```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
dB = 36.58 + 20 LOG fMHz + 20 LOG Dmi
Half Wave Dipoles (distance in Kilometers) dB = 88.15 + 20 LOG fGHz + 20 LOG Dkm
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
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
```