Chapter 6: Electric Dipoles, Thin Linear Antennas and Arrays of Dipoles and Apertures

Example 6-8.1, Page number: 174

In [6]:
import math

#Variable declaration
z = 333.0         #Driving point impedence (ohm)
r = 300.0         #twin-line impedence (ohm)
z1 = 73.0         #Self impedence of lambda/2 dipole (ohm)
z2 = 13.0         #Mutual impedence with lambda/2 spacing (ohm)

#Calculation
pv = (z-r)/(z+r)    #Reflection coefficient (unitless)
vswr = (1+pv)/(1-pv)    #Voltage Standing Wave Ratio (unitless)
gain_l2 =math.sqrt((2*z1)/(z1-z2)) #Field gain over lambda/2 dipole (unitless)
gain_l2_db = 20*math.log10(gain_l2) #Field gain (in dB)
gain_iso = (gain_l2**2)*1.64        #Gain over isotropic source (unitless)
gain_iso_db = 10*math.log10(gain_iso) #Gain over isotropic source (in dB)

#Result
print "The VSWR is", vswr
print "The field gain over lambda/2 dipole is", round(gain_l2,2), "or", round(gain_l2_db,1), "dB"
print """The gain over isotropic source is %.1f or %.1f dB
            """ % (round(gain_iso),gain_iso_db)

The VSWR is 1.11
The field gain over lambda/2 dipole is 1.56 or 3.9 dB
The gain over isotropic source is 4.0 or 6.0 dB

Example 6-8.2, Page number:175

In [5]:
import math

#Variable declaration
z = 73.0      #Self impedence of lambda/2 dipole (ohm)
zm = 64.4     #Mutual impedence with lambda/8 spacing (ohm)

#Calculation
D = math.sqrt((2*z)/(z-zm))*math.sin(math.pi/8) #Field gain over lambda/2 dipole (unitless)
D_db = 20*math.log10(D)     #Field gain over lambda/2 dipole (in dB)

gain_iso = (D**2)*1.64      #gain over isotropic source (unitless)
gain_iso_db = 10*math.log10(gain_iso)   #gain over isotropic source (in dB)

#Result
print "The field gain over lambda/2 dipole is", round(D,2), "or", round(D_db,2), "dB"
print "The gain over isotropic source is", round(gain_iso,2), "or", round(gain_iso_db,1), "dB"

The field gain over lambda/2 dipole is 1.58 or 3.96 dB
The gain over isotropic source is 4.08 or 6.1 dB

Example 6-12.1, Page number: 196

In [7]:
from math import sqrt, log10

#Variable declaration
s1 = 0.4            #Spacing 1(lambda)
s2 = 0.5            #Spacing 2(lambda)
s3 = 0.6            #Spacing 3(lambda)
R_21_1 = 6.3        #Mutual resistance for s1 (ohm)
R_21_2 = -12.691    #Murual resistance for s2 (ohm)
R_21_3 = -23.381    #Mutual resistance for s3 (ohm)  
Z = 73.13           #Self impedence of lambda/2 dipole (ohm)

#Calculation
gain_1 = sqrt(2*(Z/(Z+R_21_1)))     #Gain in fieldfor s1 (unitless)
gain_iso1 = 1.64*(gain_1**2)        #Power gain over isotropic (unitless)
gain_iso_db1 = 10*log10(gain_iso1)  #Power gain (in dBi)

gain_2 = sqrt(2*(Z/(Z+R_21_2)))     #Gain in fieldfor s2 (unitless)
gain_iso2 = 1.64*(gain_2**2)        #Power gain over isotropic (unitless)
gain_iso_db2 = 10*log10(gain_iso2)  #Power gain (in dBi)

gain_3 = sqrt(2*(Z/(Z+R_21_3)))     #Gain in fieldfor s3 (unitless)
gain_iso3 = 1.64*(gain_3**2)        #Power gain over isotropic (unitless)
gain_iso_db3 = 10*log10(gain_iso3)  #Power gain (in dBi)

#Result
print "The gain in field over half wave antenna for s1 is", round(gain_1,2)
print """The power gain over isotropic for s1 is %.2f or %.1f dBi
                """ % (gain_iso1,gain_iso_db1)
                
print "The gain in field over half wave antenna for s2 is", round(gain_2,2)
print """The power gain over isotropic for s2 is %.2f or %.2f dBi
                """ % (gain_iso2,gain_iso_db2)
                
print "The gain in field over half wave antenna for s3 is", round(gain_3,2)
print """The power gain over isotropic for s3 is %.2f or %.2f dBi
                """ % (gain_iso3,gain_iso_db3)

The gain in field over half wave antenna for s1 is 1.36
The power gain over isotropic for s1 is 3.02 or 4.8 dBi
                
The gain in field over half wave antenna for s2 is 1.56
The power gain over isotropic for s2 is 3.97 or 5.99 dBi
                
The gain in field over half wave antenna for s3 is 1.71
The power gain over isotropic for s3 is 4.82 or 6.83 dBi