# Chapter 7 Propagation of Radio Waves¶

## 7.1 Frequency calculation¶

In [1]:
from __future__ import division
import math

fcr=11*10**6;
D=1000;
h=400;
fmuf=fcr*math.sqrt(1+(D/(2*h))**2);
print("The maximum stable frequency is %g Hz"%fmuf);

The maximum stable frequency is 1.76086e+07 Hz


## 7.2 Usable frequency calculation¶

In [2]:
from __future__ import division
import math

Nmax=10**11;
phi=(math.pi)/9;
fcr=math.sqrt(81*Nmax);
print("The critical frequency is %g Hz"%fcr);
fmuf=fcr*(1/math.cos(phi));
print("The maximum usable frequency is %g Hz"%fmuf);

The critical frequency is 2.84605e+06 Hz
The maximum usable frequency is 3.0287e+06 Hz


## 7.3 Critical frequency calculation¶

In [1]:
from __future__ import division
import math

D=2000;
h=200;
fmuf=30.6*10**6;
fcr=fmuf/math.sqrt(1+(D/(2*h))**2);
print("The critical frequency is %g Hz"%fcr);

The critical frequency is 6.00115e+06 Hz


## 7.4 Skip distance calculation¶

In [4]:
from __future__ import division
import math

n=0.9;
fmuf=10*10**6;
f=10*10**6;
h=400*10**3;
Nmax=(1-n**2)*f**2/81;
print("The Nmax value is %g /m^3"%Nmax);
fcr=math.sqrt(81*Nmax);
print("The critical frequency is %g Hz"%fcr);
Dskip=2*h*math.sqrt((fmuf/fcr)**2-1);
print("The skip distance is %g m"%Dskip);

The Nmax value is 2.34568e+11 /m^3
The critical frequency is 4.3589e+06 Hz
The skip distance is 1.65179e+06 m


## 7.5 Efield calculation¶

In [2]:
from __future__ import division
import math

ht=150;
hr=2;
Is=9;
d=40*10**3;
f=1.2*10**6;
c=3*10**8;
lamda=c/f;
print("The wavelength is %d m"%lamda);
E=120*(math.pi)*ht*hr*Is/(lamda*d);
print("The electric field is %g V/m"%E);

The wavelength is 250 m
The electric field is 0.101788 V/m


## 7.6 Transmission height calculation¶

In [3]:
from __future__ import division
import math

dmax=45*10**3;
ht=(dmax/8.24)**2; #dmax=4.12[sqrt(ht)+sqrt(hr)];ht=hr;
print("The height of transmission is %g m"%ht);

The height of transmission is 2.98243e+07 m


## 7.7 Nmax calculation¶

In [ ]:
from __future__ import division
import math

fcre=2.5*10**6;
fcrf=8.5*10**6;
Nmaxe=(fcre)**2/81;
Nmaxf=(fcrf)**2/81;
print("The Nmax for e layer is %g /m^3"%Nmaxe);
print("The Nmax for f layer is %g /m^3"%Nmaxf);


## 7.8 Critical freq calculation¶

In [4]:
from __future__ import division
import math

Nmaxf1=2.5;
Nmaxf2=3.5;
Nmaxf3=1.5;#10^6*10^-6=1;
fcr1=math.sqrt(81*Nmaxf1);
fcr2=math.sqrt(81*Nmaxf2);
fcr3=math.sqrt(81*Nmaxf3);
print("The critical frequencies are %gHz %gHz %gHz"%(fcr1,fcr2,fcr3));

The critical frequencies are 14.2302Hz 16.8375Hz 11.0227Hz


## 7.9 Electron Density calculation¶

In [6]:
from __future__ import division
import math

fcr1=4.5*10**6;
fcr2=1.5*10**6;
Nmax1=(fcr1/9)**2;
Nmax2=(fcr2/9)**2;
print("The Nmax values are %g m^3 %g m^3"%(Nmax1,Nmax2));
Nmax=Nmax1-Nmax2;
print("The change in electron density is %g m^3"%Nmax);

The Nmax values are 2.5e+11 m^3 2.77778e+10 m^3
The change in electron density is 2.22222e+11 m^3


## 7.10 Frequency calculation¶

In [7]:
from __future__ import division
import math

#Note:10^6 is the power and not 10^-6 as mentioned in book
n=0.5;
N=400*10**6;
f=math.sqrt((81*N)/(1-n**2));
print("The frequency is %e Hz"%f);

The frequency is 2.078461e+05 Hz


## 7.11 Critical freq calculation¶

In [8]:
from __future__ import division
import math

D=1500;
h=250;
fmuf=37.95*10**6;
fcr=fmuf/math.sqrt(1+(D/(2*h))**2);
print("The critical frequency is %e Hz"%fcr);

The critical frequency is 1.200084e+07 Hz


## 7.12 Usable freq calculation¶

In [9]:
from __future__ import division
import math

D=2500;
h=200;
fcr=5*10**6;
fmuf=fcr*math.sqrt(1+(D/(2*h))**2);
print("The maximum usable frequency is %g Hz"%fmuf);

The maximum usable frequency is 3.16475e+07 Hz


## 7.13 virtual height calculation¶

In [10]:
from __future__ import division
import math

T=5*10**-3;
c=3*10**8;
h=c*(T/2);
print("The virtual height is given by %g m"%h);

The virtual height is given by 750000 m


## 7.14 LOS calculation¶

In [11]:
from __future__ import division
import math

ht=40;
hr=25;
f=90*10**6;
p=35;
LOS=4.12*(math.sqrt(ht)+math.sqrt(hr));
print("The line of sight distance is %g m"%LOS);

The line of sight distance is 46.6572 m


## 7.15 critical freq calculation¶

In [12]:
from __future__ import division
import math

Nmax=1.26*10**12;
fcr=math.sqrt(81*Nmax);
print("The critical frequency is %g Hz"%fcr)

The critical frequency is 1.01025e+07 Hz


## 7.16 critical freq calculation¶

In [13]:
from __future__ import division
import math

Nmax=1.24*10**12;
fcr=math.sqrt(81*Nmax);
print("The critical frequency is %g Hz"%fcr);

The critical frequency is 1.0022e+07 Hz


## 7.17 usable freq calculation¶

In [14]:
from __future__ import division
import math

fcr=6*10**6;
D=200*10**3;
h=200*10**3;
fmuf=fcr*math.sqrt(1+(D/(2*h))**2);
print("The maximum usable frequency is %g Hz"%fmuf);

The maximum usable frequency is 6.7082e+06 Hz


## 7.18 Range calculation¶

In [15]:
from __future__ import division
import math

ht=100;
hr=50;
d=1.4142*(math.sqrt(ht)+math.sqrt(hr));
print("The maximum range is %g miles"%d);

The maximum range is 24.1419 miles