Chapter07, Loop Antenna

Example No. 7.10.1, page : 7-16

In [3]:
import numpy as np
A=1 #m²(Area of loop)
N=400 #no. of turns
Q=100 #Quality factor
theta=60 #degree(angle)
Erms=10 #µV/m(field strength)
f=1 #MHz(tuned frequency)
c=3*10**8 #m/s##Speed of light
lamda=c/(f*10**6) #m(Wavelength)
Vr=Q*2*np.pi*A*N*np.cos(theta*np.pi/180)*Erms*10**-6/lamda #V(reciever input voltage)
print "Input voltage to the receiver = %0.3f mV  " %(Vr*1000)

Input voltage to the receiver = 4.189 mV

Example No. 7.10.2, page : 7-17

In [4]:
import numpy as np
N=12 #no. of turns
A=1 #m²(Area of loop)
Erms=100 #µV/m(field strength)
f=10 #MHz(tuned frequency)
theta=0 #degree(angle)
c=3*10**8 #m/s##Speed of light
lamda=c/(f*10**6) #m(Wavelength)
Vr=2*np.pi*A*N*np.cos(theta*np.pi/180)*Erms*10**-6/lamda #V(reciever input voltage)
print "Voltage induced in loop = %0.2f µV/m " %(Vr*10**6) 

Voltage induced in loop = 251.33 µV/m

Example No. 7.10.3, page : 7-17

In [7]:
N=25 #no. of turns
Vrms=150 #µV(emf induced)
f=500 #kHz(tuned frequency)
A=0.5**2 #m²(Area of loop)
theta=0 #degree(angle)
c=3*10**8 #m/s##Speed of light
lamda=c/(f*10**3) #m(Wavelength)
Erms=lamda/(2*np.pi*A*N*np.cos(theta*np.pi/180))*Vrms*10**-6 #V/m(maximum emf induced)
print "Field strength = %0.3f mV/m  "%(Erms*10**3) 

Field strength = 2.292 mV/m

Example No. 7.10.4, page : 7-17

In [11]:
N1=1.0 #no. of turns in primary
N2=8.0 #no. of turns in secondary
#a=lamda/25 
aBYlamda=1.0/25 #(temporary calculation)
#A=np.pi*a**2
A_BY_lamda_sqr=np.pi*aBYlamda**2 #(temporary calculation)
Rr1=31200*(N1*A_BY_lamda_sqr)**2 #Ω(Radiation resistance for single turn)
print "Radiation resistance for single turn loop = %0.4f Ω " %(Rr1) 
Rr2=31200*(N2*A_BY_lamda_sqr)**2 #Ω(Radiation resistance for 8 turn)
print "Radiation resistance for 8 turn loop = %0.2f Ω " %Rr2 

Radiation resistance for single turn loop = 0.7883 Ω 
Radiation resistance for 8 turn loop = 50.45 Ω

Example No. 7.10.5, page : 7-18

In [14]:
from __future__ import division
f=100 #MHz(Operating frequency)
c=3*10**8 #m/s##Speed of light
lamda=c/(f*10**6) #m(Wavelength)
a=lamda/25 #m(radius)
C=2*np.pi*a #m(Circumference)
d=2*10**-4*lamda #m(Spacing)
print "For single turn : " 
N=1 #n. of turns
RL_BY_Rr=3430.0/(C**3*f**(3.5)*N*d) #(temporary calculation)
K=1/(1+RL_BY_Rr)*100 #%(Radiation efficiency)
print "Radiation efficiency of single turn = %0.2f %%" %K
print "For Eight turn : " 
N=8 #no. of turns
RL_BY_Rr=3430/(C**3*f**(3.5)*N*d) #(temporary calculation)
K=1/(1+RL_BY_Rr)*100 #%(Radiation efficiency)
print "Radiation efficiency of eight turn = %0.2f %%" % K

For single turn : 
Radiation efficiency of single turn = 42.85 %
For Eight turn : 
Radiation efficiency of eight turn = 85.71 %

Example No. 7.10.6, page : 7-19

In [18]:
from fractions import Fraction
a=0.5 #m(radius)
f=0.9 #MHz(OPerating frequency)
c=3*10**8 #m/s##Speed of light
lamda=c/(f*10**6) #m(wavelength)
C=2*np.pi*a #m(Circumference)
if C/lamda<1/3:
    D=3/2 #Directivity
elif C/lamda>1/3:
    D=0.682*C/lamda #Directivity

print "Directivity :" ,Fraction(D)

Directivity : 3/2