{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter 1 ELECTROMAGNETIC THEORY"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## example 1.1,page no.17"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "phase velocity in meter per second= 6.54e+07 \n",
      "wavelength in meter= 2.18e-02 \n",
      "wave impedence in ohm= 2.47e+02 \n"
     ]
    }
   ],
   "source": [
    "# program to calculate wavelength , phase velocity and wave impedence .\n",
    "from math import pi,sqrt\n",
    "\n",
    "f=3*10**9;\n",
    "mur =3;\n",
    "muo =4*pi*10**-7;\n",
    "eipsilao =8.854*10**-12;\n",
    "eipsilar =7;\n",
    "mue=muo*mur;\n",
    "eipsila=eipsilao*eipsilar;\n",
    "Vp=sqrt(1/(mue*eipsila));\n",
    "lamda=Vp/f;\n",
    "eta=sqrt(mue/eipsila);\n",
    "#Result\n",
    "print\"phase velocity in meter per second= %.2e \"%Vp;\n",
    "# phase velocity .\n",
    "print\"wavelength in meter= %.2e \"%lamda # wavelength.\n",
    "print\"wave impedence in ohm= %.2e \"%eta # wave impedence ."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## example:−1.2  page no.−20"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "skin depth of aluminium in meter=8.15e-07 \n",
      "skin depth of copper in meter= 6.60e-07\n",
      "skin depth of gold in meter= 7.86e-07\n",
      "skin depth of silver in meter= 6.41e-07\n"
     ]
    }
   ],
   "source": [
    "# progarm to find out skin depth of aluminium, copper , gold and silver at frequency 10GHZ.\n",
    "f=10*10**9;\n",
    "muo=4*pi*10**-7; # permeability in free space.\n",
    "omega=2*pi*f;\n",
    "sigma_aluminium =3.816*10**7;\n",
    "sigma_copper =5.813*10**7;\n",
    "sigma_gold =4.098*10**7;\n",
    "sigma_silver =6.173*10**7;\n",
    "delta1=sqrt(2/(omega*muo*sigma_aluminium));\n",
    "delta2=sqrt(2/(omega*muo*sigma_copper));\n",
    "delta3=sqrt(2/(omega*muo*sigma_gold));\n",
    "delta4=sqrt(2/(omega*muo*sigma_silver));\n",
    "#result\n",
    "print\"skin depth of aluminium in meter=%.2e \"%delta1; # skin depth of aluminium\n",
    "print\"skin depth of copper in meter= %.2e\"%delta2; # skin depth of copper .\n",
    "print\"skin depth of gold in meter= %.2e\"%delta3; #skin depth of gold .\n",
    "print\"skin depth of silver in meter= %.2e\"%delta4; # skin depth of silver ."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## example:−1.3 page no.−24"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "for z<0, E1= A*N*x*exp(I*ko*z)\n",
      "for z<0, H1= -A*N*y*exp(I*ko*z)\n",
      "for z>0, E2= B*N*x*exp(-I*ko*z)\n",
      "for z>0, H2= B*N*y*exp(-I*ko*z)\n",
      "Matrix([[-Jo/2], [-Jo/2]])\n"
     ]
    }
   ],
   "source": [
    "#program to find the resulting fields by assuming plane waves on either side of the current sheet and enforcing the boundary conditions.\n",
    "from sympy import symbols,Matrix,exp,I\n",
    "\n",
    "E,x,E1,E2,H1,H2,z,Jo,A,B,N,n,ko,y,l,m = symbols('E,x,E1,E2,H1,H2,z,Jo,A,B,N,n,ko,y,l,m');\n",
    "E1=A*N*exp(I*ko*z)*x; # x component of elec tricfield (region z<0).\n",
    "H1=A*N*exp(I*ko*z)*(-y); # y component of magnetic field (region z<0).\n",
    "E2=B*N*exp(-I*ko*z)*x;# x component of electric field (region z>0).\n",
    "H2=B*N*exp(-I*ko*z)*y;  # y component of electric field (region z>0).\n",
    "print \"for z<0, E1=\",E1\n",
    "print \"for z<0, H1=\",H1\n",
    "print \"for z>0, E2=\",E2\n",
    "print \"for z>0, H2=\",H2\n",
    "#from boundary conditions\n",
    "c=Matrix([[-1,-1],[1,-1]]);\n",
    "d=Matrix([[A],[B]]);\n",
    "d=c.inv()*Matrix([[Jo],[0]]);\n",
    "print d;\n",
    "#result\n",
    "# A=−Jo/2; B=−Jo/2."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## example:−1.4 page no.−38."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "skin depth in meter= 2.087e-06\n",
      "propagation comstant = 479049.101381194 + 479049.101381194*I\n",
      "intrinsic impedence in ohm= 0.00824099606711155 + 0.00824099606711155*I\n",
      "reflection coefficient= (-376.991759003933 + 0.00824099606711155*I)/(377.008240996067 + 0.00824099606711155*I)\n",
      "transmission coefficient=  (0.0164819921342231 + 0.0164819921342231*I)/(377.008240996067 + 0.00824099606711155*I)\n"
     ]
    }
   ],
   "source": [
    "# program to compute propagation constan , impedence , skin depth , reflection and transmission coefficient\n",
    "from sympy import I\n",
    "from numpy import pi,sqrt\n",
    "\n",
    "f=1*10**9;\n",
    "omega=2*pi*f;\n",
    "sigma=5.813*10**7; # for copper .\n",
    "mue=4*pi*10**-7; # permeability in free space.\n",
    "delta=sqrt(2/(mue*sigma*omega)); # skin depth .\n",
    "gama=((1+I)/delta); # propagation constant .\n",
    "eta=gama/sigma; # impedence\n",
    "etao=377; # intrinsic impedence in free space .\n",
    "tao=((eta-etao)/(eta+etao)); # reflection coefficient .\n",
    "t=(2*eta)/(eta+etao); # transmission coefficient\n",
    "# result\n",
    "print \"skin depth in meter= %.3e\"%delta\n",
    "print \"propagation comstant =\",gama\n",
    "print \"intrinsic impedence in ohm=\",eta\n",
    "print \"reflection coefficient=\",tao\n",
    "print \"transmission coefficient= \",t"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## example:−1.5 page no.−42."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The wave impendaces are 377 ohm , 236 ohm\n"
     ]
    },
    {
     "data": {
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ljmHY1cy2y9geFi1hdZyy4Y5tTrlZsCCsQrrnntrKzhaHOJ2jRZI2b96QtBmw\nKDmVHGdpfEWSU27694dttoHvfz9tTcpPHAe3fYGBwKRoV1fgZDMbnqxqLXRwJ6A6ZtYs2GSTkLkt\niUxZ7uDmZDNrFmy9NTQ2QvfuaWtTPIk5uJnZMEndgC0Jk8/vmtmCInR0nKJ45RXYbbfaS5/oVC6X\nXx5WIVWzUWgPeQ2DpH0jo3AkwSA0W53NIyv0r7Jo6NQ9PozklJN334V774V36jitUmtzDHtHfw+O\nPgdFn+ZtxykLlbgiSVJPSeMlTZB0YY7jDZLmSBodfX6Xhp5O4Zx/fgirvdZaaWuSHnHmGDY1s/+2\ntS9JfBy2flm0CFZfHT78MPxNgiJyPncg5Hz+ETANeI2lcz43AL82s0PakOVtu4J49ln4+c/h7bdr\nI99CsXMMcVYlDc6x74FCK3KcYnjjDdhoo+SMQpH0ACaa2eTI0XMQcGiOcnW2yLG6WbwYzjsP/vjH\n2jAK7aG1OYatge7AapKOIDRyA1YB6iC+oFMJDB8OP6y8zB/rA1MytqcCu2WVMWBPSWMIvYrzzayO\nR60rnzvvhNVWg8MPT1uT9GltVVI3wlzCqrScU/gCOC1JpRynmeHDKzLhepyxn1HAhmb2laRewMOE\nZ8qpQObODc5sjz5af85suchrGMzsEeARSXuY2ctl1MlxAPjmmzDxfO+9aWuyFNOADTO2NyT0Gr7F\nzL7I+P6EpP+TtIaZzc4W1q9fv2+/NzQ00NDQUGp9nTb4/e/hgANg553T1qR9NDY20tjY2G45cSaf\n/waca2afR9urA9ebWdkSLPoEXX3y0ktw7rkhx26SFDH5vCxh8nlfYDrwH5aefF4H+MTMTFIP4J+5\nIhV7206fN96A/fcPE85duqStTWlJMoPbds1GAcDMPpO0U6EVOU6hVOj8Ama2SNLZwFNAB+AOMxsn\n6Yzo+ADgKOBMSYuAr4DjUlPYyUtTE5x1Fvzv/9aeUWgPcQyDMrvAUfY290F1Emf4cLjggrS1yI2Z\nPQE8kbVvQMb3WwgRiZ0KZuDAYBxOPTVtTSqLOENJJwGXAP8krEw6GrjSzMqWMsW72/XH118HB6MZ\nM2DllZOty2Ml1SezZoWQF08+CTvumLY2yZCYH0NkAI4APgY+Ag6PaxTa8g7NKLerpEXRsljHYcQI\n2H775I2CU79cdBEce2ztGoX2EDeD6RrAPDMbKGktSZuY2aTWToi8Q28mwztU0pDMCbqMctcAT+IO\nQU7E8OHYgAW5AAAcOElEQVSwzz5pa+HUKq+8Ao89FjIDOkvTZo9BUj/gAuCiaFdH4J4YsuN6h55D\n8K7+NI7CTn3w3HOVOfHsVD8LF8KZZwYP51VXTVubyiROSIzDCf/Q5wGY2TQgTgc/l3fo+pkFJK0f\nye4f7fLBVocvvoCxYz2iqpMM114L66wDxx+ftiaVS5yhpAVm1qTIHVBS55iy4/yTvwn4bbTWW/hQ\nkgO8+CL06AErrJC2Jk6tMW4c3HgjjBzpHs6tEccwPCBpACFm0unAKcBfY5zXpncosDMwKDI6XYBe\nkhaa2ZBsYe4dWj8k7b9QKu9Qp7pYvBhOOQUuuww23jhtbSqbNperAkjaD9gv2nzKzJ6JcU6b3qFZ\n5QcCj+ZKAORL+uqLnXaCm28uXw4GX65aH9x0Ezz0UJi/WibOIHoNkKTnM2b2NPB0IYJjeoc6Tgtm\nz4b334ddd01bE6eWeP/94N388sv1YxTaQ94eg6QvyT9PYGa2SmJaLa2Lv1XVCQ89BLffDkOHlq9O\n7zHUNmaw774hSN7556etTXlJosewXTmztDkOuP+CU3puuw3mzYNf/SptTaqH1jpVDwBIGlYmXRzH\nDYNTUiZMgN/9LsRE6uAR3mLTWo+hg6RLgC0l/ZqWS0nNzG5IVjWn3vjwQ/j00zD57DjtZeFCOOGE\nkGuhe/e0takuWusxHAcsJkwcrwyslPHxCDZOyXn8cejZ0ycHndJwxRWwxhpw9tlpa1J9tJbBbTzw\nB0ljzayMU4FOvfL443DiiWlr4dQCI0aEuYXRo92RrRjivJuNknSHpCcBJHWX5NHLnZLy9dfwwguw\n335tl3Wc1pg7Nwwh3XorrLtu2tpUJ3EMw10EH4b1ou0JgM/vOyXluedghx1g9dXT1iQeHlK+cjn3\n3LA89bDD0takeoljGLqY2f2E+QaiSKmLEtXKqTuGDoUDD0xbi3hkhJTvCXQHekvaOk85DylfRu6/\nP+QKv/HGtDWpbuIYhi8lrdm8IWl3YE5yKjn1hlmYX6gWw4CHlK9I3n03TDQPGgQrrZS2NtVNnJAY\n5wGPAptKGgGsRUh07jglYdy4kHd3m23S1iQ2uULK75ZZICOk/A+BXfGQ8ony1Vdw9NFhJdLOO6et\nTfXTqmGIusJ7R5+tCN3hd83smzLo5tQJjz8ewhVU0eqRkoaU98jB7efss2HbbeGMM9LWJF1KFTm4\nzeiqkl4zs1RDmnk8mdqmoSHEsDnooHTqLzSeTDSc2s/MekbbFwFNZnZNRpn/ssQYdAG+Ak7LDinv\nbbv9DBwYku/85z8+hJRNsbGS4hiGG4HlgPsJWdxE8HweVYyixeAPT+0yZw5suCF89BGsuGI6OhRh\nGDykfIUwdmxYgfT88+7dnIskw27vSOg6X5613yPaOO3m6afh+99PzygUg4eUrwzmzAnzCjfe6Eah\n1MRK1JM2/lZVu/TpA7vskm7YAg+7XX0sXgwHHwybbAK33JK2NpVLsW0773JVSX2iLnO+4x0lnVxo\nhY7TTFMTPPFEVS1TdSqEiy6C+fNDVjan9LQ2lLQS8Jqk8cBIYAZhfuE7wC6EVUq3J66hU7OMHAlr\nrhne+hwnLn/7Gzz4YJhsXm65tLWpTVodSoqW2X0P+D6wUbT7A+DfwIhy9YG9u12b9O0b1p9fe226\nevhQUvXwyitwyCEhhEoV+b2kRlKTz8sAPczsD8Wp5Tj5eeQR+NOf0tbCqRamToUjj4Q773SjkDSt\nhsQws8VA7zLp4tQREybAxx+HFUmO0xZffgmHHhoC5KXl71JPxFmu+m9JN7PEjwGAcvoxOLXH4MFw\nxBGebtFpm4UL4aijQma/Cy5IW5v6II6DWyM5QgCYWdn8GHwctvbYaSe4/vrKyO/scwyVi1lY0jx7\nNjz0ECwb51XW+ZbEHNzMrKEojRwnD++/D9Omwd57p62JU+lcckmImjpsmBuFchLrVks6iBB3fvnm\nfWaW7QntOLEYPBgOP9yHkZzWufnmsCz1pZegc+e0takv2szHIGkAcAxwLsGP4Rhg44T1cmqYwYND\nKAPHyceDD8LVV8OTT0KXLmlrU3/EmWN408y2lTTWzLaTtBLwpJmVbT2JJBs61OjUCTp1guWXDykg\n11orRFOsonDNdc+kSdCjB8yYUTlDAz7HUFk89hicemowCjvumLY21U2SQfS+jv5+FSUfmUXwfi4r\nN90ECxaEz/z58Nln8MknYXJqrbVgnXWCB+1mm8Hmm4e/W27pycArjQcfDMNIlWIUnMri6afhlFOC\ncXCjkB5xHs9HJa0OXAuMIqxQKnsojKeeyr1/3jz49NMQtnnSpDCx+eKLcNddITPYssuGBrbTTuHv\n7rvDBhuUVXUngwceCFm2HCeb556DE04Iq4969Ehbm/qmoOiqkjoBy5tZWXM+F9vdNgvekqNHw6hR\n4TNiRBiGamgISyUbGmC99UquspODDz4IaRdnzKisGDc+lJQ+//538Gv55z/DM+mUhiQT9awAnEWI\nl2TAi0B/M5tfjKLFUMqHp6kJ3n47vJ00NoYEHxtuCIcdFj7bb+9zFklxww3h3t9xR9qatMQNQ7qM\nGBGevX/8A37847S1qS2SNAwPAHOBewirkn4CrGpmZVtXkuTDs3hxaJgPPxw+ixeHRnrCCeHt1o1E\n6dhzT/j976Fnz7Q1aYkbhvR49lno3TtETO3VK21tao8kDcM7Zta9rX1JUq6Hxyy80Q4eHBrqiivC\nT38ajIRPYrePKVNghx3CXFAlDSNBcQ+PpJ7ATYQMbn/NzPccHT+UkPWwKfr8xsyG55BTt4bhkUfg\ntNPC8+bOjslQ8kQ9GYyStEdGRbsDrxdaUTUgwXe/C/36wcSJ8H//Fyawu3cP2aKefTYYD6dwBg8O\n4ZIrzSgUg6QOwM1AT4LjZ29JW2cVe9bMtjezHYE+wG3l1bKyueceOOMMGDrUjUIl0loGt+YVS7sA\nL0n6QNJkYASwi6Q3JY0tg46psMwyocHeeWeYwD7kEPjlL2HbbeGvf4Wvv25bhrOEu++GE09MW4uS\n0QOYaGaTzWwhMAg4NLOAmc3L2FwJmFlG/Sqa/v3ht7+F4cNDWlen8mitx/Cf6G9PYFPgB0BD9L0X\ncDBwSJLKVQqdO4cu75tvBn+Khx+GjTeGyy4LCcmd1hkzJvid1NBqk/WBKRnbU6N9LZB0mKRxwBOE\nyAF1jRlceilcdx288ELoiTuVSWt+DAIws8nlUaXykeBHPwqfd9+Fq64KznS/+EWIE7/KKmlrWJk0\n9xaWiTNwWR3EGlA0s4eBhyXtBfwd2DJXuX79+n37vaGhgYYasqDNzJ8fHNcmTYKXX4a1105bo9qk\nsbGRxsbGdsvJO/ksaSpwA5GByMLM7IZYFbQ9SXc8cEFUzxfAmWY2NqtMxU7QvfceXH558Nj81a+C\ngfCAX0tYuDAsB37hBejWLW1tclPoBF00z9bPzHpG2xcBTdltO+uc9wnZEGdl7a/Ytl0qZs4MK/3W\nWy+8JKywQtoa1Q9JTD53AFYmjI9mf1aOqVScSbr/Anub2XbAFVTZJF23bmEi7YUX4I03YOut4d57\nfZK6maeegk03rVyjUCQjgS0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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10705d510>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# example:−2.7.page no.−50.\n",
    "# program to plot the reflection coefficients for parallel and perpendicular polarized plane waves incident from free space on to a dielectric region with Er=2.55,versus incidence angle.\n",
    "\n",
    "from pylab import plot,subplot,title,xlabel,ylabel\n",
    "from sympy import acos,asin\n",
    "import numpy as n\n",
    "import math as m\n",
    "\n",
    "Er=2.55; # relaitve permittivity of dielectric medium .\n",
    "N1=377.; # intrinsic impedence\n",
    "N2=N1/m.sqrt(Er); # intrinsic impedence of dielectric medium.\n",
    "xb=asin(m.sqrt(1./(1.+1/2.55)));# brewster angle valid only in case of parallel polarization.\n",
    "xt=acos(m.sqrt(1.-(1./Er)**2.*m.sin(xb))); # angle of transmission .\n",
    "xi=n.arange(0,m.pi/2,0.05); # incidence\n",
    "print \"The wave impendaces are %d ohm , %d ohm\"%(N1,N2)\n",
    "# for parallel polarization angle .\n",
    "N2=N2*m.cos(xt);\n",
    "N1=N1*n.cos(xi);\n",
    "Tpar=(N2-N1)/(N2+N1);\n",
    "w=abs(Tpar);\n",
    "\n",
    "# result\n",
    "subplot(121)\n",
    "title ('parallel polarization');\n",
    "xlabel('xi(incidence angle)');\n",
    "ylabel('Tpar(reflection coefficient)');\n",
    "plot(xi,w)\n",
    "# for perpendicular polarization .\n",
    "#NOTE:− in case of this polarization . there is no brewster angle .\n",
    "xt=acos(n.sqrt(1-(1/Er)**2.*m.sin(xb)));\n",
    "n1=377.*m.cos(xt);\n",
    "n2=(377/m.sqrt(Er))*n.cos(xi);\n",
    "Tper=(n2-n1)/(n1+n2);\n",
    "z=abs(Tper);\n",
    "#result\n",
    "subplot(122)\n",
    "\n",
    "title ('perpendicular polarization');\n",
    "xlabel('xi(incidence angle)');\n",
    "#ylabel('Tper(reflection coefficient)');\n",
    "plot(xi,z);"
   ]
  }
 ],
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