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 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 6: Antennas"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 6.1, Page 137"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "from pylab import *\n",
      "%pylab inline\n",
      "#Variable Decalration\n",
      "a=3\n",
      "b=2\n",
      "dB=1\n",
      "\n",
      "#Calculation\n",
      "#Initializations\n",
      "tita=arange(-90,92,2)\n",
      "tita[45]=1\n",
      "tita1=arange(-90,92,2)\n",
      "Y=linspace(0,0,91)\n",
      "E=linspace(0,0,91)\n",
      "gE=linspace(0,0,91)\n",
      "GE=linspace(0,0,91)\n",
      "X=linspace(0,0,91)\n",
      "E1=linspace(0,0,91)\n",
      "gH=linspace(0,0,91)\n",
      "GH=linspace(0,0,91)\n",
      "for i in range(0,size(Y)-1):\n",
      "   Y[i]=math.pi*b*math.sin(tita[i]*3.142/180)\n",
      "   X[i]=math.pi*a*math.sin(tita[i]*3.142/180)\n",
      "   E[i]=(math.sin(Y[i]))/Y[i]   \n",
      "   E1[i]=math.cos(tita1[i]*3.142/180)*(math.sin(X[i]))/X[i]\n",
      "   gE[i]=(E[i])**2   #Raiation pattern in E-Plane\n",
      "   gH[i]=E1[i]**2    #Raiation pattern in H-Plane\n",
      "   GE[i]=10*math.log10(gE[i])  #Raiation pattern in E-Plane(dB)\n",
      "   GH[i]=10*math.log10(gH[i])  #Raiation pattern in H-Plane(dB)\n",
      "\n",
      "#Results\n",
      "\n",
      "figure(0)\n",
      "plot(tita,GE)   #Plotting E-Plane radiation pattern\n",
      "ylim([-30,0])\n",
      "xlim([-90,90])\n",
      "xlabel('tita degrees')\n",
      "ylabel('GE(tita)')\n",
      "figure(1)\n",
      "plot(tita1,GH)  #Plotting H-Plane radiation pattern\n",
      "ylim([-30,0])\n",
      "xlim([-90,90])\n",
      "xlabel('tita degrees')\n",
      "ylabel('GH(tita)')\n",
      "show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "WARNING: pylab import has clobbered these variables: ['linalg', 'draw_if_interactive', 'random', 'power', 'info', 'fft']\n",
        "`%pylab --no-import-all` prevents importing * from pylab and numpy\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
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K9IWWkGQwe/ZseHt7w9vbG9HR0bhe4zJkxYoV8Pb2hp+fH3bbQ09XPTZsAKKi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\nQUREBPz8/Op87Ny5EwCwbNk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       "text": [
        "<matplotlib.figure.Figure at 0x230e550>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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vf9VxntOnw5Il8Ne/wvDhsGoV/OEPNZ+S5++kMvBT33wDd98NL7wA991X/rbX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\nEEIA/x/QySImXNYyRgAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x331be90>"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 6.2, Page 159"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "from pylab import *\n",
      "%pylab inline\n",
      "#Varable Declaration\n",
      "\n",
      "N=5   #Number of elements of dipole\n",
      "s=0.25 #Space between dipole elements(wavelengths)\n",
      "phi0=0#Angle between array factor and array(degrees)\n",
      "\n",
      "#Calculation\n",
      "\n",
      "alpha=-2*3.142*s*math.cos(phi0)  #Current phase(radians)\n",
      "phi=arange(-180,182,2)\n",
      "Si=linspace(0,0,181)\n",
      "for k in range(0,180):\n",
      "    Si[k]=alpha+2*3.142*s*math.cos(phi[k]*3.142/180)\n",
      "AFR=linspace(0,0,181)\n",
      "AFI=linspace(0,0,181)\n",
      "for i in range(0,180):\n",
      "  for j in range(0,N-1):\n",
      "     AFR[i]=AFR[i]+math.cos(j*Si[i])  #Real part of Array factor\n",
      "     AFI[i]=AFI[i]+math.sin(j*Si[i])#Imaginary part of Array factor\n",
      "\n",
      "teta=linspace(-3.142,3.142,181)\n",
      "AF=linspace(0,0,181)\n",
      "for k in range(0,180):\n",
      "   AF[k]=AF[k]+(AFR[k]**2+AFI[k]**2)**0.5\n",
      "\n",
      "#Result\n",
      "\n",
      "polar(teta,AF)\n",
      "title('Polar plot of Array Factor')\n",
      "show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "WARNING: pylab import has clobbered these variables: ['power', 'draw_if_interactive', 'random', 'fft', 'linalg', 'info']\n",
        "`%pylab --no-import-all` prevents importing * from pylab and numpy\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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cMZA2mlEoFHTo0CGT5lJhheM4Wr58ObNzOj2d6P33iRwciN59l+jMGVUDUheW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\nmAgICPCCICYCAgK8IIiJgIAAL/wfoh506YJzEZ8AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x35cfc10>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 6.3, Page 160"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "from pylab import *\n",
      "%pylab inline\n",
      "#Varable Declaration\n",
      "\n",
      "N=5   #Number of elements of dipole\n",
      "s=0.25 #Space between dipole elements(wavelengths)\n",
      "phi0=90*math.pi/180 #Angle between array factor and array(radians)\n",
      "\n",
      "#Calculation\n",
      "\n",
      "alpha=-2*math.pi*s*math.cos(phi0)  #Current phase(radians)\n",
      "phi=arange(-180,185,5)\n",
      "Si=linspace(0,0,73)\n",
      "for k in range(0,73):\n",
      "    Si[k]=alpha+2*math.pi*s*math.cos(phi[k]*math.pi/180)\n",
      "\n",
      "AFR=linspace(0,0,73)\n",
      "AFI=linspace(0,0,73)\n",
      "\n",
      "for i in range(0,73):\n",
      "  for j in range(0,N):\n",
      "     AFR[i]=AFR[i]+math.cos(j*Si[i])  #Real part of Array factor\n",
      "     AFI[i]=AFI[i]+math.sin(j*Si[i])#Imaginary part of Array factor\n",
      "\n",
      "teta=phi*math.pi/180\n",
      "AF=linspace(0,0,73)\n",
      "for k in range(0,73):\n",
      "   AF[k]=AF[k]+(AFR[k]**2+AFI[k]**2)**0.5\n",
      "\n",
      "#Result\n",
      "\n",
      "polar(teta,AF)\n",
      "title('Polar plot of Array Factor')\n",
      "show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "WARNING: pylab import has clobbered these variables: ['power', 'draw_if_interactive', 'random', 'fft', 'linalg', 'info']\n",
        "`%pylab --no-import-all` prevents importing * from pylab and numpy\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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GQSMjIwQFBXGik8fj4c8//8S9e/fwyy+/cCJTlzQYZ3Lx4kWsWLECoaGhnKbH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\n5Zq42dnZMDU1rZcZqiwoKCiAs7MzMjMz0axZM53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VSoXBgwdjzJgx2LNnD/Oe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\nkih+9IgAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x23250d0>"
       ]
      }
     ],
     "prompt_number": 4
    }
   ],
   "metadata": {}
  }
 ]
}