removing problem statements

1 files changed, 418 insertions, 451 deletions

diff --git a/Elements_of_Electromagnetics/chapter_12.ipynb b/Elements_of_Electromagnetics/chapter_12.ipynb
index b6ded6a6..e098f292 100644
--- a/Elements_of_Electromagnetics/chapter_12.ipynb
+++ b/Elements_of_Electromagnetics/chapter_12.ipynb
@@ -1,452 +1,419 @@
-{

- "metadata": {

-  "name": "chapter_12.ipynb"

- },

- "nbformat": 3,

- "nbformat_minor": 0,

- "worksheets": [

-  {

-   "cells": [

-    {

-     "cell_type": "markdown",

-     "metadata": {},

-     "source": [

-      "<h1>Chapter 12: Waveguides<h1>"

-     ]

-    },

-    {

-     "cell_type": "markdown",

-     "metadata": {},

-     "source": [

-      "<h3>Example 12.1, Page number: 557<h3>"

-     ]

-    },

-    {

-     "cell_type": "code",

-     "collapsed": false,

-     "input": [

-      "from __future__ import division\n",

-      "'''\n",

-      "A rectangular waveguide with dimensions a = 2.5 cm, b = 1 cm is to \n",

-      "operate below 15.1 GHz. How many TE and TM modes can the waveguide transmit\n",

-      "if the guide is filled with a medium characterized by sigma = 0, epsilon = 4\n",

-      "epsilon_o,mu_r = 1? Calculate the cutoff frequencies of the modes. '''\n",

-      "\n",

-      "import scipy\n",

-      "\n",

-      "#Variable Declaration\n",

-      "\n",

-      "a=2.5*10**-2     #in m\n",

-      "b=1*10**-2       #in m\n",

-      "c=0\n",

-      "Ur=1             #relative permeability\n",

-      "Er=4             #relative permittivity\n",

-      "C=3*10**8        #speed of wave in m/s\n",

-      "fc=0\n",

-      "m=0\n",

-      "n=0\n",

-      "\n",

-      "#Calculations\n",

-      "\n",

-      "while (fc*10**-9 < 15.1) :\n",

-      "   fc = (C/(4*a))*scipy.sqrt(m**2+(a*n/b)**2)\n",

-      "   if (( fc*10**-9) < 15.1) :\n",

-      "       n=n+1\n",

-      "   else:\n",

-      "       print 'Maximum value of n is ',n-1\n",

-      "\n",

-      "nmax=n-1 \n",

-      "fc=0\n",

-      "m=0\n",

-      "n=0\n",

-      "while(fc*10**-9 < 15.1):\n",

-      "   fc =(C/(4*a))*scipy.sqrt(m**2+(a*n/b)**2)\n",

-      "   if((fc*10**-9) < 15.1):\n",

-      "       m=m+1\n",

-      "   else:\n",

-      "      print 'Maximum value of m is ',m-1 \n",

-      "\n",

-      "mmax=m-1\n",

-      "m=0\n",

-      "while(m<mmax+1):\n",

-      "    n=0\n",

-      "    while(n<nmax+1):\n",

-      "        p=(C/(4*a))*scipy.sqrt(m**2+(a*n/b)**2)\n",

-      "        if((p*10**-9) < 15.1) :\n",

-      "          print m,n,'transmission mode is possible'\n",

-      "          print 'frequency is',round(p*10**-9,2),'GHz'\n",

-      "        else:\n",

-      "          print m,n,'transmission mode is not possible'\n",

-      "        n=n+1\n",

-      "    \n",

-      "    m=m+1\n",

-      "        "

-     ],

-     "language": "python",

-     "metadata": {},

-     "outputs": [

-      {

-       "output_type": "stream",

-       "stream": "stdout",

-       "text": [

-        "Maximum value of n is  2\n",

-        "Maximum value of m is  5\n",

-        "0 0 transmission mode is possible\n",

-        "frequency is 0.0 GHz\n",

-        "0 1 transmission mode is possible\n",

-        "frequency is 7.5 GHz\n",

-        "0 2 transmission mode is possible\n",

-        "frequency is 15.0 GHz\n",

-        "1 0 transmission mode is possible\n",

-        "frequency is 3.0 GHz\n",

-        "1 1 transmission mode is possible\n",

-        "frequency is 8.08 GHz\n",

-        "1 2 transmission mode is not possible\n",

-        "2 0 transmission mode is possible\n",

-        "frequency is 6.0 GHz\n",

-        "2 1 transmission mode is possible\n",

-        "frequency is 9.6 GHz\n",

-        "2 2 transmission mode is not possible\n",

-        "3 0 transmission mode is possible\n",

-        "frequency is 9.0 GHz\n",

-        "3 1 transmission mode is possible\n",

-        "frequency is 11.72 GHz\n",

-        "3 2 transmission mode is not possible\n",

-        "4 0 transmission mode is possible\n",

-        "frequency is 12.0 GHz\n",

-        "4 1 transmission mode is possible\n",

-        "frequency is 14.15 GHz\n",

-        "4 2 transmission mode is not possible\n",

-        "5 0 transmission mode is possible\n",

-        "frequency is 15.0 GHz\n",

-        "5 1 transmission mode is not possible\n",

-        "5 2 transmission mode is not possible\n"

-       ]

-      }

-     ],

-     "prompt_number": 1

-    },

-    {

-     "cell_type": "markdown",

-     "metadata": {},

-     "source": [

-      "<h3>Example 12.3, Page number: 561<h3>"

-     ]

-    },

-    {

-     "cell_type": "code",

-     "collapsed": false,

-     "input": [

-      "'''\n",

-      "In a rectangular waveguide for which a = 1.5 cm, b = 0.8 cm, sigma = 0, \n",

-      "mu = mu_o and epsilon = 4epsilon_o,\n",

-      "\n",

-      "Hx=2sin(pi x/a) cos(3pi y/b)sin(pi X 10^11t - Bz) A/m\n",

-      "\n",

-      "Determine \n",

-      "(a) The mode of operation \n",

-      "(b) The cutoff frequency \n",

-      "(c) The phase constant B \n",

-      "(d) The propagation constant gamma\n",

-      "(e) The intrinsic wave impedance eta '''\n",

-      "\n",

-      "import scipy\n",

-      "import cmath\n",

-      "from numpy import *\n",

-      "\n",

-      "#Variable Declaration\n",

-      "\n",

-      "a=1.5*10**-2              #in m\n",

-      "b=0.8*10**-2              #in m\n",

-      "c=0\n",

-      "Uo=4*scipy.pi*10**-7      #permeability of free space\n",

-      "Ur=1                      #relative permeability\n",

-      "Eo=10**-9/(36*scipy.pi)   #permittivity of free space\n",

-      "Er=4                      #relative permittivity\n",

-      "C=3*10**8                 #speed of light in m/s\n",

-      "w=scipy.pi*10**11         #omega in rad/s\n",

-      "m=1\n",

-      "n=3\n",

-      "u=C/2                     #speed of wave in m/s\n",

-      "\n",

-      "#Calculations\n",

-      "\n",

-      "f=w/(2*scipy.pi)                                #frequency of wave in Hz\n",

-      "fc=u*((m*m)/(a*a)+(n*n)/(b*b))**0.5/2           #cutoff frequency in Hz\n",

-      "B=w*scipy.sqrt(1-(fc/f)**2)/u                   #phase constant in rad/m\n",

-      "eta=377/scipy.sqrt(Er)*scipy.sqrt(1-(fc/f)**2)  #intrinsic wave impedance in ohm\n",

-      "\n",

-      "#Results\n",

-      "\n",

-      "print 'The cutoff frequency =',round(fc*10**-9,2),'GHz'\n",

-      "print 'The phase constant =',round(B,2),'rad/m'\n",

-      "print 'The propagation constant =',round(B,2),'j /m'\n",

-      "print 'The intrinsic wave impedance =',round(eta,1),'ohms'"

-     ],

-     "language": "python",

-     "metadata": {},

-     "outputs": [

-      {

-       "output_type": "stream",

-       "stream": "stdout",

-       "text": [

-        "The cutoff frequency = 28.57 GHz\n",

-        "The phase constant = 1718.93 rad/m\n",

-        "The propagation constant = 1718.93 j /m\n",

-        "The intrinsic wave impedance = 154.7 ohms\n"

-       ]

-      }

-     ],

-     "prompt_number": 2

-    },

-    {

-     "cell_type": "markdown",

-     "metadata": {},

-     "source": [

-      "<h3>Example 12.4, Page number: 565<h3>"

-     ]

-    },

-    {

-     "cell_type": "code",

-     "collapsed": false,

-     "input": [

-      "'''\n",

-      "A standard air-filled rectangular waveguide with dimensions a = 8.636 cm,\n",

-      "b = 4.318 cm is fed by a 4-GHz carrier from a coaxial cable. Determine if a \n",

-      "TE_10 mode will be propagated. If so, calculate the phase velocity and \n",

-      "the group velocity. '''\n",

-      "\n",

-      "import scipy\n",

-      "\n",

-      "#Variable Declaration\n",

-      "\n",

-      "a=8.636*10**-2    #in m\n",

-      "b=4.318*10**-2    #in m\n",

-      "f=4*10**9         #in Hz\n",

-      "u=3*10**8         #speed of wave in m/s\n",

-      "\n",

-      "#Calculations\n",

-      "\n",

-      "fc=u/(2*a)\n",

-      "if(f>fc):\n",

-      "    print 'As f>fc, TE10 mode will propogate'\n",

-      "else:\n",

-      "    print 'It will not propogate'\n",

-      "\n",

-      "Up=u/scipy.sqrt(1-(fc/f)**2)    #phase velocity in m/s\n",

-      "Ug=u*u/Up                       #group velocity in m/s\n",

-      "\n",

-      "#Results\n",

-      "\n",

-      "print 'Phase velocity =',round(Up*10**-6,0),'Mm/s'\n",

-      "print 'Group velocity =',round(Ug*10**-6,1),'Mm/s'"

-     ],

-     "language": "python",

-     "metadata": {},

-     "outputs": [

-      {

-       "output_type": "stream",

-       "stream": "stdout",

-       "text": [

-        "As f>fc, TE10 mode will propogate\n",

-        "Phase velocity = 333.0 Mm/s\n",

-        "Group velocity = 270.2 Mm/s\n"

-       ]

-      }

-     ],

-     "prompt_number": 3

-    },

-    {

-     "cell_type": "markdown",

-     "metadata": {},

-     "source": [

-      "<h3>Example 12.5, Page number: 570<h3>"

-     ]

-    },

-    {

-     "cell_type": "code",

-     "collapsed": false,

-     "input": [

-      "'''\n",

-      "An air-filled rectangular waveguide of dimensions a = 4 cm, b = 2 cm \n",

-      "transports energy in the dominant mode at a rate of 2 mW. If the frequency of\n",

-      "operation is lO GHz. Determine the peak value of the electric field \n",

-      "in the waveguide. '''\n",

-      "\n",

-      "import scipy\n",

-      "\n",

-      "#Variable Declaration\n",

-      "\n",

-      "f=10*10**9          #frequency of operation in Hz\n",

-      "a=4*10**-2          #in m\n",

-      "b=2*10**-2          #in m\n",

-      "u=3*10**8           #velocity in m/s\n",

-      "Pavg=2*10**-3       #average power in W\n",

-      "\n",

-      "#Calculations\n",

-      "\n",

-      "fc=u/(2*a)                      #cutoff frequency in Hz\n",

-      "n=377/scipy.sqrt(1-(fc/f)**2)   #intrinsic wave impedance in ohms\n",

-      "E=scipy.sqrt(4*n*Pavg/(a*b))    #peak value of electric field in V/m\n",

-      "\n",

-      "#Result\n",

-      "\n",

-      "print 'Peak value of electric field =',round(E,2),'V/m'"

-     ],

-     "language": "python",

-     "metadata": {},

-     "outputs": [

-      {

-       "output_type": "stream",

-       "stream": "stdout",

-       "text": [

-        "Peak value of electric field = 63.77 V/m\n"

-       ]

-      }

-     ],

-     "prompt_number": 4

-    },

-    {

-     "cell_type": "markdown",

-     "metadata": {},

-     "source": [

-      "<h3>Example 12.6, Page number: 571<h3>"

-     ]

-    },

-    {

-     "cell_type": "code",

-     "collapsed": false,

-     "input": [

-      "'''\n",

-      "A copper-plated waveguide (sigma_e = 5.8 X 10 7 S/m) operating at 4.8 GHz \n",

-      "is supposed to deliver a minimum power of 1.2 kW to an antenna. If the guide\n",

-      "is fillcd with polystyrene (sigma = 10^17 S/m, epsilon = 2.55 epsilon_o) and\n",

-      "its dimensions are a = 4.2 cm, b = 2.6 cm, calculate the power dissipated in \n",

-      "a length 60 cm of the guide in the TE_10 mode. '''\n",

-      "\n",

-      "import scipy\n",

-      "\n",

-      "#Variable declaration\n",

-      "\n",

-      "cc=5.8*10**7             #in S/m\n",

-      "f=4.8*10**9              #in Hz\n",

-      "c=10**-17                #in S/m\n",

-      "Uo=4*scipy.pi*10**-7     #permeability of free space\n",

-      "Eo=10**-9/(36*scipy.pi)  #permittivity of free space\n",

-      "Er=2.55                  #relative permittivity\n",

-      "z=60*10**-2              #in m\n",

-      "l=4.2*10**-2             #in m\n",

-      "b=2.6*10**-2             #in m\n",

-      "P=1.2*10**3              #in W\n",

-      "\n",

-      "#Calculations\n",

-      "\n",

-      "n=377/scipy.sqrt(Er)\n",

-      "u=3*10**8/scipy.sqrt(Er)\n",

-      "fc=u/(2*l)\n",

-      "ad=c*n/(2*scipy.sqrt(1-(fc/f)**2))\n",

-      "Rs=scipy.sqrt(scipy.pi*f*Uo/cc)\n",

-      "ac=2*Rs*(0.5+(b/l)*(fc/f)**2)/(b*n*scipy.sqrt(1-(fc/f)**2))\n",

-      "a=ac\n",

-      "Pd=P*(scipy.e**(2*a*z)-1)\n",

-      "\n",

-      "#Result\n",

-      "\n",

-      "print 'power dissipated =',round(Pd,3),'W'\n"

-     ],

-     "language": "python",

-     "metadata": {},

-     "outputs": [

-      {

-       "output_type": "stream",

-       "stream": "stdout",

-       "text": [

-        "power dissipated = 6.096 W\n"

-       ]

-      }

-     ],

-     "prompt_number": 5

-    },

-    {

-     "cell_type": "markdown",

-     "metadata": {},

-     "source": [

-      "<h3>Example 12.8, Page number: 579<h3>"

-     ]

-    },

-    {

-     "cell_type": "code",

-     "collapsed": false,

-     "input": [

-      "'''\n",

-      "An air-filled resonant cavity with dimensions a = 5 cm, b = 4 cm, and \n",

-      "c = 10 cm is made of copper (sigma_e = 5.8 X 10^7 mhos/m). Find \n",

-      "(a) The five lowest order modes \n",

-      "(b) The quality factor for TE_101 mode '''\n",

-      "\n",

-      "import scipy\n",

-      "\n",

-      "#Variable Declaration\n",

-      "   \n",

-      "a=5*10**-2              #in m\n",

-      "b=4*10**-2              #in m\n",

-      "c=10*10**-2             #in m\n",

-      "C=5.8*10**7             #in mhos/m\n",

-      "Uo=4*scipy.pi*10**-7    #permeability of free space\n",

-      "u=3*10**8               #speed of wave in m/s\n",

-      "\n",

-      "#Calculations\n",

-      "\n",

-      "def f(m,n,p):\n",

-      "    fr=scipy.sqrt((m/a)**2+(n/b)**2+(p/c)**2)*u/2     #resonant frequency in Hz\n",

-      "    print round(fr*10**-9,3)\n",

-      "    \n",

-      "\n",

-      "f101=3.35*10**9\n",

-      "d=scipy.sqrt(1/(scipy.pi*f101*Uo*C))\n",

-      "Q=(a*a+c*c)*a*b*c/(d*(2*b*(a**3+c**3)+a*c*(a*a+c*c))) #quality factor\n",

-      "\n",

-      "#Results\n",

-      "\n",

-      "print 'Thus the five lowest order modes in ascending order are '\n",

-      "print 'TE101, frequency in GHz ='\n",

-      "f(1,0,1)\n",

-      "print 'TE011, frequency in GHz ='\n",

-      "f(0,1,1)\n",

-      "print 'TE102, frequency in GHz ='\n",

-      "f(1,0,2)\n",

-      "print 'TE110, frequency in GHz ='\n",

-      "f(1,1,0)\n",

-      "print 'TE111 or TM111, frequency in GHz ='\n",

-      "f(1,1,1)\n",

-      "print 'Quality factor =',round(Q,0)"

-     ],

-     "language": "python",

-     "metadata": {},

-     "outputs": [

-      {

-       "output_type": "stream",

-       "stream": "stdout",

-       "text": [

-        "Thus the five lowest order modes in ascending order are \n",

-        "TE101, frequency in GHz =\n",

-        "3.354\n",

-        "TE011, frequency in GHz =\n",

-        "4.039\n",

-        "TE102, frequency in GHz =\n",

-        "4.243\n",

-        "TE110, frequency in GHz =\n",

-        "4.802\n",

-        "TE111 or TM111, frequency in GHz =\n",

-        "5.031\n",

-        "Quality factor = 14358.0\n"

-       ]

-      }

-     ],

-     "prompt_number": 6

-    }

-   ],

-   "metadata": {}

-  }

- ]

+{
+ "metadata": {
+  "name": "",
+  "signature": "sha256:7e2f43e6e0f517c2aac74f69be1d132b3ab84b5c247c20e556eb69dbe9aedae5"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+  {
+   "cells": [
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "<h1>Chapter 12: Waveguides<h1>"
+     ]
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "<h3>Example 12.1, Page number: 557<h3>"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "from __future__ import division\n",
+      " \n",
+      "\n",
+      "import scipy\n",
+      "\n",
+      "#Variable Declaration\n",
+      "\n",
+      "a=2.5*10**-2     #in m\n",
+      "b=1*10**-2       #in m\n",
+      "c=0\n",
+      "Ur=1             #relative permeability\n",
+      "Er=4             #relative permittivity\n",
+      "C=3*10**8        #speed of wave in m/s\n",
+      "fc=0\n",
+      "m=0\n",
+      "n=0\n",
+      "\n",
+      "#Calculations\n",
+      "\n",
+      "while (fc*10**-9 < 15.1) :\n",
+      "   fc = (C/(4*a))*scipy.sqrt(m**2+(a*n/b)**2)\n",
+      "   if (( fc*10**-9) < 15.1) :\n",
+      "       n=n+1\n",
+      "   else:\n",
+      "       print 'Maximum value of n is ',n-1\n",
+      "\n",
+      "nmax=n-1 \n",
+      "fc=0\n",
+      "m=0\n",
+      "n=0\n",
+      "while(fc*10**-9 < 15.1):\n",
+      "   fc =(C/(4*a))*scipy.sqrt(m**2+(a*n/b)**2)\n",
+      "   if((fc*10**-9) < 15.1):\n",
+      "       m=m+1\n",
+      "   else:\n",
+      "      print 'Maximum value of m is ',m-1 \n",
+      "\n",
+      "mmax=m-1\n",
+      "m=0\n",
+      "while(m<mmax+1):\n",
+      "    n=0\n",
+      "    while(n<nmax+1):\n",
+      "        p=(C/(4*a))*scipy.sqrt(m**2+(a*n/b)**2)\n",
+      "        if((p*10**-9) < 15.1) :\n",
+      "          print m,n,'transmission mode is possible'\n",
+      "          print 'frequency is',round(p*10**-9,2),'GHz'\n",
+      "        else:\n",
+      "          print m,n,'transmission mode is not possible'\n",
+      "        n=n+1\n",
+      "    \n",
+      "    m=m+1\n",
+      "        "
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "Maximum value of n is  2\n",
+        "Maximum value of m is  5\n",
+        "0 0 transmission mode is possible\n",
+        "frequency is 0.0 GHz\n",
+        "0 1 transmission mode is possible\n",
+        "frequency is 7.5 GHz\n",
+        "0 2 transmission mode is possible\n",
+        "frequency is 15.0 GHz\n",
+        "1 0 transmission mode is possible\n",
+        "frequency is 3.0 GHz\n",
+        "1 1 transmission mode is possible\n",
+        "frequency is 8.08 GHz\n",
+        "1 2 transmission mode is not possible\n",
+        "2 0 transmission mode is possible\n",
+        "frequency is 6.0 GHz\n",
+        "2 1 transmission mode is possible\n",
+        "frequency is 9.6 GHz\n",
+        "2 2 transmission mode is not possible\n",
+        "3 0 transmission mode is possible\n",
+        "frequency is 9.0 GHz\n",
+        "3 1 transmission mode is possible\n",
+        "frequency is 11.72 GHz\n",
+        "3 2 transmission mode is not possible\n",
+        "4 0 transmission mode is possible\n",
+        "frequency is 12.0 GHz\n",
+        "4 1 transmission mode is possible\n",
+        "frequency is 14.15 GHz\n",
+        "4 2 transmission mode is not possible\n",
+        "5 0 transmission mode is possible\n",
+        "frequency is 15.0 GHz\n",
+        "5 1 transmission mode is not possible\n",
+        "5 2 transmission mode is not possible\n"
+       ]
+      }
+     ],
+     "prompt_number": 1
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "<h3>Example 12.3, Page number: 561<h3>"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      " \n",
+      "import scipy\n",
+      "import cmath\n",
+      "from numpy import *\n",
+      "\n",
+      "#Variable Declaration\n",
+      "\n",
+      "a=1.5*10**-2              #in m\n",
+      "b=0.8*10**-2              #in m\n",
+      "c=0\n",
+      "Uo=4*scipy.pi*10**-7      #permeability of free space\n",
+      "Ur=1                      #relative permeability\n",
+      "Eo=10**-9/(36*scipy.pi)   #permittivity of free space\n",
+      "Er=4                      #relative permittivity\n",
+      "C=3*10**8                 #speed of light in m/s\n",
+      "w=scipy.pi*10**11         #omega in rad/s\n",
+      "m=1\n",
+      "n=3\n",
+      "u=C/2                     #speed of wave in m/s\n",
+      "\n",
+      "#Calculations\n",
+      "\n",
+      "f=w/(2*scipy.pi)                                #frequency of wave in Hz\n",
+      "fc=u*((m*m)/(a*a)+(n*n)/(b*b))**0.5/2           #cutoff frequency in Hz\n",
+      "B=w*scipy.sqrt(1-(fc/f)**2)/u                   #phase constant in rad/m\n",
+      "eta=377/scipy.sqrt(Er)*scipy.sqrt(1-(fc/f)**2)  #intrinsic wave impedance in ohm\n",
+      "\n",
+      "#Results\n",
+      "\n",
+      "print 'The cutoff frequency =',round(fc*10**-9,2),'GHz'\n",
+      "print 'The phase constant =',round(B,2),'rad/m'\n",
+      "print 'The propagation constant =',round(B,2),'j /m'\n",
+      "print 'The intrinsic wave impedance =',round(eta,1),'ohms'"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "The cutoff frequency = 28.57 GHz\n",
+        "The phase constant = 1718.93 rad/m\n",
+        "The propagation constant = 1718.93 j /m\n",
+        "The intrinsic wave impedance = 154.7 ohms\n"
+       ]
+      }
+     ],
+     "prompt_number": 2
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "<h3>Example 12.4, Page number: 565<h3>"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      " \n",
+      "import scipy\n",
+      "\n",
+      "#Variable Declaration\n",
+      "\n",
+      "a=8.636*10**-2    #in m\n",
+      "b=4.318*10**-2    #in m\n",
+      "f=4*10**9         #in Hz\n",
+      "u=3*10**8         #speed of wave in m/s\n",
+      "\n",
+      "#Calculations\n",
+      "\n",
+      "fc=u/(2*a)\n",
+      "if(f>fc):\n",
+      "    print 'As f>fc, TE10 mode will propogate'\n",
+      "else:\n",
+      "    print 'It will not propogate'\n",
+      "\n",
+      "Up=u/scipy.sqrt(1-(fc/f)**2)    #phase velocity in m/s\n",
+      "Ug=u*u/Up                       #group velocity in m/s\n",
+      "\n",
+      "#Results\n",
+      "\n",
+      "print 'Phase velocity =',round(Up*10**-6,0),'Mm/s'\n",
+      "print 'Group velocity =',round(Ug*10**-6,1),'Mm/s'"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "As f>fc, TE10 mode will propogate\n",
+        "Phase velocity = 333.0 Mm/s\n",
+        "Group velocity = 270.2 Mm/s\n"
+       ]
+      }
+     ],
+     "prompt_number": 3
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "<h3>Example 12.5, Page number: 570<h3>"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      " \n",
+      "\n",
+      "import scipy\n",
+      "\n",
+      "#Variable Declaration\n",
+      "\n",
+      "f=10*10**9          #frequency of operation in Hz\n",
+      "a=4*10**-2          #in m\n",
+      "b=2*10**-2          #in m\n",
+      "u=3*10**8           #velocity in m/s\n",
+      "Pavg=2*10**-3       #average power in W\n",
+      "\n",
+      "#Calculations\n",
+      "\n",
+      "fc=u/(2*a)                      #cutoff frequency in Hz\n",
+      "n=377/scipy.sqrt(1-(fc/f)**2)   #intrinsic wave impedance in ohms\n",
+      "E=scipy.sqrt(4*n*Pavg/(a*b))    #peak value of electric field in V/m\n",
+      "\n",
+      "#Result\n",
+      "\n",
+      "print 'Peak value of electric field =',round(E,2),'V/m'"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "Peak value of electric field = 63.77 V/m\n"
+       ]
+      }
+     ],
+     "prompt_number": 4
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "<h3>Example 12.6, Page number: 571<h3>"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      " \n",
+      "\n",
+      "import scipy\n",
+      "\n",
+      "#Variable declaration\n",
+      "\n",
+      "cc=5.8*10**7             #in S/m\n",
+      "f=4.8*10**9              #in Hz\n",
+      "c=10**-17                #in S/m\n",
+      "Uo=4*scipy.pi*10**-7     #permeability of free space\n",
+      "Eo=10**-9/(36*scipy.pi)  #permittivity of free space\n",
+      "Er=2.55                  #relative permittivity\n",
+      "z=60*10**-2              #in m\n",
+      "l=4.2*10**-2             #in m\n",
+      "b=2.6*10**-2             #in m\n",
+      "P=1.2*10**3              #in W\n",
+      "\n",
+      "#Calculations\n",
+      "\n",
+      "n=377/scipy.sqrt(Er)\n",
+      "u=3*10**8/scipy.sqrt(Er)\n",
+      "fc=u/(2*l)\n",
+      "ad=c*n/(2*scipy.sqrt(1-(fc/f)**2))\n",
+      "Rs=scipy.sqrt(scipy.pi*f*Uo/cc)\n",
+      "ac=2*Rs*(0.5+(b/l)*(fc/f)**2)/(b*n*scipy.sqrt(1-(fc/f)**2))\n",
+      "a=ac\n",
+      "Pd=P*(scipy.e**(2*a*z)-1)\n",
+      "\n",
+      "#Result\n",
+      "\n",
+      "print 'power dissipated =',round(Pd,3),'W'\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "power dissipated = 6.096 W\n"
+       ]
+      }
+     ],
+     "prompt_number": 5
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "<h3>Example 12.8, Page number: 579<h3>"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      " \n",
+      "\n",
+      "import scipy\n",
+      "\n",
+      "#Variable Declaration\n",
+      "   \n",
+      "a=5*10**-2              #in m\n",
+      "b=4*10**-2              #in m\n",
+      "c=10*10**-2             #in m\n",
+      "C=5.8*10**7             #in mhos/m\n",
+      "Uo=4*scipy.pi*10**-7    #permeability of free space\n",
+      "u=3*10**8               #speed of wave in m/s\n",
+      "\n",
+      "#Calculations\n",
+      "\n",
+      "def f(m,n,p):\n",
+      "    fr=scipy.sqrt((m/a)**2+(n/b)**2+(p/c)**2)*u/2     #resonant frequency in Hz\n",
+      "    print round(fr*10**-9,3)\n",
+      "    \n",
+      "\n",
+      "f101=3.35*10**9\n",
+      "d=scipy.sqrt(1/(scipy.pi*f101*Uo*C))\n",
+      "Q=(a*a+c*c)*a*b*c/(d*(2*b*(a**3+c**3)+a*c*(a*a+c*c))) #quality factor\n",
+      "\n",
+      "#Results\n",
+      "\n",
+      "print 'Thus the five lowest order modes in ascending order are '\n",
+      "print 'TE101, frequency in GHz ='\n",
+      "f(1,0,1)\n",
+      "print 'TE011, frequency in GHz ='\n",
+      "f(0,1,1)\n",
+      "print 'TE102, frequency in GHz ='\n",
+      "f(1,0,2)\n",
+      "print 'TE110, frequency in GHz ='\n",
+      "f(1,1,0)\n",
+      "print 'TE111 or TM111, frequency in GHz ='\n",
+      "f(1,1,1)\n",
+      "print 'Quality factor =',round(Q,0)"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "Thus the five lowest order modes in ascending order are \n",
+        "TE101, frequency in GHz =\n",
+        "3.354\n",
+        "TE011, frequency in GHz =\n",
+        "4.039\n",
+        "TE102, frequency in GHz =\n",
+        "4.243\n",
+        "TE110, frequency in GHz =\n",
+        "4.802\n",
+        "TE111 or TM111, frequency in GHz =\n",
+        "5.031\n",
+        "Quality factor = 14358.0\n"
+       ]
+      }
+     ],
+     "prompt_number": 6
+    }
+   ],
+   "metadata": {}
+  }
+ ]
 }
\ No newline at end of file