# Chapter 7: Loop, Slot and Horn Antennas

### Example 7-8.1, Page number: 256

In :
from math import sqrt,pi,sin,log10

#Variable declaration
C_lambda = 0.1*pi       #Circumference (lambda)
R_m = 1.6               #Mutual resistance of two loops (ohm)

#Calculation
Rr = 197*(C_lambda)**4      #Self resistance of loop (ohm)
D1 = (1.5)*(sin(theta1))**2 #Direcivity of loop alone (unitless)
D1_db = 10*log10(D1)        #Directivity of loop alone (dBi)
D2 = 1.5*(2*sqrt(Rr/(Rr-R_m))*sin(theta2))**2
#Directivity of loop with ground plane (unitless)
D2_db = 10*log10(D2)    #Direcitivy of loop with ground plane (dBi)

#Result
print "The directivity of loop alone is %.2f or %.2f dBi" % (D1,D1_db)
print """The direcitivy of loop with ground plane is %.2f or %.0f dBi
""" %(D2,D2_db)

The directivity of loop alone is 1.50 or 1.76 dBi
The direcitivy of loop with ground plane is 12.47 or 11 dBi



### Example 7-8.2, Page number:257

In :
from math import sqrt, sin, pi, log10

#Variable declaration
Rr = 197.0        #self resistance of loop (ohm)
Rm = 157.0       #mutual resistance of two loops (ohm)

#Calculation
D = 1.5*(2*sqrt(Rr/(Rr-Rm))*sin(theta))**2  #Directivity (unitless)
D_db = 10*log10(D)      #Directivity (dBi)

#Result
print "The direcitivy is %.1f or %.1f dBi" % (D,D_db)

The direcitivy is 10.2 or 10.1 dBi


### Example 7-11.1, Page number: 261

In :
from math import pi, log10

#Variable declaration
c = pi      #Circumference (m)
f1 = 1    #Frequency (MHz)
f2 = 10   #Frequency (MHz)
d = 10e-3   #Diameter of copper wire (m)

#Calcalation
RL_Rr1 = 3430/((c**3)*(f1**3.5)*d)
RL_Rr2 = 3430/((c**3)*(f2**3.5)*d)
#Ratio of Loss resistance and radiation resistance (unitless

k1 = 1/(1+RL_Rr1)   #Radiation efficiency (unitless)
k_db1 = 10*log10(k1)    #Radiation efficiency (in dB)
k2 = 1/(1+RL_Rr2)   #Radiation efficiency (unitless)
k_db2 = 10*log10(k2)    #Radiation efficiency (in dB)

#Result
print "The radiation effiency for 1 MHz is %.1ef or %.1f dB" % (k1, k_db1)
print "The radiation effiency for 10 MHz is %.2f or %.1f dB" % (k2, k_db2)

The radiation effiency for 1 MHz is 9.0e-05f or -40.4 dB
The radiation effiency for 10 MHz is 0.22 or -6.5 dB


### Example 7-11.2, Page number: 264

In :
from math import pi,sqrt

#Variable declaration
n = 10    #Number of turns (unitless)
dia = 1e-3   #Diameter of copper wire (m)
dia_rod = 1e-2    #Diameter of ferrite rod (m)
len_rod = 10e-2    #Length of ferrite rod (m)
mu_r = 250 - 2.5j    #Relative permeability (unitless)
mu_er = 50    #Efeective relative permeability (unitless)
f = 1e6    #Frequency (Hz)
c = 3e8    #Speed of light (m/s)
mu_0 = pi*4e-7    #Absolute permeability (H/m)

#Calculations
wave_lt = c/f    #Wavelength (m)
C_l = (2*pi*radius)/(wave_lt)    #Circumference of loop (m)
Rr = 197*(mu_er**2)*(n**2)*(C_l**4)    #Radiation resistance (ohm)
cond = 1/((7e-5**2)*f*pi*mu_er)    #Conductivity (S/m)
delta = 1/(sqrt(f*pi*mu_er*cond))    #Depth of penetration(m)

RL = n*(C_l/dia)*sqrt((f*mu_0)/(pi*cond))    #Ohmic resistance (ohm)
k = Rr/(RL+abs(Rf))    #Radiation efficiency (unitless)

Q = 2*pi*f*L/(abs(Rf) + Rr + RL)    #Ratio of energy stored to energy lost per cycle (unitless)

fHP = f/Q    #Bandwidth at half power (Hz)

#Results
print "The radiation efficiency is ", round(k,11)
print "The value of Q is ", round(Q,3)
print "The half-power bandwidth is", round(fHP), "Hz"

The radiation efficiency is  6.65e-09
The value of Q is  11.076
The half-power bandwidth is 90289.0 Hz


### Example 7-17.1, Page number: 280

In :
import numpy as np

#Variable declaration
Z0 = 376.7      #Intrinsic impdence of free space (ohm)
Zd = 73 + 42.5j #Impedence of infinitesimally thin lambda/2 antenna (ohm)

#Calculation
Z1 = (Z0**2)/(4*Zd) #Terminal impedence of the lambda/2 slot antenna (ohm)

#Result
print "The terminal impedence of the thin lambda/2 slot antenna is", np.around(Z1), "ohm"

The terminal impedence of the thin lambda/2 slot antenna is (363-211j) ohm


### Example 7-17.2, Page number: 280

In :
#Variable declaration
Zd = 67     #Terminal impedence of cylindrical antenna (ohm)
Z0 = 376.7  #Intrinsic impedence of free space (ohm)
L = 0.475   #Length of complementary slot (lambda)

#Calculation
Z1 = Z0**2/(4*Zd)   #Terminal resistance of complementary slot (ohm)
w = 2*L/100         #Width of complementary slot (lambda)

#Result
print "The terminal resistance of the complementary slot is", round(Z1), "ohm"
print "The width of the complementary slot is", w, "lambda"

The terminal resistance of the complementary slot is 529.0 ohm
The width of the complementary slot is 0.0095 lambda


### Example 7-17.3, Page number: 281

In :
#Variable declaration
Zd = 710    #Terminal impdence of cylindrical dipole
Z0 = 376.7  #Intrinsic impedence of free space (ohm)

#Calculation
Z1 = Z0**2/(4*Zd)   #Terminal resistance of complementary slot (ohm)

#Result
print "The terminal resistance of the complementary slot is", round(Z1),"ohm"

The terminal resistance of the complementary slot is 50.0 ohm


### Example 7-20.1, Page number 288

In :
import math

#Variable declaration
delta_e = 0.2       #path length difference in E-plane (lambda)
delta_h = 0.375     #path length difference in H-plane (lambda)
a_e = 10            #E-plane aperture (lambda)

#Calculation
L = a_e**2/(8*delta_e)    #Horn length(lambda)
theta_e = 2*math.atan2(a_e,2*L)*180/math.pi   #Flare angle in E-plane (degrees)
theta_h = 2*math.acos(L/(L+delta_h))*180/math.pi
#Flare angle in the H-plane (degrees)
a_h = 2*L*math.tan(theta_h/2*math.pi/180)   #H-plane aperture (lambda)

hpbw_e = 56/a_e     #Half power beamwidth in E-plane (degrees)
hpbw_h = 67/a_h     #Half power beamwidth in H-plane (degrees)

D = 10*math.log10(7.5*a_e*a_h)  #Directivity (dB)

#Result
print "The length of the pyramidal horn is", L,"lambda"
print "The flare angles in E-plane and H-plane are", round(theta_e,1),"and", round(theta_h,2), "degrees"
print "The H-plane aperture is", round(a_h,1), "lambda"
print "The Half power beamwidths in E-plane and H-plane are", hpbw_e,"&",round(hpbw_h,1),\
"degrees"
print "The direcivity is", round(D,1),"dBi"

The length of the pyramidal horn is 62.5 lambda
The flare angles in E-plane and H-plane are 9.1 and 12.52 degrees
The H-plane aperture is 13.7 lambda
The Half power beamwidths in E-plane and H-plane are 5 & 4.9 degrees
The direcivity is 30.1 dBi