path: root/Microwave_and_Radar_Engineering_by_M._Kulkarni/chapter03.ipynb

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 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "chapter03:Transmission Lines"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example number 3.1, Page number 47"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#calculate Terminating impedance\n",
      "#Variable declaration\n",
      "Zo = 100       #o/p impedance(Ohms)\n",
      "s = 5          #VSWR\n",
      "\n",
      "#Calculations\n",
      "Zmax = Zo*s\n",
      "\n",
      "#Results\n",
      "print \"Terminating impedance = \",Zmax,\"Ohms\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Terminating impedance =  500 Ohms\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.2, Page number 47"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#calculate Characteristic impedance,Attenuation constant,Phase constant,Power delivered to the load\n",
      "import math\n",
      "import cmath\n",
      "\n",
      "#Varaible declaration \n",
      "R = 8             #resistance(Ohms)\n",
      "L = 2*10**-3      #inductance(H/km)\n",
      "C = 0.002*10**-6  #capacitance(F)\n",
      "G = 0.07*10**-6   #conductance(s/km)\n",
      "f = 2*10**3       #frequency(Hz)\n",
      "Vs = 2            #input signal(V)\n",
      "l = 500.          #line length(km)\n",
      "\n",
      "#Calculations\n",
      "w = 2*math.pi*f\n",
      "x = complex(R,w*L)\n",
      "y = complex(G,w*C)\n",
      "Zo = cmath.sqrt(x/y)\n",
      "gamma = cmath.sqrt(x*y)\n",
      "Is = Vs/Zo.real\n",
      "Il = Is*cmath.exp(-1*gamma*l)\n",
      "P = Il**2*Zo.real\n",
      "\n",
      "#Results\n",
      "print \"Characteristic impedance =\",Zo,\"Ohms\"\n",
      "print \"Attenuation constant =\",round(gamma.real,6),\"NP/km\"\n",
      "print \"Phase constant =\", round(gamma.imag,6),\"rad/km\"\n",
      "print \"\\ncalculation error in the textbook\"\n",
      "print \"\\nPower delivered to the load =\", round((abs(P)/1E-6),1), \"uW\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Characteristic impedance = (1012.50018135-155.813417548j) Ohms\n",
        "Attenuation constant = 0.003987 NP/km\n",
        "Phase constant = 0.025436 rad/km\n",
        "\n",
        "calculation error in the textbook\n",
        "\n",
        "Power delivered to the load = 73.3 uW\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.3, Page number 48"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#calculate Phase velocity\n",
      "import math\n",
      "\n",
      "#Varaible declaration\n",
      "f = 2*10**3       #frequency(Hz)\n",
      "B = 0.02543       #phase constant(rad/km)\n",
      "\n",
      "#Calculations\n",
      "w = 2*math.pi*f\n",
      "Vp = w/B\n",
      "\n",
      "#Results\n",
      "print \"Phase velocity =\",round((Vp/1E+3),2),\"km/sec\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Phase velocity = 494.16 km/sec\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.4, Page number 48"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#calculate Current drawn from generator,Power delivered to the load,Current flowing through the load\n",
      "\n",
      "import cmath\n",
      "import math\n",
      "\n",
      "#Variable declaration\n",
      "f = 37.5*10**6       #frequency(Hz)\n",
      "V = 200              #Voltage signal(Vrms)\n",
      "r = 200              #internal resistance(Ohms)\n",
      "Zo = 200             #characteristic impedance(Ohms)\n",
      "l = 10               #line length(m)\n",
      "Zl = 100             #resistive load(Ohms)\n",
      "c = 3*10**8          #velocity of propagation(m/s)\n",
      "\n",
      "#Calculations\n",
      "#Part a\n",
      "lamda = c/f\n",
      "Bl = (5*math.degrees(math.pi))/4\n",
      "x = complex(Zl,(Zo*math.tan(Bl)))\n",
      "y = complex(Zo,(Zl*math.tan(Bl)))\n",
      "Zi = Zo*(x/y)\n",
      "Vs = (Zi.real*Zo)/(Zi.real+Zo)\n",
      "Is = Zo/(Zi.real+Zo)\n",
      "\n",
      "#Part b\n",
      "P = Vs*Is\n",
      "\n",
      "#Part c\n",
      "Il = math.sqrt(P/Zl)\n",
      "\n",
      "#Results\n",
      "print \"Please note that the solution given in the textbook is incorrect.Hence the difference in answers\\n\"\n",
      "print \"Current drawn from generator is\",round(Is,3),\"A\" \n",
      "print \"Power delivered to the load is\",round(P,2),\"W\"\n",
      "print \"Current flowing through the load is\",round(Il,3),\"A\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Please note that the solution given in the textbook is incorrect.Hence the difference in answers\n",
        "\n",
        "Current drawn from generator is 0.413 A\n",
        "Power delivered to the load is 48.47 W\n",
        "Current flowing through the load is 0.696 A\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.5, Page number 50"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#calculate Reflection co-efficient, VSWR\n",
      "import cmath\n",
      "import math\n",
      "\n",
      "#Variable declaration\n",
      "zo = 50              #characteristic impedance(Ohms)\n",
      "f = 300*10**6        #frequency(Hz)\n",
      "zl = complex(50,50)  #terminating load(Ohms)\n",
      "c = 3*10**8          #velocity of propagation(m/s)\n",
      "\n",
      "#Calculations\n",
      "lamda = c/f\n",
      "rho = (zl-zo)/(zl+zo)\n",
      "phi = cmath.phase(rho)\n",
      "s = (1+abs(rho))/(1-abs(rho))\n",
      "\n",
      "#Results\n",
      "print \"Reflection co-efficient =\",round(abs(rho),4),\"with phase =\",round(math.degrees(phi),1)\n",
      "print \"VSWR =\",round(s,2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Reflection co-efficient = 0.4472 with phase = 63.4\n",
        "VSWR = 2.62\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.6, Page number 50"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#calculate position of the stub,Length of stub \n",
      "import math\n",
      "\n",
      "#Variable declaration\n",
      "Zl = 100.           #load resistance(Ohms)\n",
      "Zo = 600.           #characteristic impedance(Ohms)\n",
      "f = 100*10**6       #frequency(Hz)\n",
      "c = 3*10**8         #velocity of propagation(m/s)\n",
      "\n",
      "#Calculations\n",
      "lamda = c/f\n",
      "l = (lamda*math.atan(math.sqrt(Zl/Zo)))/(2*math.pi)\n",
      "l_dash = (lamda*math.atan(math.sqrt((Zl*Zo)/(Zo-Zl))))/(2*math.pi)\n",
      "\n",
      "#Results\n",
      "print \"The position of the stub is\", round(l,3),\"m\\n\"\n",
      "print \"Please note that the solution for l_dash given in the textbook is incorrect\"\n",
      "print \"Length of stub is\",round(l_dash,3),\"m\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The position of the stub is 0.185 m\n",
        "\n",
        "Please note that the solution for l_dash given in the textbook is incorrect\n",
        "Length of stub is 0.707 m\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.7, Page number 50"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#calculate Terminating impedance\n",
      "import cmath\n",
      "import math\n",
      "\n",
      "#Variable declaration\n",
      "s = 3.2            #VSWR\n",
      "Xmin = 0.237       #minimum voltage(V)\n",
      "Zo = 50            #characteristic impedance(Ohms)\n",
      "\n",
      "#Calculations\n",
      "q = math.tan(math.degrees(2*math.pi*Xmin))\n",
      "x = complex(1,-(s*q))\n",
      "y = complex(s, -q)\n",
      "Zl = Zo*(x/y)\n",
      "\n",
      "#Result\n",
      "print \"Please note that the solution given in the textbook is incorrect.Hence the difference in answers\\n\"\n",
      "print \"Terminating impedance =\", Zl,\"Ohms\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Please note that the solution given in the textbook is incorrect.Hence the difference in answers\n",
        "\n",
        "Terminating impedance = (19.6572514629-23.7885950214j) Ohms\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.8, Page number 51"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#calculate VSWR,First Vmax is loacted at load and first Vmin is located at,Vmin,Impedance at Vmin\n",
      "import math\n",
      "\n",
      "#Variable declaration\n",
      "Zo = 50.               #characteristic impedance(Ohms)\n",
      "Zl = 100.              #load resistance(Ohms)\n",
      "f = 300*10**3          #frequency(Hz)\n",
      "Pl = 50*10**-3         #load power(W)\n",
      "c = 3*10**8            #velocity of propagation(m/s)\n",
      "\n",
      "#Calculations\n",
      "lamda = c/f\n",
      "\n",
      "#Part a\n",
      "rho = (Zl-Zo)/(Zl+Zo)\n",
      "s = (1+abs(rho))/(1-abs(rho))\n",
      "\n",
      "#Part b\n",
      "#Since real Zl>Zo, first Vmax is located at the load\n",
      "Vmin_pos = lamda/4\n",
      "\n",
      "#Part c\n",
      "Vmax = math.sqrt(Pl*Zl)\n",
      "Vmin = Vmax/s\n",
      "\n",
      "#Part d\n",
      "Zin_at_Vmin = Zo/s\n",
      "Zin_at_Vmax = Zo*s\n",
      "\n",
      "#Results\n",
      "print \"VSWR = \", s\n",
      "print \"First Vmax is loacted at load and first Vmin is located at=\", Vmin_pos,\"m from the load\"\n",
      "print \"Vmax = \",round(Vmax,2),\"V\",\"\\nVmin = \",round(Vmin,2),\"V\"\n",
      "print \"Impedance at Vmin is \", Zin_at_Vmin,\"Ohm and impedance at Vmax is\",Zin_at_Vmax,\"Ohm\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "VSWR =  2.0\n",
        "First Vmax is loacted at load and first Vmin is located at= 250 m from the load\n",
        "Vmax =  2.24 V \n",
        "Vmin =  1.12 V\n",
        "Impedance at Vmin is  25.0 Ohm and impedance at Vmax is 100.0 Ohm\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.9, Page number 52"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#calculate Reflection loss, transmission loss, return loss\n",
      "\n",
      "import math\n",
      "\n",
      "#Variable declaration\n",
      "Zo = 600.           #characteristic impedance(Ohms)\n",
      "Zs = 50             #source impedance(Ohms)\n",
      "l = 200             #length of line(m)\n",
      "Zl = 500.           #load resistance(Ohms)\n",
      "\n",
      "#Calculations\n",
      "rho = (Zl-Zo)/(Zl+Zo)\n",
      "\n",
      "#Part a\n",
      "ref_l = math.log10(1/(1-((abs(rho))**2)))\n",
      "\n",
      "#Part b\n",
      "#Since, the line is lossless,\n",
      "att_l = 0\n",
      "trans_l = ref_l+att_l\n",
      "\n",
      "#Part c\n",
      "ret_l = math.log10(abs(rho))\n",
      "\n",
      "#Results\n",
      "print \"Reflection loss =\",round(ref_l,4),\"dB\"\n",
      "print \"Transmission loss =\",round(trans_l,4),\"dB\"\n",
      "print \"Return loss =\",round(ret_l,3),\"dB (Calculation error in the textbook)\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Reflection loss = 0.0036 dB\n",
        "Transmission loss = 0.0036 dB\n",
        "Return loss = -1.041 dB (Calculation error in the textbook)\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.10, Page number 52"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#calculate Characteristic impedance,Phase velocity \n",
      "\n",
      "import cmath\n",
      "import math\n",
      "\n",
      "#Variable declaration\n",
      "l = 10 #length of line(km)\n",
      "zsc = complex(1895.47,2234.29)  \n",
      "zoc = complex(216.99,-143.37)\n",
      "f = 1*10**3  #frequency(Hz)\n",
      "\n",
      "#Calculations\n",
      "zo = cmath.sqrt(zsc*zoc)\n",
      "x = cmath.sqrt(zsc/zoc)\n",
      "t = (1+x)/(1-x)\n",
      "gamma = cmath.log(t)/(l*2)\n",
      "B = gamma.imag\n",
      "w = 2*math.pi*f\n",
      "Vp = w/B\n",
      "\n",
      "#Results\n",
      "print \"There is calculation mistake throughout the problem in the textbook\\n\"\n",
      "print \"Characteristic impedance =\",zo,\"Ohms\"\n",
      "print \"Phase velocity =\",round((Vp/1E+3),3),\"*10^3 m/sec\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "There is calculation mistake throughout the problem in the textbook\n",
        "\n",
        "Characteristic impedance = (864.190238563+123.274392427j) Ohms\n",
        "Phase velocity = 45.994 *10^3 m/sec\n"
       ]
      }
     ],
     "prompt_number": 10
    }
   ],
   "metadata": {}
  }
 ]
}