{ "metadata": { "name": "", "signature": "sha256:7e2f43e6e0f517c2aac74f69be1d132b3ab84b5c247c20e556eb69dbe9aedae5" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "

Chapter 12: Waveguides

" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 12.1, Page number: 557

" ] }, { "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(mExample 12.3, Page number: 561

" ] }, { "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": [ "

Example 12.4, Page number: 565

" ] }, { "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": [ "

Example 12.5, Page number: 570

" ] }, { "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": [ "

Example 12.6, Page number: 571

" ] }, { "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": [ "

Example 12.8, Page number: 579

" ] }, { "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": {} } ] }