VK2YQA (in W5) Take the ratio of the destination antenna aperture (0.13*lambda^2 for a half wave dipole), to the surface area of a sphere, of a radius equal to the distance between the source and destination antennas (i.e. Pr/Pt). The assumption is that the source is isotropic. Massaging the above expression will produce a constant and the sum of two logs. Regards, Frank |
#6
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Bob Bob,
The formula for pathloss of a signal is = 10*log10( [lambda/(4*pi*D)]^2 ) {See any myriad of texts} where log10 is log base 10, lambda is the wavelength, D is the LOS distance from one station to another, and of course pi is ~ 3.14. For this formula to work, lambda and D need to be in the same units. Using logarithm theorems we can rewrite it as = 20*log10( lambda/(4*pi*D) ) Using more log theorems, this equals = 20*log10(lambda) - 20*log10(4*pi*D) = 20*log10(lambda) - [ 20*log10(4) + 20*log10(pi) + 20*log10(D) ] = 20*log10(lambda) - 20*log10(4) - 20*log10(pi) - 20*log10(D) lambda = c/f where c is the speed of light and f is the frequency (in the same unit system) so = 20*log10(c/f) - 20*log10(4) - 20*log10(pi) - 20*log10(D) = 20*log10(c)- 20*log(f) - 20*log10(4) - 20*log10(pi) - 20*log10(D) Now... we need to make sure we are using the same unit convention. If D is to be in MILES, c needs to be in miles per second. c ~= 3*10^8 m/s and in miles per second c ~= 186411.4 mi/s = [20*log10(c) - 20*log10(4) - 20*log10(pi)] - 20*log10(D) - 20*log(f) plug into your handy-dandy calculator = (83.4 dB) - 20*log10(D) - 20*log(f) However, f can be refered to in GHz rather than Hertz so = (83.4 dB) - 20*log10(D) - 20*log(F_in_GHz*10^9) = (83.4 dB) - 20*log10(D) - [20*log(F_in_GHz) + 20*log10(10^9)] = (83.4 dB) - 20*log10(D) - 20*log(F_in_GHz) - 20*log10(10^9) = (83.4 dB) - 20*log10(D) - 20*log(F_in_GHz) - 180 and... = (-96.6 dB) - 20*log10(D) - 20*log(F_in_GHz) Note that to be mathematically consistent, when you "add" loss to a system, you subtract a number therefore your value is actually negative. It's mostly semantics. When you say "loss" you mean subract. Hope this helps! Dario Bob Bob wrote: Hi all. No doubt I could get this reading lots and lots of text books. It might however be interesting to air a discussion on it.. Have been reading the free space pathloss formula from the ARRL antenna handbook; Loss in dB = K + 20logf + 20logD Where f is the freq in GHz and D is the distance in miles K is a constant of around 96.6dB I have known about a "fixed K" loss in an antenna system for ages. It even made mention I think in this NG recently when talking about a passive repeater system. From my own exposure to path modelling (EDX/Pathloss etc) I noted a very high dB loss per distance rate in the first (say) 100 wavelengths when looking at graphs of same. (I wasnt doing the actual job, just providing data to the engineer to compare measured with predicted. Fascinating stuff!) What I wonder is where roughly does the 96dB odd "come from". More interestingly can it be reduced by any appreciable amount. Is it maybe a antenna to "air" coupling loss, maybe even that a RX antenna cant possibly extract all of the energy from the wave as it goes past. I would appreciate any input on this. My initial forays (as a young ham) into LOS paths went through the isotropic/point source radiators and looking at the surface area of the covered "sphere" containing all of the radiated power idea. Then the RX antenna "aperture" area was used to calculate the actual received power. Needless to say it never met the actual measured values! Cheers Bob VK2YQA (in W5) |
#7
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Thank you all for your feedback/comment. So much for an easy answer!
grin) Bob Bob wrote: |
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