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## Free-Space Path Loss vs. Cable Loss

Consider a space link with 100 million kilometer distance and a transmit frequency of 2 GHz (S-Band). 1. Calculate the Free-Space Path Loss [dB].

```clear all;
clc;
F = 2;                                %transmit frequency (S-Band)[GHz]
d = 1e8;                              %[km]
L = 92.4 + 20*log10(F) + 20*log10(d); %[dB]
fprintf('Free-Space Path Loss L = %4.2f [dB] \n',L);
% Assume a typical coaxial cable with a loss of 0.3[dB/m] at S-Band.
% How long may this cable be for a total loss equal to the Free-Space
% Path Loss from above [m]?
c_l = 0.3;          %[dB/m]
l_cabel = L/c_l;    %[m]
fprintf('Equivalent Cabel Length = %4.2f [m] \n\n',l_cabel);
% 3.Discuss this comparison. What is the fundamental diference between
% the two losses?
% In the second case the loss is a due the resistance of cabel.
% Look in the web```
```Free-Space Path Loss L = 258.42 [dB]
Equivalent Cabel Length = 861.40 [m]```

## Propagation Delays

1.Calculate the two-way propagation delays[min] between Earth and spacecrafts at diferent planets (from Mercury to Saturn; consider the following average distances between Sun-Planet: 0.3871AU for Mercury, 0.723AU for Venus, 1.524AU for Mars, 5.203AU for Jupiter, 9.582AU for Saturn). Assume conjunction Sun-Planet-Earth (Mercury, Venus), or Sun-Earth-Planet

```%(Mars,Jupiter, Saturn) for an easy calculation of the minimum distances
%(Note that this is not the worst case in terms of maximum distances to be
% considered for the actual link design).
v_light   = 300000;% Speed of light in vacuum [km/s]
R_mercury = 0.3871;  %[AU]
R_venus   = 0.7230;  %[AU]
R_earth   = 1.0000;  %[AU]
R_mars    = 1.5240;  %[AU]
R_jupiter = 5.2030;  %[AU]
R_saturn  = 9.5820;  %[AU]
AU        = 149597871; %[km]
% Earth - Mercury
p_d = 2*(R_earth - R_mercury)/v_light*AU/60;
fprintf('Two-way Propagation Delay, Earth - Mercury = %4.2f [min]\n',p_d);
% Earth - Venus
p_d = 2*(R_earth - R_venus)/v_light*AU/60;
fprintf('Two-way Propagation Delay, Earth - Venus   = %4.2f  [min]\n',p_d);
% Earth - Mars
p_d = 2*(R_mars - R_earth)/v_light*AU/60;
fprintf('Two-way Propagation Delay, Earth - Mars    = %4.2f  [min]\n',p_d);
% Earth - Jupiter
p_d = 2*(R_jupiter - R_earth)/v_light*AU/60;
fprintf('Two-way Propagation Delay, Earth - Jupiter = %4.2f [min]\n',p_d);
% Earth - Saturn
p_d = 2*(R_saturn - R_earth)/v_light*AU/60;
fprintf('Two-way Propagation Delay, Earth - Saturn  = %4.2f[min]\n\n',p_d);

%2. For the various cases calculate the Free-Space Path Loss[dB], assuming
% an RF frequency of 6 GHz.
F = 6; %transmit frequency [GHz]
% Earth - Mercury
L = 92.4 + 20*log10(F) + 20*log10(R_earth - R_mercury); %[dB]
fprintf('Free-Space Path Loss, Earth - Mercury L = %4.2f [dB] \n',L);
% Earth - Venus
L = 92.4 + 20*log10(F) + 20*log10((R_earth - R_venus)); %[dB]
fprintf('Free-Space Path Loss, Earth - Venus   L = %4.2f  [dB] \n',L);
% Earth - Mars
L = 92.4 + 20*log10(F) + 20*log10((R_mars - R_earth)); %[dB]
fprintf('Free-Space Path Loss, Earth - Mars    L = %4.2f [dB] \n',L);
% Earth - Jupiter
L = 92.4 + 20*log10(F) + 20*log10((R_jupiter - R_earth)); %[dB]
fprintf('Free-Space Path Loss, Earth - Jupiter L = %4.2f [dB] \n',L);
% Earth - Saturn
L = 92.4 + 20*log10(F) + 20*log10((R_saturn - R_earth)); %[dB]
fprintf('Free-Space Path Loss, Earth - Saturn  L = %4.2f [dB] \n\n',L);

%3. Discuss the implications by the delay on operations and needs for
% spacecraft autonomy.```
```Two-way Propagation Delay, Earth - Mercury = 10.19 [min]
Two-way Propagation Delay, Earth - Venus   = 4.60  [min]
Two-way Propagation Delay, Earth - Mars    = 8.71  [min]
Two-way Propagation Delay, Earth - Jupiter = 69.86 [min]
Two-way Propagation Delay, Earth - Saturn  = 142.65[min]

Free-Space Path Loss, Earth - Mercury L = 103.71 [dB]
Free-Space Path Loss, Earth - Venus   L = 96.81  [dB]
Free-Space Path Loss, Earth - Mars    L = 102.35 [dB]
Free-Space Path Loss, Earth - Jupiter L = 120.43 [dB]
Free-Space Path Loss, Earth - Saturn  L = 126.63 [dB]```

## Satellite Design

```% Your satellite designer wants to reduce the satellite transmitter output
% power from 50 W to 25 W to save weight. How much is this reduction
% expressed in dB scale?

P1 = 50;                % [W]
P1_db = 10*log10(P1);   % 17 dBW
P2 = 25;                % [W]
P2_db = 10*log10(P2);   % 14 dBW
red = (P1_db - P2_db);  % 3  dBW

fprintf('Reduction expressed in DB scale %4.0f\n',red);

% If you want to maintain the satellite-to-ground
% station data link at the same data rate, you could achieve this by
% modifying the antenna on ground: By which factor do you have to increase
% the diameter of a your dish antenna then?
R_factor = sqrt(red);
fprintf('Diameter increase your dish antenna %4.2f \n',R_factor);```
```Reduction expressed in DB scale    3
Diameter increase your dish antenna 1.74```

Published with MATLAB® 7.10

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