# Contents

## Free-Space Path Loss vs. Cable Loss

Click for more…! 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;
close all;
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);```
```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]
mu_sun = 132712440018;          %(km^3s?2)```

Earth – Mercury

```p_d = 2*(R_earth - R_mercury)/v_light*AU/60;
fprintf('Min Two-way Propagation Delay, Earth - Mercury = %4.2f [min]\n',p_d);
figure(1);
T_mercury  = 2*pi*((R_mercury*AU)^3/mu_sun)^0.5/86400;   % solar days
T_earth = 2*pi*((R_earth*AU)^3/mu_sun)^0.5/86400; % solar days
time = 0:1:10*T_mercury;
fi_earth = rem(time,T_earth)/(T_earth)*360;
fi_mercury = rem(time,T_mercury)/(T_mercury)*360;
phase = fi_earth - fi_mercury;
dist = (R_earth^2 + R_mercury^2 - 2*R_earth*R_mercury*cosd(phase)).^0.5;
subplot(2,1,1);
plot(time/T_earth,dist);
title ('Earth - Mercury Comunication');
ylabel('Distance Earth - Mercury [AU]');
p_d = 2*dist/v_light*AU/60;
subplot(2,1,2);
plot(time/T_earth,p_d,'k');
ylabel('Two-way Propagation Delay [min]');
xlabel('Time [Earth Period]');```
`Min Two-way Propagation Delay, Earth - Mercury = 10.19 [min]` Earth – Venus

```p_d = 2*(R_earth - R_venus)/v_light*AU/60;
fprintf('Min Two-way Propagation Delay, Earth - Venus   = %4.2f  [min]\n',p_d);
figure(2);
T_venus  = 2*pi*((R_venus*AU)^3/mu_sun)^0.5/86400;   % solar days
T_earth = 2*pi*((R_earth*AU)^3/mu_sun)^0.5/86400; % solar days
time = 0:1:7*T_venus;
fi_earth = rem(time,T_earth)/(T_earth)*360;
fi_venus = rem(time,T_venus)/(T_venus)*360;
phase = fi_earth - fi_venus;
dist = (R_earth^2 + R_venus^2 - 2*R_earth*R_venus*cosd(phase)).^0.5;
subplot(2,1,1);
plot(time/T_earth,dist);
title ('Earth - Venus Comunication');
ylabel('Distance Earth - Venus [AU]');
p_d = 2*dist/v_light*AU/60;
subplot(2,1,2);
plot(time/T_earth,p_d,'k');
ylabel('Two-way Propagation Delay [min]');
xlabel('Time [Earth Period]');```
`Min Two-way Propagation Delay, Earth - Venus   = 4.60  [min]` Earth – Mars

```p_d = 2*(R_mars - R_earth)/v_light*AU/60;
fprintf('Min Two-way Propagation Delay, Earth - Mars    = %4.2f  [min]\n',p_d);
figure(3);
T_mars  = 2*pi*((R_mars*AU)^3/mu_sun)^0.5/86400;   % solar days
T_earth = 2*pi*((R_earth*AU)^3/mu_sun)^0.5/86400; % solar days
time = 0:1:6*T_mars;
fi_earth = rem(time,T_earth)/(T_earth)*360;
fi_mars  = rem(time,T_mars)/(T_mars)*360;
phase = fi_earth - fi_mars;
dist = (R_earth^2 + R_mars^2 - 2*R_earth*R_mars*cosd(phase)).^0.5;
subplot(2,1,1);
plot(time/T_earth,dist);
title ('Earth - Mars Comunication');
ylabel('Distance Earth - Mars [AU]');
p_d = 2*dist/v_light*AU/60;
subplot(2,1,2);
plot(time/T_earth,p_d,'k');
ylabel('Two-way Propagation Delay [min]');
xlabel('Time [Earth Period]');```
`Min Two-way Propagation Delay, Earth - Mars    = 8.71  [min]` Earth – Jupiter

```p_d = 2*(R_jupiter- R_earth)/v_light*AU/60;
fprintf('Min Two-way Propagation Delay, Earth - Jupiter    = %4.2f  [min]\n',p_d);
figure(4);
T_jupiter  = 2*pi*((R_mars*AU)^3/mu_sun)^0.5/86400;   % solar days
T_earth = 2*pi*((R_earth*AU)^3/mu_sun)^0.5/86400; % solar days
time = 0:1:3*T_mars;
fi_earth = rem(time,T_earth)/(T_earth)*360;
fi_jupiter = rem(time,T_jupiter)/(T_jupiter)*360;
phase = fi_earth - fi_jupiter;
dist = (R_earth^2 + R_jupiter^2 - 2*R_earth*R_jupiter*cosd(phase)).^0.5;
subplot(2,1,1);
plot(time/T_earth,dist);
title('Earth - Jupiter Comunication');
ylabel('Distance Earth - Jupiter [AU]');
p_d = 2*dist/v_light*AU/60;
subplot(2,1,2);
plot(time/T_earth,p_d,'k');
ylabel('Two-way Propagation Delay [min]');
xlabel('Time [Earth Period]');```
`Min Two-way Propagation Delay, Earth - Jupiter    = 69.86  [min]` Earth – Saturn

```p_d = 2*(R_saturn- R_earth)/v_light*AU/60;
fprintf('Min Two-way Propagation Delay, Earth - Saturn    = %4.2f  [min]\n',p_d);
figure(5);
T_saturn  = 2*pi*((R_saturn*AU)^3/mu_sun)^0.5/86400;   % solar days
T_earth = 2*pi*((R_earth*AU)^3/mu_sun)^0.5/86400; % solar days
time = 0:1:3*T_mars;
fi_earth = rem(time,T_earth)/(T_earth)*360;
fi_saturn = rem(time,T_saturn)/(T_saturn)*360;
phase = fi_earth - fi_saturn;
dist = (R_earth^2 + R_saturn^2 - 2*R_earth*R_saturn*cosd(phase)).^0.5;
subplot(2,1,1);
plot(time/T_earth,dist);
title ('Earth - Saturn Comunication');
ylabel('Distance Earth - Saturn [AU]');
p_d = 2*dist/v_light*AU/60;
subplot(2,1,2);
plot(time/T_earth,p_d,'k');
ylabel('Two-way Propagation Delay [min]');
xlabel('Time [Earth Period]');```
`Min Two-way Propagation Delay, Earth - Saturn    = 142.65  [min]` ```%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)*AU); %[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)*AU); %[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)*AU); %[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)*AU); %[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)*AU); %[dB]
fprintf('Free-Space Path Loss, Earth - Saturn  L = %4.2f [dB] \n\n',L);```
```Free-Space Path Loss, Earth - Mercury L = 267.21 [dB]
Free-Space Path Loss, Earth - Venus   L = 260.31  [dB]
Free-Space Path Loss, Earth - Mars    L = 265.85 [dB]
Free-Space Path Loss, Earth - Jupiter L = 283.93 [dB]
Free-Space Path Loss, Earth - Saturn  L = 290.13 [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 = (P2_db - P1_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?
% Pt1*A1r = Pt2*A2r  A2r/A1r = Pt1/Pt2 = 2
% Pt - Transmited Power ;
% Ar - Effective Area of receiving antena;

R_factor = sqrt(P1/P2);
fprintf('Diameter increase your dish antenna %4.2f \n',R_factor);```
```Reduction expressed in DB scale   -3
Diameter increase your dish antenna 1.41```

Published with MATLAB® 7.10