In [1]:

```
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"
```

In [2]:

```
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"
```

In [4]:

```
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"
```

In [4]:

```
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"
```