# Chapter 8: Helical Antennas

### Example 8-5.1, Page number: 309

In :
from math import sqrt

#Variable declaration
w = 5       #Width of flattened tubing at termination (mm)
Er = 2.7    #Relative permittivity of the sheet
Z0 = 50     #Characteristic impdence of the sheet

#Calculation
h = w/((377/(sqrt(Er)*Z0))-2)

#Result
print "The required thickness of the polystyrene sheet is", round(h,1),"mm"

The required thickness of the polystyrene sheet is 1.9 mm


### Example 8-5.2, Page number:315

In :
from math import sqrt, log10

#Variable declaration
n = 16.0        #Number of turns (unitless)
C = 1       #Circumference (lambda)
S = 0.25        #Turn Spacing (lambda)

#Calculation
hpbw = 52/(C*sqrt(n*S)) #Half power beamwidth (degrees)
ax_rat = (2*n + 1)/(2*n)    #Axial ratio (unitless)
gain = 12*(C**2)*n*S        #Gain of antenna (unitless)
gain_db = 10*log10(gain)    #Gain of antenna (in dBi)

print "The half power beam width is", hpbw, "degrees"
print "The axial ratio is", round(ax_rat,2)
print "The gain is", gain,"or",round(gain_db,1),"dBi"

The half power beam width is 26.0 degrees
The axial ratio is 1.03
The gain is 48.0 or 16.8 dBi


### Example 8-5.3, Page number:316

In :
from math import pi, sqrt, log10

#Variable declaration
n = 10.0    #Number of turns (unitless)
S = 0.236   #Spacing between turns (lambda)
n_a = 4.0   #Number of helical antennas in the array (unitless)

#Calculation
D = 12*n*S  #Directivity of a single antenna(unitless)
Ae = D/(4*pi)   #Effective aperture (lambda^2)

A = sqrt(Ae)    #Area of square/spacing between helixes (lambda)
Ae_total = Ae*n_a   #Total effective aperture (lambda^2)
D_array = (4*pi*Ae_total)   #Directivity of the array (unitless)
D_array_db = 10*log10(D_array)  #Direcitivity of the array (dBi)

#Result
print "The best spacing between the helixes is", round(A,1), "lambda"
print "The directivity of the array is", round(D_array),"or",round(D_array_db,1),"dBi"

The best spacing between the helixes is 1.5 lambda
The directivity of the array is 113.0 or 20.5 dBi


### Example 8-16.1, Page number:347

In :
from math import pi

#Variable declaration
gain = 24.0   #Gain (dB)
alpha = 12.7    #Pitch angle (degrees)
c_lambda = 1.05 #Circumference (lambda)
s_lambda = 0.236    #Spacing between turns (lambda)

#Calculation
D = 10**(gain/10)   #Directivity (unitless)
L = D/(12*(c_lambda**2))    #Helix length (lambda)
n = L/s_lambda              #Number of turns (unitless)
D = D/4             #Directivity for four 20-turn helixes(unitless)
Ae = D/(4*pi)       #Effective aperture of each helix (lambda^2)

#Result
print "The Axial length is", round(L),"lambda"
print "The number of turns for the axial length is",round(n)
print "The effective aperture for 20 turns is",round(Ae),"lambda^2"

The Axial length is 19.0 lambda
The number of turns for the axial length is 80.0
The effective aperture for 20 turns is 5.0 lambda^2