Problem 45494. SatCom #3: Free Space Path Loss

Created by Mark Posen

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Satellite and Space Engineering - Problem #3This is part of a series of problems looking at topics in satellite and space communications and systems engineering.Determine the "Free Space Path Loss" (dB) between a transmit and receive antenna. (Note that "Free Space Path Loss" is not the same as "Spreading Loss" (inverse-square loss), as it is defined as the loss between the input port of a transmitting isotropic antenna and the output port of a receiving isotropic antenna. As it contains (hidden inside the formula) also the formulas for the transmitting and receiving isotropic antenna gains, "Free Space Path Loss" has, perhaps surprisingly at first thought, a frequency-dependent term).You are given the distance between the transmitting and receiving antennas in a satellite link (in m) and the frequency of operation (in Hz). Calculate the "Free Space Loss" (in dB).You should take the speed of light to be 299,792,458 m/s.Hint: See <a href = "https://en.wikipedia.org/wiki/Free-space_path_loss#Free-space_path_loss_formula">https://en.wikipedia.org/wiki/Free-space_path_loss#Free-space_path_loss_formula</a> - but don't forget to convert to dB!Example: The Free Space Path Loss from an antenna on the ground to a Geostationary satellite directly overhead (roughly 35,786 km altitude) at 10 GHz is around 203.5 dB.Some future problems in this series will build on work done in previous problems, so if you get a working solution I suggest you hang onto the code!

*Satellite and Space Engineering - Problem #3*

_This is part of a series of problems looking at topics in satellite and space communications and systems engineering._

Determine the "Free Space Path Loss" (dB) between a transmit and receive antenna. (Note that "Free Space Path Loss" is *not* the same as "Spreading Loss" (inverse-square loss), as it is defined as the loss between the input port of a transmitting isotropic antenna and the output port of a receiving isotropic antenna. As it contains (hidden inside the formula) also the formulas for the transmitting and receiving isotropic antenna gains, "Free Space Path Loss" has, perhaps surprisingly at first thought, a frequency-dependent term).

You are given the distance between the transmitting and receiving antennas in a satellite link (in m) and the frequency of operation (in Hz). Calculate the "Free Space Loss" (in dB).

You should take the speed of light to be 299,792,458 m/s.

Hint: See <https://en.wikipedia.org/wiki/Free-space_path_loss#Free-space_path_loss_formula> - but don't forget to convert to dB!

Example: The Free Space Path Loss from an antenna on the ground to a Geostationary satellite directly overhead (roughly 35,786 km altitude) at 10 GHz is around 203.5 dB.

_Some future problems in this series will build on work done in previous problems, so if you get a working solution I suggest you hang onto the code!_

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Problem 45494. SatCom #3: Free Space Path Loss

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