{
 "metadata": {
  "name": "Chapter 8"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 8: Microwave Tubes and Circuits"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 8.1, Page number 336"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a)dc electron velocity\n",
      "b)dc phase constant\n",
      "c)plasma frequency\n",
      "d)reduced plasma frequency \n",
      "e)dc beam current density\n",
      "\n",
      "import math\n",
      "\n",
      "#Variable declaration\n",
      "Vo = 14.5*10**3      #beam voltage(V)\n",
      "i = 1.4              #beam current(A)\n",
      "f = 10*10**9         #frequency(Hz)\n",
      "rho_o = 10**-6       #dc electron charge density(c/m^3)\n",
      "rho = 10**-8         #RF charge density(c/m^3)\n",
      "V = 10**5            #velocity perturbations(m/s)\n",
      "eo = 8.854*10**-12\n",
      "R = 0.4\n",
      "\n",
      "#Calculations\n",
      "#Part a\n",
      "vo = 0.593*10**6*math.sqrt(Vo)        #dc electron velocity\n",
      "\n",
      "#Part b\n",
      "w = 2.*math.pi*f\n",
      "ip = w/vo                             #dc phase current\n",
      "\n",
      "#Part c\n",
      "wp = math.sqrt((1.759*10**11*rho_o)/eo)\n",
      "\n",
      "#Part d\n",
      "wq = R*wp\n",
      "\n",
      "#Part e\n",
      "Jo = rho_o * vo\n",
      "\n",
      "#Part f\n",
      "J = rho*vo+rho_o*V\n",
      "\n",
      "#Results\n",
      "print \"dc electron velocity =\",round((vo/1E+8),3),\"*10**8 m/sec\"\n",
      "print \"dc phase curent =\",round(ip,2),\"rad/sec (Calculation mistake in the textbook)\"\n",
      "print \"plasma frequency =\",round((wp/1E+8),2),\"*10**8 rad/sec\"\n",
      "print \"Reduced plasma frequency =\",round((wq/1E+8),3),\"*10**8 rad/sec\"\n",
      "print \"dc beam current density =\",round(Jo,2), \"A/m^2\"\n",
      "print \"instantaeneous beam current density =\",round(J,3),\"A/m^2\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "dc electron velocity = 0.714 *10**8 m/sec\n",
        "dc phase curent = 879.92 rad/sec (Calculation mistake in the textbook)\n",
        "plasma frequency = 1.41 *10**8 rad/sec\n",
        "Reduced plasma frequency = 0.564 *10**8 rad/sec\n",
        "dc beam current density = 71.41 A/m^2\n",
        "instantaeneous beam current density = 0.814 A/m^2\n"
       ]
      }
     ],
     "prompt_number": 73
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 8.2, Page number 337"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a)input rms voltage\n",
      "b)output rms voltage\n",
      "\n",
      "import math\n",
      "\n",
      "#Variable declaration\n",
      "Av = 15.              #voltage gain(dB)\n",
      "Pin = 5*10**-3       #input power(W)\n",
      "Rsh_in = 30*10**3    #Rsh of input cavity(Ohms)\n",
      "Rsh_out = 20.*10**3   #Rsh of output cavity(Ohms)\n",
      "Rl = 40*10**4        #load impedance(Ohms)\n",
      "\n",
      "#Calculations\n",
      "#Part a\n",
      "V1 = math.sqrt(Pin*Rsh_in)       #input rms voltage\n",
      "\n",
      "#Part b\n",
      "#Av = 20log(V2/V1) db\n",
      "V2 = V1*10**(Av/20)             #deriving V2 from above equation\n",
      "\n",
      "#Part c\n",
      "Pout = (V2**2)/Rsh_out           #output power\n",
      "\n",
      "#Results\n",
      "print \"input rms voltage =\",round(V1,2),\"V\"\n",
      "print \"output rms voltage =\",round(V2,2),\"V\"\n",
      "print \"output power =\",round((Pout/1E-3),2),\"mW\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "input rms voltage = 12.25 V\n",
        "output rms voltage = 68.87 V\n",
        "output power = 237.17 mW\n"
       ]
      }
     ],
     "prompt_number": 50
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 8.3, Page number 338"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a)input power\n",
      "b)output power\n",
      "\n",
      "import math\n",
      "\n",
      "#Variable declaration\n",
      "n = 2               #no. of modes\n",
      "Vo = 300            #beam voltage(V)\n",
      "Io = 20*10**-3      #beam current(A)\n",
      "J1X = 1.25\n",
      "\n",
      "#Calculations\n",
      "#Part a\n",
      "Pdc = Vo*Io         #input power\n",
      "\n",
      "#Part b\n",
      "Pac = (2*Pdc*J1X)/(2*math.pi*n-(math.pi/2))\n",
      "\n",
      "#Part c\n",
      "N = (Pac/Pdc)*100.  #efficiency\n",
      "\n",
      "\n",
      "#Results\n",
      "print \"Input power =\",round(Pdc,2),\"W\"\n",
      "print \"Output power =\",round(Pac,2),\"W\"\n",
      "print \"Efficiency =\",round(N,2),\"%\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Input power = 6.0 W\n",
        "Output power = 1.36 W\n",
        "Efficiency = 22.74 %\n"
       ]
      }
     ],
     "prompt_number": 60
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 8.4, Page number 338"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a)electron velocity \n",
      "b)dc transit time of electrons\n",
      "c)input voltage for maximum output voltage\n",
      "\n",
      "import math\n",
      "\n",
      "#Varaible declaration\n",
      "Vo = 900           #beam voltage(V)\n",
      "Io = 30*10**-3     #beam current(A)\n",
      "f = 8*10**9        #frequency(Hz)\n",
      "d = 1*10**-3       #gap spacing in either cavity(m)\n",
      "L = 4*10**-2       #spacing between centers of cavities(m)\n",
      "Rsh = 40*10**3     #effective shunt impedance(Ohms)\n",
      "J1X = 0.582\n",
      "X = 1.841\n",
      "\n",
      "#Calculations\n",
      "#Part a\n",
      "vo = 0.593*10**6*math.sqrt(Vo)\n",
      "\n",
      "#Part b\n",
      "To = L/vo\n",
      "\n",
      "#Part c\n",
      "w = 2*math.pi*f\n",
      "theta_o = w*To\n",
      "theta_g = (w*d)/vo\n",
      "Bo = math.sin(theta_g/2)/(theta_g/2)\n",
      "V1_max = (Vo*3.68)/(Bo*theta_o)\n",
      "\n",
      "#Part d\n",
      "Ro = Vo/Io\n",
      "Av = ((Bo**2)*theta_o*J1X*Rsh)/(Ro*X)\n",
      "\n",
      "#Results\n",
      "print \"Electron velocity =\",round((vo/1E+6),2),\"*10**6 m/sec\"\n",
      "print \"dc transit time of electrons =\",round((To/1E-8),3),\"*10**-8 sec\"\n",
      "print \"Maximum input voltage =\",round(V1_max,3),\"V\"\n",
      "print \"Volatge gain =\",round(Av,3),\"V\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Electron velocity = 17.79 *10**6 m/sec\n",
        "dc transit time of electrons = 0.225 *10**-8 sec\n",
        "Maximum input voltage = 41.923 V\n",
        "Volatge gain = 23.278 V\n"
       ]
      }
     ],
     "prompt_number": 86
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 8.5, Page number 339"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a)Find the input microwave voltage V1 in order to generate maximum output voltage\n",
      "b)Determine the voltage gain (reflecting beam loading in the output cavity)\n",
      "c)Calculate the efficiency of the amplifier neglecting beam loading\n",
      "\n",
      "import math\n",
      "\n",
      "#Variable declaration\n",
      "Vo = 1200.         #beam voltage(V)\n",
      "Io = 28*10**-3     #beam current(A)\n",
      "f = 8*10**9        #frequency(Hz)\n",
      "d = 1*10**-3       #gap spacing in either cavity(m)\n",
      "L = 4.*10**-2      #spacing between centers of cavities(m)\n",
      "Rsh = 40*10**3     #effective shunt impedance(Ohms)\n",
      "J1X = 0.582\n",
      "X = 1.841\n",
      "Go = 23.3*10**-6\n",
      "\n",
      "#Calculations\n",
      "#Part a\n",
      "vo = 0.593*10**6*math.sqrt(Vo)\n",
      "w = 2*math.pi*f\n",
      "theta_o = (w*L)/vo\n",
      "theta_g = (w*d)/vo\n",
      "Bo = math.sin(theta_g/2)/(theta_g/2)\n",
      "V1_max = (Vo*3.68)/(Bo*theta_o)\n",
      "\n",
      "#Part b\n",
      "Ro = Vo/Io\n",
      "Av = ((Bo**2)*theta_o*J1X*Rsh)/(Ro*X)\n",
      "\n",
      "#Part c\n",
      "V2 = 2*Io*J1X*Bo*Rsh\n",
      "N = ((0.58*V2)/Vo)*100\n",
      "\n",
      "#Part d\n",
      "Gb = (Go*((Bo**2)-(Bo*math.cos(theta_g))))/2\n",
      "Rb = 1/Gb\n",
      "\n",
      "#Results\n",
      "print \"The input microwave voltage V1 in order to generate maximum output voltage is\",round(V1_max,2),\"V\"\n",
      "print \"The voltage gain (reflecting beam loading in the output cavity) is\",round(Av,3)\n",
      "print \"The efficiency of the amplifier neglecting beam loading is\",round(N,3),\"%\" \n",
      "print \"The beam loading conductance is\",round((Rb/1E+3),2),\"K Ohms (Calculation mistake in the textbook)\"\n",
      "print \"The value of\",round((Rb/1E+3),2),\"K Ohms is very much comparable to Rsh and cannot be neglected because theta_g is quite high\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The input microwave voltage V1 in order to generate maximum output voltage is 58.71 V\n",
        "The voltage gain (reflecting beam loading in the output cavity) is 17.058\n",
        "The efficiency of the amplifier neglecting beam loading is 48.427 %\n",
        "The beam loading conductance is 72.68 K Ohms (Calculation mistake in the textbook)\n",
        "The value of 72.68 K Ohms is very much comparable to Rsh and cannot be neglected because theta_g is quite high\n"
       ]
      }
     ],
     "prompt_number": 111
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 8.6, Page number 341"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a)Find the value of repeller voltage Vr\n",
      "b)Find the dc necesaary to give the microwave gap of voltage of 200V\n",
      "\n",
      "import math\n",
      "\n",
      "#Variable declaration\n",
      "Vo = 500.          #beam voltage(V)\n",
      "Rsh = 20*10**3     #effective shunt impedance(Ohms)\n",
      "f = 8*10**9        #frequency(Hz)\n",
      "L = 1.*10**-3      #spacing between centers of cavities(m)\n",
      "n = 2\n",
      "e_m = 1.759*10**11\n",
      "V1 = 200\n",
      "J1X = 0.582\n",
      "\n",
      "\n",
      "#Calculations\n",
      "#Part a\n",
      "w = 2*math.pi*f\n",
      "x = (e_m*((2*math.pi*n)-(math.pi/2))**2)/(8*(w**2)*(L**2))\n",
      "y = math.sqrt(Vo/x)\n",
      "Vr = y+Vo\n",
      "\n",
      "#Part b\n",
      "Bo = 1              #Assumption\n",
      "Io = V1/(2*J1X*Rsh)\n",
      "\n",
      "#Part c\n",
      "vo = 0.593*10**6*math.sqrt(Vo)\n",
      "theta_o = (w*2*L*vo)/(e_m*(Vr+Vo))\n",
      "Bi = 1                             #Assumption\n",
      "X_dash = (V1*theta_o)/(2*Vo)\n",
      "X = 1.51                           #from graph\n",
      "J1X = 0.84\n",
      "N = ((2*J1X)/((2*math.pi*n)-(math.pi/2)))*100\n",
      "\n",
      "#Results\n",
      "print \"The value of repeller voltage is\",round(Vr,2),\"V (Calculation mistake in the textbook)\"\n",
      "print \"The dc necesaary to give the microwave gap of voltage of 200V is\",round((Io/1E-3),2),\"mA\"\n",
      "print \"The elctron efficiency is\", round(N,2),\"%\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The value of repeller voltage is 1189.36 V (Calculation mistake in the textbook)\n",
        "The dc necesaary to give the microwave gap of voltage of 200V is 8.59 mA\n",
        "The elctron efficiency is 15.28 %\n"
       ]
      }
     ],
     "prompt_number": 41
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 8.7, Page number 342"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a)Determine the efficiency of the reflex klystron\n",
      "b)Find the total power output in mW\n",
      "\n",
      "import math\n",
      "\n",
      "#Variable declaration\n",
      "n = 1               #no. of modes\n",
      "Pdc = 40*10**-3     #input power(W)\n",
      "V1_Vo = 0.278          #ratio\n",
      "\n",
      "#Calculations\n",
      "#Part a\n",
      "N = (V1_Vo*3*math.pi)/4\n",
      "\n",
      "#Part b \n",
      "Pout = (8.91*Pdc)/100\n",
      "\n",
      "#Part c\n",
      "Pl = (Pout*80)/100\n",
      "\n",
      "#Results\n",
      "print \"The efficiency of the reflex klystron is\",round(N,3)\n",
      "print \"The total power output is\",round((Pout/1E-3),2),\"W\"\n",
      "print \"The power delivered to the load is\",round((Pl/1E-3),2),\"W\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " The efficiency of the reflex klystron is 0.655\n",
        "The total power output is 3.56 W\n",
        "The power delivered to the load is 2.85 W\n"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 8.8, Page number 343"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a)Hull cut-off voltage\n",
      "b)Cut-off magnetic flux density\n",
      "\n",
      "import math\n",
      "\n",
      "#Variable declaration\n",
      "a = 0.15            #inner raddius(m)\n",
      "b = 0.45            #outer radius(m)\n",
      "Bo = 1.2*10**-3     #magnetic flux density(Wb/m^2)\n",
      "Vo = 6000.          #beam voltage(V)\n",
      "e = 1.759*10**11\n",
      "\n",
      "#Calculations\n",
      "#Part a\n",
      "V = (e*Bo*(b**2)*(1-(a**2/b**2))**2)/8\n",
      "\n",
      "#Part b\n",
      "Bc = math.sqrt(8*Vo)/(e**2)*b*(1-(a**2/b**2))**2\n",
      "\n",
      "#Part c\n",
      "wc = (e*Bo)/(math.pi*2)\n",
      "\n",
      "\n",
      "#Results\n",
      "print \"Please note that here are calculation errors in this problem. Hence, the difference in answers\\n\"\n",
      "print \"Hull cut-off voltage =\",round((V/1E+3),2),\"kV\"\n",
      "print \"Cut-off magnetic flux density =\",((Bc/1E-3)),\"mwb/m^2\"\n",
      "print \"Cyclotron frequency =\",round(wc,2),\"Hz\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Please note that here are calculation errors in this problem. Hence, the difference in answers\n",
        "\n",
        "Hull cut-off voltage = 4221.6 kV\n",
        "Cut-off magnetic flux density = 2.51765610822e-18 mwb/m^2\n",
        "Cyclotron frequency = 33594425.39 Hz\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 8.9, Page number 343"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "import math\n",
      "\n",
      "#Variable declaration\n",
      "d = 2*10**-3         #diameter of helical TWT(m)\n",
      "n = 50.              #no. of turns per cm\n",
      "v = 3*10**8          #velocity of light(m/s)\n",
      "m = 9.1*10**-31      #mass of electron\n",
      "e = 1.6*10**-19      #charge on electron\n",
      "\n",
      "#Calculations\n",
      "p = 1/n*10**-2       #pitch(m)\n",
      "c = math.pi*d        #circumference(m)\n",
      "Vp = (v*p)/c     \n",
      "\n",
      "Vo = (m*(Vp**2))/(2*e)\n",
      "\n",
      "#Results\n",
      "print \"Axial phase velociity =\",round(Vp,2),\"m/sec\"\n",
      "print \"Anode voltage =\",round(Vo,2),\"V(Calculation mistake in the textbook)\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Axial phase velociity = 9549296.59 m/sec\n",
        "Anode voltage = 259.32 V(Calculation mistake in the textbook)\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 8.10, Page number 344"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a)electron velocity\n",
      "b)dc electronic transit time\n",
      "c)input voltage for maximum output voltage\n",
      "\n",
      "import math\n",
      "\n",
      "#Variable declaration\n",
      "Vo = 900              #beam voltage(V)\n",
      "Io = 30.*10**-3       #beam current(A)\n",
      "f = 8.*10**9          #frequency(Hz)\n",
      "d = 1.*10**-3         #gap spacing in either cavity(m)\n",
      "L = 4.*10**-2         #spacing between centres of cavity(m)\n",
      "Rsh = 40.*10**3       #effective shunt impedance(Ohms)\n",
      "\n",
      "#Calculations\n",
      "#Part a\n",
      "vo = 0.593*10**6*math.sqrt(Vo)\n",
      "\n",
      "#Part b\n",
      "Tt = d/vo\n",
      "\n",
      "#Part c\n",
      "w = 2*math.pi*f\n",
      "theta_g = (w*d)/vo\n",
      "Bo = math.sin(theta_g/2)/(theta_g/2)   #Beam coupling coefficient\n",
      "theta_o = (w*L)/vo                     #dc transit angle\n",
      "#For maximum o/p volltage,\n",
      "J1X = 0.582\n",
      "X = 1.841\n",
      "V1max = (2*Vo*X)/(Bo*theta_o)\n",
      "\n",
      "#Part d\n",
      "Av = (Bo**2*theta_o*J1X*Rsh)/(Io*X)\n",
      "\n",
      "#Results\n",
      "print \"dc electron velocity =\",round((vo/1E+7),1),\"*10**7 m/sec\"\n",
      "print \"Transit time =\",round((Tt/1E-10),2),\"*10^-10 s\"\n",
      "print \"Input voltage for maximum output voltage =\",round(V1max,2),\"V\"\n",
      "print \"Voltage gain =\",round((Av/1E+6),2),\"dB\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "dc electron velocity = 1.8 *10**7 m/sec\n",
        "Transit time = 0.56 *10^-10 s\n",
        "Input voltage for maximum output voltage = 41.95 V\n",
        "Voltage gain = 23.28 dB\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 8.11, Page number 345"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a)dc electron velocity\n",
      "b)dc phase constant\n",
      "c)plasma frequency\n",
      "d)reduced plasma frequency\n",
      "e)beam current density\n",
      "\n",
      "import math\n",
      "\n",
      "#Variable declaration\n",
      "Vo = 20*10**3        #beam voltage(V)\n",
      "Io = 2               #beam current(A)\n",
      "f = 9*10**9          #frequency(Hz)\n",
      "rho_o = 10**-6       #dc electron charge density(c/m^3)\n",
      "rho = 10**-8         #RF charge density(c/m^3)\n",
      "V = 10**5            #velocity perturbations(m/s)\n",
      "eo = 8.854*10**-12\n",
      "R = 0.5\n",
      "\n",
      "#Calculations\n",
      "#Part a\n",
      "vo = 0.59*10**6*math.sqrt(Vo)\n",
      "\n",
      "#Part b\n",
      "w = 2.*math.pi*f\n",
      "ip = w/vo                             #dc phase current\n",
      "\n",
      "#Part c\n",
      "wp = math.sqrt((1.759*10**11*rho_o)/eo)\n",
      "\n",
      "#Part d\n",
      "wq = R*wp\n",
      "\n",
      "#Part e\n",
      "Jo = rho_o * vo\n",
      "\n",
      "#Part f\n",
      "J = rho*vo-rho_o*V\n",
      "\n",
      "#Results\n",
      "print \"dc electron velocity =\",round((vo/1E+7),3),\"*10**7 m/sec\"\n",
      "print \"dc phase constant =\",round(ip,2),\"rad/sec (Calculation mistake in the textbook)\"\n",
      "print \"plasma frequency =\",round((wp/1E+8),2),\"*10**8 rad/sec\"\n",
      "print \"Reduced plasma frequency =\",round((wq/1E+8),3),\"*10**8 rad/sec\"\n",
      "print \"dc beam current density =\",round(Jo,2), \"A/m^2\"\n",
      "print \"instantaeneous beam current density =\",round(J,2),\"A/m^2\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "dc electron velocity = 8.344 *10**7 m/sec\n",
        "dc phase constant = 677.73 rad/sec (Calculation mistake in the textbook)\n",
        "plasma frequency = 1.41 *10**8 rad/sec\n",
        "Reduced plasma frequency = 0.705 *10**8 rad/sec\n",
        "dc beam current density = 83.44 A/m^2\n",
        "instantaeneous beam current density = 0.73 A/m^2\n"
       ]
      }
     ],
     "prompt_number": 71
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 8.12, Page number 345"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "import math\n",
      "\n",
      "#Variable declaration\n",
      "f = 5*10**9         #frequency(Hz)\n",
      "Vo = 1000           #operating voltage(V)\n",
      "n = 1.75            #no. of turns\n",
      "Vr = -500           #repeller voltage(V)\n",
      "d = 2*10**-3        #cavity gap(m)\n",
      "\n",
      "#Calculations\n",
      "w = 2*math.pi*f\n",
      "uo = 5.93*10**5*math.sqrt(Vo)\n",
      "theta_g = (w*d)/uo\n",
      "\n",
      "#Results\n",
      "print \"Transit angle =\",round(theta_g,2),\"radians\"\n",
      "print \"\\nThe length of drift region cannot be computed as the value of F is not given\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Transit angle = 3.35 radians\n",
        "\n",
        "The length of drift region cannot be computed as the value of F is not given\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 8.13, Page number 346"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a)input RF voltage\n",
      "b)voltage gain\n",
      "\n",
      "import math\n",
      "\n",
      "#Variable declaration\n",
      "f = 10*10**9         #frequency(Hz)\n",
      "Vo = 1200            #beam voltage(V)\n",
      "Io = 30*10**-3       #beam current(A)\n",
      "d = 1*10**-3         #diameter(m)\n",
      "Rsh = 40*10**3       #shunt resistance(Ohms)\n",
      "L = 4*10**-2         #length(m)\n",
      "X = 1.84\n",
      "\n",
      "#Calculations\n",
      "#Part a\n",
      "vo = 0.59*10**6*math.sqrt(Vo)\n",
      "w = 2*math.pi*f\n",
      "theta_o = (w*L)/vo\n",
      "V1 = (2*X*Vo)/theta_o\n",
      "theta_g = (theta_o*d)/L\n",
      "Bi = (math.sin(theta_g/2))/(theta_g/2)\n",
      "V1max = V1/Bi\n",
      "\n",
      "#Part b\n",
      "J1X = 0.58      #from table\n",
      "I2 = 2*Io*J1X\n",
      "V2 = Bi*I2*Rsh\n",
      "A = V2/V1\n",
      "Av = 20*math.log10(A)\n",
      "\n",
      "#Part c\n",
      "N = ((0.58*V2)/Vo)*100\n",
      "\n",
      "#Results\n",
      "print \"Input RF voltage is\",round(V1max,2),\"V\" \n",
      "print \"Voltage gain is\",round(Av,2),\"dB\"\n",
      "print \"efficiency is\",round(N,2),\"%\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Input RF voltage is 55.23 V\n",
        "Voltage gain is 28.03 dB\n",
        "efficiency is 43.75 %\n"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 8.14, Page number 347"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a)cyclotron angular frequency\n",
      "b)Hull cut-off voltage\n",
      "\n",
      "import math\n",
      "\n",
      "#Variable declaration\n",
      "Vo = 30*10**3        #beam voltage(V)\n",
      "Io = 80              #beam current(A)\n",
      "Bo = 0.01            #Wb/m**2\n",
      "a = 4*10**-2         #length of magnetron(m)\n",
      "b = 8*10**-2         #breadth of magnetron(m)\n",
      "e = 1.6*10**-19      #charge on electron(C)\n",
      "m = 9.1*10**-31      #mass of electron\n",
      "\n",
      "#Calculations\n",
      "#Part a\n",
      "w = (e*Bo)/m\n",
      "\n",
      "#Part b\n",
      "Vhc = (e*(Bo**2)*(b**2)*((1-((a/b)**2))**2))/(8*m)\n",
      "\n",
      "#PArt c\n",
      "Bc = ((8*Vo*(m/e))**0.5)/(b*(1-((a/b)**2)))\n",
      "\n",
      "#Results\n",
      "print \"Cyclotron angular frequency =\",round((w/1E+9),3),\"*10**9 rad/s\"\n",
      "print \"Hull cut-off voltage =\",round((Vhc/1E+3),3),\"kV\"\n",
      "print \"Cut-off magnetic flux density =\",round((Bc/1E-3),3),\"mWb/m**2\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Cyclotron angular frequency = 1.758 *10**9 rad/s\n",
        "Hull cut-off voltage = 7.912 kV\n",
        "Cut-off magnetic flux density = 19.472 mWb/m**2\n"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 8.15, Page number 348"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a)input power\n",
      "b)output power\n",
      "\n",
      "import math\n",
      "\n",
      "#Variable declaration\n",
      "n = 2            #mode\n",
      "Vo = 280         #beam volatge(V)\n",
      "Io = 22*10**-3   #beam current(A)\n",
      "V1 = 30          #signal voltage(V)\n",
      "\n",
      "#Calculations\n",
      "#Part a\n",
      "Pdc = Vo*Io\n",
      "\n",
      "#Part b\n",
      "J1X = 1.25       #from table\n",
      "Pac = (2*Pdc*J1X)/((2*n*math.pi)-(math.pi/2))\n",
      "\n",
      "#Part c\n",
      "N = (Pac/Pdc)*100\n",
      "\n",
      "#Results\n",
      "print \"Input power =\",round(Pdc,2),\"W\"\n",
      "print \"Output power =\",round(Pac,2),\"W\"\n",
      "print \"Efficiency =\",round(N,2),\"%\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Input power = 6.16 W\n",
        "Output power = 1.4 W\n",
        "Efficiency = 22.74 %\n"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 8.16, Page number 348"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a)repeller voltage\n",
      "\n",
      "import math\n",
      "\n",
      "#Variable declaration\n",
      "f = 8*10**9        #frequency(Hz)\n",
      "Vo = 300           #beam voltage(V)\n",
      "Rsh = 20*10**3     #shunt resistance(Ohms)\n",
      "L = 1*10**-3       #length(m)\n",
      "V1 = 200           #gap voltage(V)\n",
      "e_m = 1.759*10**11\n",
      "n = 2              #mode\n",
      "\n",
      "#Calculations\n",
      "#Part a\n",
      "w = 2*math.pi*f\n",
      "x = (e_m*((2*math.pi*n)-(math.pi/2))**2)/(8*(w**2)*(L**2))\n",
      "y = math.sqrt(Vo/x)\n",
      "Vr = y+Vo\n",
      "\n",
      "#Part b\n",
      "Bo = 1             #assumption\n",
      "J1X = 0.582        #from table\n",
      "Io = V1/(2*J1X*Rsh)\n",
      "\n",
      "#Results\n",
      "print \"Repeller voltage =\",round(Vr,3),\"V\"\n",
      "print \"Beam current =\",round((Io/1E-3),2),\"mA\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Repeller voltage = 833.98 V\n",
        "Beam current = 8.59 mA\n"
       ]
      }
     ],
     "prompt_number": 37
    }
   ],
   "metadata": {}
  }
 ]
}