{
"metadata": {
"name": "",
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"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": {}
}
]
}