Seybold J.S. Introduction to RF Propagation

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in Figure 6.4 is for a horizontal path in a standard atmosphere at sea level.

Figure 6.5 is the same plot over a much greater frequency range for both a

standard reference atmosphere and for dry air, while Figure 6.6 provides the

total attenuation through the entire atmosphere on a vertical path.

From the plots of g, it can be seen that water vapor has an absorption line

at 22 GHz. It can also be seen that dry air has an oxygen absorption line at

60 GHz. The areas between absorption lines are called windows. Note that at

1 GHz, g~0.05 dB/km, so even a 10-km path only incurs 0.5 dB of loss. The

total loss due to atmospheric absorption for terrestrial paths is found by

multiplying the path length by the speciﬁc attenuation. It is important to

remember to multiply by 2 for radar applications since transmission must

occur in two directions to complete the “link.”

For slant paths, the calculations must allow for the variation in absorption

with altitude. This is done by treating the atmosphere as a series of horizon-

tal layers each with different pressure and temperature. While the actual

absorption will be a fairly smooth function of altitude, treating it as discrete

layers simpliﬁes computation and provides a good estimate of the resulting

attenuation. The ITU [12] provides detailed information on how to perform

the calculations.A generalized approach for slant paths is given in Chapter 11,

which is sufﬁcient for most applications.

122 ATMOSPHERIC EFFECTS

Figure 6.4 Speciﬁc attenuation due to atmospheric gases for a standard atmosphere.

For short-range communications, it is possible to operate at or near one of

the absorption lines to improve frequency re-use or stealth since it reduces the

distance a signal travels and therefore makes interference or stand-off signal

detection unlikely.

Example 6.3. Consider a point-to-point mmw link that requires SNR = 10dB

and SIR = 25 dB for proper operation. What is the maximum operating dis-

tance and minimum frequency re-use distance of this system? Given:

f = 60 GHz, l=0.005m

ANT

= 30 dB

B = 50 MHz

F = 5dB

= 20 dBm

ATMOSPHERIC ATTENUATION 123

–1

–2

–3

0 100 200 300 400 500 600 700 800 900 1000

Frequency, f(GHz)

Curves A: mean global reference atmosphere (7.5 g/m

)

B: dry atmosphere

Specific attenuation (dB/km)

Figure 6.5 Speciﬁc attenuation of a standard atmosphere and of dry air versus fre-

quency for a horizontal path. (Figure 1 from Ref. 12, courtesy of the ITU.)

The noise ﬂoor is kT

BF,so

Thus

So we have

of margin for path loss. The total path loss is

The maximum interference signal is S

min

- 25 dB =-107 dBm. Since P

20 dBm, 127 dB of path loss is required to mitigate interference. From the solid

PL d d=-

()()

+◊20 4log G 15 dB kmlp

-= --

()

min

20 82 102dBm dBm dB

min

=- + =-92 10 82 dBm

N =- + -174 77dB-W Hz dB-Hz + 5 dB = 92 dBm

124 ATMOSPHERIC EFFECTS

–1

–2

0 100 200 300 400 500 600 700 800 900 1000

Frequency, f(GHz)

Curves A: mean global reference atmosphere (7.5 g/m

at sea level)

B: dry atmosphere

Zenith attenuation (dB)

Figure 6.6 Total atmospheric attenuation at zenith versus frequency for a standard

reference atmosphere and for dry air. (Figure 3 from Ref. 12, courtesy of the ITU.)

curve in Figure 6.7, it can be estimated that the maximum operating distance

is 1.8 km and the minimum separation to avoid interference will be about 3.3

km (assuming main beam intersection of the transmitter and the victim

receiver).

Figure 6.7 shows the path loss at 60 GHz for this system both with and

without the atmospheric absorption. It is clear that the atmospheric absorp-

tion plays a signiﬁcant role. It increases the required EIRP for communication

(or reduces the communication distance), but it also permits frequency reuse

as close as 3.3 km. 䊐

6.4 LOSS FROM MOISTURE AND PRECIPITATION

Moisture in the atmosphere takes many forms, some of which play a signiﬁ-

cant role in attenuating electromagnetic waves. The effects are, of course,

frequency-dependent. Precipitation in the form of rain, freezing rain, or wet

snow is a signiﬁcant problem above about 10 GHz and is treated separately in

Chapter 10. Water vapor is essentially a gas and was treated in Section 6.3.

Suspended droplets of moisture, such as clouds or fog, is neither precipitation

nor water vapor and is therefore treated separately. Dry snow and dust also

presents a unique challenge to the modeler.

LOSS FROM MOISTURE AND PRECIPITATION 125

0 0.5 1 1.5 2 2.5 3 3.5 4

100

120

140

Path Loss + Atmospheric Loss

Path Loss Only

Max Loss for Detection

Min Loss for Interference

Path Loss at 60 GHz

Distance in km

Path Loss in dB

Figure 6.7 Path loss for a 60-GHz communication link showing the impact of atmos-

pheric absorption.

6.4.1 Fog and Clouds

The ITU provides a recommended model for fog or cloud attenuation [14]

that is valid up to 200 GHz. Application of this model and a few representa-

tive design curves for planning are presented in this section. The speciﬁc at-

tenuation due to clouds or a fog bank is

where

is the speciﬁc attenuation of the cloud in dB/km

is the speciﬁc attenuation coefﬁcient of the cloud in (dB/km)/(g/m

)

M is the liquid water density of the cloud in g/m

The ITU gives the liquid water density of a cloud or fog as

The mathematical model for the speciﬁc attenuation coefﬁcient is given as

(6.19)

where f is the frequency in GHz and

300

351= .

548= .

77 6 103 3 1=+ -

()

e¢

ee ee

()

e≤

ee ee

()

+2 ¢

≤

()

0 819

eh≤

dB km g m

()

005

g m for medium fog 300-m visibility

g m for dense fog 50

m visibility

126 ATMOSPHERIC EFFECTS

Here the temperature, T, is in kelvins. The principal and secondary relaxation

frequencies are given by

Figure 6.8 shows a plot of the speciﬁc attenuation coefﬁcient, K

, versus fre-

quency for -10°C, 0°C, and 20°C. For clouds, the 0°C curve should be used.

Values from this curve can be used along with liquid water density to estimate

the speciﬁc attenuation (dB/km) due to clouds or fog. Figure 6.9 is a plot of

the speciﬁc attenuation versus frequency of clouds or fog for a liquid water

density of 0.5 g/m

. In the absence of speciﬁc measured liquid water density,

these curves can be used to estimate the speciﬁc attenuation of clouds or fog.

Here again, the 0°C curve should be used for clouds.

To determine the total attenuation through the atmosphere due to clouds,

the elevation angle and the total columnar content of liquid water, L, must be

known. The total columnar content of liquid water may be estimated for a

given probability using the plots provided in Ref. 14. The worst-case value is

1.6 kg/m

. The expression for the total cloud attenuation is

=- -

()

590 1500 1q GHz

=--

()

20 09 142 1 294 1

. qqGHz

LOSS FROM MOISTURE AND PRECIPITATION 127

1 10 100

0.01

0.1

-10 Deg C

0 Deg C

20 Deg C

Specific Attenuation Coefficient

Frequency (GHz)

Kl in (dB/km)/(g/m^3)

Figure 6.8 Speciﬁc attenuation coefﬁcient versus frequency for clouds and fog.

(6.20)

where

L is the total columnar liquid water in kg/m

is the speciﬁc attenuation coefﬁcient in dB/km

q is the elevation angle of the path

Note that the units of L and K

are such that the end result will be in dB. Figure

6.10 shows a plot of the worst-case cloud attenuation through the atmosphere

for several different elevation angles. It can be seen that cloud attenuation

starts to become a consideration above about 10 GHz.

It is intuitive that fog will not be present during a heavy rain. Therefore if

the attenuation due to fog is less than the required rain margin, only the rain

margin need be included in the link budget. While clouds are likely to be

present during rain, the rain models are based on empirical measurements,

which include any cloud attenuation, so again the cloud attenuation need not

be included in the link budget if it is smaller than the rain margin (or vice

versa).

()

∞≥ ≥ ∞

sin q

qdB for 90 5

128 ATMOSPHERIC EFFECTS

1 10 100

0.01

-10 Deg C

0 Deg C

20 Deg C

Specific Attenuation, Kl*M vs Frequency

Frequency (GHz)

Specific Attenuation of Clouds (dB/km)

Figure 6.9 Speciﬁc attenuation versus frequency for clouds and fog, liquid water

density of 0.5 g/m

Example 6.4. Consider a ground to air communication link operating at

20 GHz. If the aircraft is a high-altitude craft, operating well above the clouds,

what is the worst-case additional path loss due to cloud cover? Assume that

the minimum operational elevation angle is 15 degrees.

Using the expression for cloud attenuation,

at 20 GHz and 0°C can be computed as

The worst-case value for L was given as

and

q= ∞15

L = 16.kgm

036= .mkg

()

∞≥ ≥ ∞

sin q

qdB for 90 5

LOSS FROM MOISTURE AND PRECIPITATION 129

1 10 100

0.01

0.1

100

5 Deg

15 Deg

45 Deg

90 Deg

Total Cloud Attenuation vs Frequency

Frequency (GHz)

Attenuation of Clouds (dB)

Figure 6.10 Total cloud attenuation versus frequency for several elevation angles

using worst-case cloud density.

The worst-case attenuation due to heavy cloud cover can then be predicted to

which is consistent with the plot in Figure 6.10. 䊐

Example 6.5. Consider a 10-GHz ship-to-shore communication link. If the

maximum communication distance is 12 km, what is the worst-case loss due to

fog?

Using

for the liquid water density and

the speciﬁc attenuation coefﬁcient is computed as

and the resulting speciﬁc attenuation is

Multiplying the speciﬁc attenuation by the maximum communication distance

of 12 km results in a maximum attenuation of

which is hardly enough loss to be concerned about, especially when compared

to the likely rain loss. Depending upon the location, fog may occur much more

often than rain, so each case must be treated separately. 䊐

6.4.2 Snow and Dust

The attenuation of electromagnetic waves due to snow or dust [13] is pre-

dominantly a function of the moisture content of the particles. For that reason,

the attenuation effects are expected to be less than those due to rain. Speciﬁc

procedures for modeling the effects of snow or dust are few and far between

and since, to the author’s knowledge, none have gained wide acceptance, a

model is not provided in this book.The recommendation is that the rain atten-

uation models more than cover the snow and dust cases and since the effects

A = 0.79 dB

g=0 066.dBkm

0 132= .mkg

T =- ∞10 C

M = 0.5 g m

A = 2.23 dB

130 ATMOSPHERIC EFFECTS

are mutually exclusive, planning for dry snow or dust is superﬂuous in most

cases. Note that snow accumulation on antennas and radomes is a separate

phenomenon from the effect of atmospheric snow.

The effect of hail will depend upon its moisture content and the size of

the hailstones relative to the wavelength of the wave. Here again, deﬁnitive

models are difﬁcult to come by. The relative infrequency of hailstorms and

their association with thunderstorms makes modeling the effects of hail inde-

pendently from rain unnecessary for most applications.

6.5 SUMMARY

There is a wide diversity of atmospheric effects that must be considered based

on the frequency of operation, the path elevation, and the local environment.

Atmospheric refraction occurs when the density gradient of the atmosphere

moves the apparent radio horizon beyond the geometric horizon for nearly

horizontal links. The effect is most often compensated for by using a 4/3 earth

radius model for determining the distance to the horizon. If detailed atmos-

pheric data are available, it is possible to ﬁnd a more accurate representation

of the radio horizon. A related phenomenon is ducting, which is attributed to

water vapor in the atmosphere. A duct may either exist at the surface or be

elevated as much as 1500 m. The effect of a duct is to trap the RF wave and

prevent the usual geometric spreading loss, resulting in excessively strong

receive signals if the receiver is located in the same duct with the transmitter.

If the receiver is not in the same duct, the result will be a signiﬁcant fade, which

can be treated as a multipath fade.

Atmospheric multipath models are based on empirical measurements (and

hence they include cross-duct fades). The current ITU model is similar to pre-

viously used models and has been shown to match empirical data very well

[10]. It consists of two different models for low-probability fades and a third,

more detailed model that is validated for all fade probabilities.

The third major effect of the atmosphere is absorption and attenuation of

RF waves. The dominant absorption effects of the atmosphere are due to

oxygen and water vapor. The absorption is generally described by a speciﬁc

attenuation in dB/km for terrestrial paths and by a total attenuation as a func-

tion of elevation angle for slant paths that exit the troposphere.

There are three forms of water that are of interest to the propagation

analyst: precipitation, water vapor, and suspended water droplets, forming

clouds or fog. Each has unique properties and affects electromagnetic waves

differently. The effect of clouds and fog is rarely signiﬁcant, but it can be a

factor, particularly for log terrestrial paths or for satellite links. The ITU

models for determining the speciﬁc attenuation due to fog and for determin-

ing the total attenuation due to clouds on a slant path were both described.

The attenuation of RF waves by snow and dust is directly related to the mois-

ture content of the particles and is small relative to rain attenuation.

SUMMARY 131