PWM_SineTriangle_Offset.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/bingsen-wang/PowerElectronics/blob/main/PWM_SineTriangle_Offset.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jAMKoELNpsK-"
      },
      "source": [
        "<center><h1><b>Pulse Width Modulation - Sine Triangle with Offset</h1></b>\n",
        "\n",
        "Dr. Bingsen Wang\n",
        "\n",
        "11/23/2023\n",
        "</center>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Hv0YxDrWU4h8"
      },
      "source": [
        "#Python Code\n",
        "The Python code illustrates the basic PWM.  "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "id": "XeGsHYTt8IXU",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 905
        },
        "outputId": "5247b43d-191c-4a88-8fd4-ad5d804355cd"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 900x900 with 2 Axes>"
            ],
            "image/png": 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XZbfmac6lqA8++OA8yx5++OHp0KFDLrvssha1Med/xPfr16/RMvO6129hWWGFFbLRRhslqe5aOnXq1CbL1m38szSr+16a+k6S1vlett122/rXo0ePbrLcwvhOWvL3vvPOO6dDhw65++67i9sFoPUJl8BSoW5GaF5ef/31+v9Y3m233RZ1l5r0pS99qX4X18svv7zJnWvfeeedXHfddenSpUv22muvFrUx51LbpoL3Y4891qI6F9T/+3//L0nywQcf5Kabbmq0zCOPPLLIZnGXJHXfyz/+8Y8ml5y2xvey6aab1u8S++c//7nJQHvdddcVt3XkkUfWP/f1N7/5TZPlXnjhhdx9991ZddVVs/322xe3C0DrEy6BpcLIkSNz8sknNxnU3nrrrey3336ZPXt2VlpppfqHui8OyyyzTH7zm9+kpqYmTz/9dL797W/PtUx36tSp2X///fP+++/n1FNPbfGGPl/84hfrN3o57bTTGmwilCTvvfdeTjjhhLIP0kxHHnlk/aM8vvOd78y1NHLy5Mk56qijlugNfRaWuudGTpw4MT/4wQ/mOj9ixIhcffXVrdKXn/3sZ2nXrl0mTpyYE044Ya6/wZEjR+bWW28tbqdv3775yU9+kiS5/fbb84tf/GKuMu+880722WefVCqVnHvuuR+LvwWApZH/9QbatF69eqVr166ZNm1azj777Fx33XXZc889s84666RLly6ZOHFiRo8enZtuuinvv/9+1lxzzdxwww1zPRKh7j/oX3755STVXT3r3tt5553Tp0+f+t/Hjx9ff7z66qvTrVu3+pnFm266KZMnT56rTJIceOCB9e3tueeeufrqq3P44YfnvPPOy4gRI/KFL3whPXr0yEsvvZSrrroq//znP/O1r31tgYLwRhttlLPOOivf/va38/TTT2fdddfNYYcdlv79++fVV1/NsGHDGmwsNGbMmFx99dXp06dPdt5557z88st58MEHM2HChPoyDz30UDp06JBBgwZl0KBBGT9+fIYPH95omTXXXDNbb711kqRTp07585//nB133DGvvPJKNt5443zlK1/JwIED88Ybb+Tyyy/PgAEDss8+++Taa69tMPY77bRTVl555RZ//iQZPnx4xo8f36B/L7/8cn3dQ4cObXSn3nl99uTDv4c51Y1FUv3b+Whbdd/9d7/73YwYMSKPPPJIzjjjjIwaNSqf/exns8wyy+TRRx/N1VdfnbXXXrt+tvmmm25Kz549s80222TgwIH1n2nMmDH1bX/08zz00EN56aWXGi0zZ9+33XbbXHLJJTniiCNyySWX5Jlnnsm+++6brl275pFHHsn111+f66+/Prvsskuj4ztmzJiMGTOm0XGq+zuqc/TRR2fatGn5zne+k69//eu5+eabs/vuu6dr16554YUXMmzYsEyaNClnnXVW9t9//0bbA6ANqAC0cVOmTKncfPPNlW9+85uVHXfcsTJgwIDKsssuW2nXrl2lW7dulTXXXLOy9957V4YNG1aZNm1ao3UkafLn3nvvnWeZ/v3719fTv3//Jss15vXXX69885vfrGy44YaVbt26VTp16lTp169fZd99963cc889xWNz9913V/bcc89Kr169Kh06dKh07969stVWW1XOO++8yuTJk+fq4/bbb1+pVCqVyy+/vMnPcdppp1UqlUrl3nvvbbLMIYccMldf3nvvvcopp5xSWWeddSqdO3eudO/evbLFFltUzj///MrMmTMrhxxyyFz1DB8+fIE/+/bbbz/P7/WVV15p9Lp5ffY5/x7mNK+x+Oh3P3369Mp5551X+eQnP1lZdtllKx07dqysuuqqlaFDh1b++te/Ntr+5ZdfPt/PVPd5GhvHefX98ccfr+yzzz6V3r17Vzp16lTp27dv5YADDqiMGTOmMnv27PprzzzzzAbXnXbaaU22U/d39FHPPfdc5f/+7/8qn/jEJyrLLLNMpXPnzpWBAwdWDj300Mrjjz8+r68TgDagplJZjFsmAgBLrEmTJmWFFVZIkvzqV78qfjYsAEs391wCwMfQ5MmT89hjj2XmzJlNlnnxxRfrXw8aNKg1ugVAGyZcAsDH0BNPPJHNN988f/3rX5ssc+ONNyZJVltttWyxxRat1TUA2ijhEgA+xs4444xMmzZtrvcfffTR/OxnP0uSnHnmmenYsWNrdw2ANsZusQDwMVRTU5Ok+lzNddZZJwceeGDWWGONzJw5Mw899FD+8Ic/ZNasWTn99NNz6KGHLt7OAtAm2NAHAD6mHnzwwdx444156KGHMnbs2EycODHt27fPqquumu222y5HHXVUPvWpTy3ubgLQRgiXAAAAFHPPJQAAAMWESwAAAIoJlwAAABQTLgEAACgmXAIAAFBMuAQAAKCYcAkAAEAx4RIAAIBiwiUAAADFhEsAAACKCZcAAAAUEy4BAAAo9rEKl79/+veZNnPa4u7G0un3v0+mGVsAAPi4+liEy0qlkmNuPyY3Pn9junTossD1TJs5LZv8epM8Nf6phdi7Nq5SSY45JrnxxqTLgo9tpk1LNtkkecrYAgBAW/SxCJdH33Z0nnrrqVw19KrU1NQscD1dO3bNpZ+7NHtcu0ce+ecjC7GHbdjRR1cD4VVXJQVjm65dk0svTfbYI3nE2AIAQFuz1IfLXz36q/z+md/nmr2vSaf2nYrr23y1zXPOkHOy81U75+WJLy+EHrZhv/pVdTnsNdckncrHNptvnpxzTrLzzsnLH/OxBQCANmapDpcvTHghx/31uJz/2fOz6nKrNuuaidMm5vyHzs+zbz/bZJn9N9o/u629Ww740wGZVTtrYXW3bXnhheS445Lzz09Wbd7YZuLEavlnmx7b7L9/sttuyQEHJLM+pmMLAABtUE2lUqks7k4sKjsM2yHvTHsnTx75ZNrVNC9H73v9vrn+2etz8MYH54q9rmiy3OuTXs8nfvGJnLjNiTnjM2csrC63HTvskLzzTvLkk0m7Zv4bxb77Jtdfnxx8cHJF02Ob119PPvGJ5MQTkzM+hmMLAABt0FI7c3nb2Nsy4tUROWXbU5odLGsrtbnzpTuTJJuuvOk8y/br3i9HfvLI/PihH2f85PHF/W1TbrstGTEiOeWU5gfL2trkzurYZtN5j2369UuOPDL58Y+T8R+zsQUAgDZqqQ2XZ486Oz269sjQdYc2+5on//1kJn0wKUmyw4Ad5lv+qC2OyrSZ0/KjB360oN1sm84+O+nRIxna/LHNk08mk6pjmx12mH/5o46q7iD7o4/Z2AIAQBu1VIbLp996OqNeG5UvrvfFdO7QudnXjXh1RJJkxS4rZlCfQfMtv1aPtbJd/+3y68d/nXenv7ug3W1bnn46GTUq+eIXk87NH9uMqI5tVlwxGTT/sc1aayXbbZf8+tfJu+8uUFcBAIDWs1SGy2ufujZJsutau7bouvtfvT9Jsl3/7Zq9lHaPT+yRqTOn5tYXbm1ZJ9uqa6tjm11bNra5vzq22W675i+l3WOPZOrU5NaPydgCAEAbtlSGy5tfuDlJ85a21qlUKhn52sgWX1cXYP/43B+bfU2bdnN1bJu1tLVOpZKMHNny6+oC7B8/JmMLAABtWJvYLXb6rOm54okrct2z1+WFCS+kU/tO6dKhS76w3hdywjYnZIUuK9SXfWfqO+l1Xq+s3n31jPvGuCbrHD95fAZfPjgzZ89MkkyZOSUTpk5IkvTv3r++XLdO3fLEkU+kQ7sOjdZTW6nNcmcvl9pKbSZ9e9JCeZbmfP3zn8lhh1UfB9KnT3Lmmckuu1TPTZqU/PKX1V1ZJ01KZs5MPv3p5HvfS9Zfv1pm9uzk6quT3/42efvt5L33knXWSU4/vTqz2JR33kl69UpWXz0ZN67pcuPHJ4MHV9tOkilTkgnVsU3/D8c23bolTzyRdGh8bFNbmyy3XPU4adLCeZYmAACwSCzxM5cjXx2ZdX+xbs4edXa+vsXXM+4b4/LysS9n5GEjM3nG5Gw/bPvMrp1dX/7hNx5OJZVs1Gejedbbp1ufjP362Iz7xriM+8a4HL350UmSgSsOrH9v3DfG5emvPd1ksEySdjXtsnGfjTN91vR5PhtzoalUkn32Sb797WrAq6mpLh99+OHksceSz3wm6d69eo/jyy8nd99dXVa6+ebV50uOH18Nok89lfzud8lzzyVjx1bD22c+8+GOro15+OFq+xvNe2zTp0+1znHjqj9HV8c2Awd++N64cdX7N5sKlkl1+ezGGyfTp8/72ZgAAMBit0SHy6vHXJ2drtop7du1z8OHP5y91t2rPujdN+6+XPv0tRkzfkye+PcT9dc8P+H5JEm/5fu1qK26zXy2XX3bFvdzjRXXSJKMGT+mxde22G23VXdq3XHHarBcc83qDOEPfpD83/8lf/pTdafV5Zevlv/EJ6plp05NLrww2X335Igjqo/56Nu3WmaZZZIDDqjOEP74x023/Xx1bNOvZWNbv5nPti0f26xRHduMaYWxBQAAFtg8po0Wr9vG3paDbzw47du1zzV7X5OVu63c4PyRfzkyE6ZOSE1qstIyK9W//9LEl5Ikq3RbpdltzZg9Iw+/8XCSBQuXfZerhrRn3nqmxde22PXXJ/vt9+HvL1U/b+65J3nkkWTAgLmvWWaZ6vHii5Of/jTZd9+5y9Tt/Prqq023XdfWKs0f28yYUZ3xTBYsXNYF4GdaYWwBAIAFtkTOXP7r/X/l0JsOTSWVfH2Lr2ervlvNVebT/T6d5Tsvn+9t/70MWGFA/ftvT307SdK9S/dmt/foPx/NtFnTkiSDVx/c4v72WrZXktTfs7lI3XVX8tnPVl9PmZKMHl19feKJTS9Xffnl6nHrrZNjjmm8zD//WT326NF0229Xxzbdmz+2efTR6vMqk+p9mC3Vqzq29fdsAgAAS6QlcubypLtOyttT3077mvY5dstjGy1z0343Nfr+5BmTkyRdOnRpdnt1S2J7L9s76/Rcp2WdTdK1Q9ckyaQPJrX42haprU3OOuvDwDVqVDJrVvX14Yc3fs20aR8uKT300KYfA/Lgg9Xjhhs23f7k6timS/PHtn5JbO/e1U2DWqprdWwzaRGPLQAAUGSJm7l8a8pbufbpD59T2X+F/vO5oqG63V/ntQnPR9U933JBZi2TpGvHVgqX7dolBx/84e/33ls9DhzY9H2QDz5YXZqaNP0YkClTPly6utNOTbdft/vrvDbh+ai651suyKxlIlwCAEAbscSFy7+8+JfMqq3Oxu2y5i4tvn6ZjtX7C6fPmt6s8rNrZ+eB1x9IsmD3WyYLFmgXivvuqx4/85n5l1lttWTttRsvc+utyQcfVO+7rHu2ZGPq7t2c3ryxzezZyQPVsV2g+y2TBQu0AABAq2uVcPnUU0/l3rpZtvmVfeup+tfb9Z/HMxebsFzn5ZI0P1yO/tfo+qW0Cxou6+7X7Nap2wJdv0Defz95/PHq66ZmJJMPZzfnFUD/8IfqcZdd5n0/5XLVsW12uBw9+sOltAsaLuvu1+zWimMLAAC02CIPl5VKJUOGDMmuu+6aaXVBYR6mzJhS/3qNFdZocXt1jyB5e8rbzSpfd79lt07dssnKmzQ4N+q1Ubn875fPt473P3g/SdKza88W9LTQnPdbNhUcp06t7iA7rzLvvFN9vElSfRxJnb/9rfqsyjnVLb19u3ljW3+/ZbduySabNDw3alRy+fzHNu9XxzY9W3FsAQCAFlvk4fK2227L22+/nRkzZuTSSy+db/lVlqs+5qJju47N2vH1wdcfzFtT3qr/fc0V10ySvP7e683qX939llv33Trt27VvcO7Ue07N6t1Xn28db7z3RpJk4IoDm9XmQlE3I7nWWtUlr4154IEPl5U2FS5///vqPZnduyef//yH7x99dPLeew3Lrlkd27zevLGtv99y662T9g3HNqeemqw+/7HNG9WxzcBWHFsAAKDFFmm4rFQqOf3009O7d+/07t0755xzznxnL3ceuHOSZGbtzLw7/d15ln34jYez7/X7Nii38cobJ0leefeVZvVx7H+qs3MffdzJnS/dmWmzpmXIwCHzreON96sB6BMrfaLJMmfef2aWP3v5bD9s+/qZziLNud+yLoD275+s0cQs8A03VI9f+MKHu8A+91x1k59PfrJh2Y2rY5tXmje29TOfW33kUTJ33lld7jpk/mNbHy4/0fTYAgAAi98iDZe33XZbHnvssWyyySbp27dv3nrrrfnOXn569U9n+/7bJ0luev6mJstd9vfL8sXrvpjr9rmuQajbbJXNsmzHZfPkv59MbaV2vn3ss2yfJB8up02SidMm5pjbj8lle1423+uT5Knx1ftEG3seZ1J9buf37v1e3p/xfu5/9f78ZvRvmlVvk95778PnW87rfsvmBND//Kd6rHt2ZlKdVTzzzLnLbrZZsuyyyZNPVh+LMj99qmPbYCfbiROrz9q8rHljm6f+ew/uRwMqAACwRFlk4bJu1nLw4MFZZZVV0rVr1xx00EHNmr28eu+rs27PdXPi8BNz37j76t+fMHVChj0xLIMvG5zrn70+D3z5gWzTb5sG13Zo1yHb9d8uU2ZOyXNvPzfffn550y8nSZ6f8Hz9cddrds0p256SDXpvMN/rJ0ydkNffez1rrrhm+nTr02iZmpqaBr/f8dId8613nkaNqu7EmjQdLqdOTR59tPp6xx2brmvPPavHDz6o1nnOOdXj3nvPXbZDh2S77aqzms/Nf2zz5erY5vnnPzzuumtyyinJBvMf20yYUF2Cu+aaHwZVAABgibTIwuXIkSPz2GOP5fTTT68PV6ecckreeuutXHvttfO8tu/yffO3w/+Wo7c4OkfddlRW/cmqGfizgfns1Z/NmPFjcsGuF+T2A25v8hmY+26wb5Lk9n/cPt9+HrzxwfnF//wit7x4SwZcMCCH33J4ztrxrBy08UHN+pwjxlU3rRm67tAmy6zcbeV8/zPfz/Kdl8+QNYbktUmvNavuJq24YnXn1iOPTFZdtfEylUrSt2+y+ebJXns1Xdd3v5scf3xy0knV+zfffDOZ1/ezb3Vsc/v8xzYHH5z84hfJLbckAwYkhx+enHVWclDzxrZ+Q6ChTY8tAACwZKipVCqVRVHxm2++mVtvvTVf/epX8+Uvfzljx47NqFGjct1112XDDTfM+uuvvyiaTZJMmj4pq/501XxylU/m/sPuX2TtJMlhNx+WYU8My6NfeTSfWvVT8y3/n2n/yU5X7pTRR4xepP1aZCZNqgbaT37yww17FpXDDkuGDavOwH5q/mMLAAAsPots5nLVVVfNEUccMdeS0H333XeRBssk6d6lew7f9PCMem1UXnznxUXWzvRZ03PLC7fkU6t+qlnBMknGvTuuWTvQLrG6d6/OQI4alby46MY206dXZzw/9SnBEgAA2oBF/iiSxeWb23wznTt0zi8f+eUia+MPT/8h/5n2n5y4zYnNvuYvL/4lu6y5yyLrU6v45jeTzp2TXy66sc0f/lDdbOjE5o8tAACw+Cy14bJf9345efDJufjxi/Pqu68u9Ppn187OeQ+el81X3TxfWP8Lzbrmg1kf5Nqnr80X1mte+SVWv37JyScnF1+cvLrwxzazZyfnnVe9X/QLbXysAADgY2KpDZdJctLgk/KJlT6RE+48YaHXPeyJYXl+wvO5eI+L066mecP4owd+lKHrDm1yV9k25aSTqs+ePGHhj22GDavuLHvxxUm7pfpPFAAAlhpL9X+5d2rfKTfvd3PuG3dfhj0xbKHV+8Z7b+Rbw7+VH+74w2y6yqbNuuYvL/4lfx7755y63akLrR+LVadOyc03V5+lOWzYwqv3jTeSb30r+eEPk02bN7YAAMDit1SHyyRZY8U1csv+t+Tku0/Og68/WFzfzNkzc+CfDszn1vlcThp8UrOv69CuQ/6075/StWPX4j4sMdZYo7rpzsknJw+Wj21mzkwOPDD53OeqM6MAAECbsdSHyyTZpt82uePAO3Lkn4/MlBlTFrieSqWSQ28+NGv3WDuX7XlZi6797FqfzWrLr7bAbS+xttkmueOO6jM3pyz42KZSSQ49NFl77eSylo0tAACw+HVY3B1oLYP6DMqY/xtTVMe0WdOy65q75qCND1pIvVpKDBqUjCkb20ybluy6a3KQsQUAgLboYzFzubAs03EZwXJRWWYZwRIAANow4RIAAIBiwiUAAADFhEsAAACKCZcAAAAUEy4BAAAoJlwCAABQTLgEAACgmHAJAABAMeESAACAYsIlAAAAxYRLAAAAigmXAAAAFBMuAQAAKCZcAgAAUEy4BAAAoJhwCQAAQDHhEgAAgGLCJQAAAMWESwAAAIoJlwAAABQTLgEAACgmXAIAAFCswyKtvVJJ3n47mT49mTkzmTAh6dAh6dSp+tO+fVJTs0i7AAAAwKK3aMNlbW3Sp8+Hv/fq1fD8W2/N/R4AAABtzqJdFlupzPt8p06LtHkAAABax+K951K4BAAAWCoIlwAAABRbtPdctm9fva/ymGOSl19Obr45mTWrurnPjBnV8wAAALR5izZc1tRUN+zp0iXp2DFZeeVF2hwAAACLh+dcAgAAUEy4BAAAoJhwCQAAQDHhEgAAgGLCJQAAAMWESwAAAIoJlwAAABQTLgEAACgmXAIAAFBMuAQAAKCYcAkAAEAx4RIAAIBiwiUAAADFhEsAAACKCZcAAAAUEy4BAAAoJlwCAABQTLgEAACgmHAJAABAMeESAACAYsIlAAAAxYRLAAAAigmXAAAAFBMuAQAAKCZcAgAAUEy4BAAAoJhwCQAAQDHhEgAAgGLCJQAAAMWESwAAAIoJlwAAABQTLgEAACgmXAIAAFBMuAQAAKCYcAkAAEAx4RIAAIBiwiUAAADFhEsAAACKCZcAAAAUEy4BAAAoJlwCAABQTLgEAACgmHAJAABAMeESAACAYsIlAAAAxYRLAAAAigmXAAAAFBMuAQAAKCZcAgAAUEy4BAAAoJhwCQAAQDHhEgAAgGLCJQAAAMWESwAAAIoJlwAAABQTLgEAACgmXAIAAFBMuAQAAKCYcAkAAEAx4RIAAIBiwiUAAADFhEsAAACKCZcAAAAUEy4BAAAoJlwCAABQTLgEAACgmHAJAABAMeESAACAYsIlAAAAxYRLAAAAigmXAAAAFBMuAQAAKCZcAgAAUEy4BAAAoJhwCQAAQDHhEgAAgGLCJQAAAMWESwAAAIoJlwAAABQTLgEAACgmXAIAAFBMuAQAAKCYcAkAAEAx4RIAAIBiwiUAAADFhEsAAACKCZcAAAAUEy4BAAAoJlwCAABQTLgEAACgmHAJAABAMeESAACAYsIlAAAAxYRLAAAAigmXAAAAFBMuAQAAKCZcAgAAUEy4BAAAoJhwCQAAQDHhEgAAgGLCJQAAAMWESwAAAIoJlwAAABQTLgEAACgmXAIAAFBMuAQAAKCYcAkAAEAx4RIAAIBiwiUAAADFhEsAAACKCZcAAAAUEy4BAAAoJlwCAABQTLgEAACgmHAJAABAMeESAACAYsIlAAAAxYRLAAAAigmXAAAAFBMuAQAAKCZcAgAAUEy4BAAAoJhwCQAAQDHhEgAAgGLCJQAAAMWESwAAAIoJlwAAABQTLgEAACgmXAIAAFBMuAQAAKCYcAkAAEAx4RIAAIBiwiUAAADFhEsAAACKCZcAAAAUEy4BAAAoJlwCAABQTLgEAACgmHAJAABAMeESAACAYsIlAAAAxYRLAAAAigmXAAAAFBMuAQAAKCZcAgAAUEy4BAAAoJhwCQAAQDHhEgAAgGLCJQAAAMWESwAAAIoJlwAAABQTLgEAACgmXAIAAFBMuAQAAKCYcAkAAEAx4RIAAIBiwiUAAADFhEsAAACKCZcAAAAUEy4BAAAoJlwCAABQTLgEAACgmHAJAABAMeESAACAYsIlAAAAxYRLAAAAigmXAAAAFBMuAQAAKCZcAgAAUEy4BAAAoJhwCQAAQDHhEgAAgGLCJQAAAMWESwAAAIoJlwAAABQTLgEAACgmXAIAAFBMuAQAAKCYcAkAAEAx4RIAAIBiwiUAAADFhEsAAACKCZcAAAAUEy4BAAAoJlwCAABQTLgEAACgmHAJAABAMeESAACAYsIlAAAAxYRLAAAAigmXAAAAFBMuAQAAKCZcAgAAUEy4BAAAoJhwCQAAQDHhEgAAgGLCJQAAAMWESwAAAIoJlwAAABQTLgEAACgmXAIAAFBMuAQAAKCYcAkAAEAx4RIAAIBiwiUAAADFhEsAAACKCZcAAAAUEy4BAAAoJlwCAABQTLgEAACgmHAJAABAMeESAACAYsIlAAAAxYRLAAAAigmXAAAAFBMuAQAAKCZcAgAAUEy4BAAAoJhwCQAAQDHhEgAAgGLCJQAAAMWESwAAAIoJlwAAABQTLgEAACgmXAIAAFBMuAQAAKCYcAkAAEAx4RIAAIBiwiUAAADFhEsAAACKCZcAAAAUEy4BAAAoJlwCAABQTLgEAACgmHAJAABAMeESAACAYsIlAAAAxYRLAAAAigmXAAAAFBMuAQAAKCZcAgAAUEy4BAAAoJhwCQAAQDHhEgAAgGLCJQAAAMWESwAAAIoJlwAAABQTLgEAACgmXAIAAFBMuAQAAKCYcAkAAEAx4RIAAIBiwiUAAADFWj1cTp81vbWbBAAAYBFr1XD5wawPsswPl0nPH/XMu9Pfbc2mAQAAWIRaNVz+8/1/ppJKpsycku6du7dm0wAAACxCrRouX5/0epKk7/J9U1NT05pNAwAAsAi1arh84703kiT9lu/Xms0CAACwiLXuzOV7H85cAgAAsPRYLMtizVwCAAAsXcxcAgAAUGzx3HPZ3cwlAADA0sSGPgAAABRrtXBZW6nN21PfTmJZLAAAwNKm1cLljNkzkiRdO3RNj649WqtZAAAAWkGrhcsPZn+QpHq/ZU1NTWs1CwAAQCtovZnLWdWZS0tiAQAAlj6tP3NpMx8AAIClTquHSzOXAAAAS5/WC5ezhEsAAIClVavvFmtZLAAAwNJnsewWCwAAwNKlVcLlrNpZmTV7VhIzlwAAAEujVgmXU2dOTZIs23HZrNBlhdZoEgAAgFbUKuFyyowpSaqb+dTU1LRGkwAAALSi1gmXMz8MlwAAACx9WnVZrM18AAAAlk6tuyx2OTOXAAAAS4KXX345N910U2bNmrVQ6mvVZbFmLgEAAJYMI0eOzNChQ7P++uvnqquuKg6ZrRsuPYYEAABgiXDIIYfk8ccfz3rrrZeDDz64OGTWVCqVSksuOOecc/Lggw+2qJE/3//nVD6oZPvtts/ynZdv0bUAAAAsWu+++25efPHFjB8/Pt26dctdd92VLbfcskV1LPKZy9pKberya9eOXRd1cwAAACwGLZ65XBCHHnZonn3+2fztwb95ziUAAMASYvTo0TnjjDNyyy23ZO211873vve97LfffunQoUOL62r5FQugJjXp1L6TYAkAALCEuOKKK3LooYdm7bXXzlVXXbXAobJOq4RLAAAAlizbbbddbrzxxuyxxx5FobJOq+wWCwAAwKI3ceLEnH/++Xn22WfnW3aNNdbIXnvttVCCZSJcAgAALDWOOOKIHH/88Tn33HNbvW3hEgAAYClQW1ubO++8M0my6aabtnr7wiUAAMBS4Mknn8ykSZOSJDvssEOrty9cAgAALAVGjBiRJFlxxRUzaNCgVm9fuAQAAFgK3H///Umqu8C2a9f6UU+4BAAAaOMqlUpGjhyZZPEsiU2ESwAAgDZn/PjxWXvttTNgwIAMGDAgvXv3zoQJE5IkF1xwQf37G264YWbNmtUqfVo4DzQBAACg1fTp0ydjx46t//2MM87I6aefnoEDB+all15aLH0ycwkAANDG1W3ms+222y62PgiXAAAAbdiMGTPy8MMPJxEuAQAAWECPPvpopk2bliQZPHjwYuuHcAkAANCG1S2J7d27d9ZZZ53F1g/hEgAAoA2re77l4py1TIRLAACANmv27Nl54IEHkize+y0T4RIAAKDNGj16dCZPnpxEuAQAAGAB1d1v2a1bt2yyySYNzo0aNSqXX355q/VFuAQAAGij6u633HrrrdO+ffsG50499dSsvvrqrdYX4RIAAKCNGjt2bJJkq622avD+nXfemWnTpmXIkCGt1hfhEgAAoI3q06dPkqRfv371702cODHHHHNMLrvsslbti3AJAADQRn35y19Okjz//PP1x1133TWnnHJKNthgg1btS4dWbQ0AAICF5uCDD87777+fCy64IH/84x/Tt2/fnHXWWa26HLZOTaVSqSzqRg477LCMHTs2o0aNWtRNAQAAsBi0yszlFltskZVXXrk1mgIAAGAxaJWZSwAAAJZuNvQBAACgmHAJAABAMeESAACAYsIlAAAAxYRLAAAAigmXAAAAFBMuAQAAKCZcAgAAUEy4BAAAoJhwCQAAQDHhEgAAgGLCJQAAAMWESwAAAIoJlwAAABQTLgEAACgmXAIAAFBMuAQAAKCYcAkAAEAx4RIAAIBiwiUAAADFhEsAAACKCZcAAAAUEy4BAAAoJlwCAABQTLgEAACgmHAJAABAMeESAACAYsIlAAAAxYRLAAAAigmXAAAAFBMuAQAAKCZcAgAAUEy4BAAAoJhwCQAAQDHhEgAAgGLCJQAAAMWESwAAAIoJlwAAABQTLgEAACgmXAIAAFBMuAQAAKCYcAkAAEAx4RIAAIBiwiUAAADFhEsAAACKCZcAAAAUEy4BAAAoJlwCAABQTLgEAACgmHAJAABAMeESAACAYsIlAAAAxYRLAAAAigmXAAAAFBMuAQAAKCZcAgAAUEy4BAAAoJhwCQAAQDHhEgAAgGLCJQAAAMWESwAAAIoJlwAAABQTLgEWstNPPz01NTXz/enatWsGDhyYgw46KA888ECDOu677755Xjtu3LhG2/7c5z6XmpqabL311k32b4cddmiyzmHDhjV6bvDgwQs0Ft/4xjcare++++5boPqS5M0338wPfvCDbLfddundu3c6deqUZZZZJn379s12222Xo446KsOGDWtyjJLkN7/5Tbp3757Pfe5zmTlz5gL3pS1o7Pue19gAwIKqqVQqlcXdCYClyZgxYzJmzJgkyXHHHZcJEyakZ8+eOf/88+vLzJ49O6+99lquvfbaPPfcc0mSo446Kj//+c/Trl27jB8/PsOHD8+bb76Zk046KUmy6aab5vjjj0+SDB06NMsuu2yDdmfOnJkePXpk8uTJad++fSZMmJAVVlhhrv4NHz4848ePz4033pgbb7wxl156aTp37pyhQ4dm/PjxefDBB5Mkl1xySUaOHFl/3f33359tt9222ePwzjvvpH///pkyZUp9n/fee+8kyc4775w+ffo0u646v/vd73LEEUdk8uTJ2XjjjbPbbrulf//+adeuXV577bXccccdeeyxx+rLn3/++fnGN74xVz0bbbRRnn766STJ448/ns0226zFfWkr6r7vkSNH5pJLLkmSvPLKKxkwYMDi7RgAS58KAItM//79K0kq/fv3b/T8zJkzK/vss08lSSVJ5Tvf+U6D87Nnz66suOKKlSSV3r17V2pra5tsa8SIEfX1JKnccMMN8+zbrrvuWtl4442bPH/IIYc0qG/XXXedZ30fdfrppze4/rTTTmvR9R911113Vdq1a1dJUvn1r3/dZLlLL720UlNTU0lSOfvssxst8+tf/7qy3HLLVT772c9WPvjgg6J+tRWXX355/XfxyiuvLO7uALAUsiwWYDHq0KFDLr300nTr1i1J8uMf/zivvfZa/fl27dplxx13TJK89dZb9TOijRk+fHjatfvwf9bvvPPOJsvOmDEjI0eOzC677DLfPq6//vpJkjvuuCNPPPHEfMsnydSpU3PhhRfWX7swfO9730ttbW2GDBmSI444oslyhx9+eA466KB51nXEEUfkvffeyx133JFOnTottD4CwMeZcAmwmHXv3j0777xzkurS1ltuuaXB+bpzSTVANuXOO+/MkCFD0rdv3/mWffDBBzNlypQGdTflxBNPrH991llnzbd8klx66aWZOHFi/TLeUtOmTctDDz2UJNl8883nW35+4RIAWPiES4AlwFprrVX/+sUXX2xwrjnhcuLEiXnsscey884715d/5ZVXMnbs2EbLDx8+PF27dm3WPZRf+tKXsvrqqydJ/vjHP87Vv4+aNWtWfvrTn2bvvffOmmuuOd/6m+M///lPKv/dIuDtt9+eb/ktt9wy5513Xv2sLwCw6AmXAEuADh061L/+6O6lAwcOzMCBA5MkI0eOzAcffDDX9XfffXdqa2sbhMuk6aWxw4cPz7bbbpsuXbrMt28dO3bMCSeckCSpra3NueeeO8/yv/vd7/Laa681mPEstcIKK6SmpiZJ8pe//CWTJk2aZ/nlllsu3/zmN7PFFls0eL+xnXyHDRvWZD3vv/9+Tj311Ky33nrp2rVrVlxxxWy55Za54IILMmvWrBx66KFz1XfTTTclSfr27TvXuSR57rnnctBBB2XVVVdN586d079//3zta1/LW2+91WQ/amtrc9ddd+XrX/96Nttss3Tv3j0dO3ZMr169MmTIkFxyySWZMWNGM0YSABYd4RJgCfCvf/2r/nW/fv3mOl8XGKdNm9ZgB9c6w4cPT+/evbPxxhtnyJAh9UGmsXA5ceLEPP74481aElvn8MMPT8+ePZMkV199dd54441Gy1UqlfzoRz/KDjvs0Kzlq8217LLLZuONN06S/Pvf/85uu+2Wp556qsX17L333rnqqqsa7NzblHHjxmXQoEH54Q9/mP/85z85/vjj8+Mf/zj/8z//kwsuuCA77bRTfaDr2bNnrrrqqlx11VX51Kc+lSS58MILc9VVV2Xo0KH1dY4YMSI77bRTVllllZx55pk55ZRT8sEHH+Siiy7Kpz/96bz//vuN9uX000/PzjvvnF/84hdZaaWV8t3vfjcXXnhhDjrooDzxxBM54ogjMnjw4EycOLHFYwIAC83i3lEIYGk2v91iK5XqjrCrr756/U6ejzzyyFxlbrjhhvrzJ5544lzn11hjjcqXvvSl+t832WSTSpLKcsstV5kxY0ajdT355JPz7HvdbrF1zjjjjPo+HHvssY1ec8stt1SSVG677bZKpVKp3HvvvQttt9jf/e53DXaframpqey4446VSy65pPLvf/+7RXW98sor9fVcfvnlc53/4IMPKhtssEElSaVfv36VN998s8H59957r7LZZptV2rdvP9/v97TTTqtva9111608++yzDc4/++yz9fU0tbvtSSedVElSOfPMM+c6N2HChMr6669fSVLZZ599muyH3WIBWNTMXAIsZr/4xS/qd4j97Gc/2+iM34477li/E+xH77v8xz/+kVdeeaXBTGTd6/fff79+I5w6w4cPz8orr5xBgwa1qJ9HH310/a62l156aSZMmDBXmXPPPTcbbbRR/ud//qdFdTfH/vvvnzPPPDPt27dPUp0lveeee/LVr341q6yySrbccsucddZZeeWVV4rbuuiii/LMM88kSc4555ysssoqDc4vt9xy+eUvf5nZs2e3qN6999476623XoP31ltvvWyzzTZJkltvvbXJa3v06FH/zNM5rbTSSvnpT3+aJLnhhhsybty4FvUJABYW4RKgFdTW1mbChAn1P+PHj89jjz2WY489Nt/4xjeSVB/5cdVVVzV6/Yorrli/3PKJJ55osKlN3dLXxsLlnOfrDB8+PDvttFOLP0OPHj3yla98JUn1USM/+9nPGpwfNWpUHnjggXzrW99qcd3Ndcopp+TRRx/N0KFDG9ynWqlU8sgjj+SUU07JmmuumaFDh+bll19e4HZ++9vfJkk6d+7cYFnrnLbaaqv6jY6a6/Of/3yj79c9suX5559v9PzJJ5+c559/vsFnnlPdvaWVSiX3339/i/oEAAuLcAnQCl5//fX06tWr/mfllVfO5ptvnp///Ofp2bNnTj755DzyyCPp1atXk3XUBcZKpZK77767/v3hw4dn/fXXz2qrrVb/3pyb9cwZLl9++eW8/PLLzXq+ZWNOOOGE+udC/uIXv2hwj+A555yT1VdfPfvvv/8C1d1cm266af70pz/lX//6Vy655JLsvvvuDTYmqlQquemmm7LpppvmgQceaHH97777bp5++ukkybrrrpuuXbs2WXbDDTdsUd3rrLNOo++vuOKKSdLkRkXLL798g7+NmTNnZuLEifX/WDHnDOqbb77Zoj4BwMIiXAK0gj59+mT48OENfkaOHJkXX3wx48ePzw9/+MMsu+yy86yjsUeSzJo1K/fee+9cm/N06dIlgwcPTpI8/vjj+c9//tPgupZs5jOn1VZbLQceeGCSagi76KKLkiRPP/10brvtthx33HFNzq4tbD179sxXvvKV/PnPf86ECRNy3XXXZdddd60//95772W//fZr8S6q48aNq3/syaqrrjrPsnWhsLmWW265Rt/v3Llzksxzme3jjz+eQw45JKuvvno6deqUHj16NPgHizrTp09vUZ8AYGH52IfL3/8+mTZtcfcCWNp16dIlO+20U4OfwYMHZ+21167f2XV+tt566/oAWhcSH3nkkUyaNKnRsFj3Xt1jLJLkrrvuykYbbZSVV155gT/LiSeeWH//5/nnn58PPvgg5557blZYYYX6ZbOtbdlll80+++yT22+/PXfddVf9bOMbb7zR5LNBmzJ58uT61/N7VEtLg3TduLXUhRdemC222CJXXnllVlpppfzsZz/LzTff3OAfKwBgcWtT4bK2NvnI498WWKWSHHNMcuONSTMe89akadOSTTZJFmBHfIAW6dSpU7bffvsk1WW2L7zwQu68884G78/po/dd1tbW5p577lngJbF11llnney1115Jqo8FOe200/L73/8+X/va1+Y7+9oahgwZkmOOOab+92effbZF19dtWpTMfxawpRv6LIinnnoqxx13XGpra7PLLrtk9OjROeaYY7Lnnns2+McKAFjcluhw+etfJzvskGywQdK7d9KxY7Kw9ok4+uhqILzqqqSZkwaN6to1ufTSZI89kkceWTh9A2jKR5fGDh8+PFtvvXWDQFRnk002qV8uOXz48PrlsaXhMkm+/e1v178+99xz06FDhwaBblHYfPPNs/vuuzer7NZbb13/um6Ja3MNGDCgfjZ5fvcvtsZzJa+//vr6EHv88cc3e6YbAFrbEh0ue/ZMPvWppHPn5O23qzOXm25aXu+vflVdDnvNNcl/96UosvnmyTnnJDvvnBRsTggwX3OGyxtuuCGPPPJIk/dP1tTUZMiQIUmS1157LRdeeGG6dOmSbbfdtrgfm2++eX3dSXLIIYekd+/exfXOy9tvv53HH3+8WWXnDJT9+/dvUTsrrLBCNtpooyTV3VunTp3aZNm6jX8WpX//+9/1r/v169domTmX8gLA4rJEh8svfjH58Y+TM8748L3/7k+xwF54ITnuuOT885P57NNQb+LEavl5razaf/9kt92SAw5IZs0q6yNAUzbYYIP6TWZGjBiRWbNmzXNznjnPXXPNNRk8ePA8dz9tibrZy3bt2uWb3/zmQqlzfsaPH5977rlnvuVuv/32JNWlxHOG4Ob6f//v/yVJPvjgg9x0002NlnnkkUfy6quvtrjulprzGZtNParkscceW+T9AID5WaLDZZ265aarrJKsuWZZXUcckXziE8l/Nzts9jXHH5+ce+68y/3oR8kTTyQ/+EFRFwHmac7763r06FH//MvGzBku6+7ZW5j9mDZtWqZOnZq11lprodU7P1/+8pfz3HPPNXn+yiuvrH9O5YknnpiePXu2uI0jjzwyG2ywQZLkO9/5ToPZw6Q6U3jUUUct8tnaJPniF79YvxHQaaed1uDxL0l1V9wTTjhhkfcDAOandfaLLzRiRPVYOmt5223Vuq69Nmnuhn21tUndI+LmtyS3X7/kyCOrs61f+1rSp09Zf4G2acyYMRkzZkySZMqUKfXHq6++ur7MgS35F66P2HnnnXPllVcmSXbcccd57kDar1+/rLPOOnnhhRfqr52X8ePH1+88+vJ/1/nX9XvNNddscC9j0vRuqsOHD8/48eMbhMAxY8bU1zV06NAWb/4zYMCAvPrqq3n11Vez8cYbZ7fddss222yT3r17Z9asWXn11Vdz++235/HHH0+7du1y/PHH5/vf/36DOuq+mwkTJtS/99BDD6VDhw7p06dP/fh06tQpf/7zn7PjjjvmlVdeycYbb5yvfOUrGThwYN54441cfvnl2WmnnbLBBhvkiiuumOcY1P0tJJnr8z/00EN56aWXGi2z8847p0+fPtloo41y1lln5dvf/naefvrprLvuujnssMPSv3//vPrqqxk2bFiDR5zUjXPd56nrx0MPPVRf5qabbkrPnj0zaNCgDBo0qEXfAwA0qbKEmzatUuncuVJJKpWf/7ysrsGDK5UePSqV6dObf83o0dW2k0rl73+ff/mxYyuVmppK5fjjF7ibQBt32mmnVZLM86fEv/71r0pNTU0lSeXiiy+eb/mjjz66kqTSu3fvSm1t7TzL3nvvvU32+ZBDDml2H7fffvt5fv5XXnml2XXN6dlnn6387Gc/q+y3336VTTbZpLLSSitVOnbsWOnYsWOlZ8+ela233rryrW99q/LUU081ev28vpvtt99+rvLvvfde5ZRTTqmss846lc6dO1d69OhRGTx4cGXYsGGVSqVSOeiggypJKmuttVaLxqDu8x9yyCFNlrn33nsb1Hf33XdX9txzz0qvXr0qHTp0qHTv3r2y1VZbVc4777zK5MmTm/w88+rHaaedtkDfAwA0pqZSaeE2eq3svvuSz3ym+nr06AXf0Ofpp5ONNkq++tXk4oubf90FF1Tv0VxxxWTChObNeO6wQ/Loo8k//5mssMKC9ReAJd/QoUNz0003ZYsttsjf/va3xd0dAFislvh7LuuWxC6/fLLxxgtez7XXVo+77tqy6+6/v3rcbrvmL6XdY49k6tTk1ltb1hYAS46nn346//rXv+ZZ5sUXX0wSS0sBIG0oXG69dfPDXWNuvrl63GGH5l9TqSQjR7b8uroA+8c/Nv8aAJYse+21V77+9a83ef7FF1/Ms//dRnzo0KGt1S0AWGIt0eFyxozk4Yerr7fdNpk2rboj6yc/may1VtKrV7LLLsn8ViK98071MSL9+1eXtzZl/Phk7bWTAQOqP717V5fCJtXlsXXvb7jhvB83sv76yTLLJH/9a/UzANA23XrrrXnggQfmen/q1Kn56le/miTZYYcdsttuu7V21wBgibNE7xb76KPVQJlUd17dcstk332roa1nz2rw++Qnq/dkPvZYNdQ15uGHq7OQ/30mdpP69EnGjv3w9zPOSE4/PRk4MHnppeb3u1276hLehx6qhtpNNmn+tQAsGWpqajJjxozsuOOO2W+//bLZZpulW7dueemll3LNNdfktddey5ZbbpnrrrtucXcVAJYIS3S4rFsSm1SD3tVXJ9tv/+F7PXsme+2V/PznyS9/Wf1pTN0zp/v1W7D2t922ZdclyRprVMPlmDHCJUBbNGLEiFx//fW5++67M2rUqFx//fWZOXNmVlxxxWy66aY57bTTctBBB6Vjx46Lu6sAsERoM+Hyl79sGCzrdOpUPc5rZrHu3CqrNL/tjy7Jbam+favHZ55p+bUALH6rrrpqjj322Bx77LGLuysA0CYssfdczpqVPPhg9fWBByZ77tl4uX/+s3qc172Ub79dPXbv3vz251ySO3hw86+r06tX9TjHc7oBAACWWktsuHz88WTy5Orr/+6Z0KiHHqoeN9yw6TJ19XTp0vz262ZNe/dO1lmn+dfV6dq1epw0qeXXAgAAtDVLbLisC3ddu1Y38mnMP/6RjBtXfb3TTk3XNXNm9dihBYuA655vuSCzlolwCQAAfLwsseGyLtxtvfWH91V+1PXXV4+rrppsvnnTdS2zTPU4fXrz2p49O6nbeX5B7rdMFizQAgAAtFWtEi6feuqp3Hvvvc0uX1ubjBpVfb3DDk2X+8MfqscvfrH6+I+mLLdc9djccDl69IdLaRc0XNbdr9mt24JdDwAA0JYs8nBZqVQyZMiQ7LrrrplWl7jm44knPlxO+pnPNF5mzJjkySerrw888MP3hw9P3nqrYdm6R5DUbewzP3VLcrt1m/sxIqNGJZdfPv863n+/euzZs3ltAgAAtGWLPFzedtttefvttzNjxoxceumlzbqmLtwts0yyxRaNl6kLeOuv/+GS2Nra5NBDk5qahmXXXLN6fP315vV5ziW57ds3PHfqqcnqq8+/jjfeqB4HDmxemwAAAG3ZIg2XlUolp59+enr37p3evXvnnHPOadbsZV24nNf9ln/8Y/X40VnLDTb48DEgdTbeuHp85ZXm9Xvs2Opxq60avn/nndXlrkOGzL+OunD5iU80r00AAIC2bJGGy9tuuy2PPfZYNtlkk/Tt2zdvvfXWfGcvK5Vk5Mjq63ndb1m3bLZul9ja2uS7302+/e25y262WbLsstVltLW18+93nz7VY91y2iSZODE55pjkssvmf32SPPVU9fjRgAoAALA0WmThsm7WcvDgwVlllVXStWvXHHTQQfOdvXzmmeQ//6m+bup+yyTZc8/q8YMPqhv1fP3ryac+ley449xlO3RIttsumTIlee65+ff9y1+uHp9//sPjrrsmp5xSnRmdnwkTqktw11zzw6AKAACwNFtk4XLkyJF57LHHcvrpp6fmvzdBnnLKKXnrrbdy7bXXNnnd8ssnvXsnn/1sdVlsU37xi+r9lfvsU132usoq1feasu++1ePtt8+/7wcfXK3rlluSAQOSww9PzjorOeig+V+bfLisd+jQ5pUHAABo62oqlUplUVT85ptv5tZbb81Xv/rVfPnLX87YsWMzatSoXHfdddlwww2z/vrrL4pmmzRpUvV5mJ/85Icb9iwqhx2WDBuWPPpodTYVAABgabfIwuWcDjvssPpwuTgde2xy4YXVZa6LaqOd6dOT1Var7hL76KOLpg0AAIAlzSJ/FMmS5JvfTDp3Tn75y0XXxh/+UL1n9MQTF10bAAAAS5qPVbjs1y85+eTk4ouTV19d+PXPnp2cd171uZtf+MLCrx8AAGBJ9bEKl0ly0knVJbEnnLDw6x42rLrk9uKLk3Yfu5EFAAA+zj52EahTp+Tmm5P77quGwYXljTeSb30r+eEPk003XXj1AgAAtAUfu3CZJGusUX3MyMknJw8+WF7fzJnJgQcmn/tcdWYUAADg4+ZjGS6TZJttkjvuSI48MpkyZcHrqVSqz9tce+3ksssWWvcAAADalA6LuwOL06BByZgxZXVMm5bsumty0EELp08AAABt0cd25nJhWWYZwRIAAEC4BAAAoJhwCQAAQDHhEgAAgGLCJQAAAMWESwAAAIoJlwAAABQTLgEAACjWYVFWXlubvPNOMn16MnNm8vbbDc+vtFLSTrwFAABo8xZpuHznnaR37w9/n/N1krz1VtKr16LsAQAAAK3BvCEAAADFhEsAAACKCZcAAAAUW6T3XK60UvW+ymOOSV5+Ofnzn+c+DwAAQNu3SMNlu3bVDXu6dEk6drR5DwAAwNLKslgAAACKCZcAAAAUEy4BAAAoJlwCAABQTLgEAACgmHAJAABAMeESAACAYsIlAAAAxYRLAAAAigmXAAAAFBMuAQAAKCZcAgAAUEy4BAAAoJhwCQAAQDHhEgAAgGLCJQAAAMWESwAAAIoJlwAAABQTLgEAACgmXAIAAFBMuAQAAKCYcAkAAEAx4RIAAIBiwiUAAADFhEsAAACKCZcAAAAUEy4BAAAoJlwCAABQTLgEAACgmHAJAABAMeESAACAYsIlAAAAxYRLAAAAigmXAAAAFBMuAQAAKCZcAgAAUEy4BAAAoJhwCQAAQDHhEgAAgGLCJQAAAMWESwAAAIoJlwAAABQTLgEAACgmXAIAAFBMuAQAAKCYcAkAAEAx4RIAAIBiwiUAAADFhEsAAACKCZcAAAAUEy4BAAAoJlwCAABQTLgEAACgmHAJAABAMeESAACAYsIlAAAAxYRLAAAAigmXAAAAFBMuAQAAKCZcAgAAUEy4BAAAoJhwCQAAQDHhEgAAgGLCJQAAAMWESwAAAIoJlwAAABQTLgEAACgmXAIAAFBMuAQAAKCYcAkAAEAx4RIAAIBiwiUAAADFhEsAAACKCZcAAAAUEy4BAAAoJlwCAABQTLgEAACgmHAJAABAMeESAACAYsIlAAAAxYRLAAAAigmXAAAAFBMuAQAAKCZcAgAAUEy4BAAAoJhwCQAAQDHhEgAAgGLCJQAAAMWESwAAAIoJlwAAABQTLgEAACgmXAIAAFBMuAQAAKCYcAkAAEAx4RIAAIBiwiUAAADFhEsAAACKCZcAAAAUEy4BAAAoJlwCAABQTLgEAACgmHAJAABAMeESAACAYsIlAAAAxYRLAAAAigmXAAAAFBMuAQAAKCZcAgAAUEy4BAAAoJhwCQAAQDHhEgAAgGLCJQAAAMWESwAAAIoJlwAAABQTLgEAACgmXAIAAFBMuAQAAKCYcAkAAEAx4RIAAIBiwiUAAADFhEsAAACKCZcAAAAUEy4BAAAoJlwCAABQTLgEAACgmHAJAABAMeESAACAYsIlAAAAxYRLAAAAigmXAAAAFBMuAQAAKCZcAgAAUEy4BAAAoJhwCQAAQDHhEgAAgGLCJQAAAMWESwAAAIoJlwAAABQTLgEAACgmXAIAAFBMuAQAAKCYcAkAAEAx4RIAAIBiwiUAAADFhEsAAACKCZcAAAAUEy4BAAAoJlwCAABQTLgEAACgmHAJAABAMeESAACAYsIlAAAAxYRLAAAAigmXAAAAFBMuAQAAKCZcAgAAUEy4BAAAoJhwCQAAQDHhEgAAgGLCJQAAAMWESwAAAIoJlwAAABQTLgEAACgmXAIAAFBMuAQAAKCYcAkAAEAx4RIAAIBiwiUAAADFhEsAAACKCZcAAAAUEy4BAAAoJlwCAABQTLgEAACgmHAJAABAMeESAACAYsIlAAAAxYRLAAAAigmXAAAAFBMuAQAAKCZcAgAAUEy4BAAAoJhwCQAAQDHhEgAAgGLCJQAAAMWESwAAAIoJlwAAABQTLgEAACgmXAIAAFBMuAQAAKCYcAkAAEAx4RIAAIBiwiUAAADFhEsAAACKCZcAAAAUEy4BAAAoJlwCAABQTLgEAACgmHAJAABAMeESAACAYsIlAAAAxYRLAAAAigmXAAAAFBMuAQAAKCZcAgAAUEy4BAAAoJhwCQAAQDHhEgAAgGLCJQAAAMWESwAAAIoJlwAAABQTLgEAACgmXAIAAFBMuAQAAKCYcAkAAEAx4RIAAIBiwiUAAADFhEsAAACKCZcAAAAUEy4BAAAoJlwCAABQTLgEAACgmHAJAABAMeESAACAYsIlAAAAxYRLAAAAigmXAAAAFBMuAQAAKCZcAgAAUEy4BAAAoJhwCQAAQDHhEgAAgGLCJQAAAMWESwAAAIoJlwAAABQTLgEAACgmXAIAAFBMuAQAAKCYcAkAAEAx4RIAAIBiwiUAAADFhEsAAACKCZcAAAAUEy4BAAAoJlwCAABQTLgEAACgmHAJAABAMeESAACAYsIlAAAAxYRLAAAAigmXAAAAFBMuAQAAKCZcAgAAUEy4BAAAoJhwCQAAQDHhEgAAgGLCJQAAAMWESwAAAIoJlwAAABQTLgEAACgmXAIAAFBMuAQAAKCYcAkAAEAx4RIAAIBiwiUAAADFhEsAAACKCZcAAAAUEy4BAAAoJlwCAABQTLgEAACgmHAJAABAMeESAACAYsIlAAAAxYRLAAAAigmXAAAAFBMuAQAAKCZcAgAAUEy4BAAAoJhwCQAAQDHhEgAAgGLCJQAAAMWESwAAAIoJlwAAABQTLgEAACgmXAIAAFBMuAQAAKCYcAkAAEAx4RIAAIBiwiUAAADFhEsAAACKCZcAAAAUEy4BAAAoJlwCAABQTLgEAAD4GHr55Zdz0003ZdasWQulPuESAADgY2jkyJEZOnRo1l9//Vx11VXFIVO4BAAA+Bg65JBD8vjjj2e99dbLwQcfXBwyayqVSqUlF5xzzjl58MEHW9TIE088kcmTJ2fw4MEtug4AAIBF7913382LL76Y8ePHp1u3brnrrruy5ZZbtqgOM5cAAAAUa/HM5YI47LDDMnbs2IwaNWpRNwUAAEAzjR49OmeccUZuueWWrL322vne976X/fbbLx06dGhxXS2/AgAAgDbviiuuyKGHHpq11147V1111QKHyjrCJQAAwMfQdtttlxtvvDF77LFHUais455LAACApcTEiRNz/vnn59lnn51v2TXWWCN77bXXQgmWiXAJAACw1DjiiCNy/PHH59xzz231toVLAACApUBtbW3uvPPOJMmmm27a6u0LlwAAAEuBJ598MpMmTUqS7LDDDq3evnAJAACwFBgxYkSSZMUVV8ygQYNavX3hEgAAYClw//33J6nuAtuuXetHPeESAACgjatUKhk5cmSSxbMkNhEuAQAA2pzx48dn7bXXzoABAzJgwID07t07EyZMSJJccMEF9e9vuOGGmTVrVqv0aeE80AQAAIBW06dPn4wdO7b+9zPOOCOnn356Bg4cmJdeemmx9MnMJQAAQBtXt5nPtttuu9j6IFwCAAC0YTNmzMjDDz+cRLgEAABgAT366KOZNm1akmTw4MGLrR/CJQAAQBtWtyS2d+/eWWeddRZbP4RLAACANqzu+ZaLc9YyES4BAADarNmzZ+eBBx5Isnjvt0yESwAAgDZr9OjRmTx5chLhEgAAgAVUd79lt27dsskmmzQ4N2rUqFx++eWt1hfhEgAAoI2qu99y6623Tvv27RucO/XUU7P66qu3Wl+ESwAAgDZq7NixSZKtttqqwft33nlnpk2bliFDhrRaX4RLAACANqpPnz5Jkn79+tW/N3HixBxzzDG57LLLWrUvwiUAAEAb9eUvfzlJ8vzzz9cfd91115xyyinZYIMNWrUvHVq1NQAAABaagw8+OO+//34uuOCC/PGPf0zfvn1z1llntepy2Do1lUqlsqgbOeywwzJ27NiMGjVqUTcFAADAYtAqM5dbbLFFVl555dZoCgAAgMWgVWYuAQAAWLrZ0AcAAIBiwiUAAADFhEsAAACKCZcAAAAUEy4BAAAoJlwCAABQTLgEAACgmHAJAABAMeESAACAYsIlAAAAxYRLAAAAigmXAAAAFBMuAQAAKPb/Aek3vCPrZEh9AAAAAElFTkSuQmCC\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "import matplotlib\n",
        "from os import linesep\n",
        "from numpy import linspace,cos,pi,sin,random,arccos,heaviside\n",
        "import matplotlib.pyplot as plt\n",
        "from matplotlib import animation,rc\n",
        "rc('animation', html='jshtml')\n",
        "plt.rcParams.update({\"font.family\" : \"serif\",\"mathtext.fontset\" : \"cm\"})\n",
        "\n",
        "#functions\n",
        "def carr(f,t): #carrier\n",
        "  return 1/pi*arccos(cos(2*pi*f*t))\n",
        "\n",
        "def m(MI,f,theta,t): #modulation function\n",
        "  return (MI*cos(2*pi*f*t + theta) + 1)/2\n",
        "\n",
        "def h(ct,mt): #PWM switching function\n",
        "  return heaviside(mt-ct,0)\n",
        "\n",
        "#parameters\n",
        "Nf = 250 # number of frames\n",
        "Nppf = 10 # number of points per frame\n",
        "fc = 12 # carrier frequency\n",
        "fm = 1 # signal\n",
        "MI = 0.9 # modulation index\n",
        "\n",
        "#time series\n",
        "t=linspace(0,1,Nf*Nppf)\n",
        "ct = carr(fc,t) #carrier time-domain signal\n",
        "mt = m(MI,fm,0,t) #modulation function time series\n",
        "ht = h(ct,mt) #pwm signal time series\n",
        "\n",
        "#set up figures\n",
        "fig = plt.figure(figsize=(9,9))\n",
        "fig.tight_layout()\n",
        "ax_frame = [[[0, 0.5, 1, .4], [-.02,1.1], [-.1,1.1]], #sine & triangle\n",
        "            [[0, 0,   1, .4], [-.02,1.1], [-.1,1.1]], # pwm\n",
        "            ]# [pos-boundary, xlim, ylim] for subplots\n",
        "ax_lbl=[['$c(t),$', '$t$'], [r'$h(t)$', '$t$'],] #yx axes labels\n",
        "clst=['g','b','r'] #colors of lines\n",
        "ax_lst=[] #axis list or the list of subplots\n",
        "lines = [] #array for all lines\n",
        "for k in range(len(ax_frame)):\n",
        "  xn,xm,yn,ym = ax_frame[k][1]+ax_frame[k][2]\n",
        "  ax=fig.add_axes(ax_frame[k][0],xlim=[xn,xm], ylim=[yn,ym],fc='none') #no fc\n",
        "  ax.axis('off') #turn off axis frames\n",
        "  ax_lst.append(ax)\n",
        "  ax.annotate(\"\", (xm, 0), (xn, 0),arrowprops={'arrowstyle':\"->\"}) #x-axis\n",
        "  ax.annotate(\"\", (0,ym), (0,yn),arrowprops={'arrowstyle':\"->\"}) #y-axis\n",
        "  if k==0:\n",
        "    lines.append(ax.plot([], [], clst[k], lw=1.5)[0]) #triangle carrier\n",
        "    lines.append(ax.plot([], [], clst[k+2], lw=3)[0]) #sine reference\n",
        "    y_text=ax.text(0.1,ym,'$m(t)$',size=24,va='center',color=clst[k+2]) # addtional ylabel\n",
        "  else:\n",
        "    lines.append(ax.plot([], [], clst[k], lw=3)[0]) #pwm\n",
        "  ax.text(xm-.02,0,ax_lbl[k][-1],size=24,va='top',ha='right') #x-axis label\n",
        "  y_text=ax.text(0.01,ym,ax_lbl[k][0],size=24,va='center',color=clst[k]) #y label\n",
        "ax_lst[0].text(0.5,ax_frame[0][2][1]+0.1,'Sine and Triangle',va='bottom',ha='center',size=20)\n",
        "ax_lst[1].text(0.5,ax_frame[0][2][1]+0.1,'PWM Signal',va='top',ha='center',size=20)\n",
        "\n",
        "# animation function. This is called sequentially\n",
        "def animate(i):\n",
        "  lines[0].set_data(t[:(i+1)*Nppf],ct[:(i+1)*Nppf])\n",
        "  lines[1].set_data(t[:(i+1)*Nppf],mt[:(i+1)*Nppf])\n",
        "  lines[2].set_data(t[:(i+1)*Nppf],ht[:(i+1)*Nppf])\n",
        "  return\n",
        "\n",
        "anim = animation.FuncAnimation(fig, animate, frames=Nf, interval=50)\n",
        "anim #uncomment to generate animation in the output area\n",
        "# to save the animation, uncomment the following three lines\n",
        "fn = r\"PWM_sineTriangle_Offset.mp4\"\n",
        "writervideo = animation.FFMpegWriter(fps=25)\n",
        "anim.save(fn, writer=writervideo,dpi = 120)"
      ]
    }
  ]
}