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diff --git a/Antennas_and_Wave_Propagation/chapter12.ipynb b/Antennas_and_Wave_Propagation/chapter12.ipynb new file mode 100644 index 00000000..5d140dce --- /dev/null +++ b/Antennas_and_Wave_Propagation/chapter12.ipynb @@ -0,0 +1,195 @@ +{ + "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": {} + } + ] +}
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