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},
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"worksheets": [
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h1>Chapter 7: Loop, Slot and Horn Antennas<h1>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 7-8.1, Page number: 256<h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from math import sqrt,pi,sin,log10\n",
"\n",
"#Variable declaration\n",
"C_lambda = 0.1*pi #Circumference (lambda)\n",
"R_m = 1.6 #Mutual resistance of two loops (ohm)\n",
"theta1 = 90*pi/180 #Angle of radiation (radians)\n",
"theta2 = 2*pi/10 #Angle of radiation (radians)\n",
"\n",
"#Calculation\n",
"Rr = 197*(C_lambda)**4 #Self resistance of loop (ohm)\n",
"D1 = (1.5)*(sin(theta1))**2 #Direcivity of loop alone (unitless)\n",
"D1_db = 10*log10(D1) #Directivity of loop alone (dBi)\n",
"D2 = 1.5*(2*sqrt(Rr/(Rr-R_m))*sin(theta2))**2\n",
" #Directivity of loop with ground plane (unitless)\n",
"D2_db = 10*log10(D2) #Direcitivy of loop with ground plane (dBi)\n",
"\n",
"#Result\n",
"print \"The directivity of loop alone is %.2f or %.2f dBi\" % (D1,D1_db)\n",
"print \"\"\"The direcitivy of loop with ground plane is %.2f or %.0f dBi\n",
" \"\"\" %(D2,D2_db)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The directivity of loop alone is 1.50 or 1.76 dBi\n",
"The direcitivy of loop with ground plane is 12.47 or 11 dBi\n",
" \n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 7-8.2, Page number:257<h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from math import sqrt, sin, pi, log10\n",
"\n",
"#Variable declaration\n",
"Rr = 197.0 #self resistance of loop (ohm)\n",
"Rm = 157.0 #mutual resistance of two loops (ohm)\n",
"theta = 2*pi/10 #Angle of radiation (radians)\n",
"\n",
"#Calculation\n",
"D = 1.5*(2*sqrt(Rr/(Rr-Rm))*sin(theta))**2 #Directivity (unitless)\n",
"D_db = 10*log10(D) #Directivity (dBi)\n",
"\n",
"#Result\n",
"print \"The direcitivy is %.1f or %.1f dBi\" % (D,D_db)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The direcitivy is 10.2 or 10.1 dBi\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 7-11.1, Page number: 261<h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from math import pi, log10\n",
"\n",
"#Variable declaration\n",
"c = pi #Circumference (m)\n",
"f1 = 1 #Frequency (MHz)\n",
"f2 = 10 #Frequency (MHz)\n",
"d = 10e-3 #Diameter of copper wire (m)\n",
"\n",
"#Calcalation\n",
"RL_Rr1 = 3430/((c**3)*(f1**3.5)*d) \n",
"RL_Rr2 = 3430/((c**3)*(f2**3.5)*d)\n",
" #Ratio of Loss resistance and radiation resistance (unitless\n",
" \n",
"k1 = 1/(1+RL_Rr1) #Radiation efficiency (unitless)\n",
"k_db1 = 10*log10(k1) #Radiation efficiency (in dB)\n",
"k2 = 1/(1+RL_Rr2) #Radiation efficiency (unitless)\n",
"k_db2 = 10*log10(k2) #Radiation efficiency (in dB)\n",
"\n",
"#Result\n",
"print \"The radiation effiency for 1 MHz is %.1ef or %.1f dB\" % (k1, k_db1)\n",
"print \"The radiation effiency for 10 MHz is %.2f or %.1f dB\" % (k2, k_db2)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The radiation effiency for 1 MHz is 9.0e-05f or -40.4 dB\n",
"The radiation effiency for 10 MHz is 0.22 or -6.5 dB\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 7-11.2, Page number: 264</h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from math import pi,sqrt\n",
"\n",
"#Variable declaration\n",
"n = 10 #Number of turns (unitless)\n",
"dia = 1e-3 #Diameter of copper wire (m)\n",
"dia_rod = 1e-2 #Diameter of ferrite rod (m)\n",
"len_rod = 10e-2 #Length of ferrite rod (m)\n",
"mu_r = 250 - 2.5j #Relative permeability (unitless)\n",
"mu_er = 50 #Efeective relative permeability (unitless)\n",
"f = 1e6 #Frequency (Hz)\n",
"c = 3e8 #Speed of light (m/s)\n",
"mu_0 = pi*4e-7 #Absolute permeability (H/m)\n",
"\n",
"#Calculations\n",
"wave_lt = c/f #Wavelength (m)\n",
"radius = dia_rod/2\n",
"C_l = (2*pi*radius)/(wave_lt) #Circumference of loop (m)\n",
"Rr = 197*(mu_er**2)*(n**2)*(C_l**4) #Radiation resistance (ohm)\n",
"Rf = 2*pi*f*mu_er*(mu_r.imag/mu_r.real)*mu_0*(n**2)*(pi*radius**2)/len_rod #Loss resistance(ohm)\n",
"cond = 1/((7e-5**2)*f*pi*mu_er) #Conductivity (S/m)\n",
"delta = 1/(sqrt(f*pi*mu_er*cond)) #Depth of penetration(m)\n",
"\n",
"RL = n*(C_l/dia)*sqrt((f*mu_0)/(pi*cond)) #Ohmic resistance (ohm)\n",
"k = Rr/(RL+abs(Rf)) #Radiation efficiency (unitless)\n",
"\n",
"L = mu_er*(n**2)*(radius**2)*mu_0/len_rod #Inductance (H)\n",
"Q = 2*pi*f*L/(abs(Rf) + Rr + RL) #Ratio of energy stored to energy lost per cycle (unitless)\n",
"\n",
"fHP = f/Q #Bandwidth at half power (Hz)\n",
"\n",
"\n",
"#Results\n",
"print \"The radiation efficiency is \", round(k,11)\n",
"print \"The value of Q is \", round(Q,3)\n",
"print \"The half-power bandwidth is\", round(fHP), \"Hz\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The radiation efficiency is 6.65e-09\n",
"The value of Q is 11.076\n",
"The half-power bandwidth is 90289.0 Hz\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 7-17.1, Page number: 280<h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import numpy as np\n",
"\n",
"#Variable declaration\n",
"Z0 = 376.7 #Intrinsic impdence of free space (ohm)\n",
"Zd = 73 + 42.5j #Impedence of infinitesimally thin lambda/2 antenna (ohm)\n",
"\n",
"#Calculation\n",
"Z1 = (Z0**2)/(4*Zd) #Terminal impedence of the lambda/2 slot antenna (ohm)\n",
"\n",
"#Result\n",
"print \"The terminal impedence of the thin lambda/2 slot antenna is\", np.around(Z1), \"ohm\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The terminal impedence of the thin lambda/2 slot antenna is "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(363-211j) ohm\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 7-17.2, Page number: 280<h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"Zd = 67 #Terminal impedence of cylindrical antenna (ohm)\n",
"Z0 = 376.7 #Intrinsic impedence of free space (ohm)\n",
"L = 0.475 #Length of complementary slot (lambda)\n",
"\n",
"#Calculation\n",
"Z1 = Z0**2/(4*Zd) #Terminal resistance of complementary slot (ohm)\n",
"w = 2*L/100 #Width of complementary slot (lambda)\n",
"\n",
"#Result\n",
"print \"The terminal resistance of the complementary slot is\", round(Z1), \"ohm\"\n",
"print \"The width of the complementary slot is\", w, \"lambda\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The terminal resistance of the complementary slot is 529.0 ohm\n",
"The width of the complementary slot is 0.0095 lambda\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 7-17.3, Page number: 281<h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"Zd = 710 #Terminal impdence of cylindrical dipole\n",
"Z0 = 376.7 #Intrinsic impedence of free space (ohm)\n",
"\n",
"#Calculation\n",
"Z1 = Z0**2/(4*Zd) #Terminal resistance of complementary slot (ohm)\n",
"\n",
"#Result\n",
"print \"The terminal resistance of the complementary slot is\", round(Z1),\"ohm\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The terminal resistance of the complementary slot is 50.0 ohm\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 7-20.1, Page number 288<h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Variable declaration\n",
"delta_e = 0.2 #path length difference in E-plane (lambda)\n",
"delta_h = 0.375 #path length difference in H-plane (lambda)\n",
"a_e = 10 #E-plane aperture (lambda)\n",
"\n",
"\n",
"#Calculation\n",
"L = a_e**2/(8*delta_e) #Horn length(lambda)\n",
"theta_e = 2*math.atan2(a_e,2*L)*180/math.pi #Flare angle in E-plane (degrees)\n",
"theta_h = 2*math.acos(L/(L+delta_h))*180/math.pi\n",
" #Flare angle in the H-plane (degrees)\n",
"a_h = 2*L*math.tan(theta_h/2*math.pi/180) #H-plane aperture (lambda)\n",
"\n",
"hpbw_e = 56/a_e #Half power beamwidth in E-plane (degrees)\n",
"hpbw_h = 67/a_h #Half power beamwidth in H-plane (degrees)\n",
"\n",
"D = 10*math.log10(7.5*a_e*a_h) #Directivity (dB)\n",
"\n",
"#Result\n",
"print \"The length of the pyramidal horn is\", L,\"lambda\"\n",
"print \"The flare angles in E-plane and H-plane are\", round(theta_e,1),\"and\", round(theta_h,2), \"degrees\"\n",
"print \"The H-plane aperture is\", round(a_h,1), \"lambda\"\n",
"print \"The Half power beamwidths in E-plane and H-plane are\", hpbw_e,\"&\",round(hpbw_h,1),\\\n",
"\"degrees\"\n",
"print \"The direcivity is\", round(D,1),\"dBi\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The length of the pyramidal horn is 62.5 lambda\n",
"The flare angles in E-plane and H-plane are 9.1 and 12.52 degrees\n",
"The H-plane aperture is 13.7 lambda\n",
"The Half power beamwidths in E-plane and H-plane are 5 & 4.9 degrees\n",
"The direcivity is 30.1 dBi\n"
]
}
],
"prompt_number": 10
}
],
"metadata": {}
}
]
}