Chapter 5. Loop Antennas

Example 5.1, Page 239

#Assuming lamda = 50
lamda=50

#Given radius = lamda/25
radius=lamda/25

def rad_res(radius,turns,lamda):
    S=pi*radius**2
    res=31171*turns**2*S**2/lamda**4
    print 'Radiation resistance for %d turns is: %f Ohms'%(turns,res)
    
rad_res(radius,1,lamda)
rad_res(radius,8,lamda)

Radiation resistance for 1 turns is: 0.787572 Ohms
Radiation resistance for 8 turns is: 50.404629 Ohms

#Given data is radius of loop and wire, frequency, conductivity

lamda=50.0

a=lamda/25
b=lamda*10**-4
f=100*10**6
space=4*10**-4*lamda
cond=5.7*10**7
omega=2*pi*f
mu_0=4*pi*10**-7
rad_res1=0.788
rad_res50=50.43

Rl=(a/b)*sqrt(omega*mu_0/(2*cond))
ecd1=rad_res1/(rad_res1+Rl)
print "Radiation efficiency of a single turn loop antenna is : %f"%(ecd1*100)

N=8
Rp_R0=0.38
R_ohmic=(N*a/b)*sqrt(omega*mu_0/(2*cond))*(1+Rp_R0)
ecd2=rad_res50/(rad_res50+R_ohmic)
print "Radiation efficiency of an 8 turn loop antenna is : %f"%(ecd2*100)

Radiation efficiency of a single turn loop antenna is : 42.809924
Radiation efficiency of an 8 turn loop antenna is : 81.270876

Example 5.3, Page 243

lamda=50

#Radius
a=lamda/25

S=pi*a**2

print 'Physical area of loop:',S

#Effective aperture
Aem=(3*lamda**2)/(8*pi)

comp=Aem/S

print 'Electrically the loop is',comp,'times bigger than physical area,'

Physical area of loop: 12.5663706144
Electrically the loop is 23.7471524162 times bigger than physical area,

Example 5.4, Page no. 260

#To design a resonant loop antenna omega=12 & circumference=1.125*lamda
omega=12
f=100*10**6
v=3*10**8
lamda=v/f
circum=1.125*lamda
a=circum/(2*pi)
print "The radius of the loop is: %f m"%(a)

b=(2*pi*a)/(exp(omega/2.0))
print "The radius of the wire is : %f m"%b

print "The axial directivity is calculated as 3.6 dB."
print "There is no need of a lumped element to resonate the radiator, since the antenna is self-resonant."

The radius of the loop is: 0.537148 m
The radius of the wire is : 0.008366 m
The axial directivity is calculated as 3.6 dB.
There is no need of a lumped element to resonate the radiator, since the antenna is self-resonant.