Practical_Antenna_Handbook_0071639586

34 p a r t I I : F u n d a m e n t a l s
so the UHF and microwave communities tend to use a derivative parameter, N, called
the refractivity of the atmosphere:
N = ( n – 1) × 10 6 (2.20)
N tends to vary from about 280 to 320 and, since n varies with altitude, so will N. In
nonhomogeneous atmospheres (the usual case), these parameters will vary approximately
linearly for several tenths of a kilometer. All but a few microwave relay systems
can assume an approximately linear reduction of n and N with increasing altitude, although
airborne radios and radars cannot. There are two methods for calculating N:
and
⎛ ⎞
P
⎝
⎜
⎠
⎟ ⎛ ⎝ ⎜
⎞
N = 77.6 e H
⎠
⎟
T
+ 4810 s rel (2.21)
T
⎛ × ⎞
N = 77.6 ⎜
3.73 10 5
e
s
2
⎟
T ⎝ T ⎠
(2.22)
where P = atmospheric pressure in millibars (1 torr = 1.3332 mbar)
T = temperature in kelvins
e s = saturation vapor pressure of atmospheric water in millibars
H rel = relative humidity expressed as a decimal fraction (rather than a
percentage)
Ray path curvature (K) can be expressed as a function of either n or N, provided that the
assumption of a linear gradient d n /d h holds true:
1
K =
⎛ r ⎞
odn
⎝
⎜1 +
d ⎠
⎟
h
(2.23)
or
K =
⎛
⎝
⎜
1
d / d
N h
1 + 157
⎞
⎠
⎟
(2.24)
For the near-surface region, where d n /d h varies at about 3.9 × 10 –8 m, the value of K
is 1.33. For most terrestrial microwave paths, this value (K = 4 3 = 1.33) is called a standard
refraction, and is used in calculations in the absence of additional data. For regions
above the linear zone close to the surface, you can use another expression of refractivity:
N
a
= N e
s
−Ce ( hr − ht
)
(2.25)