LRT

 Link Budget
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System Overview

Link Budget

Communications Design

Cost Analysis

References

Source Code

Link Budget Calculations

This initial steps to calculating the link budgets of the satellite system was determining the physical constants of the environment and objects we would be dealing with. The following table details some of the values we used to complete the calculations.

Mass of the Earth 5.9736e24 kg
Radius of the Earth 6371e3 m
Mass of the Moon 7.349e22 kg
Radius of the Moon 1738e3 m
Distance from Earth to the Moon 384400e3 m
Distance from Moon to Lagrangian Point L2 6.1528e7 m
Distance from L2 to Lunar Orbit 6.1556e7 m
Distance from Lunar Orbit to Earth 3.8440e8 m
Orbital height for lunar satellite 1838e3 m
System temperature at Moon observatory 20 K
System temperature at space satellites 20K 
System temperature on Earth 298 K
Bandwidth 8.16e9 Hz
Eo/No using 256-QAM with turbo code 14 dB
Carrier Frequency 19.48 GHz
Boltzman's Constant (k) 1.3607e-23  J K-1


Antenna Gains

To calculate the antenna gain for each satellite the formula used was the following.

Gain=10*log10(Apperture_Effeciency*(4*pi/lamda2)*(pi*Radius2))
G=10*log10(n*(4*pi/lamda2)*(pi*R2))   [1]

For each antenna, the receive and transmit gain were assumed to be the same. The values for the four antennas in use through the system are summarized below.

Antenna Name Radius Aperture Efficiency Corresponding Gain
Lunar Base Antenna 150m .9 95.2772 dB
Space Satellites (2) 2.5m .75 58.9224 dB
Earth Station (DSN) 17m .94 76.5532 dB

 

Noise Calculations

Noise calculations were made for each antenna system. The formula used for this calculation was the following.

Noise Power=10*log10(Boltzman's Constant*System Temp.*Bandwidth

Pn=k*T*B   [2]

The tabulated values for each of the receiver systems can be seen below.

Antenna Name System Temperature Noise Power (dB)
Lunar Base Antenna 20 K -116.5352 dB
Space Satellites (2) 20 K -116.5352 dB
Earth Station (DSN) 298 K -104.8033 dB


Link Budget Calculations

Link Budget calculations were completed for each of three different link paths. Using the data from the above tables and the formula listed below, the required transmit power was solved. Rain fading was accounted for in the design by adding 1dB of link budget to the overall design. This margin would allow for variation in the amount of power received on Earth during non-ideal conditions. The final total power for communication is shown below. This is a relatively small amount of power for transmitting data over such large distances. This can partially be attributed to link design which will be explained in more detail on the Channel Design page. The formulae used to calculate the link budgets were the following.

Received Power=(Eo/No) + Noise Power at Receiver Antenna + 10*log10(Data Rate/Bandwidth)

Pr=(Eo/No) + Pn + 10*log10(DR/B)   [3]

Transmit Power=Received Power-Transmitter Gain-Receiver Gain+Path Loss

Pt=Pr-Gt-Gr+20*log10(4*pi/lambda)+20*log10(R)+Rain Fade   [4]

Tabulated results for all links are shown below.

Link Path Lunar Base to Satellite at Lagrangian Point L2 Satellite at Lagrangian Point L2 to Satellite in lunar orbit Satellite in lunar orbit to  Earth station (DSN)
Noise Power Recv. (dB) -116.2072 -116.2072 -104.4754
Distance (m) 6.1528e7 6.1556e7 3.8440e8
Gt (dB) 95.4187 59.0639 59.0639
Gr (dB) 59.0639 59.0639 76.6947
Transmit Power (dB) -32.7748 3.5839 13.5953
Transmit Power (W) 5.2786e-4 2.2824 22.8841

Total Transmit Power = 25.1670 W