# Chapter 11: Frequency Independent Antennas, Antenna Miniaturization and Fractal Antennas¶

## Example 11.1, Page No. 634¶

In [19]:
import scipy
import math
#For a given D0 of 8dB optimum sigma is 0.157

sigma=0.157
tau=0.865

alpha=math.degrees(math.atan((1-tau)/(4*sigma)))
print "Angle between edges:",alpha

print "Active Region Bandwidth:",B_ar

f_max=(216000000.0)
f_min=(54000000.0)
B=f_max/f_min
B_s=B*B_ar
print "Designed Bandwidth:",B_s

v=300000000
lamda_max=v/f_min
print "Maximum wavelength:",lamda_max,"m"

print "Total length of structure:",L,"m"

N=1+(log(B_s)/(log(1/tau)))
print "Number of elements:",int(N)

sigma_1=sigma/sqrt(tau)
print "Relative mean spacing:",sigma_1

def toFeet(m):
return m*3.2804

l_max=toFeet(lamda_max)/2
ratio=l_max*int(alpha)/0.75

Z_a=120*(log(ratio)-2.25)
print "Average characteristic impedance of elements:",Z_a,"ohms"

R_in=50.0
ratio_2=Z_a/R_in

Z0=1.2*R_in
print "Average characteristic impedance of feeder line:",Z0,"ohms"

s=(3.0/4)*cosh(Z0/120.0)
print "Center-to-center spacing of feeder conductors:",s,"in."

Angle between edges: 12.1321360732
Active Region Bandwidth: 1.752806
Designed Bandwidth: 7.011224
Maximum wavelength: 5.55555555556 m
Total length of structure: 5.53939644496 m
Number of elements: 14
Relative mean spacing: 0.168807445799
Average characteristic impedance of elements: 327.864640314 ohms
Average characteristic impedance of feeder line: 60.0 ohms
Center-to-center spacing of feeder conductors: 0.845719473905 in.