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{
"metadata": {
"name": ""
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h1>Chapter 12: The Cylindrical Antenna and the Moment Method (MM)<h1>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 12-12.1, Page number: 472<h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from math import pi\n",
"import numpy as np\n",
"\n",
"#Variable declaration\n",
"N = 3 #Piecewise sinusoidal dipole modes (unitless)\n",
"l = 1/10.0 #Dipole length (lambda)\n",
"z11_exact = 0.4935 - 3454j #Exact impedence vector(ohm)\n",
"z11_apprx = 0.4944 - 3426j #approximate impedence vector(ohm)\n",
"z12_exact = 0.4935 + 1753j #Exact impedence vector(ohm)\n",
"z12_apprx = 0.4945 + 1576j #approximate impedence vector(ohm)\n",
"z13_exact = 0.4935 + 129.9j #Exact impedence vector(ohm)\n",
"z13_apprx = 0.4885 + 132.2j #approximate impedence vector(ohm)\n",
"\n",
"#Calculations\n",
"N2 = N + 1 #Number of equal segments (unitless)\n",
"d = l/4 #Length of each segment (lambda)\n",
"Rmn = 20*(2*pi*d)**2 #Real part of elements of Z-matrix, Zmn (VA)\n",
"zmat_apprx = np.array([[(z11_apprx+z13_apprx), z12_apprx],\n",
" [2*z12_apprx, z11_apprx]])\n",
" #Z(impedence) matrix (unitless)\n",
"vmat = np.array([0,1]) #Voltage matrix (unitless)\n",
"i1,i2 = np.linalg.solve(zmat_apprx,vmat) #Current matrix (unitless)\n",
"i_ratio = i2/i1 #Current ratio (unitless)\n",
"zin = vmat[1]/i2 #Input impedence (ohm)\n",
"\n",
"\n",
"zmat_exact = np.array([[(z11_exact+z13_exact), z12_exact],\n",
" [2*z12_exact, z11_exact]])\n",
"i1_e,i2_e = np.linalg.solve(zmat_exact,vmat) #Current matrix (unitless)\n",
"i_ratio_exact = i2_e/i1_e #Current ratio (unitless)\n",
"zin_exact = vmat[1]/i2_e #Input impedence (ohm)\n",
"\n",
"\n",
"#Result\n",
"print \"The current ratio is \", np.around(i_ratio,4)\n",
"print \"This is nearly equal to 1.9,\" \\\n",
" \"indicating a nearly triangular current distribution\"\n",
"print \"The input impdence is \", np.around(zin,3), \"ohm using approximate values\"\n",
"print \"The input impedence is \", np.around(zin_exact,3), \"ohm using exact values\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The current ratio is (2.09+0.0013j)\n",
"This is nearly equal to 1.9,indicating a nearly triangular current distribution\n",
"The input impdence is (1.891-1917.848j) ohm using approximate values\n",
"The input impedence is (2.083-1605.074j) ohm using exact values\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 12-12.2, Page number: 473<h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from math import tan, pi\n",
"import numpy as np\n",
"\n",
"#Variable declaration\n",
"z_load = 2.083 + 1605j #conjugate matched load (ohm)\n",
"e0 = 1.0 #Electric field magnitude (unitless)\n",
"l = 1/10.0 #length of dipole (lambda)\n",
"imag = 0+1j #Imaginary number \n",
"\n",
"z11_exact = 0.4935 - 3454j #Exact impedence vector(ohm)\n",
"z11_apprx = 0.4944 - 3426j #approximate impedence vector(ohm)\n",
"z12_exact = 0.4935 + 1753j #Exact impedence vector(ohm)\n",
"z12_apprx = 0.4945 + 1576j #approximate impedence vector(ohm)\n",
"z13_exact = 0.4935 + 129.9j #Exact impedence vector(ohm)\n",
"z13_apprx = 0.4885 + 132.2j #approximate impedence vector(ohm)\n",
"\n",
"#Calculation\n",
"d = l/4 #Length of each segment (lambda)\n",
"vm = (2*e0/(2*pi))*tan(2*pi*d/2) #Voltage vector (VA)\n",
"z22 = z11_exact + z_load #Impedence matrix for loaded dipole (VA)\n",
"zmat_exact = np.array([[(z11_exact+z13_exact), z12_exact],\n",
" [2*z12_exact, z22]])\n",
" #Z(impedence) matrix (unitless)\n",
"vmat = np.array([vm,vm]) #Voltage matrix (unitless)\n",
"i1,i2 = np.linalg.solve(zmat_exact,vmat) #Current matrix (unitless)\n",
"i3 = i1 #Current vector (unitless)\n",
"\n",
"e_zn = (60*tan(2*pi*d/2))*imag #Free space electric field (V/m)\n",
"\n",
"e_s = i1*e_zn + i2*e_zn + i3*e_zn #Scattered field (V/m)\n",
"\n",
"sigma = 4*pi*(abs(e_s)**2)/(abs(e0)**2) #Radar Cross section (lambda**2)\n",
"\n",
"#Result\n",
"print \"The radar cross section using exact values of Z matrix is\", round(sigma,4),\\\n",
" \"lambda^2\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The radar cross section using exact values of Z matrix is 0.1805 lambda^2\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 12-12.3, Page number: 475<h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import numpy as np\n",
"\n",
"#Variable declaration\n",
"z11_exact = 2-1921j #Exact impedence vector (ohm)\n",
"z12_exact = 1.9971-325.1j #Exact impedence vector (ohm)\n",
"\n",
"z11_apprx = 1.9739-1992j #Approximate impedence vector (ohm)\n",
"z12_apprx = 1.9739-232.8j #Approximate impedence vector (ohm)\n",
"\n",
"vmat = np.array([1,0])\n",
"\n",
"#Calculations\n",
"zmat_exact = np.array([[z11_apprx, z12_apprx],\n",
" [z12_apprx, z11_apprx]]) \n",
" #Impedence matrix (unitless)\n",
"i1,i2 = np.linalg.solve(zmat_exact,vmat)\n",
" #Current matrix (unitless)\n",
"zin = 1/i1\n",
"\n",
"#Result\n",
"print \"The input impedence for order N = 2 is\", np.around(zin,3), \"ohm\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The input impedence for order N = 2 is (1.539-1964.795j) ohm\n"
]
}
],
"prompt_number": 4
}
],
"metadata": {}
}
]
}
|
