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LinkBudget:
FIXME FIXME
%%\[ \frac{C}{N_0} = EIRP - Losses + (G/T) - k - B = 7.8 dB\] %B=12kHz
%\[ \frac{C}{N_0} = EIRP - Losses + (G/T) - k - B = 3.6 dB\] %B=20kHz
%%\[ \frac{C}{N_0} = EIRP - Losses + (G/T) - k - B = -3.3 dB\] %B=40kHz
%\hspace{9cm}(optimistic !!)
%%\[ \frac{C}{N_0} + B = -3 +4 -(1 + 135 + 0.6 + 3) + 6 -(-222) -81.5 = 7.8 dB \]
%%\[ \frac{C}{N_0} = 7.8 dB \]
%\begin{description}[xxxxxxxxxxxxxxxxx]
%\item[TxPower] $0.5W = -3 dBW$
%\item[Rx G/T] $6dB$
%\item[AntennaGain] $4 dBi$ ($~65\% $ of time)
%\item[FSPL] $310km$,$434Mhz$ $\rightarrow 135dB$ % $-20log_{10}(310km) -20log_{10}(434Mhz)-32.45 = -135 dB$
%\item[Sky Thermal Noise] $4^o C \rightarrow -222dBJ/K$ % $k=10 log_{10}(kTB) = -222dBJ/K$ (at $4\angle C, 1 Hz N_0$) %noise at normalized bandwith = 1 Hz
%%\item[Bandwidth] $B=12KHz=81.5dBHz$ %$B=20*log10( 12kHz [Hz]) = 81.5 [dBHz]$
%\item[Bandwidth] $B=20KHz=86dBHz$
%%\item[Bandwidth] $B=40KHz=92dBHz$
%\item[$L\rightarrow C$ polarisation] $-3dB$
$\frac{C}{N_0}=EIRP - Losses + (G/T) - k - B $
70cm: %\[ \frac{C}{N_0} + B = -3 +4 -(1 + 135 + 0.6 + 3) + 6 -(-222) -81.5 = 7.8 dB \]
downlink 70cm: $\frac{C}{T}= (10*math.log(0.5,10) + 8.3) - (1 + 135 + 0.6 + 3 ) + 6 - 81.5 = -209.8 dB$
k=-228.6 dB (J/K) -> 1K
Noise: $N=N_0 B=k T B$
Carrier Power: $C=\frac{P}{4 \pi R^2} G_r A_{eff}
Antenna Gain: $\roh \frac{\pi^2 D^2}{\lambda^2}$:
$EIRP = P_T * G_T$
Free Space Loss: \lbracket\frac{4 \pi R}{\lambda}\rbracket^2
$\frac{E_b}{N_0}=\frac{C}{N}\frac{B}{r}
Transmission Power: 10 log10( [W])
Antennagain Sat:
wavelength: 2m / 70cm
antenna length: ~0.5m (wenn nicht faltbar ~0.25m)
(2m/0.5m = 1/4 -> gain: ~ 2 dBi)
2m/0.25 = 1/8 -> gain: < 2 dBi
(0.7m/0.5m = 1.5 -> gain: 3.01 dBi)
0.7m/0.25m = 3 -> gain: 4.47 dBi
aktuell: 2m: 2dBi 70cm: 4.4dBi
Antennagain Boden:
Gain: 6 dBd / 8.3 dbi
G/T: 8.3 - 1 + 25 - 4 - NoiseTemp = 8.3 - 2 = 6
Loss:
Alignment-Loss: 0,2..1dB
FreeSpaceLoss (AntennaAparture + spreading of radiated power) = 20*log10(d [km]) + 20*log10(f [Mhz]) + 32.45 =
2m: 82.3dB + 43dB = 125dB
70cm: 82.3dB + 52.7dB = 135dB
Atmosphärendämpfung: <1dB (0.6dB)
Polarisation Linear(send) auf Circular(Empfang): 3dB
Bandbreite: 20*log10( 12kHz [Hz]) = 81.5 [dBHz]
more realistic to calculate Satellite Antenna Gain with 0 dBi since the antenna is neither pointed (no attitude control) in our direction, nor do we even know in which direction is is pointed
(actually, considering the fading from atitude changes, that's propably optimistic even)
P_r = (P_t * G_t * A_ e) / (4 \pi R^2 )
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