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Signal to Noise Ratio Between Spacecraft Transmitter and Receiver Antenna

  1. Jan 28, 2012 #1
    1. The problem statement, all variables and given/known data
    Determine the SNR for the spacecraft that uses a transmitter power of
    16 W at a frequency of 2.4 GHz. The transmitter and receiver antenna
    gain are 28 dBi and 60 dBi, respectively. The distance from the space-
    craft to ground is 2 ϫ 1010 m, the effective noise temperature of antenna
    plus receiver is 14 degrees Kelvin, and a bit rate of 120 kbps. Assume
    the bandwidth of the system to be half of the bit rate, 60 kHz.


    2. Relevant equations
    The equation below calculates received power in free space (no loss due to non free space).
    Pr = Pt * (λ/(4πd))^2 * (Gt * Gr)

    Pr is received power.
    Pt is transmitted power.
    λ is wavelength.
    d is distance.
    Gt is transmitter gain.
    Gr is receiver gain.

    Also, SNR = Pr/Pn [Pn = noise power]

    3. The attempt at a solution
    I calculated Pr plugging in the following...
    Pt = 16 W
    λ = 0.125 m
    d = 2E10 m
    Gt = 28 dBi = 630.96
    Gr = 60 dBi = 1,000,000

    giving me Pr = 2.497 * 10^(-15) W = -146.03 dBW

    The main problem is I don't know how to calculate Pn, or how/why bandwidth, bit rate, and temp come into play here. Textbook not very helpful and struggled deciphering meaning on wikipedia.
     
  2. jcsd
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