Satellite Communications & RF Systems Engineering
Satellite EIRP, G/T & Carrier-to-Noise C/N0 Formula
Calculate Effective Isotropic Radiated Power EIRP_dBW = P_tx + G_tx - L_feed, Carrier-to-Noise Spectral Density C/N_0 = EIRP - L_path + G/T + 228.6 dB-Hz, and Digital Demodulator E_b / N_0.
Watch the sign on Boltzmann’s constant -228.6 dBW/(K*Hz) in satellite link budgets!
Geostationary and LEO satellite transponder link budgets combine transmitter power, dish gain, path attenuation, and cryogenic/LNB receiver noise in decibels: (1) Effective Isotropic Radiated Power is EIRP_dBW = P_tx_dBW + G_tx_dBi - L_feed_dB; (2) because Boltzmann’s constant is k_B = 1.38065e-23 J/K, 10 * LOG10(k_B) equals -228.60 dBW/(K*Hz)—meaning subtracting 10*LOG10(k_B) ADDS +228.60 dB to form Carrier-to-Noise Spectral Density C/N_0 (dB-Hz) = EIRP_dBW - L_path_dB + G_over_T_dBK + 228.6; and (3) Energy-per-Bit to Noise-Density Ratio is E_b / N_0 (dB) = C/N_0 - 10 * LOG10(R_bps)! The #1 student trap in RF spreadsheets is subtracting 228.6 instead of adding it, producing an impossible -359 dB-Hz link!
Verify on Transponder_Power P_tx = 20.0 dBW (100 W, B2), Transmit_Dish_Gain G_tx = 42.0 dBi (B3), Waveguide_Feed_Loss L_feed = 2.0 dB (B4 -> EIRP = 20 + 42 - 2 = 60.00 dBW in E2), Total_Downlink_Loss L_path = 206.0 dB (FSPL + clear-sky atmospheric loss, B5), Earth_Station_G_over_T = 15.0 dB/K (B6), and Information_Bit_Rate R_bps = 10,000,000 bps (10 Mbps = 70.0 dB-Hz, B7): C/N_0 equals 60.0 - 206.0 + 15.0 + 228.6 = 97.60 dB-Hz (E3); E_b / N_0 equals 97.60 - 70.00 = 27.60 dB (E4); and Demodulator Status clears the 10.0 dB lock threshold with +17.60 dB rain-fade margin ("Demodulator Lock (Eb/N0 >= 10 dB)" in E5)!
| Satellite Ku-Band Link Metric (Ptx=20dBW, Gtx=42dBi, Lf=2dB, Lp=206dB, G/T=15dB/K, 10Mbps) | Formula | Verified Output |
|---|---|---|
| Effective Isotropic Radiated Power EIRP | P_tx_dBW + G_tx_dBi - L_feed_dB | 60.00 dBW (1.0 MW Isotropic) |
| Carrier-to-Noise Density C/N_0 | EIRP - L_path + G_over_T + 228.6 | 97.60 dB-Hz |
| Bit Energy-to-Noise Ratio E_b / N_0 | C/N_0 - 10 * LOG10(R_bps) | 27.60 dB (17.60 dB @ 100 Mbps) |
| Rain-Fade Demodulator Gate (10 dB) | Eb/N0 >= 10 dB Lock Threshold | Demodulator Lock (Eb/N0 >= 10 dB) |
Satellite C/N0 & Digital Eb/N0 Link-Budget Formula
Validate L_feed >= 0, L_path > 0, and R_bps > 0 before taking LOG10(R_bps)!
=LET(p_tx, B2, g_tx, B3, l_fd, B4, l_pt, B5, g_ot, B6, r_bp, B7, IF(OR(l_fd < 0, l_pt <= 0, r_bp <= 0), "Invalid RF Link Input", LET(ei_r, p_tx + g_tx - l_fd, cn_0, ei_r - l_pt + g_ot + 228.6, ROUND(cn_0 - 10 * LOG10(r_bp), 2))))Heavy Rain-Attenuation Outage Test Formula
Spike L_path from 206 dB to 226 dB (+20 dB tropical Ku-band rain fade) in cell B5: E_b / N_0 drops from 27.60 dB to 7.60 dB, triggering "Link Outage (Eb/N0 < 10 dB)"!
=IF(ISTEXT(E4), E4, IF(E4 >= 10, "Demodulator Lock (Eb/N0 >= 10 dB)", "Link Outage (Eb/N0 < 10 dB)"))Try the example
Use the original values or change them to test your understanding.