Chapter 4: Radiowave Propagation in Ionosphere

Example 4.1, page 130

In [1]:
import math

#Initialisation
h=400                                            #height in Km
pd=1*10**8                                       #plasma density at height D
pe=1*10**10                                     #plasma density at height E
pf=3*10**11                                      #plasma density at height F
Wd=20*10**3                                      #thickness of D
We=40*10**3                                      #thickness of E
Wf=190*10**3                                     #thickness of F

#Calculation
tecd=Wd*pd                                       #total electron content at D
tece=We*pe                                       #total electron content at E
tecf=Wf*pf                                       #total electron content at F
tec=tecd+tece+tecf                               
tec1=tec*math.sqrt(2)                            #total electron content

#Results
print'(2) TEC (D) = %.1f x 10^12 el/m^2'%(tecd/10**12)
print'    TEC (E) = %.1f x 10^14 el/m^2'%(tece/10**14)
print'    TEC (F) = %.2f x 10^16 el/m^2'%(tecf*10**-16)
print'(3) TEC = %.1f x 10^16 el/m^2'%(tec1/10**16)

(2) TEC (D) = 2.0 x 10^12 el/m^2
    TEC (E) = 4.0 x 10^14 el/m^2
    TEC (F) = 5.70 x 10^16 el/m^2
(3) TEC = 8.1 x 10^16 el/m^2

Example 4.2, page 134

In [2]:
import math

#Initialisation
N=5*10**11                                    #Electron density in F layer

#Calculation
F=9*math.sqrt(N)                              #f0F frequency

#Results
print'(1) hmin = 200Km  hmax = 400Km'         #from graph
print'(2) F = %.1f Mhz'%(F*10**-6)

(1) hmin = 200Km  hmax = 400Km
(2) F = 6.4 Mhz

Example 4.3, page 136

In [4]:
import math

#Initialisation
fc=6.3*10**6                            #frequency in hertz

#Calculation
f=fc*math.sqrt(2)                       #maximum usable frequency

#Results
print'Maximum usable frequency = %.3f MHz'%(f*10**-6)

Maximum usable frequency = 8.910 MHz

Example 4.4, page 137

In [5]:
import math

#Initialisation
tec=10**17                                   #total electron content
H=200*10**3                                  #thickness of F layer
 
#Calculation
pd=tec/H                                      #plasma density at F
fc=9*math.sqrt(pd)
ouf=3.6*fc*0.8                               #optimum usable frequency
muf=fc*1.788                                 #maximum usable frequency

#Results
print'Maximum usable frequency = %.1f MHz'%(fc*10**-6)
print'Optimum usable frequency < %.3f MHz'%(ouf*10**-6)
print'Maximum usable frequency (30) = %.1f MHz'%(muf*10**-6)

Maximum usable frequency = 6.4 MHz
Optimum usable frequency < 18.328 MHz
Maximum usable frequency (30) = 11.4 MHz

Example 4.5, page 138

In [25]:
import math

#Initialisation
d=1000                                          #distance in km
re=6370                                         #earth radius in km
dt=30                                           #in degree

#Calculation
teta=d*(2*re)**-1                               #theta in radians
tet=teta*180*math.pi**-1                       #theta in degree
w1=90-dt-tet
a=math.sin(w1*3.14/180)/re
a1=math.sin((90+dt)*3.14/180)
h=(a1*a**-1)-re                                  #height
#Results
print'(1) virtual height of the reflection point = %d km'%h           #wrong value calculated in textbook

(1) virtual height of the reflection point = 330 km

Example 4.6, page 142

In [14]:
import math

#Initialisation
d=200                            #height in Km
f=700                            #frequency in Khz

#Calculation
T1e=0.4                          #from graph 4.10
T2e=0.9
T3e=1.7
T1f=1.3
T2f=2.8
T3f=4.3
Tef=0.3
Tef1=2.7
Tef2=0.5

#Results
print'(1) Time delay of E layer, Td(1E) = %.1f ms'%T1e
print'                           Td(2E) = %.1f ms'%T2e
print'                           Td(2E) = %.1f ms'%T3e
print'    Time delay of F layer, Td(1F) = %.1f ms'%T1f
print'                           Td(2F) = %.1f ms'%T2f
print'                           Td(2F) = %.1f ms'%T3f
print'(2) Time delay of E and F for a distance of 500 km, Td(E,F) = %.1f ms'%Tef
print'(3) Td(1F,3F) = %.1f ms'%Tef1
print'    Td(1E,3E) = %.1f ms'%Tef2

(1) Time delay of E layer, Td(1E) = 0.4 ms
                           Td(2E) = 0.9 ms
                           Td(2E) = 1.7 ms
    Time delay of F layer, Td(1F) = 1.3 ms
                           Td(2F) = 2.8 ms
                           Td(2F) = 4.3 ms
(2) Time delay of E and F for a distance of 500 km, Td(E,F) = 0.3 ms
(3) Td(1F,3F) = 2.7 ms
    Td(1E,3E) = 0.5 ms

Example 4.7, page 147

In [18]:
import math

#Initialisation
f=1.5*10**9                                        #frequency in Hz
tec=10**18                                         #total electron content
g=5*10**-3                                         #geomagnetic field intensity
a=3.36*10**2

#Calculation
teta= a*g*tec*(f**-2)                             #Faraday rotation in Radian
c=0.8422
x=20*math.log10(c)                                #loss value in dB

#Results
print'(1) Faraday rotation = %.1f Rad'%teta
print'(2) Loss = %f dB'%x

(1) Faraday rotation = 0.7 Rad
(2) Loss = -1.491695 dB

Example 4.8, page 149

In [21]:
import math

#Initialisation
tec1=10**18                           #total electron content
f=1.5                                 #frequency in Hertz
tec2= 10**17                          #total electron content

#Calculation
teta = 600                            #Faraday rotation in mRadian
T=5                                   #time delay in ns
gd=0.5                                #time delay difference in ns

#Results
print'(1) Faraday rotation = %d mRad'%teta
print'(2) Time delay = %d ns'%T
print'(3) G/D = %.1f ns'%gd

(1) Faraday rotation = 600 mRad
(2) Time delay = 5 ns
(3) G/D = 0.5 ns

Example 4.9, page 158

In [11]:
import math

#Initialisation
phi=166                                            #in radian                                           
t=35*math.pi/180                                  #geographic latitude in radian
t1=60*math.pi/180                                  #zenith angle in radian
N=80*math.pi/180                                  #in radian
x=92
y=35
h=35
p=1.2



#Calculation
m=0.11-0.49*math.cos(t)
fe=0.004*(1+0.021*166)**2                            #minimum value of f0E
A=1+0.0094*(phi-66)                                  #A value
B=(math.cos(N))
B1=B**m                                              #B value
C=x+y*math.cos(t)                                    #C value
D=math.cos(t1)**p                                    #D value
F=(A*B*C*D)**(0.25)                                  #exact value of f0E                             

#Results
print'(1) Minimum value of f0E = %.2f x 10^-2 MHz'%(fe*100)
print'(2) f0E = %.2f MHz'%F                                           #wrong value calculated in textbook

(1) Minimum value of f0E = 8.05 x 10^-2 MHz
(2) f0E = 2.05 MHz

Example 4.10, page 159

In [62]:
import math

#Initialisation
g=50                                            #geomagnetic latitude in degree
R12=100                                         #solar activity number
x=60*math.pi/180                                #zenith angle in radians

#Calculation
f0=4.35+0.0058*g-0.00012*g**2
f100=5.35+0.011*g-0.00023*g**2
fs=f0+0.01*(f100-f0)*R12
n=0.093+(0.00461*g)-(0.000054*(g**2))+(0.0031*R12)            #wrong value calculated in textbook
F1=fs*(math.cos(x))**n                              #critical frequency

#Results
print'Critical Frequency = %.2f MHz'%F1          #wrong value calculated in textbook

Critical Frequency = 3.77 MHz

Example 4.11, page 164

In [61]:
import math

#Initialisation
R12=150                                          #12 month average value
fs0=4.416
fs100=5.473
n=0.23
x=45*math.pi/180                                 #zenith angle in radians                    

#Calculation
f1=63.7+0.728*R12+0.00089*R12**2
fs=fs0+0.01*(fs100-fs0)*R12
F1=fs*(math.cos(x))**n                            #critical frequency                               #zenith angle in radians

#Results
print'(1) R12 = %d'%R12
print'(2) F12 = %d'%f1
print'(3) f0F1 = %.2f MHz'%F1

(1) R12 = 150
(2) F12 = 192
(3) f0F1 = 5.54 MHz
In [ ]: