# Chapter 5: Propagation in 3 KHz to 30 MHz Band¶

## Example 5.2, page 186¶

In [8]:
import math

#Initialisation
f=5                                    #frequency in Hz
er=15                                  #ground characteristics
s=0.01                                 #for vertically polarized waves
c=3*10**8                              #speed of light
e0=8.85*10**-12                        #permitivity of free space
d=80000                                #distance in m

#Calculation
a=5**0.333
df=50/a                                 #distance in metre
h=c*(f*10**6)**-1                       #wavelength
b=s/(2*math.pi*f*e0*10**6)
b1=math.sqrt(er**2+b**2)
p=(math.pi*d)/(h*b1)

#from fig 5.8
As = 0.05                             #attenuation factor

#Results
print'p = %d'%p
print'|As| = %.2f'%As

p = 107
|As| = 0.05


## Example 5.3, page 191¶

In [51]:
import math

#Initialisation
c=3*10**8                              #speed of light
f=10*10**6                             #frequency in Hz
e0=8.85*10**-12                        #permitivity of free space
er=10                                  #ground characteristics
s=0.005
d=30000
pt=200                                  #transmitter power in watt
gt=1                                     #gain of transmitter antenna

#Calculation
h=c*f**-1                               #wavelength
e=er*e0
b=s/(2*math.pi*f*e)
b1=math.sqrt(er**2+b**2)
p=(math.pi*d)/(h*b1)                     #wrong value calculated in textbook
i=((er*e0*2*3.14*f)/s)
b2=math.atan(i)
b3=b2*180/math.pi
a1=((2+0.3*p)/(2+p+0.6*p**2))
a2=math.sqrt(p/2)*(5*10**-82)*math.sin(-b3)
As=a1-a2                                       #attenuation function
pr=pt*gt*gr*h**2/(4*math.pi*d)**2
pr1=pr*(2*As)**2                            #wrong value calculated in textbook

#Results
print'Received signal power Pr = %.2f pW'%(pr1*10**12)         #wrong value calculated in textbook

Received signal power Pr = 13.35 pW


## Example 5.4, page 192¶

In [10]:
import math

#Initialisation
f=0.5                               #frequency in MHz
Pa=100                              #transmitter power
Po=1000
e120=68                            #from figure 5.10
e220=85                            #from figure 5.9
e230=80
e330=60                             #from figure 5.10
e380=48
e350=50                            #from figure 5.10
e250=75                            #from figure 5.9
e260=73
e160=60                            #from figure 5.10
e180=48

#Calculation
ETR=e120-e220+e230-e330+e380
ERT=e350-e250+e260-e160+e180                        #wrong value calculated in textbook
ER=(ETR+ERT)/2                                      #field strength at the receiving end
Ea=ER+(10*math.log10(Pa*Po**-1))
lb=137.2+(20*math.log10(f))-ER

#Results
print'(1) Electric field = %.1f dB'%Ea              #wrong value calculated in textbook due to value ER
print'(2) Basic loss path = %.1f dB'%lb             #wrong value calculated in textbook due to value ER

(1) Electric field = 33.0 dB
(2) Basic loss path = 88.2 dB


## Example 5.5, page 196¶

In [1]:
import math

#Initialisation
f1=2.5                                  #frequency in MHz
f2=6.3                                  #frequency in MHz
K=1.1                                   # K factor

#Calculation
fse=1.05*f1*2                                  #frequency in MHz
fsf=K*f2*2                                  #frequency in MHz

#Results
print'Frequency for E layer = %.2f MHz'%fse
print'Frequency for F layer = %.2f MHz'%fsf

Frequency for E layer = 5.25 MHz
Frequency for F layer = 13.86 MHz


## Example 5.7, page 201¶

In [87]:
import math

#Initialisation
f=10                                   #frequency in MHz
delta=14.5                              #in degree
d=1750                                  #distance in Km
re=6370                                #radius of earth in Km
pt=100                                #transmitter power in watt
lm=30                                   #in dB
P11=3775                               #in Km

#Calculation
a=(delta+(d/(2*re)))*(180*3.14**-1)
j=math.cos(a)
a1=(d*(2*re)**-1)*(180*3.14**-1)
j1=math.sin(a1)
P=4*re*(j1*j**-1)                                   #path length
pt1=10*math.log10(pt*10**-3)
FSL=32.4+20*math.log10(f)+20*math.log10(3775)       #free space loss
Et=136.6+pt1+20*math.log10(f)-FSL-lm                 #median value

#Results
print'(1) Path length = %d km'%P11
print'(2) Median value = %.2f dB'%Et

(1) Path length = 3775 km
(2) Median value = -7.34 dB


## Example 5.8, page 202¶

In [15]:
import math

#Initialisation
et=20                                     #in dB
gr=2                                     #antenna gain in dB
f=15                                     #frequency in MHz

#Calculation
pr=et+gr-(20*math.log10(f))-107.2          #received signal power in dB
pr1=10**(pr/10)                             #received signal power in W

#Results
print'Power Recieved signal = %.2f pW'%(pr1*10**12)

Power Recieved signal = 13.42 pW


## Example 5.9, page 202¶

In [11]:
import math

#Initialisation
pr=-108.7                                   #received signal power in dB
fa=50                                       #noise tempreture
b=2700                                      #frequency in Hz
N=5                                         #noise figure in dB

#Calculation
snr=pr-fa-(10*math.log10(b))+204               #signal to noise ratio
snr1=snr-N

#Results
print'Received signal to noise ratio = %.1f dB'%snr
print'Output signal to noise ratio = %.1f dB'%snr1

Received signal to noise ratio = 11.0 dB
Output signal to noise ratio = 6.0 dB


## Example 5.10, page 205¶

In [67]:
import math

#Initialisation
d=3000                                    #distance in Km
re=6370                                   #radius of earth in Km
phi=72                                    #angle in degree
N=5*10**11                                #electron density

#Calculation
teta1=teta*180/math.pi                    #degree
dt=90-teta1-phi                           #Elevation angle
a=re/(math.sin(phi*math.pi/180))
b=math.sin((teta1+phi)*math.pi/180)
h=(a*b)-re                                 #Height in Km
fc=9*math.sqrt(N)                          #frequency in MHz
MUF=fc*(math.cos(phi*math.pi/180))**-1      #Maximum working frequency

#Results
print'(1) Elevation angle = %.1f degree'%dt
print'(2) Height h = %.1f km'%h
print'(3) MUF = %.1f MHz'%(MUF*10**-6)

(1) Elevation angle = 4.5 degree
(2) Height h = 307.1 km
(3) MUF = 20.6 MHz


## Example 5.11, page 208¶

In [16]:
import math

#Initialisation
d=2500                                      #distance in Km
re=6370                                     #radius of earth in Km
dt=6                                        #elevation angle in degree
f1=15                                       #frequency in MHz
los1=42                                     #loss

#Calculation
teta1=teta*180/math.pi               #in degree
phi=90-dt-teta1
l=(2*re*math.sin(teta))/math.sin(phi*math.pi/180)
fsl=32.4+(20*math.log10(f1))+(20*math.log10(l))        #Free space loss
pr=57+6-fsl-los1                                    #receving power in dB
pr1=10**(pr/10)                                    #receving power in Watt

#Results
print'Power = %.2f pW'%(pr1*10**12)

Power = 47.60 pW

In [19]: