20230511 EE110 Sample Final Exam Solutions.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "e436f359",
   "metadata": {},
   "source": [
    "# Question 1: Write the equation for the function of the plot shown below in terms of scaled and delayed delta, step, and/or ramp functions. Show your reasoning behind each height change and slope change for full credit.  Points will be taken off for each incorrect (missing, extra, incorrect delay, incorrect scale factor) ramp and step function.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "c31569f3",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "def u(t):\n",
    "    return 0.5*(np.sign(t)+1)\n",
    "def r(t):\n",
    "    return t*u(t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "c2984521",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t=np.linspace(-1,8,200)\n",
    "def f(t):\n",
    "    return 2*u(t-2)-1.5*u(t-3)-.5*r(t-6)+.5*r(t-7)\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(1,1,1)\n",
    "fig.subplots_adjust(left=0.25, bottom=0.25)\n",
    "legend='$f(t) $'\n",
    "[line] = ax.plot(t, f(t), linewidth=2, color='blue',label=legend)\n",
    "ax.set_xlabel('Time (s)',fontsize=12)\n",
    "ax.set_ylabel('Arbritrary units',fontsize=12) \n",
    "ax.legend()\n",
    "ax.set_title('Plot of abritary waveform')\n",
    "ax.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "39a0380b",
   "metadata": {},
   "source": [
    "At t=2 there is a step up of 2 which is denoted as $2u(t)$, then at t=3, there is a step down of 1.5 (2 to 0.5) which is $-1.5u(t-3)$.  At t=6 there is a negative ramp of -.5 which is $-0.5r(t-6)$ which then flattens out thus the slope at t=7 is equal and opposite which is $0.5r(t-7)$.\n",
    "\n",
    "$f(t)=2u(t-2)-1.5u(t-3)-.5r(t-6)+.5r(t-7)$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2238b940",
   "metadata": {},
   "source": [
    "# Question 2: Using any convolution method, find the equation for the convolution and sketch it over time. Make sure to clearly label 5$\\tau$, if appropriate. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b51527cc",
   "metadata": {},
   "source": [
    "$g(t)= u(t)-u(t-10)$\n",
    "\n",
    "$h(t)=\\frac{1}{2}\\times e^{-\\frac{t}{2}}u(t)$\n",
    "\n",
    "$f(t)=g(t)*h(t)$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3cb9ce33",
   "metadata": {},
   "source": [
    "The common convolution is $z(t)=u(t)*e^{-\\frac{t}{2}}u(t)$\n",
    "$z(t)=u(t)*e^{-\\frac{t}{2}}u(t)=L^{-1}\\left(G(s)\\times H(s)=\\frac{1}{s} \\times \\frac{1}{s+\\frac{1}{2}} \\right)$\n",
    "$z(t)=\\left(1-e^{-\\frac{t}{2}} \\right)u(t)$\n",
    "\n",
    "$f(t)=g(t)*h(t)=z(t)-z(t-10)=\\left(1-e^{-\\frac{t}{2}} \\right)u(t)-\\left(1-e^{-\\frac{t-10}{2}} \\right)u(t-10)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "6f56e882",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def z(t):\n",
    "    return u(t)*(1-np.exp(-t/2))\n",
    "def f(t):\n",
    "    return z(t)-z(t-10)\n",
    "t=np.linspace(-1,20,200)\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(1,1,1)\n",
    "fig.subplots_adjust(left=0.25, bottom=0.25)\n",
    "legend='$f(t) $'\n",
    "[line] = ax.plot(t, f(t), linewidth=2, color='blue',label=legend)\n",
    "ax.set_xlabel('Time (s)',fontsize=12)\n",
    "ax.set_ylabel('Arbritrary units',fontsize=12) \n",
    "ax.legend()\n",
    "ax.set_title('Plot of abritary waveform')\n",
    "ax.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6002837e",
   "metadata": {},
   "source": [
    "$5 \\tau =10s$ and can been seen for t=0 to 10, and t=10 to 20."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "397e16d0",
   "metadata": {},
   "source": [
    "# Q3 Match  the step responses\n",
    "$h_1(t)=2e^{-t}u(t)$ This function's step response will go from 0 to 2 with an asymptotic approach from 0 to 5s as $tau=1s$.\n",
    "\n",
    "$h_2(t)=2\\left( \\delta(t) -e^{-t}u(t) \\right)$ This function's step response  will go from 2 to 0 with an exponential decay from 0 to 5s as $tau=1s$.\n",
    "\n",
    "$h_3(t)=\\frac{1}{500m}e^{-\\frac{t}{500m}}u(t)$ This function's step response will go from 0 to 1 with an asymptotic approach from 0 to 2.5s as $tau=.5s$.\n",
    "\n",
    "$h_4(t)=\\delta(t)-\\frac{1}{500m}e^{-\\frac{t}{500m}}u(t)$This function's step response  will go from 1 to 0 with an exponential decay from 0 to 2.5s as $tau=.5s$.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "c61a5764",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy import *\n",
    "s =symbols(\" s\",positive=True)\n",
    "time, tau =symbols(\" time, tau\",real=True)\n",
    "def convolution(g,h):\n",
    "    #The ().subs method replaces t with tau the dummy variable.\n",
    "    gtmp=g.subs(time,tau)\n",
    "    #The ().subs method replaces t with t-tau the dummy variable.\n",
    "    htmp=h.subs(time,time-tau)\n",
    "    #use -oo instead of zero, otherwise delta functions will not work.\n",
    "    #Make sure at least one function multiplied by u(t).\n",
    "    return integrate(gtmp*htmp,(tau,-oo,time))\n",
    "h1=2*exp(-time)*Heaviside(time)\n",
    "g=Heaviside(time)\n",
    "f1=convolution(h1,g)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "913cee4d",
   "metadata": {},
   "source": [
    "The step response of $h_1(t)$="
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "57045473",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 2 \\cdot \\left(1 - e^{- time}\\right) \\theta\\left(time\\right)$"
      ],
      "text/plain": [
       "2*(1 - exp(-time))*Heaviside(time)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "ca409679",
   "metadata": {},
   "outputs": [],
   "source": [
    "h2=2*(DiracDelta(time)-exp(-time)*Heaviside(time))\n",
    "f2=convolution(h2,g)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0bb3290d",
   "metadata": {},
   "source": [
    "The step response of $h_2(t)=$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "56688348",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 2 \\left(\\theta\\left(time\\right)\\right)^{2} - 2 \\theta\\left(time\\right) + 2 e^{- time} \\theta\\left(time\\right)$"
      ],
      "text/plain": [
       "2*Heaviside(time)**2 - 2*Heaviside(time) + 2*exp(-time)*Heaviside(time)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f2.simplify().expand()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0bc8e64f",
   "metadata": {},
   "source": [
    "Note: $\\left( u(t) \\right)^2=u(t)$ so the step response becomes $2e^{-time}u(time)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "a8e60ed6",
   "metadata": {},
   "outputs": [],
   "source": [
    "h3=1/.5*exp(-time/.5)*Heaviside(time)\n",
    "f3=convolution(h3,g)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ed8648eb",
   "metadata": {},
   "source": [
    "The step response of $h_3(t)=$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "b0859fa4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left(1 - e^{- 2 time}\\right) \\theta\\left(time\\right)$"
      ],
      "text/plain": [
       "(1 - exp(-2*time))*Heaviside(time)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "c31a7c3c",
   "metadata": {},
   "outputs": [],
   "source": [
    "h4=DiracDelta(time)-1/.5*exp(-time/.5)*Heaviside(time)\n",
    "f4=convolution(h4,g)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "69f41fee",
   "metadata": {},
   "source": [
    "The step response of $h_4(t)=$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "ed523b17",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left(\\theta\\left(time\\right)\\right)^{2} - \\theta\\left(time\\right) + e^{- 2 time} \\theta\\left(time\\right)$"
      ],
      "text/plain": [
       "Heaviside(time)**2 - Heaviside(time) + exp(-2*time)*Heaviside(time)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f4.simplify().expand()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d5ecdd55",
   "metadata": {},
   "source": [
    "Note: $\\left( u(t) \\right)^2=u(t)$ so the step response becomes $e^{-2 time}u(time)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "2e4c1a32",
   "metadata": {},
   "outputs": [],
   "source": [
    "f1= lambdify(time, f1, modules=['numpy'])\n",
    "f2= lambdify(time, f2, modules=['numpy'])\n",
    "f3= lambdify(time, f3, modules=['numpy'])\n",
    "f4= lambdify(time, f4, modules=['numpy'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "be3f1a20",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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0LCvUbdsC7dqVFe1/n8AlC8ciTkSkJ/n5QGqqDN980wabN1vjxAlxNPij1KsnFuhOnQAfn7I/W7QQr7qJqsIiTkRUQ3//Dfz8s/g6fBg4cQIoLq4HwLvKc5ycgG7dAF9foHNnsVi3a8fPqalmWMSJiLR04wbw00/AgQPAoUPApUvVt2/YEPDzE4t26at1a15dk/6wiBMRVeH2bSApqaxw//579e3btQMCAkrQsOEpTJ3aER072nBSEzIoFnEion+pVMAvvwDffw/88ANw8mTVj3fJ5UD37kDPnuIrMFCcIEWc8CQT7dt3ZAEng2MRJyKLdvs2sG+fWLh//FFcYasy1tZAjx7AgAFA//5AQAAnRCHpsYgTkcX580/g22+BXbuAI0eqnkO8c2exYA8YAPTuLS68QWRKWMSJyCL88QcQGyu+0tMrb+PgAAQHA4MHAyEhgLu7cWMk0hWLOBHVWZcuAdu3A19/Lc6KVpm2bYEhQ8TX00/zUS8yLyziRFSn3LoFfPUV8MUXQGpq5W18fYFRo8RX27bGjY9In1jEicjsFRYCe/cC27YB8fGAUlmxjb+/WLRHjhTnGCeqC1jEichsnT8PfPYZEB1d+ajyjh2B0FBg3DjA09Po4REZHIs4EZmVggJxZPmGDUBycsX3mzUDxo8Hnn9eHF1OVJexiBORWcjMBNasATZurHjVbWsLjB4NTJ4M9OsnPtNNZAlYxInIpKWmApGR4qNhKpXme+3aAdOni7fMXVwkCY9IUiziRGRylEqxaEdGAseOab5naws89xzw0kviI2FcTIQsGYs4EZmMggJxkNry5eKsauU1bQrMnAnMmAG4ukoRHZHpYREnIsnl5QGffgqsWAEoFJrvde4MzJsnjjDnXOVEmljEiUgy9+8DUVHibfOHB6s98wzw5ptAnz68ZU5UFckXyktJScGwYcPQrFkzyGQy7N69u9r2kyZNgkwmq/Dq0KGDuk10dHSlbQoKCgycDRFp48ED4OOPxUlX3n5bs4CPHAmkpYlLgfbtywJOVB3Ji3heXh46d+6M1atXa9U+KioKCoVC/bp27RoaN26M5557TqOdo6OjRjuFQgE7OztDpEBEWlIqxclZ2rQB/vc/4OZN8bi1tfhc99mz4oA2Pz9p4yQyF5LfTg8JCUFISIjW7Z2cnODk5KTe3717N+7cuYPJkydrtJPJZHBzc9NbnERUc4IAfPMNsGABcOFC2XGZTJyYZfFi4IknJAuPyGxJXsRra+PGjRg4cCBatmypcTw3NxctW7aESqVCly5dsHTpUnTt2rXKfgoLC1FYWKjez8nJAQAolUooK5uIWQel59e2H3PE3Jn7iRPA//5njZ9/1rzxN2xYCRYvVsHHp/QcY0dpGPy5M3d99aUNmSAIQq2/op7IZDLs2rULI0aM0Kq9QqGAh4cHtm/fjjFjxqiPHz16FBcvXoSPjw9ycnIQFRWF+Ph4nDp1Cm3atKm0r8WLFyMiIqLC8e3bt8Pe3r5G+RBZstu35fjyy/Y4cMATglD2wbaPzz94/vlzaNv2joTREZmu/Px8jB8/Hvfu3YOjo2O1bc26iC9btgwfffQRbty4AdtqFgEuKSmBr68vevfujVWrVlXaprIrcQ8PD9y8efOR38RHUSqVSExMRFBQEGxsbGrVl7lh7paXe1ERsGKFgPfft0JBQdnNvjZtBHz4oQohIUKdHqxmqT93gLnrK/ecnBy4uLhoVcTN9na6IAjYtGkTQkNDqy3gAGBlZYXu3bvjQvkP4x4il8shr+QhVBsbG739MuqzL3PD3C0j9+Rk4OWXgXPnyo41agQsWgTMnCmDra3Z/pOjM0v6uT+Mudcud13Ol3x0ek0lJyfj4sWLmDJlyiPbCoKAjIwMuLu7GyEyIstz86a4+EjfvmUF3MpKwIwZKly4AMydK06XSkT6Jfl/i3Nzc3Hx4kX1/pUrV5CRkYHGjRvD09MT4eHhuH79OrZu3apx3saNG9GjRw907NixQp8RERHw9/dHmzZtkJOTg1WrViEjIwNr1qwxeD5ElkQQgC1bgNde03zWu3v3Evz3v8l45ZWnYWPDJcWIDEXyIp6WloZ+/fqp98PCwgAAEydORHR0NBQKBTIzMzXOuXfvHmJjYxEVFVVpn3fv3sX06dORlZUFJycndO3aFSkpKXjqqacMlwiRhfnrL2DqVGDfvrJjjo7AsmXAiy+qsG9fjnTBEVkIyYt43759Ud3Yuujo6ArHnJyckJ+fX+U5K1euxMqVK/URHhE9pPTqe+5c4N69suNjxwIrVwLu7nXncTEiUyd5ESci86FQiOt3f/dd2bFmzYANG4AhQ6SLi8hSme3ANiIyrm+/BTp00CzgL7wAnDnDAk4kFRZxIqrWgwfiY2OjRgF3/p2fxdUViIsTb6s/9pi08RFZMt5OJ6IqnTkjruN99mzZsdGjgfXrAWdn6eIiIhGvxImoAkEQC3X37mUFvH59cQWyr75iAScyFbwSJyIN+fnASy8B27aVHevUCdixA2jfXrq4iKgiXokTkdrly0BgoGYBf+UV4NgxFnAiU8QrcSICAPzwAzBhQtngtQYNgM2bgeeekzYuIqoar8SJLJwgAO+8Iz4mVlrAn3wS+OUXFnAiU8crcSILVlAATJkCbN9edmzECPHRsVquwEtERsArcSILlZ0N9O9fVsBlMuDdd4HYWBZwInPBK3EiC3T2LDB0KPDnn+K+vT3w5ZfiVTgRmQ8WcSILk5goTtiS8+8iY82aAXv3Ar6+0sZFRLrj7XQiCxITIw5gKy3gvr7iADYWcCLzxCJOZCE++UR8hKx0mdBnnwVSUoDmzaWNi4hqjkWcqI4TBODtt4HZs8VtAJg6VRzA1qCBtLERUe2wiBPVYSoVMGOG+Bx4qQULxPW/63FEDJHZ419jojqquBiYPFlzCtVVq4BXX5UuJiLSLxZxojpIqQReeEFctAQQr7q3bgX++19p4yIi/WIRJ6pjioqA8ePFz7wBwMYG+PprYPhwaeMiIv1jESeqQwoLgbFjgbg4cV8uB779Fhg8WNq4iMgwWMSJ6gilEhgzBtizR9y3sxOLeXCwtHERkeGwiBPVASqV+Bl4aQG3txdnYevfX9q4iMiwWMSJzFxJCTB9etkgNjs74LvvgH79pI2LiAxP8ufEU1JSMGzYMDRr1gwymQy7d++utn1SUhJkMlmF1++//67RLjY2Ft7e3pDL5fD29sauXbsMmAWRNAQBmDcP2LRJ3K9XD/jmGxZwIksheRHPy8tD586dsXr1ap3OO3/+PBQKhfrVpk0b9XupqakYO3YsQkNDcerUKYSGhmLMmDE4duyYvsMnktTbb4vPfgOAlZW4rOiQIdLGRETGI/nt9JCQEISEhOh8XtOmTdGoUaNK34uMjERQUBDCw8MBAOHh4UhOTkZkZCRiYmIqPaewsBCFhYXq/Zx/V4hQKpVQlk42XUOl59e2H3PE3A2X++rVVnj3XWv1/oYNxRgxQoApfKv5c2fulkafuevSh+RFvKa6du2KgoICeHt7Y+HChehX7v5hamoq5s2bp9F+0KBBiIyMrLK/ZcuWISIiosLxhIQE2Nvb6yXmxMREvfRjjpi7fh054o4PP+yu3p8+/TRcXK4gPl7vX6pW+HO3TMy9dvLz87Vua3ZF3N3dHRs2bICfnx8KCwvxxRdfYMCAAUhKSkLv3r0BAFlZWXB1ddU4z9XVFVlZWVX2Gx4ejrCwMPV+Tk4OPDw8EBwcDEdHx1rFrFQqkZiYiKCgINjY2NSqL3PD3PWf++HDMkRFWUMQZACA8HAVIiLaA2ivt69RW/y5M3fmXnOld4K1YXZFvG3btmjbtq16PyAgANeuXcOKFSvURRwAZDKZxnmCIFQ4Vp5cLodcLq9w3MbGRm+/jPrsy9wwd/3k/ttvwMiR4qQuADBpEvDuu9aQyayrPU8q/Lkzd0ujj9x1OV/ygW364O/vjwsXLqj33dzcKlx1Z2dnV7g6JzInN24AISHA3bvi/qBB4mpk1fzflIjquDpRxE+ePAl3d3f1fkBAQIXPJRISEhAYGGjs0Ij04sEDce7zzExx39dXnA/dQi92iOhfkt9Oz83NxcWLF9X7V65cQUZGBho3bgxPT0+Eh4fj+vXr2Lp1KwBx5Pnjjz+ODh06oKioCNu2bUNsbCxiS1d7ADBnzhz07t0by5cvx/DhwxEXF4f9+/fj8OHDRs+PqLYEAXjxRSAtTdz39AS+/x5wcJA2LiKSnuRFPC0tTWNkeengsokTJyI6OhoKhQKZpZcfAIqKivDaa6/h+vXrqF+/Pjp06IDvv/8eg8ut8BAYGIgdO3Zg4cKFePvtt9G6dWvs3LkTPXr0MF5iRHry7rtls7E1aCBOp+rmJm1MRGQaJC/iffv2hSAIVb4fHR2tsf/GG2/gjTfeeGS/o0ePxujRo2sbHpGkvv1WnNAFED/7/vJLoFMnaWMiItNRJz4TJ6qLMjKA0NCy/ffe45rgRKRJ5yJeUFBQ4Rm2r776CvPnz8dPP/2kt8CILNmtW8CIEUDpnA/PPw+8+aakIRGRCdK5iIeGhmL27Nnq/VWrVmHcuHH44IMPEBwcjHhTmzKKyMyUlIhF++pVcf+pp4DPPuOjZERUkc5F/JdffsEzzzyj3l+1ahWef/553L17FyNHjsSKFSv0GiCRpXnnHeDHH8VtFxcgNlZcXpSI6GE6F/F//vkHzZs3ByA+Dnb58mW8+uqrcHR0xJQpU3DmzBm9B0lkKfbtAxYvFretrMRR6S1aSBoSEZkwnYu4vb097t27BwA4dOgQGjZsiG7dugEA7OzskJubq98IiSzE1avA+PHic+GAeEU+YIC0MRGRadP5ETMfHx+sWbMGLVu2xNq1a9GvXz/1nOSZmZlw4wOsRDorKgKeew64fVvcHzaMA9mI6NF0LuJvv/02hg4dii5dusDW1hb79+9Xv/f999/D19dXrwESWYKFC4Hjx8XtVq2ALVvE2+lERNXRuYj3798f586dQ3p6Orp06YJWrVppvNelSxd9xkdU5yUkAB9+KG7b2Ihzoj/2mLQxEZF50Pn/+ikpKXB2dsbIkSM1CjgATJgwAYWlayQS0SNlZwMvvFC2v3y5uLgJEZE2dC7i/fr1w2+//Vbpe+fPn9eYB52IqlZSAkycCPz9t7j/zDPAnDnSxkRE5kXnIl7dPOdKpRJW/CCPSCtRUWXPg7u6AtHR/ByciHSj1WfiOTk5uHv3rno/KytLY2UxAHjw4AG2bNnC0elEWjh9WnP0+datYiEnItKFVkV85cqVWLJkCQBAJpPhP//5T6XtBEHAW2+9pb/oiOqgoiLxc3ClUtx/7TUgOFjamIjIPGlVxIODg9GwYUMIgoA33ngDr776Kjw9PTXayOVy+Pj4oE+fPgYJlKiuWLoUOHVK3PbxESd1ISKqCa2KeEBAAAICAgAAeXl5mDZtGpo1a2bQwIjqouPHgWXLxO169cTnweVyaWMiIvOl83PiixYtMkQcRHXegwfiaHSVStz/v/8DunaVNiYiMm9aFfGtW7diyJAhcHZ2xtatWx/Z/oXyD74SEQDg7beBc+fE7W7dgPnzpY2HiMyfVkV80qRJOHr0KJydnTFp0qRq28pkMhZxooccOQJ8/LG4LZeLt9FtbKSNiYjMn1ZF/MqVK3B3d1dvE5H2CguBqVM1Vyfz9pY2JiKqG7Qq4i1btqx0m4ge7YMPrNS30bt3B+bNkzYeIqo7OD8UkQFdu9YQy5eLf82srYHPPhP/JCLSB51HpwPAtm3bsH37dly9ehUPHjzQeE8mk+HSpUt6CY7InJWUAGvXdkFRkQwA8PrrQOfOEgdFRHWKzlfiy5cvxwsvvIDMzEx07twZffr00Xj17t1bp/5SUlIwbNgwNGvWDDKZDLt37662/bfffougoCA0adIEjo6OCAgIwL59+zTaREdHQyaTVXgVFBTomi5RjW3caIVz55wBAK1bi4+UERHpk85X4hs2bMCsWbPwySef6CWAvLw8dO7cGZMnT8aoUaMe2T4lJQVBQUF477330KhRI2zevBnDhg3DsWPH0LXcQ7eOjo44f/68xrl2dnZ6iZnoUW7cAMLDy/6P/OmnQP36EgZERHWSzkU8KyuryrnTayIkJAQhISFat4+MjNTYf++99xAXF4e9e/dqFHGZTMbFWEgyr70G5OSIt9FfeKEEAwZw+AkR6Z/ORdzPzw+XLl1C//79DRGPzkpKSnD//n00btxY43hubi5atmwJlUqFLl26YOnSpRpF/mGFhYUoLCxU7+fk5AAQl1dVlq5UUUOl59e2H3NkibknJ8sQEyP+1XJwKMQ776igVFrWQ+GW+HMvxdyZu7760oZMqG6B8EqkpaXh+eefx5dffgk/Pz+dg6s2GJkMu3btwogRI7Q+58MPP8T777+Pc+fOoWnTpgCAo0eP4uLFi/Dx8UFOTg6ioqIQHx+PU6dOoU2bNpX2s3jxYkRERFQ4vn37dtjb29coH7I8xcUyhIX1RWamIwBg5swMBAdflTgqIjIn+fn5GD9+PO7duwdHR8dq2+pcxH18fJCVlYXbt2/Dzc0Nzs7Omh3KZDhVukSTjnQt4jExMZg6dSri4uIwcODAKtuVlJTA19cXvXv3xqpVqyptU9mVuIeHB27evPnIb+KjKJVKJCYmIigoCDYWNk2XpeW+apUVXntNfIbM11eFBQu+wzPPWEbu5Vnaz7085s7ca5t7Tk4OXFxctCriOt9Od3Z2houLS42D05edO3diypQp+Prrr6st4ABgZWWF7t2748KFC1W2kcvlkFeynJSNjY3efhn12Ze5sYTcs7KAJUvEbZkM+OQTAf/8Yxm5V4W5M3dLo4/cdTlf5yKelJSk6yl6FxMTgxdffBExMTEYMmTII9sLgoCMjAz4+PgYITqyVG++Cfw7lAJTpgDduwuIj5c2JiKq22o02Ys+5ebm4uLFi+r9K1euICMjA40bN4anpyfCw8Nx/fp19eppMTExeOGFFxAVFQV/f39kZWUBAOrXrw8nJycAQEREBPz9/dGmTRvk5ORg1apVyMjIwJo1a4yfIFmEI0eA0gX+GjUC3ntP0nCIyELoXMRTUlIe2UaXCV/S0tLQr18/9X5YWBgAYOLEiYiOjoZCoUBmZqb6/U8//RTFxcWYNWsWZs2apT5e2h4A7t69i+nTpyMrKwtOTk7o2rUrUlJS8NRTT2kdF5G2SkqAuXPL9t99F2jSBLDAAbpEZGQ6F/G+fftCJpNV20alUunUX3Vj60oLcyltbuevXLkSK1eu1DoGotrYsQM4flzc9vEBXnpJ2niIyHLoXMQPHjxY4djNmzcRFxeHn3/+mbesyaI8eACEh5ftr1jBBU6IyHh0LuJ9+vSp9PioUaMwY8YM/Pjjj3jmmWdqHRiROYiKAko/7XnmGSA4WNp4iMiy6HUuyP/85z/YsWOHPrskMlnZ2WUD2KysxKtwIiJj0msRv3PnjsaEKUR12eLFwP374vbUqUCHDpKGQ0QWSOfb6eVHipcqLCzE6dOnER4eDn9/f70ERmTKzp0DNmwQtxs2LJvkhYjImHQu4o8//nilo9MFQUDbtm2xevVqvQRGZMreegsofQhj/nzA1VXaeIjIMulcxDdt2lShiNvZ2eHxxx9H9+7dYWXFJRepbvvlF2D3bnG7WTNg3jxJwyEiC6ZzEZ80aZIBwiAyH2+9Vbb9f/8HcJE7IpIKL5uJdPDTT+ILAFq3Bl58Udp4iMiysYgTaUkQgAULyvaXLAEsdKEmIjIRLOJEWtqzBzh2TNz28QHGjZM2HiIiFnEiLahUwMKFZfvvvCNO8EJEJCX+M0SkhR07gDNnxG1/f2DYMGnjISICalDEY2NjUVJSYohYiEySSqU5mcu77wKPWMiPiMgodC7izz33HFq2bIl3330X2dnZhoiJyKR89RXwxx/idp8+QP/+0sZDRFRK5yKelJSEgIAAREREwNPTE6GhoTh69KghYiOSXEkJsHRp2f7//Z90sRARPUznIt67d2989dVXuHr1Kt544w389NNP6NmzJ/z8/BAdHc0FUKhOiY0V50kHgJ49gX79pI2HiKi8Gg9sc3d3x5IlS5CZmYlt27bBysoKU6ZMQYsWLRAeHg6FQqHPOImMrqREHIVe6v/+j5+FE5FpqfXo9CtXruDYsWO4cOECrK2t4ePjg6ioKDz55JPYu3evPmIkksSePcDp0+J2jx5AUJC08RARPaxGRVwQBOzZsweDBg1C+/btsX37drzyyiv4888/ceDAAfz555/o27cv5nFlCDJTgqA5Ip1X4URkinReAGX58uVYv349rl69is6dO+Ozzz7D+PHjIZfL1W2aNm2K119/Hf34ASKZqe+/B06eFLf9/ICQEGnjISKqjM5FfOHChXj22WcRHR2NPn36VNmudevW+D8O5SUztWxZ2fbbb/MqnIhMk05FXKVS4cyZM2jatCkee+yxats2b94cixYtqlVwRFL4+WfgyBFxu0MHzs5GRKZLp8/EBUFAhw4d+Fw41WnLl5dtv/EG50gnItOl0z9P9erVg5ubm16nXU1JScGwYcPQrFkzyGQy7N69+5HnJCcnw8/PD3Z2dmjVqhXWr19foU1sbCy8vb0hl8vh7e2NXbt26S1mqrt++w0ofaiiRQuuVEZEpk3na4xx48Zh69ategsgLy8PnTt3xurVq7Vqf+XKFQwePBi9evXCyZMn8dZbb2H27NmIjY1Vt0lNTcXYsWMRGhqKU6dOITQ0FGPGjMGx0nUkiaqwYkXZ9rx5gK2tdLEQET2KzgPbunTpgp07d6J///4YOXIk3N3dIXto1M/IkSO17i8kJAQhOgz9Xb9+PTw9PREZGQkAaN++PdLS0rBixQqMGjUKABAZGYmgoCCEh4cDAMLDw5GcnIzIyEjExMRo/bXIsvz1F7Btm7jdqBEwbZqk4RARPZLORfyFF14AAFy/fh1JSUkV3pfJZFCpVLUOrCqpqakIDg7WODZo0CBs3LgRSqUSNjY2SE1NrfCM+qBBg9SFvzKFhYUaU8bm5OQAAJRKJZRKZa1iLj2/tv2YI3PKfeVKKyiV1gCAl15Swc6uBLUJ25xy1zfmztwtjT5z16UPnYv4wYMHdT1Fr7KysuDq6qpxzNXVFcXFxbh58ybc3d2rbJOVlVVlv8uWLUNERESF4wkJCbC3t9dL7ImJiXrpxxyZeu65ufWwbl0wAGvY2KjQvn0i4uP1sw6AqeduSMzdMjH32snPz9e6rc5FvLpnw43l4dv3giBUOF5Zm4ePlRceHo6wsDD1fk5ODjw8PBAcHAxHR8daxatUKpGYmIigoCDY2NjUqi9zYy65f/ihFR48EK/CJ00Cxo8fUOs+zSV3Q2DuzJ2511zpnWBt6FzEpebm5lbhijo7Oxv16tWDs7NztW0evjovTy6Xa8w6V8rGxkZvv4z67MvcmHLuSiWwbp24LZMBr79uDRsba731b8q5GxpzZ+6WRh+563J+jYr4hQsX8Omnn+LcuXN48OCBxnsymQw//fRTTbrVSkBAQIWFVRISEtCtWzd14gEBAUhMTNT4XDwhIQGBgYEGi4vM165d4qA2ABgyBGjTRtp4iIi0pXMRP3PmDPz9/dG8eXNcvHgRnTp1ws2bN3H9+nV4eHigdevWOvWXm5uLixcvqvevXLmCjIwMNG7cGJ6enggPD8f169fVj7XNmDEDq1evRlhYGKZNm4bU1FRs3LhRY9T5nDlz0Lt3byxfvhzDhw9HXFwc9u/fj8OHD+uaLlmAqKiy7blzJQuDiEhnOj8n/tZbb2HQoEE4e/YsBEHAxo0bce3aNezduxcFBQV4p/wCzFpIS0tD165d0bVrVwBAWFgYunbtqp53XaFQIDMzU93ey8sL8fHxSEpKQpcuXbB06VKsWrVK/XgZAAQGBmLHjh3YvHkzOnXqhOjoaOzcuRM9evTQNV2q49LSyqZY7dgR6N9f2niIiHSh85X4iRMnsHbtWlj9Oxdl6extQ4YMwWuvvaZ+Jltbffv2VQ9Mq0x0dHSFY3369MGJEyeq7Xf06NEYPXq01nGQZSp/FT57Nhc6ISLzovOV+J07d9C4cWNYWVnBxsYGd+7cUb/XrVu3RxZXIlOhUAA7d4rbjRsDEyZIGw8Rka50LuLNmzfHzZs3AQBPPPEEUlJS1O+dPn0aDRs21F90RAa0fj3Uk7lMnw7oaToAIiKj0fl2+tNPP40jR45gxIgRmDBhAhYtWgSFQgFbW1tER0fj+eefN0ScRHpVWCgWcQCwtgZmzpQ2HiKimtC5iC9YsAA3btwAALz55pvIysrCl19+CZlMhjFjxmBF+RUkiEzUV18B2dni9qhRgIeHtPEQEdWEzkXcw8MDrVq1AgBYW1tj1apVWLVqld4DIzKktWvLtmfPli4OIqLa0Okz8YKCAtSvX1+rNb+JTFVGBnD0qLjdqRPAOYCIyFzpVMTt7Ozg7OyMBg0aGCoeIoMr/SwcAGbM4GNlRGS+dB6dPmzYMOzatcsQsRAZ3P37wJdfitsNGwIch0lE5kznz8THjRuHKVOm4MUXX8TIkSPh7u5eYXUwX19fvQVIpE/btgG5ueL2hAmAg4O08RAR1YbORXzQoEEAxJnUtmzZovFe6XKfKpVKP9ER6ZEglK1WBgAvvyxdLERE+qBzEd+0aVO163ITmarUVODXX8Vtf3+gc2dp4yEiqi2di/ikSZMMEAaR4ZUf0MarcCKqC3Qe2Na/f3/8/vvvlb73xx9/oD+XgSITdOuWOMELADz2GPDcc9LGQ0SkDzoX8aSkJOTk5FT63v3793VawYzIWL74QpxqFQAmTwbq15c2HiIifdC5iFdHoVDAnqtIkIkRBGDTprL9adOki4WISJ+0+kw8Li4OcXFx6v2lS5eiSZMmGm0ePHiApKQkdO3aVb8REtVSenrZgLbAQKBdO2njISLSF62K+G+//Yavv/4aACCTyXDgwAFYWWlexMvlcvj4+CAqKkr/URLVwsaNZdsvvihdHERE+qZVEQ8PD0d4eDgAwMrKCgcPHsRTTz1l0MCI9CE/H9i+Xdy2twfGjJE2HiIifdL5EbOSkhJDxEFkELt2AaXjMMeM4QxtRFS36HVgG5GpKT+gbcoU6eIgIjIEra7EW7VqhV27dqFz587w8vKqdsY2mUyGS5cu6S1Aopq6cgU4cEDcbtMG6NlT2niIiPRNqyLep08fODo6qrc57SqZg+josu0XX+SSo0RU92hVxDdv3qzeji7/LyORiVKpgNJfWysr4IUXpI2HiMgQdPpM/MGDB+jZsyf279+v1yDWrl0LLy8v2NnZwc/PD4cOHaqy7aRJkyCTySq8OnTooG4THR1daZuCggK9xk2m6+BB4No1cTskBGjWTNp4iIgMQaciXr9+ffz666+oV0/nQe1V2rlzJ+bOnYsFCxbg5MmT6NWrF0JCQpCZmVlp+6ioKCgUCvXr2rVraNy4MZ57aDJsR0dHjXYKhQJ2dnZ6i5tM27ZtZdtcs4eI6iqdR6cHBATgl19+0VsAH3/8MaZMmYKpU6eiffv2iIyMhIeHB9aVX/i5HCcnJ7i5ualfaWlpuHPnDiZPnqzRTiaTabRzc3PTW8xk2vLzgdhYcdvJCRg6VNp4iIgMRedL6o8++gjDhw+Hm5sbRo4ciYYNG9b4ixcVFSE9PR3z58/XOB4cHIwjR45o1cfGjRsxcOBAtGzZUuN4bm4uWrZsCZVKhS5dumDp0qXVTglbWFiIwtIVMgD1Ii9KpRJKpVLblCpVen5t+zFHUuQeGytDbq74qz1qVAmsrVWQ4lvPnztztzTMXT+569KHTBAEQZfOHRwcUFRUhOLiYgCAvb29xmh1mUyGe/fuadXXjRs30Lx5c/z8888IDAxUH3/vvfewZcsWnD9/vtrzFQoFPDw8sH37dowpNxXX0aNHcfHiRfj4+CAnJwdRUVGIj4/HqVOn0KZNm0r7Wrx4MSIiIioc3759Oxd1MTNLl/ZAerp45+Xddw+jQ4dbEkdERKS9/Px8jB8/Hvfu3VM/GVYVna/ER40apfdHzB7uTxAErb5GdHQ0GjVqhBEjRmgc9/f3h7+/v3q/Z8+e8PX1xSeffIJVq1ZV2ld4eDjCwsLU+zk5OfDw8EBwcPAjv4mPolQqkZiYiKCgINjY2NSqL3Nj7Nyzs4GMDPHX2tNTwP/+1wNWEk1pxJ87c2fulkOfuVe13HdldC7i+nzEzMXFBdbW1sjKytI4np2dDVdX12rPFQQBmzZtQmhoKGxtbatta2Vlhe7du+PChQtVtpHL5ZDL5RWO29jY6O2XUZ99mRtj5R4bKz5eBgATJsggl0v//ebPnblbGuZeu9x1OV/SaVdtbW3h5+eHxMREjeOJiYkat9crk5ycjIsXL2KKFnNpCoKAjIwMuLu71ypeMn3lR6U//7x0cRARGUONiviff/6Jl156CU8++SScnZ3x5JNP4qWXXsKVK1d07issLAyff/45Nm3ahHPnzmHevHnIzMzEjBkzAIi3uV+oZKaOjRs3okePHujYsWOF9yIiIrBv3z5cvnwZGRkZmDJlCjIyMtR9Ut10/jxw/Li43bUr4O0tbTxERIam8+30jIwM9OvXD/n5+QgMDISfnx+ysrIQHR2NnTt3IikpCV26dNG6v7Fjx+LWrVtYsmQJFAoFOnbsiPj4ePVoc4VCUeGZ8Xv37iE2NrbKtcvv3r2L6dOnIysrC05OTujatStSUlK4fGodV/4qPDRUujiIiIxF5yI+d+5cNGnSBPv374enp6f6+NWrVxEUFIR58+bh4MGDOvU5c+ZMzJw5s9L3KvsM3snJCfn5+VX2t3LlSqxcuVKnGMi8CUJZEbeyAsaNkzYeIiJj0Pl2+i+//IKIiAiNAg4ALVu2xOLFi3Hs2DG9BUekraNHgT//FLcHDgQ4/IGILIHORdzJyQlOTk6VvteoUaNaP45FVBM7d5Zt//e/0sVBRGRMOhfx8ePH4/PPP6/0vc8++wz/5b+gZGQlJcDXX4vbtrbAQ9MGEBHVWVp9Jv7tt9+qt/38/PDNN9/gqaeewn//+1+4ubkhKysLMTExyM7OrrAQCZGhHT4M3Lghbg8aBDRqJGk4RERGo1URHz16NGQyGcrP0Hrt2jWkpaVVaBsaGorx48frL0KiR/jqq7LtsWOli4OIyNi0KuK6jjYnMhaVCvjmG3FbLgeefVbaeIiIjEmrIt6nTx8A4qpjSUlJaNeuXYXR6URSSE4G/v5b3B48GHBwkDYeIiJj0mlgW7169TB06NBq5yAnMqbyo9J5K52ILI1ORdzKygotWrTQaYUVIkMpLhYXPAGA+vWBoUOljYeIyNh0fsRsypQpWLNmDVSlS0URSeTAAeDWv0uFDx0KNGggbTxERMam87Srtra2OH/+PNq3b49nn30W7u7uGmt/y2QyzJs3T69BElWGt9KJyNLpXMTffPNN9fbHH39c4X0WcTKGoiJg1y5xu0EDcVAbEZGl0bmI12S5USJ9S0oC7twRt4cNEz8TJyKyNDoX8dIlQqvyzz//1DgYIm2Vm0QQo0ZJFwcRkZR0HthWGUEQEB8fj1GjRqFFixb66JKoSioVsHu3uG1nBzzzjKThEBFJRucr8fIuXbqETZs2YcuWLVAoFLC1tcUoXhaRgR09WjbBy6BBQMOG0sZDRCQVnYt4QUEBvv76a2zcuBGHDh2CIAiQyWQICwvD/Pnz4ezsbIg4idRKB7QBwH/+I10cRERS0/p2+vHjxzFjxgy4ublh0qRJOHHiBCZNmoTvvvsOgiBg2LBhLOBkcIJQ9nm4tbU4qI2IyFJpdSXeqVMnnD17FgAQEBCAF198EWPHjkWDBg1w7949gwZIVN7p00DpAxJ9+wKNG0saDhGRpLQq4mfOnIFMJsOQIUPw/vvvw9vb29BxEVWq/Kj0kSOli4OIyBRodTs9MjISnTp1wnfffQcfHx8EBATg888/x/379w0dH5GG8p+HDx8uXRxERKZAqyI+e/ZsnDx5Er/88gumT5+O33//HdOnT4e7uzumT58OmUymMfUqkSFcvAj8+qu47e8PNG8ubTxERFLT6Tnxbt26Yd26dVAoFNiyZQu6deuGb775BoIgYMqUKfjoo49wq3RFCiI9K38VzlvpREQ1nOzFzs4OoaGhSEpKwh9//IH58+cjPz8fr7/+Ojw8PPQdIxEAzc/D+WgZEZEeZmxr3bo13nvvPWRmZmLPnj14pgbTZ61duxZeXl6ws7ODn58fDh06VGXbpKQk9e378q/ff/9do11sbCy8vb0hl8vh7e2NXeUv48js/P03cOyYuN2xI/DEE9LGQ0RkCvQy7SoAWFlZYejQofi2/OWSFnbu3Im5c+diwYIFOHnyJHr16oWQkBBkZmZWe9758+ehUCjUrzZt2qjfS01NxdixYxEaGopTp04hNDQUY8aMwbHSKkBm5/vvxWfEAeDZZ6WNhYjIVOitiNfUxx9/jClTpmDq1Klo3749IiMj4eHhgXXr1lV7XtOmTeHm5qZ+WVtbq9+LjIxEUFAQwsPD0a5dO4SHh2PAgAGIjIw0cDZkKN99V7bNCV6IiES1mju9toqKipCeno758+drHA8ODsaRI0eqPbdr164oKCiAt7c3Fi5ciH79+qnfS01NrbCm+aBBg6ot4oWFhSgsLFTv5+TkAACUSiWUSqW2KVWq9Pza9mOO9JF7QQGQkFAPgAxNmgjo0qUY5vCt5M+duVsa5q6f3HXpQ9IifvPmTahUKri6umocd3V1RVZWVqXnuLu7Y8OGDfDz80NhYSG++OILDBgwAElJSejduzcAICsrS6c+AWDZsmWIiIiocDwhIQH29va6plapxMREvfRjjmqT+4kTTZGXFwAA8PG5hn37TuorLKPgz90yMXfLpI/c8/PztW4raREv9fAz5qWLqlSmbdu2aNu2rXo/ICAA165dw4oVK9RFXNc+ASA8PBxhYWHq/ZycHHh4eCA4OBiOjo465fMwpVKJxMREBAUFwcbGplZ9mRt95L5vX9mnPi+91AyDB7vrKzyD4s+duTN3y6HP3EvvBGtD0iLu4uICa2vrClfI2dnZFa6kq+Pv749t27ap993c3HTuUy6XQy6XVzhuY2Ojt19GffZlbmqauyCIg9oAwNYWCAmpB3P7FvLnztwtDXOvXe66nC/pwDZbW1v4+flVuP2QmJiIwMBArfs5efIk3N3Lrs4CAgIq9JmQkKBTn2Qafv0VKH1QoW9fwMFB0nCIiEyK5LfTw8LCEBoaim7duiEgIAAbNmxAZmYmZsyYAUC8zX39+nVs3boVgDjy/PHHH0eHDh1QVFSEbdu2ITY2FrGxseo+58yZg969e2P58uUYPnw44uLisH//fhw+fFiSHKnmOCqdiKhqkhfxsWPH4tatW1iyZAkUCgU6duyI+Ph4tGzZEgCgUCg0nhkvKirCa6+9huvXr6N+/fro0KEDvv/+ewwePFjdJjAwEDt27MDChQvx9ttvo3Xr1ti5cyd69Ohh9PyodvbuLdtmESci0iR5EQeAmTNnYubMmZW+Fx0drbH/xhtv4I033nhkn6NHj8bo0aP1ER5JJDu7bJY2Hx/g3//XERHRvySf7IWoKuVnaRs6VNpYiIhMEYs4mSx+Hk5EVD0WcTJJSiVQ+oCBiwvw1FPSxkNEZIpYxMkkpaYC9++L24MGAeWmxicion+xiJNJ+vHHsu0arG5LRGQRWMTJJJUv4sHB0sVBRGTKWMTJ5GRlASf/XePEzw9o2lTaeIiITBWLOJmcffvKtnkrnYioaiziZHLK30oPCZEuDiIiU8ciTiZFpQISEsRtJyeAM+USEVWNRZxMSloacPu2uB0UBNQziYmBiYhME4s4mZQffijb5ufhRETVYxEnk1L+8/BBg6SLg4jIHLCIk8m4dQv45Rdxu2NHoEULaeMhIjJ1LOJkMhITy1Yt4610IqJHYxEnk8Hnw4mIdMMiTiZBEID9+8Xt+vWBnj2ljYeIyBywiJNJ+OMP4K+/xO1evQA7O2njISIyByziZBJKr8IBYOBA6eIgIjInLOJkEljEiYh0xyJOkisuBg4eFLednYHOnaWNh4jIXLCIk+TS04F798TtAQMAK/5WEhFphf9ckuR4K52IqGZYxElyLOJERDVjEkV87dq18PLygp2dHfz8/HDo0KEq23777bcICgpCkyZN4OjoiICAAOwrP0sIgOjoaMhksgqvgoICQ6dCOsrLA44cEbdbtQK8vKSNh4jInEhexHfu3Im5c+diwYIFOHnyJHr16oWQkBBkZmZW2j4lJQVBQUGIj49Heno6+vXrh2HDhuHkyZMa7RwdHaFQKDRednz42OQcPgwUFYnbvAonItKN5Ks1f/zxx5gyZQqmTp0KAIiMjMS+ffuwbt06LFu2rEL7yMhIjf333nsPcXFx2Lt3L7p27ao+LpPJ4ObmpnUchYWFKCwsVO/n5OQAAJRKJZRKpS4pVVB6fm37MUePyj0hwQqANQCgT59iKJWCsUIzOP7cmbulYe76yV2XPiQt4kVFRUhPT8f8+fM1jgcHB+NI6T3WRygpKcH9+/fRuHFjjeO5ublo2bIlVCoVunTpgqVLl2oU+YctW7YMERERFY4nJCTA3t5eq1geJTExUS/9mKOqct+9uw+ARgAAlSoR8fFFxgvKSPhzt0zM3TLpI/f8/Hyt20paxG/evAmVSgVXV1eN466ursjKytKqj48++gh5eXkYM2aM+li7du0QHR0NHx8f5OTkICoqCj179sSpU6fQpk2bSvsJDw9HWFiYej8nJwceHh4IDg6Go6NjDbIro1QqkZiYiKCgINjY2NSqL3NTXe43bwKXL4vHunQRMG5c3bqfzp87c2fulkOfuZfeCdaG5LfTAfHWd3mCIFQ4VpmYmBgsXrwYcXFxaNq0qfq4v78//P391fs9e/aEr68vPvnkE6xatarSvuRyOeRyeYXjNjY2evtl1Gdf5qay3MuPXwwKktXZ7w1/7szd0jD32uWuy/mSFnEXFxdYW1tXuOrOzs6ucHX+sJ07d2LKlCn4+uuvMfARI6KsrKzQvXt3XLhwodYxk/6UztIGiJO8EBGRbiQdnW5raws/P78KnyEkJiYiMDCwyvNiYmIwadIkbN++HUOGDHnk1xEEARkZGXB3d691zKQ/SUnin/XqcelRIqKakPx2elhYGEJDQ9GtWzcEBARgw4YNyMzMxIwZMwCIn1Vfv34dW7duBSAW8BdeeAFRUVHw9/dXX8XXr18fTk5OAICIiAj4+/ujTZs2yMnJwapVq5CRkYE1a9ZIkyRVkJUF/P67uN29O9CwobTxEBGZI8mL+NixY3Hr1i0sWbIECoUCHTt2RHx8PFq2bAkAUCgUGs+Mf/rppyguLsasWbMwa9Ys9fGJEyciOjoaAHD37l1Mnz4dWVlZcHJyQteuXZGSkoKnnnrKqLlR1ZKTy7b79pUsDCIisyZ5EQeAmTNnYubMmZW+V1qYSyWV3oOtxsqVK7Fy5Uo9REaGUv7HyCJORFQzks/YRpap/Ofh1Qx/ICKiarCIk9Hx83AiIv1gESej4+fhRET6wSJORsfPw4mI9INFnIyOn4cTEekHizgZFT8PJyLSHxZxMip+Hk5EpD8s4mRU5T8P79NHsjCIiOoEFnEyqtIrcWtrzpdORFRbLOJkNH//DZw7J27z83AiotpjESejSUkp2+atdCKi2mMRJ6M5fLhsm0WciKj2WMTJaA4dEv+UyYCAAGljISKqC1jEyShycoBTp8RtHx+gUSNJwyEiqhNYxMkojh2ToaRE3H76aWljISKqK1jEySh+/lmm3mYRJyLSDxZxMoojR8qKeK9eEgZCRFSHsIiTwRUXy3DsmFjEW7YEWrSQOCAiojqCRZwM7vJlJzx4IBZx3konItIfFnEyuHPnnNXbLOJERPrDIk4Gd+5cY/U2izgRkf6wiJNBCULZlXijRoC3t7TxEBHVJSziZFAXLgD37skBiKuWWfE3johIb0zin9S1a9fCy8sLdnZ28PPzw6HS+TmrkJycDD8/P9jZ2aFVq1ZYv359hTaxsbHw9vaGXC6Ht7c3du3aZajwqRrlHy3jrXQiIv2SvIjv3LkTc+fOxYIFC3Dy5En06tULISEhyMzMrLT9lStXMHjwYPTq1QsnT57EW2+9hdmzZyM2NlbdJjU1FWPHjkVoaChOnTqF0NBQjBkzBseOHTNWWvSvn38u+xXj8+FERPpVT+oAPv74Y0yZMgVTp04FAERGRmLfvn1Yt24dli1bVqH9+vXr4enpicjISABA+/btkZaWhhUrVmDUqFHqPoKCghAeHg4ACA8PR3JyMiIjIxETE2OcxP6VnQ3s3GmFM2ceR2amFaytjfrlJffTT+KVuFwuoFs32SNaExGRLiQt4kVFRUhPT8f8+fM1jgcHB+PIkSOVnpOamorg4GCNY4MGDcLGjRuhVCphY2OD1NRUzJs3r0Kb0sJfmcLCQhQWFqr3c3JyAABKpRJKpVKXtDRcvizD7Nn1AHSucR/mTSzcfn4lsLIqQS2+lWan9PemNr8/5oq5M3dLo8/cdelD0iJ+8+ZNqFQquLq6ahx3dXVFVlZWpedkZWVV2r64uBg3b96Eu7t7lW2q6hMAli1bhoiIiArHExISYG9vr21KFVy82AgAF8/29v4N8fGXpQ5DEomJiVKHIBnmbpmYe+3k5+dr3Vby2+kAIJNp3mYVBKHCsUe1f/i4rn2Gh4cjLCxMvZ+TkwMPDw8EBwfD0dHx0UlU4eZNwNGxEGfPnkWHDh1gbWH301UqFRSKdMyb1wV2du2kDseolEolEhMTERQUBBsbG6nDMSrmztyZe82V3gnWhqRF3MXFBdbW1hWukLOzsytcSZdyc3OrtH29evXg7OxcbZuq+gQAuVwOuVxe4biNjU2tfiDu7sCkSUrEx1/D4ME+sLExif83GY1SKSA+/h/Y2dXu+2jOavs7ZM6YO3O3NPrIXZfzJR2dbmtrCz8/vwq3HxITExEYGFjpOQEBARXaJyQkoFu3burEq2pTVZ9ERETmSPLLwrCwMISGhqJbt24ICAjAhg0bkJmZiRkzZgAQb3Nfv34dW7duBQDMmDEDq1evRlhYGKZNm4bU1FRs3LhRY9T5nDlz0Lt3byxfvhzDhw9HXFwc9u/fj8OHD0uSIxERkSFIXsTHjh2LW7duYcmSJVAoFOjYsSPi4+PRsmVLAIBCodB4ZtzLywvx8fGYN28e1qxZg2bNmmHVqlXqx8sAIDAwEDt27MDChQvx9ttvo3Xr1ti5cyd69Ohh9PyIiIgMRfIiDgAzZ87EzJkzK30vOjq6wrE+ffrgxIkT1fY5evRojB49Wh/hERERmSTJZ2wjIiKimmERJyIiMlMs4kRERGaKRZyIiMhMsYgTERGZKRZxIiIiM2USj5iZotL52HWZw7YqSqUS+fn5yMnJsbipCJk7c2fuloO56yf30rpTWoeqwyJehfv37wMAPDw8JI6EiIgs0f379+Hk5FRtG5mgTam3QCUlJbhx4wYcHByqXf1MG6Urol27dq1WK6KZI+bO3Jm75WDu+sldEATcv38fzZo1g5VV9Z9680q8ClZWVmjRooVe+3R0dLS4X+xSzJ25Wxrmztxr41FX4KU4sI2IiMhMsYgTERGZKRZxI5DL5Vi0aBHkcrnUoRgdc2fuloa5M3dj4sA2IiIiM8UrcSIiIjPFIk5ERGSmWMSJiIjMFIs4ERGRmWIRN7J3330XgYGBsLe3R6NGjaQOx+DWrl0LLy8v2NnZwc/PD4cOHZI6JINLSUnBsGHD0KxZM8hkMuzevVvqkIxm2bJl6N69OxwcHNC0aVOMGDEC58+flzoso1i3bh06deqknuwjICAAP/zwg9RhSWLZsmWQyWSYO3eu1KEY3OLFiyGTyTRebm5uRvv6LOJGVlRUhOeeew4vv/yy1KEY3M6dOzF37lwsWLAAJ0+eRK9evRASEoLMzEypQzOovLw8dO7cGatXr5Y6FKNLTk7GrFmzcPToUSQmJqK4uBjBwcHIy8uTOjSDa9GiBd5//32kpaUhLS0N/fv3x/Dhw3H27FmpQzOq48ePY8OGDejUqZPUoRhNhw4doFAo1K9ff/3VeF9cIEls3rxZcHJykjoMg3rqqaeEGTNmaBxr166dMH/+fIkiMj4Awq5du6QOQzLZ2dkCACE5OVnqUCTx2GOPCZ9//rnUYRjN/fv3hTZt2giJiYlCnz59hDlz5kgdksEtWrRI6Ny5s2Rfn1fiZBBFRUVIT09HcHCwxvHg4GAcOXJEoqjI2O7duwcAaNy4scSRGJdKpcKOHTuQl5eHgIAAqcMxmlmzZmHIkCEYOHCg1KEY1YULF9CsWTN4eXlh3LhxuHz5stG+NhdAIYO4efMmVCoVXF1dNY67uroiKytLoqjImARBQFhYGJ5++ml07NhR6nCM4tdff0VAQAAKCgrQsGFD7Nq1C97e3lKHZRQ7duzAiRMncPz4calDMaoePXpg69atePLJJ/H333/jnXfeQWBgIM6ePQtnZ2eDf31eietBZQMbHn6lpaVJHaYkHl7GVRCEWi/tSubhlVdewenTpxETEyN1KEbTtm1bZGRk4OjRo3j55ZcxceJE/Pbbb1KHZXDXrl3DnDlzsG3bNtjZ2UkdjlGFhIRg1KhR8PHxwcCBA/H9998DALZs2WKUr88rcT145ZVXMG7cuGrbPP7448YJxkS4uLjA2tq6wlV3dnZ2hatzqnteffVV7NmzBykpKXpf0teU2dra4oknngAAdOvWDcePH0dUVBQ+/fRTiSMzrPT0dGRnZ8PPz099TKVSISUlBatXr0ZhYSGsra0ljNB4GjRoAB8fH1y4cMEoX49FXA9cXFzg4uIidRgmxdbWFn5+fkhMTMR//vMf9fHExEQMHz5cwsjIkARBwKuvvopdu3YhKSkJXl5eUockKUEQUFhYKHUYBjdgwIAKI7InT56Mdu3a4c0337SYAg4AhYWFOHfuHHr16mWUr8cibmSZmZm4ffs2MjMzoVKpkJGRAQB44okn0LBhQ2mD07OwsDCEhoaiW7duCAgIwIYNG5CZmYkZM2ZIHZpB5ebm4uLFi+r9K1euICMjA40bN4anp6eEkRnerFmzsH37dsTFxcHBwUF9J8bJyQn169eXODrDeuuttxASEgIPDw/cv38fO3bsQFJSEn788UepQzM4BweHCuMeGjRoAGdn5zo/HuK1117DsGHD4OnpiezsbLzzzjvIycnBxIkTjROAZOPiLdTEiRMFABVeBw8elDo0g1izZo3QsmVLwdbWVvD19bWIR40OHjxY6c944sSJUodmcJXlDUDYvHmz1KEZ3Isvvqj+XW/SpIkwYMAAISEhQeqwJGMpj5iNHTtWcHd3F2xsbIRmzZoJI0eOFM6ePWu0r8+lSImIiMwUR6cTERGZKRZxIiIiM8UiTkREZKZYxImIiMwUizgREZGZYhEnIiIyUyziREREZopFnIiIyEyxiBPVMY9aUa/0lZSUhEmTJpnk4jyHDh2CXC7H1atXtT7nzp07aNSoEXbv3m24wIhMDGdsI6pjjh49qrG/dOlSHDx4EAcOHNA47u3tjX/++Qc5OTno2rWrMUOsliAI6vn2V69erdO5ERER2LZtG86ePQtbW1sDRUhkOljEieq4SZMm4ZtvvkFubq7UoWjlhx9+wODBg/H777+jbdu2Op37999/o0WLFtiyZQvGjx9voAiJTAdvpxNZsMpup8tkMrzyyivYvHkz2rZti/r166Nbt244evQoBEHAhx9+CC8vLzRs2BD9+/fXWLGt1P79+zFgwAA4OjrC3t4ePXv2xE8//aRVTOvWrUP37t0rFPADBw6gb9++cHZ2Rv369eHp6YlRo0YhPz9f3cbV1RVBQUFYv3697t8MIjPEIk5EFXz33Xf4/PPP8f777yMmJgb379/HkCFD8L///Q8///wzVq9ejQ0bNuC3337DqFGjUP6G3rZt2xAcHAxHR0ds2bIFX331FRo3boxBgwY9spAXFRVh//796Nevn8bxP//8E0OGDIGtrS02bdqEH3/8Ee+//z4aNGiAoqIijbZ9+/bFzz//jLt37+rt+0FkqrieOBFVUFhYiISEBDRo0ACAeHU+YsQIHDx4ECdOnIBMJgMA/PPPP5g7dy7OnDkDHx8f5OfnY86cORg6dCh27dql7m/w4MHw9fXFW2+9hWPHjlX5dTMyMvDgwQP4+vpqHE9PT0dBQQE+/PBDdO7cWX28slvmvr6+KCkpwdGjR/HMM8/U6vtAZOp4JU5EFfTr109dwAGgffv2AICQkBB1AS9/vHQU+ZEjR3D79m1MnDgRxcXF6ldJSQmeeeYZHD9+HHl5eVV+3Rs3bgAAmjZtqnG8S5cusLW1xfTp07FlyxZcvny5yj5Kz71+/bouKROZJRZxIqqgcePGGvulI72rOl5QUABAHFgGAKNHj4aNjY3Ga/ny5RAEAbdv367y6z548AAAYGdnp3G8devW2L9/P5o2bYpZs2ahdevWaN26NaKioir0UXpuaV9EdRlvpxOR3ri4uAAAPvnkE/j7+1faxtXV9ZHnV1boe/XqhV69ekGlUiEtLQ2ffPIJ5s6dC1dXV4wbN07drvTc0r6I6jIWcSLSm549e6JRo0b47bff8Morr+h8funt+UuXLlXZxtraGj169EC7du3w5Zdf4sSJExpFvPRWu7e3t85fn8jcsIgTkd40bNgQn3zyCSZOnIjbt29j9OjRaNq0Kf755x+cOnUK//zzD9atW1fl+S1atECrVq1w9OhRzJ49W318/fr1OHDgAIYMGQJPT08UFBRg06ZNAICBAwdq9HH06FE4OzvDx8fHMEkSmRAWcSLSq+effx6enp744IMP8NJLL+H+/fto2rQpunTpgkmTJj3y/AkTJmD16tUoLCyEXC4HIA5sS0hIwKJFi5CVlYWGDRuiY8eO2LNnD4KDg9XnCoKAPXv2YPz48RoD8IjqKs7YRkQm5caNG/Dy8sLWrVsxduxYnc796aefEBwcjLNnz6Jdu3YGipDIdLCIE5HJefPNN/HDDz8gIyMDVlbaP0TTr18/PPHEE/jss88MGB2R6eDtdCIyOQsXLoS9vT2uX78ODw8Prc65c+cO+vTpg5kzZxo4OiLTwStxIiIiM8XJXoiIiMwUizgREZGZYhEnIiIyUyziREREZopFnIiIyEyxiBMREZkpFnEiIiIzxSJORERkpv4fMv2NcDHg/s8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "axis_color = 'lightgoldenrodyellow'\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(1,1,1)\n",
    "fig.subplots_adjust(left=0.25, bottom=0.25)\n",
    "time = np.arange(-1, 5, 0.001)\n",
    "[line] = ax.plot(time, f1(time), linewidth=2, color='blue')\n",
    "ax.set_xlabel('Time (s)',fontsize=12)\n",
    "ax.set_ylabel('Arbritrary units',fontsize=12) \n",
    "plt.title('$f_1(t)$, Plot C')\n",
    "ax.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "54f9bdb3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(1,1,1)\n",
    "fig.subplots_adjust(left=0.25, bottom=0.25)\n",
    "[line] = ax.plot(time, f2(time), linewidth=2, color='blue')\n",
    "ax.set_xlabel('Time (s)',fontsize=12)\n",
    "ax.set_ylabel('Arbritrary units',fontsize=12) \n",
    "plt.title('$f_2(t)$, Plot B')\n",
    "ax.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "d0493944",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(1,1,1)\n",
    "fig.subplots_adjust(left=0.25, bottom=0.25)\n",
    "[line] = ax.plot(time, f3(time), linewidth=2, color='blue')\n",
    "ax.set_xlabel('Time (s)',fontsize=12)\n",
    "ax.set_ylabel('Arbritrary units',fontsize=12) \n",
    "plt.title('$f_3(t)$ Plot D')\n",
    "ax.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "bdbe1bbb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(1,1,1)\n",
    "fig.subplots_adjust(left=0.25, bottom=0.25)\n",
    "time = np.arange(-1, 5, 0.001)\n",
    "[line] = ax.plot(time, f4(time), linewidth=2, color='blue')\n",
    "ax.set_xlabel('Time (s)',fontsize=12)\n",
    "ax.set_ylabel('Arbritrary units',fontsize=12) \n",
    "plt.title('$f_4(t)$, Plot A')\n",
    "ax.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1a483bd8",
   "metadata": {},
   "source": [
    "# Q4 Create Bode plot for\n",
    "$H(s)=100\\times \\frac{s^2}{(a+10)(s+1000)}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "d32b0e5e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1200x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "Z=[0,0]\n",
    "P=[10,1000]\n",
    "G=100\n",
    "SN=1\n",
    "SD=1\n",
    "wbreak=[]\n",
    "w_type=[]\n",
    "equation=' '\n",
    "phase=' '\n",
    "for i in Z:\n",
    "    wbreak.append(i)\n",
    "    w_type.append(\"Z\")\n",
    "    if i==0:\n",
    "        equation=equation+\"+20*t\"\n",
    "        phase=phase+\"+90\"\n",
    "    if i!=0:\n",
    "        equation=equation+\"+20*r(t-1*{})\".format(np.log10(i))\n",
    "        phase=phase+\"+45*r(t-1*{})\".format(np.log10(i)-1)\n",
    "        phase=phase+\"-45*r(t-1*{})\".format(np.log10(i)+1)\n",
    "    if i!=0:\n",
    "        SN=SN*i\n",
    "for i in P:\n",
    "    wbreak.append(i)\n",
    "    w_type.append(\"P\")\n",
    "    if i==0:\n",
    "        equation=equation+\"-20*t\"\n",
    "        phase=phase+\"-90\"\n",
    "    if i!=0:\n",
    "        equation=equation+\"-20*r(t-1*{})\".format(np.log10(i))\n",
    "        phase=phase+\"-45*r(t-1*{})\".format(np.log10(i)-1)\n",
    "        phase=phase+\"+45*r(t-1*{})\".format(np.log10(i)+1)\n",
    "    if i!=0:\n",
    "        SD=SD*i\n",
    "\n",
    "ratio=20*np.log10(SN/SD*G)\n",
    "equation=equation+\"+{}\".format(ratio)\n",
    "\n",
    "w_mag=[]\n",
    "w_phase=[]\n",
    "flag=1\n",
    "\n",
    "\n",
    "for i in range(0,len(wbreak)):\n",
    "\n",
    "    if wbreak[i]==0:\n",
    "        w_mag.append(.1)\n",
    "        w_mag.append(1)\n",
    "        w_mag.append(10)\n",
    "    if wbreak[i]!=0:\n",
    "        w_mag.append(wbreak[i])\n",
    "        w_mag.append(wbreak[i]/100.)\n",
    "        w_mag.append(wbreak[i]/10.)\n",
    "        w_mag.append(wbreak[i]/1000.)\n",
    "        w_mag.append(wbreak[i]*10.)\n",
    "        w_mag.append(wbreak[i]*100.)\n",
    "        w_mag.append(wbreak[i]*1000.)\n",
    "            \n",
    "mag=[]\n",
    "pha=[]\n",
    "\n",
    "w_mag=np.unique(np.log10(w_mag))\n",
    "\n",
    "\n",
    "for i in w_mag:\n",
    "\n",
    " \n",
    "    temp=equation.replace(\"t\",str(i))\n",
    "    temp2=phase.replace(\"t\",str(i))\n",
    "    mag.append(eval(temp))\n",
    "    pha.append(eval(temp2))\n",
    "\n",
    " \n",
    "fig, (ax,ax1) = plt.subplots(1,2,figsize=(12,5))  \n",
    "fig.subplots_adjust(left=0.25, bottom=0.25)        \n",
    "[line] = ax.semilogx(10**w_mag,mag, linewidth=1, color='black')\n",
    "[line] = ax1.semilogx(10**w_mag,pha, linewidth=1, color='black')           \n",
    "ax.set_xticks(10**w_mag)\n",
    "ax1.set_xticks(10**w_mag)\n",
    "ytick=np.arange(min(pha),max(pha)+45,45)\n",
    " \n",
    "ax1.set_yticks(ytick)\n",
    "ax.set_xlabel('$\\omega$(r/s)',fontsize=12)\n",
    "ax.set_ylabel('Magnitude (dB)', color='b', fontsize=12) \n",
    "ax1.set_ylabel('Phase($^o$)', color='b', fontsize=12 ) \n",
    "ax1.set_xlabel('$\\omega$[r/s]',fontsize=12)\n",
    "ax.grid()\n",
    "ax1.grid()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aff50f30",
   "metadata": {},
   "source": [
    "# Q5 Derive the transfer function of the following circuit:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "0e79ce89",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import schemdraw as schemdraw\n",
    "import schemdraw.elements as elm\n",
    "with schemdraw.Drawing() as d:\n",
    "    d += (op := elm.Opamp(leads=True,fill='red'))\n",
    "    d += elm.Line().down(d.unit/4).at(op.in2)\n",
    "    d += elm.Ground(lead=False)\n",
    "    d += (Rin := elm.Resistor().at(op.in1).left().idot().label('$R_{1}$', loc='bot').label('$v_{in}$', loc='left'))\n",
    "    d += elm.Line().up(d.unit/2).at(op.in1)\n",
    "    d += elm.Capacitor().tox(op.out).label('$C_1$')\n",
    "    d += elm.Line().toy(op.out).dot()\n",
    "    d += elm.Line().right(d.unit/10).at(op.out)\n",
    "    d += (R2 := elm.Resistor().right().label('$R_{2}$', loc='bot'))\n",
    "    d += (op2 := elm.Opamp(leads=True,fill='red').anchor('in1'))\n",
    "    d += elm.Line().down(d.unit/4).at(op2.in2)\n",
    "    d += elm.Ground(lead=False)\n",
    "    d += elm.Line().up(d.unit/2).at(op2.in1).idot()\n",
    "    d += elm.Capacitor().tox(op2.out).label('$C_2$')\n",
    "    d += elm.Line().toy(op2.out).dot()\n",
    "\n",
    "    d += elm.Line().right(1).at(op2.out).label('$v_{out}$', loc='rgt')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fcebc494",
   "metadata": {},
   "source": [
    "Assuming and ideal OPAMP, $H_1(s)=-\\frac{1}{ s R_1 C_1}$ and $H_2(s)=-\\frac{1}{ s R_2 C_2}$ \n",
    "\n",
    "$H(s)=\\frac{V_{OUT}(s)}{V_{IN}(s)}=H_1(s) \\times H_2(s)=\\frac{1}{s^2}$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "beb12815",
   "metadata": {},
   "source": [
    "# Q6 \n",
    "Assume the OPAMP below has the transfer function of:\n",
    "$H_{opamp}(s)=\\frac{10^6}{s}$\n",
    "Mathematically derive the maximum frequency for which the circuit will behave ideally.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "702130e2",
   "metadata": {},
   "outputs": [
    {
     "data": {
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      ],
      "text/plain": [
       "<schemdraw.backends.mpl.Figure object at 0x0000020F63506350>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with schemdraw.Drawing() as d:\n",
    "    d += (op := elm.Opamp(leads=True,fill='red'))\n",
    "    d += (out := elm.Line(at=op.out).length(.75))\n",
    "    d += elm.Line().up().at(op.in1).length(1.5).dot()\n",
    "    d.push()\n",
    "    d += elm.Resistor().left().label('$R_1=10k \\Omega$')\n",
    "    d += elm.Ground()\n",
    "    d.pop()\n",
    "    d += elm.Resistor().tox(op.out).label('$R_f=90k \\Omega$')\n",
    "    d += elm.Line().toy(op.out).dot()\n",
    "    d += elm.Line().right(1).at(op.out).label('$v_{out}$', loc='rgt')\n",
    "    d += elm.Line().left(1).at(op.in2).label('$v_{in}$', loc='lft')\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "73923d98",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "image/svg+xml": [
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       " <metadata>\n",
       "  <rdf:RDF xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n",
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      ],
      "text/plain": [
       "<schemdraw.backends.mpl.Figure object at 0x0000020F667B72E0>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from schemdraw import dsp \n",
    "d = schemdraw.Drawing()\n",
    "a1=d.add(dsp.Arrow(l=d.unit/2).label('+', loc='right',ofst=(-.6, .2)).label('$In$', loc='left'))\n",
    "sm = d.add(dsp.SumSigma())\n",
    "a2=d.add(dsp.Arrow(l=d.unit/2))\n",
    "delay1 = d.add(dsp.Box(w=2, h=1, label='$H_{OPAMP}(s)$', anchor='W'))\n",
    "a3=d.add(dsp.Arrow('right', l=d.unit/2, xy=delay1.E,label='Out'))\n",
    "#a4=d.add(dsp.Arrow(xy=sm.S, theta=-90,l=d.unit/2,reverse=True).label('-', loc='right',ofst=(.6, .2)))\n",
    "d.add(dsp.Dot(xy=a3.center))\n",
    "l1=d.add(dsp.Line('down', xy=a3.center, l=.5*d.unit))\n",
    "l2=d.add(dsp.Arrow('left', l=.5*d.unit))\n",
    "g2 = d.add(dsp.Box(w=1.1, h=1, label='$\\\\beta$', anchor='E'))\n",
    "l3=d.add(dsp.Line('left', tox=sm.S, xy=g2.W))\n",
    "l4=d.add(dsp.Arrow('up', toy=sm.S,label='-'))\n",
    "d.draw() \n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "9758394c",
   "metadata": {},
   "outputs": [],
   "source": [
    "R1, R2,Avol,B,Av=symbols(\"R1, R2, Avol,B,Av\", real=True, positive=True)\n",
    "s, Out, In=symbols(\"s, Out, In\" )\n",
    "H=Avol/s\n",
    "Q=solve(Out-H*In+Out*B*H  ,Out)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fe20c056",
   "metadata": {},
   "source": [
    "Let $$H_{OPAMP}(s)=\\frac{A_{vol}}{s}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "565b2a1c",
   "metadata": {},
   "outputs": [],
   "source": [
    "H=Avol/s"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7ae46ce2",
   "metadata": {},
   "source": [
    "Put into terms the solver can understand (set expresion to zero)\n",
    "$$ Out-In\\times H_{OPAMP}(s)+Out \\times \\beta \\times H_{OPAMP}(s)=0$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a4c4eb03",
   "metadata": {},
   "source": [
    "Use the solver to find Out in terms on In"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "10fb6198",
   "metadata": {},
   "outputs": [],
   "source": [
    "Q=solve(Out-H*In+Out*B*H  ,Out)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "0292da81",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{Avol In}{Avol B + s}$"
      ],
      "text/plain": [
       "Avol*In/(Avol*B + s)"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a8f9e452",
   "metadata": {},
   "source": [
    "$\\beta=\\frac{R_1}{R_1+R_f}=\\frac{10k}{10k+90k}=0.1$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d5a8c0e9",
   "metadata": {},
   "source": [
    "$A_{vol}=10^6$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4b5a0cc0",
   "metadata": {},
   "source": [
    "$s=j\\omega$\n",
    "\n",
    "$|j\\omega|=\\omega$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e25c4c57",
   "metadata": {},
   "source": [
    "$|j\\omega|<<|A_{vol}\\beta|$\n",
    "\n",
    "$\\omega<<A_{vol}\\beta$\n",
    "\n",
    "$\\omega<<10^5$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "63a93b67",
   "metadata": {},
   "source": [
    "If this is true then the gain of the OPAMP will be $1+\\frac{R_f}{R_1}$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bded7a7a",
   "metadata": {},
   "source": [
    "# Q7 \n",
    "Design a filter with the following specifications: The cutoff frequency of a low-pass filter needs to be 200Hz with a non-inverting DC gain of 10 (20dB).  The attenuation slope needs to be -20dB/dec.  Minimize the number of OPAMPS used.\n",
    "$H(s)=\\frac{2 \\pi 1000 }{s+2\\pi 1000}$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "296f1990",
   "metadata": {},
   "source": [
    "Given the specification (20dB slope) we will need  a first order low pass filter with a non-inverting gain stage. Assuming an ideal OPAMP circuit $Gain=1+\\frac{R_f}{R_{in}}$  One has to assume a value  for one resistor and solve for the other.  One good pair  for a gain of 10 is $R_f=90k\\Omega$ and $R_{in}=10k\\Omega$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a6bd585d",
   "metadata": {},
   "source": [
    "To design the cutoff frequency use $\\frac{1}{R_{filter}C_{filter}}=2\\pi1000$  Assume a value for the capacitor and solve for the resistance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "62a560ac",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "15915.494309189535"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Cfilter=100e-9\n",
    "wo=2*np.pi*100\n",
    "Rfilter=1/wo/Cfilter\n",
    "Rfilter"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1f106f1c",
   "metadata": {},
   "source": [
    "set $R_{filter}=16k\\Omega$ .  The circuit can be seen below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "c4770510",
   "metadata": {},
   "outputs": [
    {
     "data": {
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with schemdraw.Drawing() as d:\n",
    "\n",
    "    d += (op := elm.Opamp(leads=True).fill('blue'))\n",
    "    d += (out := elm.Line(at=op.out).length(.75))\n",
    "    d += elm.Line().up().at(op.in1).length(1.5).dot()\n",
    "    d.push()\n",
    "    d += elm.Resistor().left().label('$R_{in}$')\n",
    "    d += elm.Ground()\n",
    "    d.pop()\n",
    "    d += elm.Resistor().tox(op.out).label('$R_f$')\n",
    "    d += elm.Line().toy(op.out).dot()\n",
    "    d += elm.Resistor().left().at(op.in2).idot().label('$R_{filter}$')\n",
    "    d += elm.SourceV().down().reverse().label('$v_{in}$')\n",
    "    d += elm.Line().right().dot()\n",
    "    d += elm.Capacitor().up().label('$C_{filter}$').hold()\n",
    "    d += elm.Line().tox(out.end)\n",
    "    d += elm.Gap().toy(op.out).label(['–','$v_o$','+'])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a4855f63",
   "metadata": {},
   "source": [
    "# Q8   \n",
    "$H(s)=\\frac{100}{s^2+100}$\n",
    "We can see that the pole is at $\\pm 10j$, which is not on the left hand plane, so it it is out of control.  We can see the step response of the system oscillates by taking the inverse Laplace transform of  the transfer function $H(s)$.\n",
    "$$L^{-}\\left(\\frac{100}{s^2+100}\\right)=sin(10t)u(t)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a4ab2c48",
   "metadata": {},
   "source": [
    "To make a new system that takes the system described by H(s), make a system with an summer, a feedback transfer function, G(s), and the original H(s) function that the system has a block diagram that results in:\n",
    "$$\n",
    "Q(s)=\\frac{H(s)}{1+G(s)\\times  H(s)}\n",
    "$$\n",
    "Where $Q(s)$ is the transfer function of the complete system. The figure below is the block diagram of a simple control system that will create Q(s)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "6f265dc4",
   "metadata": {},
   "outputs": [
    {
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     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import schemdraw as schem\n",
    "import schemdraw.elements as e\n",
    "from schemdraw import dsp \n",
    "d = schem.Drawing()\n",
    "a1=d.add(dsp.Arrow(l=d.unit/2).label('+', loc='right',ofst=(-.6, .2)).label('$In$', loc='left'))\n",
    "sm = d.add(dsp.SumSigma())\n",
    "a2=d.add(dsp.Arrow(l=d.unit/2))\n",
    "delay1 = d.add(dsp.Box(w=2, h=1, label='$H(s)$', anchor='W'))\n",
    "a3=d.add(dsp.Arrow('right', l=d.unit/2, xy=delay1.E,label='Out'))\n",
    "#a4=d.add(dsp.Arrow(xy=sm.S, theta=-90,l=d.unit/2,reverse=True).label('-', loc='right',ofst=(.6, .2)))\n",
    "d.add(dsp.Dot(xy=a3.center))\n",
    "l1=d.add(dsp.Line('down', xy=a3.center, l=.5*d.unit))\n",
    "l2=d.add(dsp.Arrow('left', l=.5*d.unit))\n",
    "g2 = d.add(dsp.Box(w=1.1, h=1, label='$G(s)$', anchor='E'))\n",
    "l3=d.add(dsp.Line('left', tox=sm.S, xy=g2.W))\n",
    "l4=d.add(dsp.Arrow('up', toy=sm.S,label='-'))\n",
    "d.draw()\n"
   ]
  },
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   "metadata": {},
   "source": [
    "Now that we have the block diagram for the new system, Q(s), we need to design G(s) to ensure all the poles are int he the LHP.  It can be help to break up H(s) into the numerator and denominator.\n",
    "$$H(s)=\\frac{N(s)}{D(s)}$$\n",
    "In this example $N(s)=1$, and $D(s)=s-1$.\n",
    "Substitute N(s) and D(s) into Q(s)\n",
    "$$Q(s)=\\frac{H(s)}{1+G(s)H(s)}=\\frac{N(s)}{D(s)}\\times\\frac{1}{1+G(s)\\times\\frac{N(s)}{D(s)}}=\\frac{N(s)}{D(s)+G(s)\\times N(s)}$$\n",
    "\n",
    "If we look at the above equation we see the numerator of Q(s) is the same as the numerator as H(s), and the original D(s) of H(s) is in Q(s)'s denominator.  What has changed is that the new denominator has a new term summed to the original D(s): G(s)N(s) now to make sure all the poles of Q(s) are int he LHP, we just have to choose a G(s) that makes roots of $D(s)+G(s)N(s)$ all on the LHP."
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    "In this example: \n",
    "$$Q(s)=\\frac{1}{s^2+100+G(s)\\times 1}$$\n",
    "What $G(s)\\times 1$ will turn the real part of the poles at $\\pm10j$, negative?\n",
    "In this case we need proportional feedback times derivative, so $G(s)=sK$.\n",
    "The pole becomes:\n",
    "The new Q(s) becomes:\n",
    "$$Q(s)=\\frac{100}{s+100+Ks\\times 10}=\\frac{100}{s+10Ks+100}$$  if K>0, then the system will be in control.\n",
    "\n",
    "**How did I determine we needed Ks control?**\n",
    "If we look at the quadratic equation for D(s) of the original transfer function:\n",
    "$$Roots_{1,2}(Poles)=\\frac{-b\\pm \\sqrt{b^2-4ac}}{2}$$\n",
    "\n",
    "a=1, b=0, c= 100\n",
    "$$Roots_{1,2}(Poles)=\\frac{0\\pm \\sqrt{0-400}}{2}=\\pm 10j$$\n",
    "\n",
    "To have the poles haver a negative real part, we need b to be a positive, real number.\n",
    "\n",
    "$$Q(s)=\\frac{100}{s^2+100+G(s)\\times 100}=\\frac{1}{s^2+bs+100}$$\n",
    "where $bs=G(s)\\times 100$  Solve for G(s):\n",
    "\n",
    "$$G(s)=\\frac{bs}{100}$$  repalce K for b to put the expression into control format.\n",
    "\n",
    "$$G(s)=\\frac{Ks}{100}$$ \n",
    "\n",
    "Now:\n",
    "\n",
    "$$Q(s)=\\frac{100}{s^2+\\frac{K}{100}s+100}$$\n",
    "\n",
    "Substitute back into the quadratic equation:\n",
    "\n",
    "a=1, b=$\\frac{K}{100}$, c= 100\n",
    "$$Roots_{1,2}(Poles)=\\frac{-\\frac{K}{100}\\pm \\sqrt{\\left( \\frac{K}{100}\\right)^2-400}}{2}$$\n",
    "If K>0  then $\\sqrt{\\left(\\frac{K}{100}\\right)^2-400}$ will always be less than $\\frac{K}{100}$ and the roots can never be greater than or equal to zero so the system will be in control.  That being said the closer K is to zero, the greater the ration between the imaginary part of the pole will be to the real part of the pole and the system will be more underdamped. (more oscillations)\n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "ab600fc0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$10 \\sin{\\left(10 t \\right)} u\\left(t\\right)$$"
      ],
      "text/plain": [
       "10⋅sin(10⋅t)⋅u(t)"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from lcapy import s, j, pi, f, transfer, j2pif,t,exp\n",
    "from sympy import *\n",
    "K= symbols(\"K\", positive=True)\n",
    "import numpy as np\n",
    "from matplotlib.pyplot import savefig\n",
    "H=transfer(100/(s**2+100)).simplify()\n",
    "hi=H(t)\n",
    "hi\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "ac019471",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$100 \\cdot \\left(\\frac{1}{100} - \\frac{\\cos{\\left(10 t \\right)}}{100}\\right) u\\left(t\\right)$$"
      ],
      "text/plain": [
       "    ⎛ 1    cos(10⋅t)⎞     \n",
       "100⋅⎜─── - ─────────⎟⋅u(t)\n",
       "    ⎝100      100   ⎠     "
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "FF=1/s*H\n",
    "ff=FF(t)\n",
    "ff"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "c5f3c203",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\frac{100}{10 K s + s^{2} + 100}$$"
      ],
      "text/plain": [
       "       100       \n",
       "─────────────────\n",
       "          2      \n",
       "10⋅K⋅s + s  + 100"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "G=s/10*K\n",
    " \n",
    "Q=H/(1+G*H).normal()\n",
    "Q"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "5dad3789",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\frac{100}{s^{2} + 200 s + 100}$$"
      ],
      "text/plain": [
       "      100       \n",
       "────────────────\n",
       " 2              \n",
       "s  + 200⋅s + 100"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q=Q.subs(K,20)\n",
    "Q"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "05bf505f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='Re(s)', ylabel='Im(s)'>"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "22ede2b3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\left\\{ -100 - 30 \\sqrt{11} : 1, \\  -100 + 30 \\sqrt{11} : 1\\right\\}$$"
      ],
      "text/plain": [
       "{-100 - 30⋅√11: 1, -100 + 30⋅√11: 1}"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q.poles()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3da29ead",
   "metadata": {},
   "source": [
    "We can see the  poles are now on the LHP."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "fee7af3d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(<Axes: xlabel='$\\\\omega (r/s)$', ylabel='Magnitude(dB)'>,\n",
       " <Axes: xlabel='$\\\\omega (r/s)$', ylabel='Transfer function phase (radians)'>)"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "A = Q.subs(j * f)\n",
    "fv = np.logspace(-1, 3, 400)\n",
    "A.plot(fv, log_frequency=True,ylabel=\"Magnitude(dB)\",xlabel='$\\omega (r/s)$')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f034f93e",
   "metadata": {},
   "source": [
    "# Q9\n",
    "This was too hard to recreate in a notebook.  The bode plot is that of a second order low-pass filter because the phase changes by $180^o$ and the slope is 40dB/dec.  Looking at the frequency at which the phase is $-90^o$ or finding the intercept of the low frequency gain and the high frequency slope, $\\omega_0=10^4 r/s$.  THe low frequency  Gain is 20dB or 10.  THe magnitude of  the cutoff frequency is around 17dB or $10^{17/20}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "4d2c438c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle 7.07945784384138$"
      ],
      "text/plain": [
       "7.079457843841379"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Gain_LF=10\n",
    "wo=10^4\n",
    "Gain_wo=10**(17/20)\n",
    "Gain_wo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "64e5ed39",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle 0.706268772311377$"
      ],
      "text/plain": [
       "0.7062687723113772"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "zeta=Gain_LF/Gain_wo/2\n",
    "zeta"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3b802ab6",
   "metadata": {},
   "source": [
    "$H(s)=\\frac{(10^4)^2}{s^2+2\\times .706 \\times 10^4 \\times s+(10^4)^2}$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "68797473",
   "metadata": {},
   "source": [
    "# Q10\n",
    "Shown below are four signals.  Which signals could be turned into a DC power with the application of a filter? (No half-wave rectifiers, full-wave rectifiers, or multipliers.)\n",
    "\n",
    "What kind of filter do you need to convert the signal?\n",
    "\n",
    "Which signal would provide the most DC power after filtering?\n",
    "\n",
    "Explain in as much detail as possible making sure to use the Fourier expansion in your answer. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "bac095d2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from scipy import signal\n",
    "import numpy as np\n",
    "\n",
    "def u(t):\n",
    "    return 0.5 * (np.sign(t) + 1)\n",
    "def r(t):\n",
    "    return t*u(t)\n",
    "\n",
    "# Simulation time=3s due to delay +15 due to 5tau\n",
    "t=np.linspace(-.1,10,1000)\n",
    "\n",
    "major_ticks = np.arange(0, 11, 1)\n",
    "major_ticksy = np.arange(-2,2,.5)\n",
    "fig, (ax1, ax2, ax3, ax4) = plt.subplots(4, 1, sharex=True)\n",
    "ax1.plot(t,.5*(signal.sawtooth(2 * np.pi * 1 * t,width=0)+1))\n",
    "ax1.set_xticks(major_ticks)\n",
    "ax1.grid()\n",
    "ax1.set_yticks(major_ticksy) \n",
    "ax2.set_xticks(major_ticks)\n",
    "ax2.set_yticks(major_ticksy)\n",
    "ax3.set_xticks(major_ticks)\n",
    "ax3.set_yticks(major_ticksy)\n",
    "ax4.set_xticks(major_ticks)\n",
    "ax4.set_yticks(major_ticksy)\n",
    "ax2.grid()\n",
    "ax3.grid()\n",
    "ax4.grid()\n",
    "ax4.set_xlabel(\"Time (ms)\")\n",
    "ax1.set_ylabel(\"Signal A (V)\")\n",
    "ax2.set_ylabel(\"Signal B (V)\")\n",
    "ax3.set_ylabel(\"Signal C (V)\")\n",
    "ax4.set_ylabel(\"Signal D (V)\")\n",
    "ax2.plot(t,.5*(signal.square(2 * np.pi * 1 * t)))\n",
    "ax3.plot(t,np.sin(2 * np.pi * 1 * t)**3)\n",
    "ax4.plot(t,1+.25*(signal.sawtooth(2 * np.pi * 1 * t,width=0)+1))\n",
    "fig.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a00d91c7",
   "metadata": {},
   "source": [
    "The average of signal A is non-zero by inspection, so it can be converted with a low pass filter into a DC power supply.  The average of a signal is the first term of the Fourier expansion and is given by $a_0=\\frac{1}{T}\\int_0^T x(t)dt=\\int_0^T(-t+1)dt$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "b96a7dbf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{1}{2}$"
      ],
      "text/plain": [
       "1/2"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t=symbols(\"t\", real=True)\n",
    "a0_A=integrate(-t + 1, (t,0,1))\n",
    "a0_A"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cb5411b0",
   "metadata": {},
   "source": [
    "We can see that The average is one half and so this can be filtered with a low pass filter into a DC signal."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b5e6fb06",
   "metadata": {},
   "source": [
    "The average of signal B is zero by inspection, so it cannot be converted with a low pass filter into a DC power supply.  The average of a signal is the first term of the Fourier expansion and is given by $a_0=\\frac{1}{T}\\int_0^T x(t)dt=\\int_0^{1/2}0.5dt-\\int_{1/2}^1 0.5dt$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "d225860a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAoAAAAOCAYAAAAWo42rAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAz0lEQVQoFXWS4Q2CMBCFhQkIbqAjqBvgBsoGOkf/GUbQFXQENjAyAhtA2AC/V3tGG2hyeXdfH71LSzKO48KWc64KeYeuiQrWiiVmBLyoL+hDG2iGiO3J2zTAM5qZKbAB1UdX1d6IHolGIFpP6kKnm7EA9JFJpZ8PLdIwy4TnD+U6MQ9IM82tb+s5g/GlTpyazQzWrdOM1lL3Fi9jn3tktyZWsYvaTqzteu7A7YRxA2vU1RtJboAePZiZXG1L4iT2+9ba0E8xEPopdoTe3r/YGx/SQ0OZAIYmAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$\\displaystyle 0$"
      ],
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a0_B=integrate(.5, (t,0,.5))-integrate(.5, (t,.5,1))\n",
    "a0_B"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "66880352",
   "metadata": {},
   "source": [
    "We can see that the average is zero and so this cannot be filtered with a low pass filter into a DC signal."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f69b9360",
   "metadata": {},
   "source": [
    "The average of signal C is zero by inspection, so it cannot be converted with a low pass filter into a DC power supply.  The average of a signal is the first term of the Fourier expansion and is given by $a_0=\\frac{1}{T}\\int_0^T x(t)dt=\\int_0^1 sin(2 \\pi t)^3dt$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "034f3080",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAoAAAAOCAYAAAAWo42rAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAz0lEQVQoFXWS4Q2CMBCFhQkIbqAjqBvgBsoGOkf/GUbQFXQENjAyAhtA2AC/V3tGG2hyeXdfH71LSzKO48KWc64KeYeuiQrWiiVmBLyoL+hDG2iGiO3J2zTAM5qZKbAB1UdX1d6IHolGIFpP6kKnm7EA9JFJpZ8PLdIwy4TnD+U6MQ9IM82tb+s5g/GlTpyazQzWrdOM1lL3Fi9jn3tktyZWsYvaTqzteu7A7YRxA2vU1RtJboAePZiZXG1L4iT2+9ba0E8xEPopdoTe3r/YGx/SQ0OZAIYmAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$\\displaystyle 0$"
      ],
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a0_C=integrate(sin(2*np.pi*t)**3, (t,0,1)) \n",
    "a0_C"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "571c8e4a",
   "metadata": {},
   "source": [
    "We can see that the average is zero and so this cannot be filtered with a low pass filter into a DC signal."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c1a5bbd5",
   "metadata": {},
   "source": [
    "The average of signal D is non-zero by inspection, so it can be converted with a low pass filter into a DC power supply.  The average of a signal is the first term of the Fourier expansion and is given by $a_0=\\frac{1}{T}\\int_0^T x(t)dt=\\int_0^1(-.5t+1)dt$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "592ee6b9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAACMAAAAPCAYAAABut3YUAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAB1klEQVRIDb2V0VECQQyGT4cCTuzg6AC0A+xAW9AO9BHeHO0A7EDpQCwBOoAS1A7w+3Zub/ZuTgad08yEZP+EJJvN7mW73S77L55MJsNmLrAcLsR7WULT6XTI8gUeoX8mpr0qvgUOd6XTGfLdNfi6xKJ4A8tZRFxdGvnTK41P6AYwkIEPprKQGfIi/gn9AX0lBi8jjjSH5Ka38AK+xyds3GJUruAM/Rah40/IxDfpH4hjV67B7PJJYluDh1wJVqnHlfZ7ZcxfNySJLY+R7EgOfnCnuyjGpFuShlbHShLZLDIx1dXaANdNh632tD0cN/Y4rCEga4/PAk9hu+bMBJ8uOkO8OhHcQkwUb1h0sIhn7I+wNtlB96izPymGuA7uwqQmicTa21UdJ7o3ymOe6dN5MSQwsDP07a0xcUIWVOBfdFoMAZ2HPrJ6c2JSsFd4FdctMu+sGBJdkmCArDqCHnZcJvZBbbtZfe34rjsphkAO7DmyObAWGF/dOfaBiRvk8IZXunm1vW6S1VaDJkAgd/UB+4qGb0mJF0gHdgkeBlG8pDFYHGI/GXL1WqP74kuhm0d+LQENJlmlSb33DpbnPEcGQt+gmDQNKGZBbdRWeOyeG7ZrfjrCxr8A25kMLVAsxr4AAAAASUVORK5CYII=\n",
      "text/latex": [
       "$\\displaystyle 1.25$"
      ],
      "text/plain": [
       "1.25000000000000"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a0_D=integrate(-.5*t + 1.5, (t,0,1))\n",
    "a0_D"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "291dc885",
   "metadata": {},
   "source": [
    "Given that signal D has the largest $a_0$, it would make the best source to create a DC signal."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "30827416",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n",
      "FFT A\n",
      "1\n",
      "FFT B\n",
      "2\n",
      "FFT C\n",
      "3\n",
      "FFT D\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1600x800 with 8 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.fftpack import fft\n",
    "from scipy import signal\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "#Amplitude of the square wave\n",
    "A=1.0\n",
    "#Freqeuncy in Hz of square wave\n",
    "F=1\n",
    "# Numeber of times the square wave is sampled\n",
    "N = 2**8\n",
    " \n",
    "#Number of periods to simulate\n",
    "NC=10.  #Make sure to include the ., this makes NC a floating point number.\n",
    " \n",
    "# Simulation time\n",
    "T=NC/F\n",
    "dT=T/N\n",
    "#Create X-axis data\n",
    "t = np.linspace(-.001, T, N,endpoint=False)\n",
    "#Create sin wave data\n",
    " \n",
    "#y=A*signal.square(2*np.pi*F*x,duty=D)+1\n",
    "y=[0,0,0,0]\n",
    "\n",
    "y[0]=.5*(signal.sawtooth(2 * np.pi * 1 * t,width=0)+1) \n",
    "y[1]= .5*(signal.square(2 * np.pi * 1 * t))\n",
    "y[2]= np.sin(2 * np.pi * 1 * t)**3\n",
    "y[3]=1+.25*(signal.sawtooth(2 * np.pi * 1 * t,width=0)+1) \n",
    "#Create  fake data so that an axis appears at 0\n",
    "x2 = np.linspace(0.0, T, 2)\n",
    "y2=x2*0\n",
    "# Plot sin wave with a closed circle\n",
    "fig, ((ax, ax1, ax2, ax3),(ax4, ax5, ax6, ax7)) = plt.subplots(2,4,figsize=(16,8))\n",
    "\n",
    "plotlist=[ax, ax1, ax2, ax3]\n",
    "plotlist2=[ax4, ax5, ax6, ax7]\n",
    "k=0\n",
    "for plot in y:\n",
    "    plotlist[k].plot(t, t*0,color='black')\n",
    "    plotlist[k].plot(t, plot)\n",
    "    plotlist[k].set_title('signal {}'.format(k+1))\n",
    "    plotlist[k].set_ylabel('V',fontsize=12)\n",
    "    plotlist[k].set_xlabel('Time (ms)',fontsize=12)\n",
    "    plotlist[k].grid()\n",
    "    k=k+1\n",
    "k=0\n",
    "AA=[\"A\",\"B\",\"C\",\"D\"]\n",
    "for plot in y:\n",
    "    print(k)\n",
    "    print('FFT {}'.format(AA[k]))  \n",
    "    yf = fft(plot)\n",
    "    xf = np.linspace(0.0, 1.0/(2.0*dT), int(N/2))\n",
    "    yf[0]=yf[0]/2.\n",
    "    plotlist2[k].plot(xf, xf*0, lw=2)\n",
    "    plotlist2[k].plot(xf, 2.0/N * np.abs(yf[0:int(N/2)]), 'o', lw=2) \n",
    "    plotlist2[k].vlines(xf, [0], 2.0/N * np.abs(yf[0:int(N/2)]), lw=2)\n",
    "    plotlist2[k].set_xlim(-.5,12)\n",
    "    plotlist2[k].grid()\n",
    "    plotlist2[k].set_title('FFT {}'.format(AA[k]))\n",
    "    plotlist2[k].set_xlabel('Frequency (kHz)',fontsize=12)\n",
    "    plotlist2[k].set_ylabel('Amplitude(V)',fontsize=12)\n",
    "    k=k+1\n",
    "plt.tight_layout(pad=0.5, w_pad=.5, h_pad=1.0)  \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "455f8050",
   "metadata": {},
   "source": [
    "Looking at the figure above we see that the fundamental frequency for all signals is 1kHz, and the first term in the FFT ($a_0$) is 0.5,0,0,ans 1.25 for signals 1,2,3, and 4 (FFT A, B,C, and D).  We want to pass everything near zero and block everything with a non-zero frequency.  Only a low-pass filer can do this without the sue of a rectifier."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "10fb3372",
   "metadata": {},
   "source": [
    "[It was too hard to complete the explanation in the notebook so here is a video.](https://www.youtube.com/watch?v=Awq-Lk34ezc&feature=youtu.be)\n",
    "\n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "10366f4a",
   "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": "3.10.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}