Worked Examples

Note

Example — GEO propagation delay

Altitude $35786\,km$, vertical approximation.

$$t=\frac{d}{c}=\frac{35786\times10^3}{3\times10^8}\approx\boxed{119\,ms}\ \text{(one way)}.$$

The slant path is longer ($120$–$140\,ms$ one way), and a round trip is roughly $250\,ms$.

[!NOTE]

Example — Free-space path loss

Downlink at $f=4\,GHz$, slant range $d=40000\,km$.

$$L_{fs}=32.44+20\log_{10}(40000)+20\log_{10}(4000)\approx\boxed{196.5\,dB}.$$

[!NOTE]

Example — EIRP

$P_t=20\,W$, $G_t=40\,dBi$, feeder loss $2\,dB$.

$$P_t=10\log_{10}20=13.01\,dBW,\quad EIRP=13.01+40-2=\boxed{51.01\,dBW}.$$

[!NOTE]

Example — Noise power

$T_s=500\,K$, $B=1\,MHz$.

$$N=-228.6+10\log_{10}500+10\log_{10}10^6\approx\boxed{-141.6\,dBW}.$$

[!NOTE]

Key Point — Revision — Satellite Communication

• Chain: uplink $\to$ transponder (Rx, LNA, convert, filter, HPA) $\to$ downlink.

• GEO altitude $\approx35786\,km$ from $T^2=4\pi^2a^3/\mu$ at one sidereal day.

• LEO low delay/many satellites; GEO high delay/fixed antenna; MEO for GNSS.

• Bands: C (6/4), Ku (14/11–12), Ka (30/20); uplink higher, rain fade grows with frequency.

• Earth-station figure of merit is $G/T$; $EIRP=P_t+G_t-L_t$.

• $C/N_0=EIRP+G/T-L_{fs}-L_{other}+228.6$; $E_b/N_0=C/N_0-10\log_{10}R_b$.

• VSAT = small terminal (IDU + ODU with BUC/LNB); star (two-hop) or mesh (one-hop).

• Rain attenuation dominates above 10 GHz; DAMA suits bursty traffic.