Problem 45806. SatCom #8: Satellite Link Budget

Created by Mark Posen

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<div style = "text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; "><div style="block-size: 399px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 199.5px; transform-origin: 407px 199.5px; vertical-align: baseline; "><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 150.092px 7.75px; transform-origin: 150.092px 7.75px; unicode-bidi: normal; "><span style="font-weight: 700; ">Satellite and Space Engineering - Problem #8</span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 360.592px 7.75px; transform-origin: 360.592px 7.75px; unicode-bidi: normal; "><span style="font-style: italic; ">This is part of a series of problems looking at topics in satellite and space communications and systems engineering.</span></span></div><div style="block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 382.633px 7.75px; transform-origin: 382.633px 7.75px; unicode-bidi: normal; "><span style="font-style: italic; ">lf you have competed the previous exercises in this series, you will have more-or-less everything that you need to complete this problem.</span></span></div><div style="block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 381.592px 7.75px; transform-origin: 381.592px 7.75px; unicode-bidi: normal; "><span style="">Knowing the parameters of a radio transmitter and receiver, determine the wanted signal power (dBW) in the radio receiver (in this case we are thinking of a satellite receiver, but the approach is generic to all radio receivers).</span></span></div><div style="block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 380.425px 7.75px; transform-origin: 380.425px 7.75px; unicode-bidi: normal; "><span style="">You are given power (dBW) of the signal applied to the transmitting dish antenna, the diameters (m) and efficiencies (%) of the transmitting and receiving dishes, the path length (km) between the transmitting and receiving antennas, and the frequency of the transmitted signal (GHz). </span></span></div><div style="block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.7833px 7.75px; transform-origin: 28.7833px 7.75px; unicode-bidi: normal; "><span style="">Hint: See</span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.75px; transform-origin: 1.94167px 7.75px; unicode-bidi: normal; "><span style=""> </span></span><a target='_blank' href = "https://en.wikipedia.org/wiki/Link_budget#Equation"><span style=""><span style="">https://en.wikipedia.org/wiki/Link_budget#Equation</span></span></a><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 186.308px 7.75px; transform-origin: 186.308px 7.75px; unicode-bidi: normal; "><span style=""> - For this simplified exercise, you should ignore transmitter, receiver and miscelaneous losses.</span></span></div><div style="block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384px 7.75px; transform-origin: 384px 7.75px; unicode-bidi: normal; "><span style="">Example: For a Ka-Band GSO space-to-Earth link at 17.7 GHz and of path length 41,130.13 km, where the satellite antenna has an input RF power of 9.5 dBW, a diameter of 75cm and an efficiency of 70%, and the signal is received on an Earth-station antenna of diameter 65cm and efficiency 65%, the RF power in the satellite receiver is around -119.1 dBW.</span></span></div><div style="block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 380.433px 7.75px; transform-origin: 380.433px 7.75px; unicode-bidi: normal; "><span style="font-style: italic; ">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!</span></span></div></div></div>

Satellite and Space Engineering - Problem #8
This is part of a series of problems looking at topics in satellite and space communications and systems engineering.
lf you have competed the previous exercises in this series, you will have more-or-less everything that you need to complete this problem.
Knowing the parameters of a radio transmitter and receiver, determine the wanted signal power (dBW) in the radio receiver (in this case we are thinking of a satellite receiver, but the approach is generic to all radio receivers).
You are given power (dBW) of the signal applied to the transmitting dish antenna, the diameters (m) and efficiencies (%) of the transmitting and receiving dishes, the path length (km) between the transmitting and receiving antennas, and the frequency of the transmitted signal (GHz). 
Hint: See https://en.wikipedia.org/wiki/Link_budget#Equation - For this simplified exercise, you should ignore transmitter, receiver and miscelaneous losses.
Example: For a Ka-Band GSO space-to-Earth link at 17.7 GHz and of path length 41,130.13 km, where the satellite antenna has an input RF power of 9.5 dBW, a diameter of 75cm and an efficiency of 70%, and the signal is received on an Earth-station antenna of diameter 65cm and efficiency 65%, the RF power in the satellite receiver is around -119.1 dBW.
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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Augusto Mazzei on 26 Feb 2022

actually the wikipedia page is referring for the TX and RX antennas a power expressed in dBm, not dBW. Can you make some check?

https://en.wikipedia.org/wiki/Decibel_watt

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Problem 45806. SatCom #8: Satellite Link Budget

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