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diff --git a/Elements_of_Electromagnetics/chapter_12.ipynb b/Elements_of_Electromagnetics/chapter_12.ipynb new file mode 100644 index 00000000..b6ded6a6 --- /dev/null +++ b/Elements_of_Electromagnetics/chapter_12.ipynb @@ -0,0 +1,452 @@ +{
+ "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": {}
+ }
+ ]
+}
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