Chapter 24: Space Wave Propagation

Example 24-9.1, Page number: 808

In [1]:
from math import sqrt

#Variable declaration
tx_h = 49.0       #Transmitting antenna height (m)
rx_h = 25.0       #Receiving antenna height (m)
f = 100e6       #Frequency (Hz)
tx_p = 100.0      #Transmitted power (W)
c = 3e8         #Speed of light (m/s)
a = 6370        #Earth's radius (km)

#Calculations
wave_lt = c/f   #Wavelength (m)
d0 = sqrt(2*(4.0/3.0)*(a/1000.0))*(sqrt(tx_h)+sqrt(rx_h))
#Line of Sight (LOS) distance (km)
d = d0*1000     #LOS (m)
Er = (88*sqrt(tx_p)/(wave_lt*(d**2)))*tx_h*rx_h

#Result
print "The Line of Sight distance is", round(d0,2), "km"
print "The received signal strength is", round(Er,6), "W"

#The mistake is in the calculation of (88*sqrt(tx_p)/(wave_lt*(d**2))) where four orders of
#magnitude are ignored in the resulting calculation.

The Line of Sight distance is 49.46 km
The received signal strength is 0.000147 W

Out[1]:
'The mistake is in the calculation of (88*sqrt(tx_p)/(wave_lt*(d**2))) where four orders of\nmagnitude are ignored in the resulting calculation.'

Example 24-9.2, Page number: 809

In [4]:
from math import sqrt

#Variable declaration
tx_h = 144      #Transmitting antenna height (m)
rx_h = 25       #Receiving antenna height (m)
a = 6370        #Radius of earth (km)

#Calculations
los = 4.12*(sqrt(tx_h) + sqrt(rx_h))    #Line of sight distance (km)

#Result

The Radio horizon distance from radar is 49.46 km


Example 24-9.3, Page number: 809

In [8]:
from math import sqrt

#Variable declaration
tx_h = 100      #Transmitting antenna height (m)
rx_h = 16       #Receiving antenna height (m)
tx_p = 40e3     #Transmitting antenna power radiation (W)
f = 100e6       #Frequency (Hz)
d = 10e3        #Distance (m)
c = 3e8         #Speed of light (m/s)
E = 1e-3        #Signal strength (V/m)

#Calculations
los = 4.12*(sqrt(tx_h) + sqrt(rx_h))    #LOS distance (km)
wave_lt = c/f       #Wavelength (m)

Es = (88*sqrt(tx_p)/(wave_lt*(d**2)))*tx_h*rx_h
#Field strength at distance d (V/m)

dsig = sqrt(88*sqrt(tx_p)*tx_h*rx_h/(wave_lt*E))
#Distance at which field strength reduces to 1mV/m

#Result
print "The LOS distance is", los, "km"
print "The field strength at 10km is", round(Es,5),"V/m"
print "The distance at which field strength is 1mV/m is", round(dsig,-1), "m"

The LOS distance is 57.68 km
The field strength at 10km is 0.09387 V/m
The distance at which field strength is 1mV/m is 96880.0 m


Example 24-9.4, Page number: 809

In [9]:
from math import pi

#Variable declaration
gain = 10       #Antenna gain (dB)
Wt = 500         #Power radiation (W)
d = 15e3        #Distance (m)
Wr = 2e-6       #Received power (W)

#Calculations
Ae = Wr*(4*pi*(d**2))/(Wt*gain)  #Effective area (m^2)

#Result
print "The effective area of the receiving antenna is", round(Ae,2), "m^2"

The effective area of the receiving antenna is 1.13 m^2


Example 24-9.5, Page number: 809

In [10]:
from math import sqrt

#Variable declaration
h = 1000        #Height of duct (m)
delM = 0.036    #Change in refractive modulus (unitless)
c = 3e8         #Speed of light (m/s)

#Calculations
wl_max = 2.5*h*sqrt(delM*1e-6)  #Maximum wavelength (m)
fmax = c/wl_max     #Maximum frequency (Hz)

#Result
print "The maximum frequency that can be transmitted is", round(fmax/1e6,1),"MHz"

The maximum frequency that can be transmitted is 632.5 MHz


Example 24-12.1, Page number: 812

In [18]:
from math import pi,sqrt

#Variable declaration
gain = 10       #Gain of transmitting antenna (dB)
P = 100         #Radiating power (W)
f = 1e6        #Frequency (Hz)
rx_gain = 15    #Gain of receiving antenna (dB)
d = 20e3        #Distance (m)
c = 3e8         #Speed of light (m/s)
v = 1000        #scattering volume (m^3)
sigma = 0.1     #Effective scattering cross-section (m^2)

#Calculations
wl = c/f        #Wavelength (m)
Pr_a = P*gain*rx_gain*(wl**2)/(4*pi*(4*pi*(d**2)))
#Received power in case (a) (W)
F = (2*sqrt(sigma*v))/(d*sqrt(pi))    #Attenuation Factor (unitless)
Pr_b = Pr_a*F   #Received power in case (b) (W)

#Result
print "The received power in case (a) is", round(Pr_a,5), "W"
print "The received power in case (b) is", round(Pr_b,10), "W"

The received power in case (a) is 0.02137 W
The received power in case (b) is 1.20581e-05 W


Example 24-14.1, Page number: 813

In [19]:
from math import log10

#Variable declaration
d = 3000      #Distance (km)
f = 3e3         #Frequency (MHz)

#Calculations
path_l = 32.45 + 20*log10(f) + 20*log10(d)

#Result
print "The path loss between the two points is", round(path_l,3), "dB"

The path loss between the two points is 171.535 dB