Chapter 5: Point Source and Their Arrays

Example 5-6.1, Page number: 90

import math
import scipy.integrate

#Variable declaration
def integrand(theta, phi):
    return (math.cos(theta)*math.sin(theta))
            #Integrand (unitless)
Um = 1      #Maximum radiation intensity (unitless)

#Calculation
P = scipy.integrate.dblquad(integrand, 0, 2*math.pi,
                             lambda x: 0, lambda x: math.pi/2)
                        #Total power radiated (relative to Um)
D = (4*math.pi)/P[0]    #Directivity (unitless)

#Result
print "The directivity is ", round(D)

The directivity is  4.0

Example 5-6.2, Page number: 91

import math
import scipy.integrate

#Variable declaration
def integrand(theta, phi):
    return (math.cos(theta)*math.sin(theta))
            #Integrand (unitless)
Um = 1      #Maximum radiation intensity (unitless)

#Calculation
P = scipy.integrate.dblquad(integrand, 0, 2*math.pi,
                             lambda x: 0, lambda x: math.pi/2)
                        #Total power radiated (relative to Um)
D = (4*math.pi)/(2*P[0])    #Directivity (unitless)

#Result
print "The directivity is ", round(D)

The directivity is  2.0

Example 5-6.3, Page number: 91

import math, scipy.integrate

#Variable declaration
def integrand(theta, phi):
    return (math.sin(theta)**2)
                #Integrand (unitless)
Um = 1          #Maximum radiation intensity (unitless)

#Calculation
P = scipy.integrate.dblquad(integrand, 0, 2*math.pi,
                             lambda x: 0, lambda x: math.pi)
                    #Total radiated power (relative to Um)
D = 4*math.pi/P[0]  #Directivity (unitless)

#Result             
print "The directivity is", round(D,2)

The directivity is 1.27

Example 5-6.4, Page number: 91

import math, scipy.integrate

#Variable declaration
def integrand(theta, phi):
    return (math.sin(theta)**3)
                #Integrand (unitless)
Um = 1          #Maximum radiation intensity (unitless)

#Calculation
P = scipy.integrate.dblquad(integrand, 0, 2*math.pi,
                             lambda x: 0, lambda x: math.pi)
                    #Total radiated power (relative to Um)
D = 4*math.pi/P[0]  #Directivity (unitless)

#Result                
print "The directivity is", round(D,2)

The directivity is 1.5

Example 5-6.5, Page number: 92

import math, scipy.integrate

#Variable declaration
def integrand(theta, phi):
    return (math.sin(theta)*math.cos(theta)**2)
                #Integrand (unitless)
Um = 1          #Maximum radiation intensity (unitless)

#Calculation
P = scipy.integrate.dblquad(integrand, 0, 2*math.pi,
                             lambda x: 0, lambda x: math.pi/2)
                    #Total radiated power (relative to Um)
D = 4*math.pi/P[0]  #Directivity (unitless)

#Result                
print "The directivity is", round(D,2)

The directivity is 6.0

Example 5-6.6, Page number:93

import math

#Variable declaration
lobes = [0.25,0.37,0.46,0.12,0.07]  #Normalized power of lobes (unitless)

#Calculation
ohm_a = 0                   #Beam area (sr)
sum_lobes = 0               #Sum of all lobes (unitless)
for i in lobes:
    ohm_a += 2*math.pi*(math.pi/36)*(i)
    sum_lobes += i

D = 4*math.pi/ohm_a         #Directivity (unitless)
D_db = 10*math.log10(D)     #Directivity (in dBi)
e_m = lobes[0]/sum_lobes    #Beam efficiency (unitless)

#Result
print "The directivity is", round(D), "or", round(D_db,1), "dBi"
print "The beam efficiency is", round(e_m, 2)

The directivity is 18.0 or 12.6 dBi
The beam efficiency is 0.2

Example 5-21.1, Page number: 146

import math

#Variable declaration
a = 25              #Height of vertical conducting wall (m)
r = 100             #Distance to the receiver (m)
wave_lt = 10e-2     #Transmitter dimension (m)

#Calculation
k = math.sqrt(2/(r*wave_lt))    #contant (unitless)
S_av = (r*wave_lt)/(4*(math.pi**2)*(a**2))  #Relative signal level (unitless)
S_av_db = 10*math.log10(S_av)   #Signal level (in db)

#Result
print "The signal level at the receiver is", round(S_av,5), "or", round(S_av_db), "dB"

The signal level at the receiver is 0.00041 or -34.0 dB