{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "36f06e08",
   "metadata": {},
   "outputs": [],
   "source": [
    "import sympy as s\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "88070726",
   "metadata": {},
   "outputs": [],
   "source": [
    "w, L, C, R = s.symbols(\"\\omega L C R\", real=True, positive=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "6850d158",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - \\frac{i L \\omega}{C L \\omega^{2} - 1} + R$"
      ],
      "text/plain": [
       "-I*L*\\omega/(C*L*\\omega**2 - 1) + R"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z1 = R+s.simplify(s.I/(1/(w*L) - w*C))\n",
    "z1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "02c2377b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\sqrt{\\frac{L^{2} \\omega^{2}}{\\left(C L \\omega^{2} - 1\\right)^{2}} + R^{2}}$"
      ],
      "text/plain": [
       "sqrt(L**2*\\omega**2/(C*L*\\omega**2 - 1)**2 + R**2)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "abs(z1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "5c957d6d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - \\frac{L \\omega}{R \\left(C L \\omega^{2} - 1\\right)}$"
      ],
      "text/plain": [
       "-L*\\omega/(R*(C*L*\\omega**2 - 1))"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s.im(z1)/s.re(z1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "317d0bdc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\sqrt{\\frac{L^{2} \\omega^{2}}{\\left(C L \\omega^{2} - 1\\right)^{2}} + R^{2}}$"
      ],
      "text/plain": [
       "sqrt(L**2*\\omega**2/(C*L*\\omega**2 - 1)**2 + R**2)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "e1 = abs(z1)\n",
    "e1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "9de81cf0",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1336847.9376977843\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "x = np.linspace(800000,1500000,1000 ) # radians per second\n",
    "c=4.7e-6\n",
    "l = 4.7e-6\n",
    "f1 = s.lambdify(w, e1.subs([(R, 1000), (C, c), (L, l)]))\n",
    "y = f1(x/(2*np.pi))\n",
    "    \n",
    "ax.plot(x/1000,y)\n",
    "ax.grid()\n",
    "ax.set_xlabel(\"freq (K Hz)\")\n",
    "ax.set_ylabel(\"Impedance (ohms)\")\n",
    "ax.set_title(\"Frequency Response\")\n",
    "\n",
    "\n",
    "print ((2*np.pi)/np.sqrt(c*l))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "b0b1f729",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{C L R \\omega^{2} - i L \\omega}{C L \\omega^{2} - i C R \\omega - 1}$"
      ],
      "text/plain": [
       "(C*L*R*\\omega**2 - I*L*\\omega)/(C*L*\\omega**2 - I*C*R*\\omega - 1)"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xl = s.I*w*L\n",
    "xc = s.I/(w*C)\n",
    "z2 = s.cancel(1/(1/xl+1/(R-xc)))\n",
    "\n",
    "z2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "72a51d3d",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{L \\omega \\sqrt{C^{2} R^{2} \\omega^{2} + 1}}{\\sqrt{C^{2} L^{2} \\omega^{4} + C^{2} R^{2} \\omega^{2} - 2 C L \\omega^{2} + 1}}$"
      ],
      "text/plain": [
       "L*\\omega*sqrt(C**2*R**2*\\omega**2 + 1)/sqrt(C**2*L**2*\\omega**4 + C**2*R**2*\\omega**2 - 2*C*L*\\omega**2 + 1)"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "e2 = s.simplify(abs(z2))\n",
    "e2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "2387682d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{L \\omega}{\\sqrt{C^{2} L^{2} \\omega^{4} - 2 C L \\omega^{2} + 1}}$"
      ],
      "text/plain": [
       "L*\\omega/sqrt(C**2*L**2*\\omega**4 - 2*C*L*\\omega**2 + 1)"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "e2.subs(R,0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "1d8a837d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Frequency Response')"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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n2VuhVubmlnfcuHFLVTX3f1aoaqtOQBvgY6AdEAm8A1x/qm1ycnK0qebOndvkbQNVsJR5b2mldn1ouv79062Nfrc1yvzwu2u01/+9r+VHq31+LG8Ey3k+HaFW5uaWF1iiJ8ipblT1nA9sV9UiVa0G3gZGuRCH8XNutt8/kQv6tedoTR1zN1gf/SawuZH4dwIjRCRORAQ4D1jvQhzGzy3eXkx8VDh9O/huYPXTMaxbKmkJ0cxYbY+kTGBr9cSvqguBacAyYLUTw/OtHYfxf4vzijmzq28HVj8d4WHCxAHt+XhDIeVHa9wOx5gmc+V/lKo+rKp9VLW/qt6gqtZGzhyjtKKKDfsOu/ri1olcMrAjR6rrmL3eXuYygcs/bqWMOc6SvBIAV1/cOpHcrm3ISIpmxqq9bodiTJNZ4jd+aXGeZ2D1wZ1T3A7lGGFhwsQBHZi3qYjDR6rdDseYJjll4heRGBG5UkSeFJF/icgUEXlQRPq1VoAmNC3KK2ZgZgoxkb4fWP10XTKwA1U1Vt1jAtdJE7+IPAJ8AYwEFgLPAW8CNcDvROQjERnYKlGakFJZVcvq/IOud9NwMkM6t6FjcgzTV1p1jwlMEadYt0hVHz7JuidEJB3o4oOYTIhbvquEmjplmAsjbnmjvrrn5QV5HKyoJjku0u2QjDktJ73jV9UZxy8TkTARSXLWF6rqEl8GZ0LT4u0liEBOV/+84wf42qCOVNcqH6yxu34TeBp9uCsir4lIkojEA2uAdSLyQ9+HZkLVYmdg9eRY/72THpiZTPd28by9bLfboRhz2rxp1dNXVQ8BlwEfAN2AG3wZlAldNbV1LNtZ4jfdNJyMiHDFmZksyitmV3GF2+EYc1q8SfyRIhKJJ/G/5/Sv0/pdepqQsHbPISpcGlj9dF06uCMA/15ud/0msHiT+J8D8oB44FMR6Qoc8mVQJnR9ue0AAMP9/I4fPCNzjeieytvL8ut7njUmIDSa+FX1KVXtpKoTnZ4+dwDjWiE2E4IWbDtAdrt40pP8o8/7xlx+ZiZ5BypYvqvU7VCM8Zo3D3dTROReEXlCRJ4SkaeAJ1ohNhNiqmvrWLy9mJHZbd0OxWsX9W9PdEQYby/LdzsUY7zmTVXP+0AWnp40lzaYjGlRq/IPUl5Vy6jsNLdD8VpiTCQX9GvPf1bu5Uh1rdvhGOOVU73AVS9GVR/weSQm5NXX74/oHjh3/ABX53bmvZV7mLl2H5cO7uR2OMY0yps7/ldE5HYR6SAiqfWTzyMzIWf+1v30aZ9IanyU26GcllHZbemSGsdrC3e6HYoxXvEm8VcBfwQW8N9qHntj17SoozW1LMkrCaj6/XphYcK1wzqzcHsxW4vK3A7HmEZ5k/i/D/RQ1SxV7eZM3X0dmAktK3aWcrSmjpEBVs1T78qcTCLChKmL7K7f+D9vEv8WwF5NND41f+sBwgSGB2jiT0+MYXzfDKYtzedojT3kNf7Nm8RfDqwQkefqm3M6TTqNaTELth2gX8dkv+6fpzHXDetCSUU1M9daP/3Gv3nTqucdZzLGJyqralm+s4RbR3dzO5RmGdMjjcw2sfzzyx18fVBHt8Mx5qQaTfyq+nJrBGJC19IdJVTXKiMC8MFuQ2Fhwg0juvLbDzawds9B+nVMdjskY07Imzd3RzujbW0SkW0isl1EtrVGcCY0fLaliMhwYVgAdMzWmGuHdiE2MpyXvshzOxRjTsqbOv4X8HTRMAYYCuQ6P41pEZ9u2k9O1zbER3tT8+jfkuMiuSKnE++t2MP+sqNuh2PMCXmT+A+q6gfOiFsH6iefR2ZCQuHhI6zfe4ize7VzO5QWc/OoblTV1tkLXcZvnWqw9TNF5Exgroj8UURG1i9zlhvTbJ9t2g/A2T2DJ/H3SE/gnF7teOXLHVTV1LkdjjH/41R/Wz9+3Hxug88KnNvy4ZhQ8+nmItISoujbIcntUFrUrWO6cdOLi5i+ag+Xn5npdjjGHOOkiV9Vrc9941N1dcpnm/dzTq92hIWJ2+G0qLN7ptE7I5FnP9nKZYM7BV35TGDzplVPstMX/xJnelxErJ2aabY1ew5SXF7F2b0Cpxtmb4kId4/LZlNBGbPX2wtdxr9483D3ReAwcLUzHQJe8mVQJjR8uqkIgLOCqH6/oYsHdKBLahxPz9tqQzMav+JN4s9W1YdVdZszPQI0q5M2Z1SvaSKyQUTWi8jI5uzPBKZPN+2nX8ck0hKi3Q7FJyLCw7jznGxW7ipl/lZrCGf8hzeJv1JExtTPiMhooLKZx30S+FBV+wCDgPXN3J8JMIePVLNsZ0lQNeM8kStyOpGeGM3Tc7e4HYoxX/Em8d8JPC0ieSKSB/wVuKOpB3SeD5yN58UwVLVKVUubuj8TmD7dtJ+aOmVskCf+6IhwJp3dnflbD7Akr9jtcIwBQLytexSRJABVPdSsA4oMBp4H1uG5218K3Keq5cd9bxIwCSAjIyNn6tSpTTpeWVkZCQkJzQk54ARCmZ9fdZSVRTU8NS6O8BZo8eLPZT5ao/zw00o6xAs/GhaDSMu08PHnMvtKqJW5ueUdN27cUlXN/Z8VqnrCCbgeCDvF+mxgzMnWn2K7XKAGGO7MPwk8eqptcnJytKnmzp3b5G0Dlb+Xuaa2Tgc/MlPvn7q8xfbp72We/MV27frQdP10U2GL7dPfy+wLoVbm5pYXWKInyKmneoGrLbBcROqHWywCYoAewDnAfuBHTbgI5QP5qrrQmZ/WxP2YALVsZwklFdWcd0a626G0mmuHdeb5T7fxx5kbGdMjrcXu+o1pipPW8avqk8CZwOtAO+A8Z343cIOqXqGqm0/3gKq6D9glIr2dRefhqfYxIWL2ugIiwyXoH+w2FB0Rzn3n92RV/kFmrbN2/cZdp+wOUVVrgY+cqSV9F3hVRKKAbcAtLbx/48dmry9geLe2JMUE7mhbTXH5kE48+8lWHpu5kfP6pBMR7k3bCmNaniv/8lR1harmqupAVb1MVUvciMO0vu37y9laVB5S1Tz1IsLDePCCPmwuLOP1xbvcDseEMLvlMK1qjtN9wflnZLgciTsu6JfBiO6pPDFrIwcrq90Ox4QoS/ymVX24Zh992ifSOTXO7VBcISL87JK+lFZW85c5p/2IzJgW4U0nbRki8oKIfODM9xWR23wfmgk2+w4eYcmOEiYO6OB2KK7q1zGZa4d2ZvL8PLYVlbkdjglB3tzxTwZmAh2d+U3A/T6KxwSxmWv3ATBxQHuXI3HfA+N7ExMZziP/WWcduJlW503iT1PVN4E6AFWtAWp9GpUJSu+v3kvP9AR6pCe6HYrr2iVG88D4XnyyqYgZq/e6HY4JMd4k/nIRaYtn1C1EZARw0KdRmaBTdPgoi/KKuSjEq3kaumlUFgM6JfPIf9bZg17TqrxJ/A8A7wHZIvIFMAVPO3xjvDZz7T5UPX3UG4/wMOG3lw/gQNlR/jhzg9vhmBDSaOJX1WV4umgYhadXzn6qusrXgZng8sGavXRvF0+vjNDpYMsb/Tslc8vobry6cCdLd1jvnaZ1eNOq5ztAgqquVdU1QIKI3O370EywKDp8lC+3FTOxfwfro+YEHhjfi47JsXz/zZVUVNW4HY4JAd5U9dyuDfrLd96yvd1nEZmgM33VHmrrlEsHd2z8yyEoPjqCx68exI7iCn73gVX5GN/zJvGHS4PbNBEJB6J8F5IJNu8s302/jkn0zLDWPCczontbbh3djSkLdnw1FrExvuJN4v8QeENEzhOR8/D01vmhb8MywWJbURkr8w/yjSGd3A7F7/3wgt70SE/gwWmrOFhhrXyM73iT+B8C5gJ3OdMc4EFfBmWCxzsr9hAm8LVBVs3TmJjIcJ64ehD7y47y0Fur7MUu4zPetOqpU9VnVPVKZ3rO6a7ZmFNSVd5ZvpvRPdLISIpxO5yAMDAzhQcv7M2Ha/cxeX6e2+GYIOVNq57RIvKRiGwSkW0isl1EtrVGcCawLdtZys7iCi4dbNU8p+P2s7pz/hnp/Ob99azYVep2OCYIeVPV8wLwBDAGGIpnzNyhvgzKBIdpS/OJjQzngn6h2QVzU4kIj101iPTEGL7z6jJKK6rcDskEGW8S/0FV/UBVC1X1QP3k88hMQCs/WsN7K3ZzycAOJIbYSFstISUuiqe/dSaFh49w79QV1NTWuR2SCSLeJP65IvJHERkpImfWTz6PzAS0Gav2Ul5Vy7XDOrsdSsAa3DmFX13Wn083FfGb9619v2k5pxxz1zHc+ZnbYJkC57Z8OCZYTF28kx7pCZzZpY3boQS0a4Z2YeO+Ml78Yju9MhK4dlgXt0MyQaDRxK+q41ojEBM8NhUcZtnOUn568RnWRUML+MnEPmwpKuNn764hKy2eEd3buh2SCXBeDb0oIheLyIMi8vP6ydeBmcD1xuJdRIaLvbTVQiLCw/jLdUPokhrH7VOWsH7vIbdDMgHOm+aczwLX4OmKWYCrgK4+jssEqCPVtby1LJ8JfdvTNiHa7XCCRnJsJFNuG058VAQ3vbiIXcUVbodkApg3d/yjVPVGoERVHwFGAr18G5YJVO+u2E1pRTU3jLR7g5bWKSWWKbcN42hNHTe+uIhDR+3NXtM03iT+SudnhYh0BKoBG03D/A9V5aUv8ujTPpHh3VLdDico9cpI5MWbc9l7sJLHlx6xPn1Mk3iT+KeLSArwR2AZkIenozZjjrFoezEb9h3m5lFZ9lDXh3K6pvLM9TnsPlzH9S8stORvTps3ffU8qqqlqvoWnrr9Pqr6M9+HZgLN5Pl5JMdGWhcNrWBc73TuGRLNxn2HLfmb03bS5pwicvkp1qGqb/smJBOI9pRWMmtdAd8+qxuxUeFuhxMSBqdH8NwNA7njlaVc/8JCptw6jDbxNlSGadyp7vi/5ky34emv51vO9A/gVt+HZgLJi59vB+CGEfZQtzWN65POczfksLHgMFc+O5/dpZWNb2RC3kkTv6reoqq3AJFAX1W9QlWvAPo5y5pFRMJFZLmITG/uvoy7SiuqeG3RTr4+qCOZbeLcDifkjOuTziu3DqPw8FGu+Nt8NhUcdjsk4+e8ebjbWVX3NpgvAFrivfH7gPUtsB/jsikLdlBRVcsd53R3O5SQNbx7W968YyS1qlz5zHyW5BW7HZLxY94k/jkiMlNEbhaRm4EZwOzmHFREMoGL8VQbmQBWUVXDS19s59w+6fRpn+R2OCHtjA5JvH3XKNomRPPNfyzk38vz3Q7J+ClvWvXcAzwLDHKm51X1u8087p/xDN9ofc0GuDcX76Kkopq7xma7HYoBOqfG8dZdoxjSOYXvvbGS336wnto6e9HLHEu8GddTRLoCPVV1tojEAeGq2qSKRBG5BJioqneLyFjgB6p6yQm+NwmYBJCRkZEzderUphyOsrIyEhISmrRtoGqtMtfUKQ99WklqjPB/I2J9frxTsfN8rJo65Z/rq5i3q4ZB7cK5Y2A0cZGB/25FqJ3n5pZ33LhxS1U1939WqOopJ+B2YDGw1ZnvCcxpbLtT7O+3QD6eF8H2ARXAP0+1TU5OjjbV3Llzm7xtoGqtMr/65Q7t+tB0/Xh9Qasc71TsPJ/YlPnbtfuPZ+g5f/hYV+eX+j4oHwu189zc8gJL9AQ51Zs6/u8Ao4FDzoViM5De1CuQqv5YVTNVNQu4FvhYVa9v6v6MO45U1/KXjzdzZpcUxvZu53Y45iRuGJnF67ePoLK6lsufmc8rX+6ovwEzIcybxH9UVb8a9FNEIvAMxGJC2OuLdrL34BG+P6G3dc/g54Z1S+X9e89iRPe2/OydNdzz+nIOHbE3fUOZN4n/ExH5CRArIuOBfwH/aYmDq+o8PUH9vvFvlVW1PD13KyO6pzIq2wYFCQRtE6KZfPNQHrywNx+u2cdFf/6M+Vv2ux2WcYk3if9HQBGwGrgDeB/4qS+DMv5tyoI89pcdtbv9ABMWJtw9tgf/unMk0RFhfPMfC3n43TVUVNW4HZppZd4MvVgnIi8DC/FU8WxUqyQMWaUVVfxt3lbO6dWOoVnW9XIgOrNLG2bcexa//3ADk+fn8cmmIn5/xUCG25COIcObEbguBrYCTwF/BbaIyEW+Dsz4pyfnbObwkWp+PLGP26GYZoiNCucXX+/Ha7cPp6ZOueb5L/nhv1ZSXF7V+MYm4HlT1fM4ME5Vx6rqOcA44E++Dcv4o61FZbyyYAfXDO1ib+kGiVHZacz63tncNTabfy/fzbmPz+PNxbuos5e+gpo3if+wqm5pML8NsF6gQtBv319PTGQ4D4y3kTeDSVxUBA9d2If37zuLnukJPPjWKq58dj7Ldpa4HZrxEW8S/xIRed/pq+cmPC16FovI5afqs98Ely+27Gf2+kLuHpdNu0QbRD0Y9cpI5I1JI/nDlQPZVVLJ5X+bzz2vLbOB3YNQow93gRg8PXKe48wXAbF4+upXwAZkCXJVNXX8/N01ZLaJ5dbR3dwOx/hQWJhwdW5nLh7Qgec+2crzn21j1toCbhmdxV1js0mJs4FegoE3rXpuaY1AjP/6+2fb2FpUzks3DyUm0kbXCgXx0RE8MKE31w3vwmMzN/H8Z9t4beFObhnTjdvGdCM5ttlDchgXNZr4RaQb8F0gq+H3VfXrvgvL+IudByp4as5mJg5oz7g+Te6pwwSoDsmxPH71IG4/uxtPzt7MU3M289IX2/n2mO7cMiaLpBi7AAQib6p63sEz9OJ/sG6UQ4qq8rN31xARJvz8kn5uh2Nc1Kd9Es9cn8PaPQd5cvZm/jR7Ey98vo0bRnblplFZpCfGuB2iOQ3eJP4jqvqUzyMxfue9lXv4ZFMRP7+kL+2T7T+2gX4dk3n+xlzW7D7IXz7ezN/mbeXvn23n8iGd+PZZ3emRHjpdJgcybxL/kyLyMDALOFq/UFWX+Swq47rCQ0f4+btrGdw5hRtH2gDq5lj9OyXz3A25bCsq4x+fb2fa0nymLt7F+WdkcMvoLEZlt7XuPPyYN4l/AHADcC7/repRZ94EIVXlx2+v5kh1LY9fPYiIcG9a/ZpQ1L1dAr/5xgAeGN+LKfPzeOXLHcxeX0D3dvFcP7wrV+Rk2oNgP+RN4r8K6N6wa2YT3KYtzWfOhkJ+evEZZLezP91N49ISonlgQm/uHteDGav28s+FO/jl9HX8YeYGLh3UiW8O78LAzGT7K8BPeJP41wApQKFvQzH+YE9pJb/8zzqGZaVam31z2mIiw7kiJ5MrcjJZs/sgry7cwTvL9/DGkl30TE/gipxMLhvcyZ4ZucybxJ8CbBCRxRxbx2/NOYNMTW0d976+nDpV/njVQMLC7O7MNF3/Tsn89vKB/HjiGcxYtZe3lubzuw828IcPNzC6RxpX5mQyoW97YqPs3ZDW5k3if9jnURi/8OfZm1myo4Qnrx1M17bxbodjgkRSTCTXDevCdcO6kLe/nLeX5fPWst3cN3UFsZHhnHtGOhcP6MC43ul2EWgl3ry5+0lrBGLc9dnmIp6et4Vrcjtz6eBObodjglRWWjwPTOjN/ef3YuH2Yqav2sPMtfuYsWqvXQRa0UkTv4gc5sRj6wqgqmr98gaJwsNH+N4bK+jRLoFffN1e1DK+FxYmjMxuy8jstjzy9X4s2l7MjNV7v7oIxESGMaZHGuedkcG5fdLJSLJnAi3ppIlfVRNbMxDjjqqaOu7+5zLKjtbw2u0j7C7LtLqI8DBG9UhjVI+0ry4CM9fuY/b6Qmav97QpGdApmXP7pJNSUcvZdWrPn5rJmzp+E8Qefm8tS3aU8JfrhtArw671xl0NLwK/+LqyqaCMORsKmLO+kKc+3owqPL16NqOy0xjTM40xPdLomBLrdtgBxxJ/CPvnlzt4fdFO7hqbzdcGdXQ7HGOOISL0bp9I7/aJ3D22B8XlVTzzzicUhafx+ZYDvLdyDwDd28Uzpkcao3ukMTK7rXUc5wVL/CFq4bYD/OK9tYzt3Y4fTOjtdjjGNCo1PorRnSIZO3YIqsrGgsN8vnk/X2zZz7Sl+UxZsIMwgTM6JDE0K5Vh3VIZmpVqAwedgCX+ELS54DC3T1lCl7ZxPHntEMKtvtQEGBGhT/sk+rRP4ttndaeqpo7lO0uYv/UAi/OKmbp4J5Pn5wHQLS2eoVltGJqVSm5WKllt40L+DWJL/CGm8NARbn5pMdGR4bx8yzDrR8UEhaiIMIZ3b8vw7m0BqK6tY83ugyzOK2bR9hJmrSvgzSX5AKTERTIoM4VBnVMY3DmZgZkppCWE1l8FlvhDSNnRGm6ZvJiSiirevGMknVPj3A7JGJ+IDA9jSJc2DOnShklnQ12dsqWojCV5JazKL2XFrlL++vFm6pwG65ltYj0XgswUBmQmc0aHpKC+KbLEHyKOVNdy1z+XsmHfYf5xUy79OyW7HZIxrSYsTOiVkUivjES+ObwLABVVNazZfYgVu0pYuesgK3aWMmPV3q+2yWwTS98OSfTtmMQZHZLo2yGJzDaxQVFNZIk/BFTX1nHPa8v4bPN+HrtqEON62xCKxsRFRTCsm+chcL2iw0dZu+cg6/YeYt2eQ6zbe4iP1hegzl8GiTER9O3guRD0bp9Iz/QEeqYnkhwXWH8dWOIPcjW1ddw/dQWz1xfy6GX9uTIn0+2QjPFb7RKjGds7nbENbo4qqmrYuO/wMReDNxbvorK69pjtPBeBBHpmJH71MzU+yo1iNKrVE7+IdAamABl4uoR4XlWfbO04QkFtnfLgtFXMWL2Xn158BjeMsJG0jDldcVERXz0vqFdXp+wurWRLYRmbCw+zqaCMzYVlTFuaT3nVfy8IbeOj6N4unqy28WSlxdMtrf5zHHFR7t13u3HkGuD7qrpMRBKBpSLykaqucyGWoFVdW8cP/rWSd1fs4YHxvfj2Wd3dDsmYoBEWJnROjaNzahzj+vz3rwNVZe/BI2wuLGNzwWE2FRxm+/5y5m4sYv/S/GP2kZEUTVZb52LgXBC6pcXTOTXW5xeFVk/8qroX2Ot8Piwi64FOgCX+FlJdp3zn1WXMWlfADy/ozXfG9XA7JGNCgojQMSWWjimxnNOr3THrDh+pZseBCrbvLydvfznbD3h+zlpXQHH5sQMcpiVE0yU1lujqI/QYVEFmm5ZtgSeqJ+qAs3WISBbwKdBfVQ8dt24SMAkgIyMjZ+rUqU06RllZGQkJoTN84NFa5U+Ly9lQKnyrTxTjswLroVNThdp5BitzMCmvVgoq6igsV4oq6yiqVIoq6igsr+X/RsaRGtO0ca/HjRu3VFVzj1/uWuIXkQTgE+DXqvr2qb6bm5urS5YsadJx5s2bx9ixY5u0baApraji9ilLWJJXwu+uGMA1Q7u4HVKrCaXzXM/KHPyaW14ROWHid+XpgohEAm8BrzaW9I13dhVXcNNLi8gvruTOQdEhlfSNMafHjVY9ArwArFfVJ1r7+MFoVX4pt05eTHWt8sptw6jcudrtkIwxfqxpFUfNMxq4AThXRFY400QX4ggKs9cVcM1zXxITGc5bd438qq8SY4w5GTda9XyOZ/hG0wx1dcrTc7fwxOxN9O+YzAs355KeaMPTGWMaZ2/uBqCyozX84M2VfLh2H98Y0onfXj6AmEgbMtEY4x1L/AFm+/5yJk1Zwrb95fz04jO4bUy3oOg0yhjTeizxB5D3V+/lobdWEREmvHLrMEb1SHM7JGNMALLEHwCOVNfy6PR1vLpwJ4M6p/DX64ZYX/rGmCazxO/nthQe5p7XlrNh32HuOLs7P7igN5HhbjTGMsYEC0v8fkpVeX3RLh6dvo64qHAm3zL0mK5ijTGmqSzx+6F9B4/w0Fur+GRTEaN7tOWJqweTkWRNNY0xLcMSvx9RVd5ZsZuH311Lda3yy0v7cf3wroSFWasdY0zLscTvJ4oOH+Wn76xm5toCcrq24bGrBtEtLd7tsIwxQcgSv8vq6pSpi3fxuw/Wc6Smjp9M7MNtY7oTbnf5xhgfscTvoo37DvOTf69m6Y4SRnRP5dffGEB2u+Dra9wY418s8bugsqqWpz7ezN8/3UZiTASPXzWIy8/sZG/gGmNahSX+VqSqfLhmH79+fz35JZVclZPJjyeeQWp8lNuhGWNCiCX+VrJuzyF+OX0tX24rpk/7RKZOGsEI60LZGOMCS/w+dqDsKE98tInXF+0kOTaSRy/rz3VDOxNhb98aY1xiid9HjtbU8sqCHTw5ZzMVVbXcODKL+8/vSUqcVesYY9xlib+F1dYp767YzRMfbSK/pJKzeqbx80v60jMj0e3QjDEGsMTfYlSVuRsL+cOHG9mw7zD9Oibxm28M4KyeadZaxxjjVyzxt4ClO0r4/QcbWJRXTNe2cTx13RAuGdDBulowxvglS/zNsG7PIf40exMfrSsgLSGaRy/txzVDuxAVYQ9ujTH+yxJ/E6zbc4in5mzmw7X7SIyO4IHxvbhtTDfio+3XaYzxf5apTsPxCf++83py6+huJMdFuh2aMcZ4zRK/FyzhG2OCiSX+U1iz+yB//XiLJXxjTFCxxH8cVWXh9mL+Nm8rn24qsoRvjAk6lvgddXXKnA2F/G3eFpbvLCUtIYoHL+zN9SO6khRjCd8YEzxCPvFX19bxn5V7ePaTrWwqKKNzaiyPXtafq3IyiYkMdzs8Y4xpcSGb+CuranlzyS6e/3Qbu0sr6dM+kSevHczFAzpYB2rGmKAWcon/YEU1Uxbk8dL8PIrLq8jt2oZHL+vHuN7p1rWCMSYkuJL4ReRC4EkgHPiHqv7O18csOHSEFz7fzqtf7qC8qpZz+6Rz19hshmal+vrQxhjjV1o98YtIOPA0MB7IBxaLyHuqus4Xxysor+PHb6/iraW7qamr42uDOnLnOdmc0SHJF4czxhi/58Yd/zBgi6puAxCRqcClQIsn/p/8ezWvL6wkMmI3Vw/NZNJZ2XRpG9fShzHGmIAiqtq6BxS5ErhQVb/tzN8ADFfVe4773iRgEkBGRkbO1KlTT/tYM7ZVUVpRxcU940iJDp0HtmVlZSQkJLgdRquyMoeGUCtzc8s7bty4paqae/xyv324q6rPA88D5Obm6tixY097H2PHwrx582jKtoHMyhwarMzBz1fldeM2eDfQucF8prPMGGNMK3Aj8S8GeopINxGJAq4F3nMhDmOMCUmtXtWjqjUicg8wE09zzhdVdW1rx2GMMaHKlTp+VX0feN+NYxtjTKgLnaYuxhhjAEv8xhgTcizxG2NMiLHEb4wxIabV39xtChEpAnY0cfM0YH8LhhMIrMyhwcoc/Jpb3q6q2u74hQGR+JtDRJac6JXlYGZlDg1W5uDnq/JaVY8xxoQYS/zGGBNiQiHxP+92AC6wMocGK3Pw80l5g76O3xhjzLFC4Y7fGGNMA5b4jTEmxAR14heRC0Vko4hsEZEfuR1PSxORziIyV0TWichaEbnPWZ4qIh+JyGbnZxu3Y21pIhIuIstFZLoz301EFjrn+g2ny++gISIpIjJNRDaIyHoRGRns51lEvuf8u14jIq+LSEywnWcReVFECkVkTYNlJzyv4vGUU/ZVInJmU48btIm/waDuFwF9getEpK+7UbW4GuD7qtoXGAF8xynjj4A5qtoTmOPMB5v7gPUN5n8P/ElVewAlwG2uROU7TwIfqmofYBCesgfteRaRTsC9QK6q9sfThfu1BN95ngxceNyyk53Xi4CezjQJeKapBw3axE+DQd1VtQqoH9Q9aKjqXlVd5nw+jCcZdMJTzpedr70MXOZKgD4iIpnAxcA/nHkBzgWmOV8JqjKLSDJwNvACgKpWqWopQX6e8XQbHysiEUAcsJcgO8+q+ilQfNzik53XS4Ep6vElkCIiHZpy3GBO/J2AXQ3m851lQUlEsoAhwEIgQ1X3Oqv2ARluxeUjfwYeBOqc+bZAqarWOPPBdq67AUXAS0711j9EJJ4gPs+quht4DNiJJ+EfBJYS3Oe53snOa4vltGBO/CFDRBKAt4D7VfVQw3Xqaa8bNG12ReQSoFBVl7odSyuKAM4EnlHVIUA5x1XrBOF5boPnDrcb0BGI53+rRIKer85rMCf+kBjUXUQi8ST9V1X1bWdxQf2fgM7PQrfi84HRwNdFJA9P9d25eOq/U5wqAQi+c50P5KvqQmd+Gp4LQTCf5/OB7apapKrVwNt4zn0wn+d6JzuvLZbTgjnxB/2g7k7d9gvAelV9osGq94CbnM83Ae+2dmy+oqo/VtVMVc3Cc04/VtVvAXOBK52vBVuZ9wG7RKS3s+g8YB1BfJ7xVPGMEJE45995fZmD9jw3cLLz+h5wo9O6ZwRwsEGV0OlR1aCdgInAJmAr8H9ux+OD8o3B82fgKmCFM03EU+c9B9gMzAZS3Y7VR+UfC0x3PncHFgFbgH8B0W7H18JlHQwscc71O0CbYD/PwCPABmAN8AoQHWznGXgdzzOMajx/2d12svMKCJ6WiluB1XhaPDXpuNZlgzHGhJhgruoxxhhzApb4jTEmxFjiN8aYEGOJ3xhjQowlfmOMCTGW+E3QEpF7nZ4sX/XBvkVEPhaRJGe+rMG6iSKySUS6HrfNzSLy1+OWzRORkw6mLSJTRaRnS8dvQpslfhPM7gbGq+cFr680ePOzOSYCK/W4LjJE5DzgKeAiVd3RAsd5Bk+/RMa0mJb4D2CM3xGRZ/G87POBiLwIJAPZzrKdInIv8CzQxdnkflX9QkTa4nmpphOwABgP5Kjq/uMO8S2OGw9VRM4G/g5MVNWtpxnv14FfOrOxQJSqdgM+AyaLSIT+t3MyY5rF7vhNUFLVO4E9wDhV/ZOzuC9wvqpeh6d/nz+p6lDgCpwunoGHgc9VtR/wb/57YTjeaDy9RdaLxvNG7WWquuEUoV0jIivqJyDXifc9VR2sqoOBlXh6pkRV6/C8pTrI27Ib0xi74zeh5D1VrXQ+nw/09XQDA0CS08vp2cDlAKo6Q0RKTrKvVPWMgVCvGpiP55X7+04Rwxuqek/9jIjMa7hSRB4EKlX16QaLC/H0UBlKPZIaH7LEb0JJeYPPYcAIVT3S8AsNLgSNqRGRMOeOHDxjA1wNzBGRn6jqb043OBE5H7gKz8WnoRig8n+3MKZprKrHhKpZwHfrZ0RksPPxU+CbzrKL8HSGdiIb8Twv+IqqVuAZGexbInJaQwI6LYCeBq5q8FdJvV54OiozpkVY4jeh6l4g1xm0eh1wp7P8EeBsEVmLp8pn50m2n4Gnd9BjqGoxngFDfuo8sPXWzXh6ZXzHqf9/H0BEMvBU/ew7jX0Zc0rWO6cxp+AM+JJ7fKseZ4CMKao63sfH/x5wSFVf8OVxTGixO35jmkA9A2D8vf4FLh8q5b8DbxvTIuyO3xhjQozd8RtjTIixxG+MMSHGEr8xxoQYS/zGGBNiLPEbY0yI+X9ULtN7YiOi7wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "x = np.linspace(0,100000,1000 ) # radians per second\n",
    "c=4.7e-5\n",
    "l = 4.7e-4\n",
    "f1 = s.lambdify(w, e2.subs([(R, 1), (C, c), (L, l)]))\n",
    "y = f1(x/(2*np.pi))\n",
    "    \n",
    "ax.plot(x/1000,y)\n",
    "ax.grid()\n",
    "ax.set_xlabel(\"freq (K Hz)\")\n",
    "ax.set_ylabel(\"Impedance (ohms)\")\n",
    "ax.set_title(\"Frequency Response\")\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a5be1d3e",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}