[NLRS] Path loss calculations

[wb0ljc@juno.com]

Hi all,

Mike, KM0T, asked about path loss calculations 
that included humidity, antenna gain and NF in the
calculation.

I have been using some info that I found either in 
the old QST column "The New Frontier" that was
published in the mid 80's, or the info was in the
ARRL UHF/Microwave Experimenters Manual.
Both would be by the same author, Bob Atkins, KA1G.
I wrote a calculator program to do the calculations.

There are some assumptions made here but the  results
should be accurate enough to give us an idea of what
to expect over a given path.

Here is how it works:

Transmitted signal:

1) FSPL = 36.6 + 20 Log (Frequency in MHz) + 20 Log (distance in Miles)
        the result is in dB. FSPL is free space path loss.

2) EIRP =    Pt + Ga -Lf
        EIRP- effective isotropic radiated power
        Pt-- Transmitted power in dBm
        Ga--Transmit Antenna gain in dBi
        Lf--Transmitter total feed line loss in dB.

3) Pr = EIRP - FSPL
       Pr-- total power of the received signal in dBm
   
Receiver sensitivity:

4) Convert NF to Temp in degrees Kelvin
     T(�K) = Tr = 290�K [ 10^(NF in dB / 10) - 1]

5) Ts = Ta + (Lr - 1)* 290 +Lr * Tr
      Ts--receive system Noise Temperature in �K
      Ta--Antenna Noise Temperature (here assumed to be 290 �K)
             This could be lower if the antenna is looking at cold sky.
      Lr-  Receive feed line loss expressed as a RATIO, NOT in dB.
      Tr--Receiver noise temperature in �K. See #4 for conversion 
             from NF in dB.
 
6) Rs  = 10 Log ( receiver bandwidth in Hz)  + 10 Log ( Ts) -198.6
      Sensitivity is in dBm for a 0 dB Signal to Noise Ratio.

7) SNR = Pr (from #3)  - Rs - Gr (receive antenna gain in dBi)
           SNR will tell you how much the received signal is above
             or below the receiver noise floor.

8) Humidity. There is a chart for 24 GHz in QST June 1985 
       " The New Frontier column".
        Convert the distance in miles to kilometers.
        Find the  excess loss per kM for the air Temperature
        and relative humidity. 
        Multiply the loss per kM by the total path length in kM.
        Subtract this value from the SNR.
                             
       I had been using a value of 0.55 dB/kM for 100 % Relative
       Humidity at 35 �C. the values in the QST chart are
       slightly less.
       It can be surprising how fast the loss can added up on
       the longer paths.

Please let me know if you find any errors or have any questions.
I hope it will be  useful to you.
             
73,  Gary  WB0LJC
   


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