DTU Satellite Systems and Design Course CubeSat Communication

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Danish Space Research Institute Danish Small Satellite Programme Digital Communication - 4 To proceed, we rewrite the “Ebno” equation in the dB-domain: or 10⋅log(E b /N 0 ) = 10⋅log(P r ) - 10⋅log(B/1 Hz) - 10⋅log(k/1 J/K) - 10⋅log(T/1 K) [dB] E b /N 0 = P r - 10⋅log(B/1 Hz) - 10⋅log(k/1 J/K) - 10⋅log(T/1 K) [dB] where E b /N 0 is now expressed in dB and P r in dBW or dBm. As usual proper reference values must be used to make the arguments to the logs dimensionless. We complete ignore the inconsistency of writing E b /N 0 in the dB expression. E b /N 0 is now a symbol, not a calculation. Combining this with the link budget equation P r = P t + G t + G r -L p [dB], we get: E b /N 0 = (P t + G t ) + G r - L p - 10⋅log(B/1 Hz) - 10⋅log(k/1 J/K) - 10⋅log(T/1 K) [dB] The quantity P t + G t is denoted EIRP (Equivalent Isotropically Radiated Power): E b /N 0 = EIRP + G r - L p - 10⋅log(B/1 Hz) - 10⋅log(k/1 J/K) - 10⋅log(T/1 K) [dB] FH 2001-08-27 Cubesat_Communication.ppt Slide # 20
Danish Space Research Institute Danish Small Satellite Programme Digital Communication - 5 We now introduce the path loss equation: d Lp = 32.45 + 20 ⋅log⎜ ⎟ + 20 ⋅log 1km ⋅ into the Ebno equation and get: E b /N 0 = EIRP + G r – 32.45 - 20⋅log(d/1 km) - 20⋅log(f/1 MHz) - 10⋅log(B/1 Hz) - 10⋅log(k/1 J/K) - 10⋅log(T/1 K) [dB] The dB-value of Boltzmann’s constant is calculated to 10⋅log(k/1 J/K) = -228.60 dB and introduced into the equation. In addition the equation is restructured a little: E b /N 0 = EIRP + (G r - 10⋅log(T/1 K)) – 32.45 + 228.60 - 20⋅log(d/1 km) - 20⋅log(f/1 MHz) - 10⋅log(B/1 Hz) [dB] FH 2001-08-27 Cubesat_Communication.ppt ⎛ ⎝ ⎞ ⎠ ⎛ ⎜ ⎝ f 1⋅ MHz ⎞ ⎟ ⎠ /continued... Slide # 21
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DTU Satellite Systems and Design Course CubeSat Communication

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