# Chapter 2 : Basic Principles in Radiowave Propagation¶

## Example 2.1, page 25¶

In [5]:
import math

#Initialisation
sig=0.005                                #sigma
ur=1                                     #relative permeability
er=12                                    #relative permittivity
eo=8.85*10**-12                          #permittivity of a free space
f1=10*10**3                              #frequency of radio wave 1
f2=10*10**9                              #frequency of radio wave 2

#Calculation
c1=sig/(2*math.pi*f1*eo*er)              #conductivity at f1
c2=sig/(2*math.pi*f2*eo*er)              #conductivity at f2

#Result
print'conductivity at f1 = %.1f >> 1'%c1
print'conductivity at f2 = %.1f x10^-4 >> 1'%(c2*10**4)

conductivity at f1 = 749.3 >> 1
conductivity at f2 = 7.5 x10^-4 >> 1


## Example 2.2, page 26¶

In [40]:
#Initialisation
c1=3*10**8                                    #speed of light in m/s
f1=100*10**6                                  #frequency in hertz
f2=1*10**9                                    #frequency in hertz

#Calculation
v1=c1/(9)                                   #velocity in m/s
v2=c1                                       #velocity in m/s
h1=v1*f1**-1                                #wavelength at f1, v1
h2=v2*f1**-1                                #wavelength at f1, v2
h3=v1*f2**-1                                #wavelength at f2, v1
h4=v2*f2**-1                                #wavelength at f2, v2

#Result
print'Velocity,'
print'V1 = %.2f x10^7 m/s'%(v1*10**-7)
print'V2 = %.2f x10^8 m/s'%(v2*10**-8)
print'\nfor f1 = 100 MHz'
print'lambda1 = %f m'%h1
print'lambda2 = %d m'%h2
print'\nfor f2 = 1 GHz'
print'lambda1 = %.2f cm'%(h3*10)
print'lambda2 = %d cm'%(h4*10**2)

Velocity,
V1 = 3.33 x10^7 m/s
V2 = 3.00 x10^8 m/s

for f1 = 100 MHz
lambda1 = 0.333333 m
lambda2 = 3 m

for f2 = 1 GHz
lambda1 = 0.33 cm
lambda2 = 30 cm


## Example 2.3, page 37¶

In [34]:
import math
import cmath

#Initialisation
s=0.08                                     #medium conductivit
w=10**7                                    #angular velocity
e=8.85*10**-7                              #permitivity if free space
u=14                                       #medium permeability
uo=4*3.14*10**-7                           #permeability of free space

#Calculation
f=w*(2*3.14)**-1                          #frequency
a=math.sqrt(f*math.pi*s*uo)               #attenuation
b=a                                       #phase
d=complex(a,b)
y=d                                       #propagation constants
z=math.log10(0.5)/(-math.log10(math.exp(1))*2*a)   #Depth of the land

#Result
print'(1) Attenuation = %.1f Np/m'%a
print'    Propagation constant = %.1f'%y.real
print'(2) Depth of land = %.2f m'%z

(1) Attenuation = 0.7 Np/m
Propagation constant = 0.7
(2) Depth of land = 0.49 m


## Example 2.6, page 38¶

In [42]:
#Initialisation
W=100*10**-12                         #power in watt
no=120*math.pi

#Calculation
Em=math.sqrt(2*no*W)                   #effective value of E
Ee=Em/math.sqrt(2)                     #effective value of E
Hm=math.sqrt((2*10**-10)/(no))         #effective value of H
He=Hm/math.sqrt(2)                     #effective value of H

#Result
print'Em = %.1f uV/m'%(Em*10**6)
print'Ee = %.1f uV/m'%(Ee*10**6)
print'Hm = %.3f uA/m'%(Hm*10**6)
print'He = %.2f uA/m'%(He*10**6)

Em = 274.6 uV/m
Ee = 194.2 uV/m
Hm = 0.728 uA/m
He = 0.52 uA/m


## Example 2.7, page 39¶

In [43]:
#Initialisation
f=7.5                                   #frequency in GHz
Pt=30                                   #transmitter power in dBm
Pth=-78                                 #RX threshold

#Calculation
FSL=92.4+(20*math.log10(f*d))            #FSL
RSL=Pt-(0.4*FSL)-La                      #RSL

#Result
print'(1) Received signal level (RSL) = %.1f dBm'%RSL
print'(2) Fade margin = %.1f dB'%FM

(1) Received signal level (RSL) = -41.8 dBm
(2) Fade margin = 36.2 dB


## Example 2.8, page 45¶

In [44]:
#Initialisation
Pt=10                                        #transmitter power in watt
Gt=5                                         #antenna power in dBm
Lt=2                                         #feeder loss in dB
d=8000                                       #distance in meter
no=120*math.pi

#Calculation
EIRP=Pt+Gt-Lt
x=EIRP*10**-1
Ed=math.sqrt(30*EIRP2)/d                     #Electric Field Intensity
W=(Ed**2)/(2*no)                             #power in watt

#Result
print'EIRP = %.1f W'%EIRP2
print'|Ed| = %.2f mV/m'%(Ed*10**3)
print'W = %.1f nW/m^2'%(W*10**9)

EIRP = 20.0 W
|Ed| = 3.06 mV/m
W = 12.4 nW/m^2


## Example 2.9, page 47¶

In [1]:
#Initialisation
FSL=128                              #FSL in dB
Lb=135                               #Sum of FSL and medium loss Lm
Lc=5
Gt=30                                #transmitter gain in dB
Gr=30                                #reciever gain in dB

#Calculation
Lm=Lb-FSL                            #medium loss in dB
Lm1=10**(Lm*10**-1)                  #medium loss
Pt=Lc+Lb-Gt-Gr+Pr                    #power in dBm
Pt1=10**(Pt*10**-1)                  #power in watt

#Result
print'Medium Loss = %d'%Lm1
print'Pt = %.1f mW'%(Pt1)

Medium Loss = 5
Pt = 100.0 mW


## Example 2.10, page 50¶

In [47]:
#Initialisation
ri1=1.00025                         #refractive index
ri2=1.00023                         #refractive index
h1=1                                #height in Km
h2=1.5                              #height in Km
n=1.00026                           #variation

#Calculation
deln=ri1-ri2
delh=h2-h1
d=deln/delh

#Result

Radiowave curvature radius, R = 25006 Km


## Example 2.11, page 51¶

In [48]:
#Initialisation
R=25000                                       #path curvature radius in Km

#Calculation
K=R*(R-Re)**-1                               #K factor
Re1=K*Re                                     #equivalent radii of the Earth
R1=(1*Re1**-1)-(1*Re**-1)+(1*R**-1)
d=1*R1**-1                                   #equivalent radii of the path

#Result
print'K = %.3f'%K
print'Re1 = %d'%Re1
print'R1 = %d'%d
print'Therefore, R1 ~ infinity'

K = 1.342
Re1 = 8548
R1 = 147573952589676412928
Therefore, R1 ~ infinity