PROPAGATION FORMULAS 1.1 DBW FROM VOLTAGE OR POWER 2 (Voltage in microvolts X 10-6) Power in dBW = 10 Log 50 ohms 2 (Voltage in volts) Power in dBW = 10 Log 50 ohms Power in dBW = 10 Log (Power in watts) Note: dBW = dBm - 30 dB 1.2 FREQUENCY TO WAVELENGTH Wavelength in Meters = 300 fMHz Wavelength in Feet = 984 f MHz 1.3 FREE SPACE LOSS Half Wave Dipole (distance in miles) dB = 32.28 + 20 LOG fMHz + 20 LOG Dmi Isotropic radiator (distance in miles) dB = 36.58 + 20 LOG fMHz + 20 LOG Dmi Half Wave Dipoles (distance in Kilometers) dB = 88.15 + 20 LOG fGHz + 20 LOG Dkm Isotropic radiator (distance in kilometers) 1.4 dB = 92.45 + 20 LOG fGHz + 20 LOG Dkm EARTH CURVATURE d in miles, h in feet d in kilometers, h in meters General d d h= 1 2 1.5K h= d1d 2 K=∞ h = 0 h = 0 K = 4/3 d d h= 1 2 2 d d h= 1 2 17 K = 2/3 h = d1d 2 d d h = 1 2 8. 5 K=1 h = 0 . 67 d1d 2 h = 12.75K d1d 2 12. 75 Where h = the change in vertical distance from a horizontal reference line, in feet/meters d1 = the distance from a point to one end of the path in miles/kilometers d2 = the distance from the same point to the other end of the path, in miles/kilometers K = the equivalent earth radius factor 1.5 FRESNEL ZONE Feet F1 = 72.1 d 1d 2 (f GHz )D d1, d2, D in miles Meters F1 = 17.3 d 1d 2 (f GHz )D d1, d2, D in kilometers Where: F1 = first Fresnel zone radius in feet/meters d1 = distance from one end of path to reflection point d2 = D - d1 D = Total length of path f = frequency in GHz Note: These formulas provide the distance to the first Fresnel Zone. If "0.6" Fresnel is required then multiply by "0.6". 1.6 DISTANCE TO RADIO HORIZON K= 1 K = 4/3 3Kh 2 D = General D = 1.5h D = 2h Where: D = distance to the radio horizon in miles K = the equivalent earth radius factor h = height in feet 1.7 uV = FIELD STRENGTH TO SENSITIVITY 39.5 * (uV / m) fMHz FdBuV / m = 20 Log E( uV / m) FdBuV / m = 105 + 10 Log P(Watts) + 20 Log(fMHz) FdBuV / m = 75 + 10 Log P(milliWatts) + 20 Log(fMHz) dBW = dBm - 70.65 + 20 Log(fMHz) m2 Where F = field strength in dB microvolts per meter P = power f = frequency Note: For 50 ohms, referenced to a dipole. 1.8 DOPPLER SHIFT v( km / h) = 1079 ∗ ∆fHz fMHz ∆fHz = 0.009266∗ v (km / h)∗ fMHz v( m / h) = 670.6 ∗ ∆fHz = 0.00149∗ v (m / h)∗ fMHz Where v = velocity 1.9 NEAR FIELD / FAR FIELD BOUNDARY GdBd 983 Far Field Starts at: ∗10 10 (meters) fMHz GdBd 3226 Far Field Starts at: ∗10 10 (feet) fMHz Where: GdBd = Gain referenced to a dipole 1.10 NOISE POWER PN(Watts) = kTB Where: k = Boltzman’s constant = 1.38∗10 −23 ∆fHz fMHz J K B = Bandwidth in Hz T = 290 Kelvin Noise power in dBm is PN = -143.9 + 10Log(BkHz) FORMULA REFERENCES: 1-1 Engineering Considerations for Microwave Communications Systems, Fourth Edition, GTE Lenkurt Inc., 1975 Microvolt 0.10 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.20 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.30 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.40 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.50 0.51 0.52 0.53 dBW -156.99 -156.16 -155.41 -154.71 -154.07 -153.47 -152.91 -152.38 -151.88 -151.41 -150.97 -150.55 -150.14 -149.76 -149.39 -149.03 -148.69 -148.36 -148.05 -147.74 -147.45 -147.16 -146.89 -146.62 -146.36 -146.11 -145.86 -145.63 -145.39 -145.17 -144.95 -144.73 -144.52 -144.32 -144.12 -143.93 -143.73 -143.55 -143.36 -143.19 -143.01 -142.84 -142.67 -142.50 MICROVOLT TO dBW and dBm dBm dBm dBm Microvolt dBW Microvolt dBW -126.99 -141.72 -111.72 -136.48 -106.48 0.58 1.06 -126.16 -141.57 -111.57 -136.40 -106.40 0.59 1.07 -125.41 -141.43 -111.43 -136.32 -106.32 0.60 1.08 -124.71 -141.28 -111.28 -136.24 -106.24 0.61 1.09 -124.07 -141.14 -111.14 -136.16 -106.16 0.62 1.10 -123.47 -141.00 -111.00 -136.08 -106.08 0.63 1.11 -122.91 -140.87 -110.87 -136.01 -106.01 0.64 1.12 -122.38 -140.73 -110.73 -135.93 -105.93 0.65 1.13 -121.88 -140.60 -110.60 -135.85 -105.85 0.66 1.14 -121.41 -140.47 -110.47 -135.78 -105.78 0.67 1.15 -120.97 -140.34 -110.34 -135.70 -105.70 0.68 1.16 -120.55 -140.21 -110.21 -135.63 -105.63 0.69 1.17 -120.14 -140.09 -110.09 -135.55 -105.55 0.70 1.18 -119.76 -139.96 -109.96 -135.48 -105.48 0.71 1.19 -119.39 -139.84 -109.84 -135.41 -105.41 0.72 1.20 -119.03 -139.72 -109.72 -135.33 -105.33 0.73 1.21 -118.69 -139.61 -109.61 -135.26 -105.26 0.74 1.22 -118.36 -139.49 -109.49 -135.19 -105.19 0.75 1.23 -118.05 -139.37 -109.37 -135.12 -105.12 0.76 1.24 -117.74 -139.26 -109.26 -135.05 -105.05 0.77 1.25 -117.45 -139.15 -109.15 -134.98 -104.98 0.78 1.26 -117.16 -139.04 -109.04 -134.91 -104.91 0.79 1.27 -116.89 -138.93 -108.93 -134.85 -104.85 0.80 1.28 -116.62 -138.82 -108.82 -134.78 -104.78 0.81 1.29 -116.36 -138.71 -108.71 -134.71 -104.71 0.82 1.30 -138.61 -108.61 -134.64 -104.64 -116.11 0.83 1.31 -115.86 -138.50 -108.50 -134.58 -104.58 0.84 1.32 -115.63 -138.40 -108.40 -134.51 -104.51 0.85 1.33 -115.39 -138.30 -108.30 -134.45 -104.45 0.86 1.34 -115.17 -138.20 -108.20 -134.38 -104.38 0.87 1.35 -114.95 -138.10 -108.10 -134.32 -104.32 0.88 1.36 -114.73 -138.00 -108.00 -134.26 -104.26 0.89 1.37 -114.52 -137.90 -107.90 -134.19 -104.19 0.90 1.38 -114.32 -137.81 -107.81 -134.13 -104.13 0.91 1.39 -114.12 -137.71 -107.71 -134.07 -104.07 0.92 1.40 -113.93 -137.62 -107.62 -134.01 -104.01 0.93 1.41 -113.73 -137.53 -107.53 -133.94 -103.94 0.94 1.42 -113.55 -137.44 -107.44 -133.88 -103.88 0.95 1.43 -113.36 -137.34 -107.34 -133.82 -103.82 0.96 1.44 -113.19 -137.25 -107.25 -133.76 -103.76 0.97 1.45 -137.17 -107.17 -133.70 -103.70 -113.01 0.98 1.46 -112.84 -137.08 -107.08 -133.64 -103.64 0.99 1.47 -112.67 -136.99 -106.99 -133.58 -103.58 1.00 1.48 -112.50 -136.90 -106.90 -133.53 -103.53 1.01 1.49 0.54 0.55 0.56 0.57 1.54 1.55 1.56 1.57 1.58 1.59 1.60 1.61 1.62 1.63 1.64 1.65 1.66 1.67 1.68 1.69 1.70 1.71 1.72 1.73 1.74 1.75 1.76 1.77 1.78 1.79 1.80 1.81 1.82 1.83 1.84 1.85 1.86 1.87 1.88 1.89 1.90 1.91 1.92 1.93 1.94 1.95 1.96 1.97 1.98 1.99 2.00 -142.34 -142.18 -142.03 -141.87 -133.24 -133.18 -133.13 -133.07 -133.02 -132.96 -132.91 -132.85 -132.80 -132.75 -132.69 -132.64 -132.59 -132.54 -132.48 -132.43 -132.38 -132.33 -132.28 -132.23 -132.18 -132.13 -132.08 -132.03 -131.98 -131.93 -131.88 -131.84 -131.79 -131.74 -131.69 -131.65 -131.60 -131.55 -131.51 -131.46 -131.41 -131.37 -131.32 -131.28 -131.23 -131.19 -131.14 -131.10 -131.06 -131.01 -130.97 -112.34 -112.18 -112.03 -111.87 -103.24 -103.18 -103.13 -103.07 -103.02 -102.96 -102.91 -102.85 -102.80 -102.75 -102.69 -102.64 -102.59 -102.54 -102.48 -102.43 -102.38 -102.33 -102.28 -102.23 -102.18 -102.13 -102.08 -102.03 -101.98 -101.93 -101.88 -101.84 -101.79 -101.74 -101.69 -101.65 -101.60 -101.55 -101.51 -101.46 -101.41 -101.37 -101.32 -101.28 -101.23 -101.19 -101.14 -101.10 -101.06 -101.01 -100.97 1.02 1.03 1.04 1.05 2.01 2.02 2.03 2.04 2.05 2.06 2.07 2.08 2.09 2.10 2.11 2.12 2.13 2.14 2.15 2.16 2.17 2.18 2.19 2.20 2.21 2.22 2.23 2.24 2.25 2.26 2.27 2.28 2.29 2.30 2.31 2.32 2.33 2.34 2.35 2.36 2.37 2.38 2.39 2.40 2.41 2.42 2.43 2.44 2.45 2.46 2.47 -136.82 -136.73 -136.65 -136.57 -130.93 -130.88 -130.84 -130.80 -130.75 -130.71 -130.67 -130.63 -130.59 -130.55 -130.50 -130.46 -130.42 -130.38 -130.34 -130.30 -130.26 -130.22 -130.18 -130.14 -130.10 -130.06 -130.02 -129.98 -129.95 -129.91 -129.87 -129.83 -129.79 -129.76 -129.72 -129.68 -129.64 -129.61 -129.57 -129.53 -129.49 -129.46 -129.42 -129.39 -129.35 -129.31 -129.28 -129.24 -129.21 -129.17 -129.14 -106.82 -106.73 -106.65 -106.57 -100.93 -100.88 -100.84 -100.80 -100.75 -100.71 -100.67 -100.63 -100.59 -100.55 -100.50 -100.46 -100.42 -100.38 -100.34 -100.30 -100.26 -100.22 -100.18 -100.14 -100.10 -100.06 -100.02 -99.98 -99.95 -99.91 -99.87 -99.83 -99.79 -99.76 -99.72 -99.68 -99.64 -99.61 -99.57 -99.53 -99.49 -99.46 -99.42 -99.39 -99.35 -99.31 -99.28 -99.24 -99.21 -99.17 -99.14 1.50 1.51 1.52 1.53 2.48 2.49 2.50 2.51 2.52 2.53 2.54 2.55 2.56 2.57 2.58 2.59 2.60 2.61 2.62 2.63 2.64 2.65 2.66 2.67 2.68 2.69 2.70 2.71 2.72 2.73 2.74 2.75 2.76 2.77 2.78 2.79 2.80 2.81 2.82 2.83 2.84 2.85 2.86 2.87 2.88 2.89 2.90 2.91 2.92 2.93 2.94 -133.47 -133.41 -133.35 -133.30 -129.10 -129.07 -129.03 -129.00 -128.96 -128.93 -128.89 -128.86 -128.82 -128.79 -128.76 -128.72 -128.69 -128.66 -128.62 -128.59 -128.56 -128.52 -128.49 -128.46 -128.43 -128.39 -128.36 -128.33 -128.30 -128.27 -128.23 -128.20 -128.17 -128.14 -128.11 -128.08 -128.05 -128.02 -127.98 -127.95 -127.92 -127.89 -127.86 -127.83 -127.80 -127.77 -127.74 -127.71 -127.68 -127.65 -127.62 -103.47 -103.41 -103.35 -103.30 -99.10 -99.07 -99.03 -99.00 -98.96 -98.93 -98.89 -98.86 -98.82 -98.79 -98.76 -98.72 -98.69 -98.66 -98.62 -98.59 -98.56 -98.52 -98.49 -98.46 -98.43 -98.39 -98.36 -98.33 -98.30 -98.27 -98.23 -98.20 -98.17 -98.14 -98.11 -98.08 -98.05 -98.02 -97.98 -97.95 -97.92 -97.89 -97.86 -97.83 -97.80 -97.77 -97.74 -97.71 -97.68 -97.65 -97.62