{ "cells": [ { "cell_type": "markdown", "id": "27e03969", "metadata": {}, "source": [ "# Filter Networks #\n", "\n", "### Approach ###\n", "\n", "Analysing simple RC networks for the purpose of producing phase shifts of sine waves which in turn might be useful later for producing oscillatory networks." ] }, { "cell_type": "code", "execution_count": 3, "id": "693e7655", "metadata": {}, "outputs": [], "source": [ "from IPython.display import Image\n", "from sympy import Matrix, symbols, Symbol, init_printing, Function, dsolve, checkodesol, sin, cos,exp, pi, Eq, \\\n", " solveset, collect, cancel, simplify, lambdify, acos, atan, sqrt, I, integrate, factor, factor_list, Matrix, expand, \\\n", " conjugate, Rational, sympify\n", "import sympy\n", "import matplotlib.pyplot as plt\n", "from scipy.signal import find_peaks\n", "from scipy.integrate import solve_ivp\n", "import numpy as np\n", "from sympy.abc import phi\n", "from functools import reduce\n", "init_printing()" ] }, { "cell_type": "code", "execution_count": 4, "id": "d8541032", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'1.13.1'" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from system_eqns import systemEqns\n", "import sympy \n", "sympy.__version__" ] }, { "cell_type": "markdown", "id": "0a699a5b", "metadata": {}, "source": [ "## The simplest network\n", "\n", "A network containing only one capacitor and resistor" ] }, { "cell_type": "code", "execution_count": 5, "id": "effe33dd", "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Image(url='https://images.kiwiheretic.xyz/RC-filter0.jpg', width=600)" ] }, { "cell_type": "markdown", "id": "6057575f", "metadata": {}, "source": [ "This is the simplest RC filter I can think of. It only contains one current path for $ \\textit{i} $.\n", "\n", "Therefore:\n", "\n", "$$ V_{in} = V_c + R \\textit{i} $$\n", "\n", "However $ \\textit{i} = C \\frac{d V_c}{dt} $ and we want to think about the case where $ V_{in} = A \\sin( 2 \\pi f t) $ and so we have:\n", "\n", "$$ A \\sin (2 \\pi f t ) = V_c(t) + R C \\frac{d V_c}{dt} $$\n" ] }, { "cell_type": "code", "execution_count": 6, "id": "ec4b6463", "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle \\left( V_{in}, \\ V_{c}, \\ C, \\ R, \\ i, \\ t, \\ f, \\ A, \\ \\tau, \\ \\omega\\right)$" ], "text/plain": [ "(V_{in}, V_c, C, R, i, t, f, A, τ, ω)" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Vin, Vc, C, R, i, t, f, A, tau, w = symbols(\"V_{in} V_c C R i t f A tau omega\", real=True, positive=True)\n", "Vin, Vc, C, R, i, t, f, A, tau, w" ] }, { "cell_type": "code", "execution_count": 7, "id": "cd33a7be", "metadata": {}, "outputs": [], "source": [ "def multiplyIt(x, y):\n", " return sympify(x)*sympify(y)" ] }, { "cell_type": "code", "execution_count": 8, "id": "0fb16257", "metadata": {}, "outputs": [], "source": [ "# Define the voltage across the capacitor as a function of time\n", "VC = Function(\"V_c\")" ] }, { "cell_type": "code", "execution_count": 9, "id": "2ff1f3dd", "metadata": {}, "outputs": [], "source": [ "# Define \"driving term\" of the differential equation\n", "dt =A*sin(2*pi*f*t)" ] }, { "cell_type": "code", "execution_count": 11, "id": "ba8ccfa4", "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle A \\sin{\\left(2 \\pi f t \\right)} = C R \\frac{d}{d t} V_{c}{\\left(t \\right)} + V_{c}{\\left(t \\right)}$" ], "text/plain": [ " d \n", "A⋅sin(2⋅π⋅f⋅t) = C⋅R⋅──(V_c(t)) + V_c(t)\n", " dt " ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Present the differential equation of the circuit\n", "eqn1 = Eq(dt , VC(t) + R * C * VC(t).diff(t))\n", "eqn1" ] }, { "cell_type": "code", "execution_count": 12, "id": "d0b3ec67", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/latex": [ "$\\displaystyle V_{c}{\\left(t \\right)} = - \\frac{2 \\pi A C R f \\cos{\\left(2 \\pi f t \\right)}}{4 \\pi^{2} C^{2} R^{2} f^{2} + 1} + \\frac{A \\sin{\\left(2 \\pi f t \\right)}}{4 \\pi^{2} C^{2} R^{2} f^{2} + 1} + C_{1} e^{- \\frac{t}{C R}}$" ], "text/plain": [ " -t \n", " ───\n", " 2⋅π⋅A⋅C⋅R⋅f⋅cos(2⋅π⋅f⋅t) A⋅sin(2⋅π⋅f⋅t) C⋅R\n", "V_c(t) = - ──────────────────────── + ───────────────── + C₁⋅ℯ \n", " 2 2 2 2 2 2 2 2 \n", " 4⋅π ⋅C ⋅R ⋅f + 1 4⋅π ⋅C ⋅R ⋅f + 1 " ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Solve for the voltage across the capacitor wrt time\n", "dsoln = dsolve(eqn1, VC(t))\n", "dsoln" ] }, { "cell_type": "markdown", "id": "4a3c5e39", "metadata": {}, "source": [ "### Find value for $ C_1 $\n", "At this point we want to find $ C_1 $ by setting $ V_c(0) = 0 $. This seems reasonable that the capacitor starts off with no charge on it." ] }, { "cell_type": "code", "execution_count": 13, "id": "a93838da", "metadata": {}, "outputs": [], "source": [ "c1 = Symbol('C1')" ] }, { "cell_type": "code", "execution_count": 14, "id": "e7608c5e", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "c1 in dsoln.free_symbols" ] }, { "cell_type": "code", "execution_count": 15, "id": "804836bb", "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAALAAAAAfCAYAAABH/UdlAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuNSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/xnp5ZAAAACXBIWXMAABJ0AAASdAHeZh94AAAKCElEQVR4nO2ce7BXVRXHPyBpvoK0h2b5CJREpR9gEyZj6ihGk/madJwRwybMoTLFR6E1X7+aqPgAdRRRS8QeZjHR5Gg+0AbFFz5AIR8hkmQ6lYD4CBW9/bH2gcPh/H733B/XS5d+35nfnHP2Wnvt/bu/ddZee+21bo+2tjZaaKG7oteGnkB3gO3RwDhgR+Dnkk7cwFNqIaFLFNj2OOBIoD/wNvAQME7S/Cbl7Q48ATwjqVZCrwFnAF8GPga8DDwKTJA0J/HMBA5MXVYBixP9uoKszwGTgW+keb/ezJxb+GDQs4vG2R+4GvgSoTSrgLttb9OkvCuAy4ABtjfNE2yPIpT1beAYYDfgm+n5pBzrYOAsYHugH3AzMMX2oMJYXwfmS/q9pJclvdHknFv4ANAlFljSIfln2yOB14B9gT/aXgAMqNPdks7J9T2SePEmEMv6AGBuou0DXA+cIWliTsaLwKzshbHdF+gD/EnSK6ltCvBjYA/CumP7OWDXdN8GzJB0RDN/gxY+GGwoH3hrQgmXpecjgGeBrxLK0wNYCHwf+HXWyfbmwCXAUZKW2/4HMIikwMClwMMF5V0NSUvT7RBgBTAvyd0+yX0feDzXZRhwHzAN+BnwVrNf+P8Rtm8ERgC7SHpzPeQMIVbV0ZKuz9M2lAJfTijdg+n5k0AbcJ+kN2z3A7YA7pf0n1y/H6a2J9LzAqAGYHtXYB/g2ArjDwG2AlbY7glsDrwDnCbpLzm+FcBngdmZpd5YYPtY4FfAZElj2uGdTLhfl0g6o6L8LwAjgdPLlNf2p4Fzga8A2xL7lBnEirsszyvpMdszgPNs35x347rKB14N25cRlu0oSe+l5s8Di3ITqxHWbmGu387AycDZOXHzCQsM4dNCvKntYTDhatTSXO4ArpM0qcC3J/GSz60gs7thXrru2Ygp7QlOBF4C3AH55xMGYHKJzL7AY8AJwCPARGAR8APgQdvblsi7ANiO0IHV6FIFtj2RsJAHSlqUIw0Ensw914iN0/u5tonAR4EXbK+yvYr4wgNt9yAsNkCVTdZg4AFJCyU9TliXMbb3KvDVgL9JWl7l+20I2B5lu832/h3s+iywEih+5yKuJPTktKobWNu7AQcBtxRW0AxXA58ATpZ0uKQfSTqQ+I37E8q/FiQ9AjwDfCetmkAXKrDty1mjvM8UyANZYxEgFGf1s+3hREhsSKJln2OA3sAuhDUm8ZWNv0W67gJsAzyV0SQtJnzvkYVuNTZO60ta/RYAfdJyvg5sH0dstGdK+k0HxH+L2Mes0ydZ3+FE2PKq4rSAN4GRtrcskXszEYs/OGvoqjjwVYRyHA4ss71dIr1BuAp7AhfluvQl+ce2P0T4zJcma5mX+2K6HSRpuu3bgSvTZm824VcPBkYTy9/9xEvwPpD3dQHuImLVZ+baasDdTX3p7oF5xN9jL+DveYLtrYjf5F3gex2UexDwHhE3L+KAdL2zsMIi6XXbswkFHwrMLPSdna4HE25fl1ngMUTkYSbhrGef0wll3ZK1XYingLG2RxBuwseJ2O9akLQCeIW0kSOiGZcAYwnLOYfY+D3IGt94CPC8pJUFcXcBu9reAyC5JQPZSC1wQrbKlbkRPwE+BUwsWTHrIlnOGvB0nchD/3R9ro6Iv6brbiW0Oem6X9bQVXHgHu2wrEWXdHTu8XZCKevJ3j53/zYRH57QgH8cET8uts/Mz0NSG/CRdubd3VG6kUs+7CmEVT63gzJ3ADYhDFQZeqfra3XoWXufIkHSa7ZXEm4E0MqF6FawvRjYqQ75XnudIMGNkkY1EJmtekULPAnYFBjbRPw2iyAsa8jVPJYSYVegpcDdDZNY1zLVgMOAG4mNUR5zGwmTtMz2EmB3270krbJ9KHH4cJek3zYxxyzq8OE69MzC9q5Dz9qX16FvnhsjFDgdk7bwP4BG7lZJnDrL/TgMmCrpz00MOQ/4GuH/LyJCWe8Qp6ClsL0D8FNC0fsQ8fqxku4E/pnYymK5EOE7KPdxIR3dU+Ijp/BZH+CFrK0XVPJRW9h4kSnwXkQUpi9woaRny5hTyO0hYlN8JKGw+xKHFhC+779Ys1kr4t50HW67Zz4SYXvrJOstyiMY/Yl9ytysodNcCNufAW4iAtSrgPOaWYI6Q04zMjpr/t0Q2UZuBHA0sAQ4rwH/lNTniLTRhdyJqaQ227OAo2z3k7Qw31nS87bvJEJl3yUOSjKYiEhNqeN7D03X7CXo1DDaKuAUSQPS5CbVCUZ3hZxmZHTW/LsbMgUeRZxmniqpNGnJ9k5EwpVyyluG6el6SB36GMJyX2F7hu0LbN8DnEq4DmfX6TeciC//IWvoNAVOubJz0/0rwL+JE68ul1NVhu3RthelY2l3xvy7IRayJsvuDknTG/DWiBf9sXZkTicU9PgyoqTngb2BqcAXgdMI1+VyYKikV4t9bPcmDsJulbQkay91IVIFxXjgKkkdPYXJ0t82yQ+Uo9Vop1qikZyqlRTtzaVRpUWj+TcL2/sRBzdDiAOCEyRNXV+5SUbTcpIPWnWleZfQma1Z4/OWyXzH9iRgvO1BuezBPM8SIpmnKo4nIhtrnQmso8C2hxLZR08WaVWQksanEce3RdooIgtsGpHHsATYOY13EmtOWhrJySopbgA2A75NVFI8WvxDNZoLuUqLDvQp+75TgcX5pPs62IrI15iWPt0RDxPx3Wtsn08s58OAOZLmFXgnEr/pucCh6zNoSg0YB0yXdH+e1qvA2Bv4JZGMoQKt3aoJ25sROZ0XSnqg0L9StUTiLZVTtZKikYxEK620aNRnfSHpNuC2NObUzpTdVZD0aooTTyBWrfcIo3NrCe9KR+XNAba3XJ+EdsLIXUvJSlO0wNcCv5N0r20VaA2rJlLuwFTgHkk3lUyiUrVEO3IqVVJUmMs6lRYV+rQASJpNhLqq8M4CZnXCmE8D55TRViuwo3S8H3BcHTkNqyZsDyPcgidtH576jJT0VAerJfatJ4fqlRSNZEBJpUWj+VeYcwsbCNlJXH9i0zZM0rt1eBtWTSTfpF5Uo3K1RAU51wMXE4k244GFxROqdmRASaVFhT4A2D6L8MEzbAa02T491zZC0n3tyWph/ZFZ4H2IiMCCXELIJsB+tk8idqlVqibqoSPVEo0wGPhFFhxPc1tke0oHLWWN5istrgFuyT1fRJTb5NM9X2pCbgtNIFPgGaxrHW8gcjPHE8v0QCK1MUONtasoGiFfLVGWpb9FveB5jqe0ksJ2VklxZr2+JajRZJ5v8tWz6mZsvw4sLZ44tdA1yHIhllPI/rH9JvHDzE/+Zt2qifYgaU7FaolG6EglRXuo0cWVFqnCoV967AnsmGLiSyW9WLdjCw1R9SSuvaqJKqhSLdEIlSop2sMGrLTYm4jePEFsPp3uO5ow3kIOPVr/nbKF7oz/Arz7dhA4YWFAAAAAAElFTkSuQmCC", "text/latex": [ "$\\displaystyle \\frac{2 \\pi A C R f}{4 \\pi^{2} C^{2} R^{2} f^{2} + 1} + V_{c}{\\left(0 \\right)}$" ], "text/plain": [ " 2⋅π⋅A⋅C⋅R⋅f \n", "───────────────── + V_c(0)\n", " 2 2 2 2 \n", "4⋅π ⋅C ⋅R ⋅f + 1 " ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Solve for C1\n", "c1eq = solveset(dsoln.subs([(t,0)]), c1).args[0]; c1eq" ] }, { "cell_type": "code", "execution_count": 16, "id": "bc4fa20e", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle \\frac{2 \\pi A C R f}{4 \\pi^{2} C^{2} R^{2} f^{2} + 1}$" ], "text/plain": [ " 2⋅π⋅A⋅C⋅R⋅f \n", "─────────────────\n", " 2 2 2 2 \n", "4⋅π ⋅C ⋅R ⋅f + 1" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# We will assume VC = 0 at t = 0. No charge on capacitor at start. \n", "c1eq.args[0]" ] }, { "cell_type": "markdown", "id": "2aa9fc95", "metadata": {}, "source": [ "At this point I am going to try and ignore the transient part of the solution" ] }, { "cell_type": "code", "execution_count": 17, "id": "e61d4d03", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle - \\frac{2 \\pi A C R f \\cos{\\left(2 \\pi f t \\right)}}{4 \\pi^{2} C^{2} R^{2} f^{2} + 1} + \\frac{A \\sin{\\left(2 \\pi f t \\right)}}{4 \\pi^{2} C^{2} R^{2} f^{2} + 1} + C_{1} e^{- \\frac{t}{C R}}$" ], "text/plain": [ " -t \n", " ───\n", " 2⋅π⋅A⋅C⋅R⋅f⋅cos(2⋅π⋅f⋅t) A⋅sin(2⋅π⋅f⋅t) C⋅R\n", "- ──────────────────────── + ───────────────── + C₁⋅ℯ \n", " 2 2 2 2 2 2 2 2 \n", " 4⋅π ⋅C ⋅R ⋅f + 1 4⋅π ⋅C ⋅R ⋅f + 1 " ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eqn1 = dsoln.rhs; eqn1" ] }, { "cell_type": "code", "execution_count": 18, "id": "c7a07a11", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle - \\frac{2 \\pi A C R f \\cos{\\left(2 \\pi f t \\right)}}{4 \\pi^{2} C^{2} R^{2} f^{2} + 1} + \\frac{A \\sin{\\left(2 \\pi f t \\right)}}{4 \\pi^{2} C^{2} R^{2} f^{2} + 1}$" ], "text/plain": [ " 2⋅π⋅A⋅C⋅R⋅f⋅cos(2⋅π⋅f⋅t) A⋅sin(2⋅π⋅f⋅t) \n", "- ──────────────────────── + ─────────────────\n", " 2 2 2 2 2 2 2 2 \n", " 4⋅π ⋅C ⋅R ⋅f + 1 4⋅π ⋅C ⋅R ⋅f + 1" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "nonTransient = sum(eqn1.args[1:])\n", "nonTransient" ] }, { "cell_type": "code", "execution_count": 19, "id": "9d2e8ec0", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle \\frac{2 \\pi A C R f \\left(2 \\pi C R f \\sin{\\left(2 \\pi f t \\right)} + \\cos{\\left(2 \\pi f t \\right)}\\right)}{4 \\pi^{2} C^{2} R^{2} f^{2} + 1}$" ], "text/plain": [ "2⋅π⋅A⋅C⋅R⋅f⋅(2⋅π⋅C⋅R⋅f⋅sin(2⋅π⋅f⋅t) + cos(2⋅π⋅f⋅t))\n", "───────────────────────────────────────────────────\n", " 2 2 2 2 \n", " 4⋅π ⋅C ⋅R ⋅f + 1 " ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Find the voltage at the output\n", "vout = simplify(A * sin(2*pi*f*t) - nonTransient)\n", "vout" ] }, { "cell_type": "code", "execution_count": 20, "id": "1833b696", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle 4 \\pi^{2} \\omega^{2} + 1$" ], "text/plain": [ " 2 2 \n", "4⋅π ⋅ω + 1" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "c3_2 = ((2*pi*C*R*f)**2 + 1).subs(C*R*f, w)\n", "c3_2" ] }, { "cell_type": "code", "execution_count": 21, "id": "e441c722", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle \\operatorname{acos}{\\left(\\frac{1}{4 \\pi^{2} \\omega^{2} + 1} \\right)}$" ], "text/plain": [ " ⎛ 1 ⎞\n", "acos⎜───────────⎟\n", " ⎜ 2 2 ⎟\n", " ⎝4⋅π ⋅ω + 1⎠" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Now compute the phase shift at the output\n", "alpha = acos(1/c3_2)\n", "alpha" ] }, { "cell_type": "markdown", "id": "68fba51d", "metadata": {}, "source": [ "### Find magnitude and phase of voltage across $ V_c $ ###\n", "\n", "We do this initially by comparing the coefficients of the sin and cos terms but later on we have at doing this\n", "using complex analysis." ] }, { "cell_type": "code", "execution_count": 22, "id": "54b227ef", "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle \\left( \\frac{A \\sin{\\left(2 \\pi f t \\right)}}{4 \\pi^{2} C^{2} R^{2} f^{2} + 1}, \\ - \\frac{2 \\pi A C R f \\cos{\\left(2 \\pi f t \\right)}}{4 \\pi^{2} C^{2} R^{2} f^{2} + 1}\\right)$" ], "text/plain": [ "⎛ A⋅sin(2⋅π⋅f⋅t) -2⋅π⋅A⋅C⋅R⋅f⋅cos(2⋅π⋅f⋅t) ⎞\n", "⎜─────────────────, ──────────────────────────⎟\n", "⎜ 2 2 2 2 2 2 2 2 ⎟\n", "⎝4⋅π ⋅C ⋅R ⋅f + 1 4⋅π ⋅C ⋅R ⋅f + 1 ⎠" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "nonTransient.args" ] }, { "cell_type": "code", "execution_count": 23, "id": "5b88db11", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle \\frac{A}{4 \\pi^{2} C^{2} R^{2} f^{2} + 1}$" ], "text/plain": [ " A \n", "─────────────────\n", " 2 2 2 2 \n", "4⋅π ⋅C ⋅R ⋅f + 1" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Get sine coefficient\n", "sincf = reduce(multiplyIt, (filter(lambda x:type(x) not in [sin],nonTransient.args[0].args)))\n", "sincf" ] }, { "cell_type": "code", "execution_count": 24, "id": "620dff99", "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle - \\frac{2 \\pi A C R f}{4 \\pi^{2} C^{2} R^{2} f^{2} + 1}$" ], "text/plain": [ " -2⋅π⋅A⋅C⋅R⋅f \n", "─────────────────\n", " 2 2 2 2 \n", "4⋅π ⋅C ⋅R ⋅f + 1" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Get cosine coefficient\n", "coscf = reduce(multiplyIt, (filter(lambda x:type(x) not in [cos],nonTransient.args[1].args)))\n", "coscf" ] }, { "cell_type": "code", "execution_count": 25, "id": "dca40fff", "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle \\frac{A}{\\sqrt{4 \\pi^{2} C^{2} R^{2} f^{2} + 1}}$" ], "text/plain": [ " A \n", "──────────────────────\n", " ___________________\n", " ╱ 2 2 2 2 \n", "╲╱ 4⋅π ⋅C ⋅R ⋅f + 1 " ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "c3 = sqrt(cancel(sincf**2 + coscf**2))\n", "c3" ] }, { "cell_type": "markdown", "id": "ad029c95", "metadata": {}, "source": [ "We might like to find out the amplitude and phase of the above formula given that it has both a sin and cosine term in it. The result will be a superposition which will have a different amplitude and phase of any of them separately. \n", "\n", "If we remember that for $ C_1 \\sin( \\theta ) + C_2 \\cos (\\theta) = C_3 * \\cos ( \\theta + \\alpha ) $. The constants $ C_1, C_2 \\mathrm{and} C_3 $ have nothing to do with the constant of integration $ C_1 $ mentioned above. It is simply because I am running out of meaningful variable names.\n", "\n", "Then:\n", "\n", "$$ C_3^2 = C_1^2 + C_2^2 $$\n", "\n", "and\n", "\n", "we can try to reduce this formula:\n", "\n", "$$ C_1 \\sin( \\theta ) + C_2 \\cos (\\theta) = C_3 * \\cos ( \\theta + \\alpha ) $$\n", "$$ \\Rightarrow C_1 \\sin( \\theta ) + C_2 \\cos (\\theta) = C_3 * \\cos ( \\theta ) \\cos (\\alpha ) - C_3 * \\sin ( \\theta ) \\sin (\\alpha ) $$\n", "$$ \\Rightarrow C_1 = C_3 * \\sin (\\alpha ) \\textrm{ and } C_2 = C_3 * \\cos (\\alpha ) $$\n", "$$ \\Rightarrow \\tan( \\alpha ) = C_1 / C_2 $$\n", "$$ \\Rightarrow \\tan^2( \\alpha ) = C_1^2 / C_2^2 $$\n", "$$ \\Rightarrow \\tan^2( \\alpha ) + 1 = C_1^2 / C_2^2 + C_2^2/C_2^2 =\\frac{C_1^2 + C_2^2}{C_2^2} $$\n", "$$ \\Rightarrow \\cos^2( \\alpha ) = \\frac{C_2^2}{C_1^2 + C_2^2} $$\n", "$$ \\Rightarrow \\alpha = \\cos^{-1} \\left( \\sqrt {\\frac{ C_2^2 } { C_1^2 + C_2^2 }} \\right) $$" ] }, { "cell_type": "code", "execution_count": 26, "id": "ebe53008", "metadata": {}, "outputs": [], "source": [ "from sympy import Mul, sympify, re, im\n", "import math " ] }, { "cell_type": "code", "execution_count": 27, "id": "8475e93c", "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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LWxZ+f74PZSkKqV90jtHWLxLPO0duno/6IyYSEhISEjpD2SyChISEhIQeI00ECQkJCeMc/w9kDaNs/4/w+AAAAABJRU5ErkJggg==", "text/latex": [ "$\\displaystyle - \\frac{2 \\pi A C R f \\cos{\\left(2 \\pi f t \\right)}}{4 \\pi^{2} C^{2} R^{2} f^{2} + 1} + \\frac{2 \\pi A C R f e^{- \\frac{t}{C R}}}{4 \\pi^{2} C^{2} R^{2} f^{2} + 1} + \\frac{A \\sin{\\left(2 \\pi f t \\right)}}{4 \\pi^{2} C^{2} R^{2} f^{2} + 1}$" ], "text/plain": [ " -t \n", " ─── \n", " C⋅R \n", " 2⋅π⋅A⋅C⋅R⋅f⋅cos(2⋅π⋅f⋅t) 2⋅π⋅A⋅C⋅R⋅f⋅ℯ A⋅sin(2⋅π⋅f⋅t) \n", "- ──────────────────────── + ───────────────── + ─────────────────\n", " 2 2 2 2 2 2 2 2 2 2 2 2 \n", " 4⋅π ⋅C ⋅R ⋅f + 1 4⋅π ⋅C ⋅R ⋅f + 1 4⋅π ⋅C ⋅R ⋅f + 1" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "simpeq2 = dsoln.args[1].subs(c1, c1eq.args[0])\n", "simpeq2" ] }, { "cell_type": "code", "execution_count": 28, "id": "ee48e2dd", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "sin" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "type(simpeq2.args[0].args[-1])" ] }, { "cell_type": "code", "execution_count": 29, "id": "03cfa076", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle \\frac{A}{4 \\pi^{2} C^{2} R^{2} f^{2} + 1}$" ], "text/plain": [ " A \n", "─────────────────\n", " 2 2 2 2 \n", "4⋅π ⋅C ⋅R ⋅f + 1" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "simpeq2.coeff(simpeq2.args[0].args[-1])" ] }, { "cell_type": "code", "execution_count": 30, "id": "2e9fd9f3", "metadata": {}, "outputs": [], "source": [ "u = symbols('u')" ] }, { "cell_type": "code", "execution_count": 31, "id": "66f6c8ec", "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle \\frac{A \\sin{\\left(2 \\pi f t \\right)}}{4 \\pi^{2} C^{2} R^{2} f^{2} + 1}$" ], "text/plain": [ " A⋅sin(2⋅π⋅f⋅t) \n", "─────────────────\n", " 2 2 2 2 \n", "4⋅π ⋅C ⋅R ⋅f + 1" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "simpeq2.args[0]" ] }, { "cell_type": "code", "execution_count": 32, "id": "2baf1a6a", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle \\frac{A}{4 \\pi^{2} C^{2} R^{2} f^{2} + 1}$" ], "text/plain": [ " A \n", "─────────────────\n", " 2 2 2 2 \n", "4⋅π ⋅C ⋅R ⋅f + 1" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Get sine coefficient\n", "c1 = reduce(multiplyIt, (filter(lambda x:type(x) not in [sin],simpeq2.args[0].args)))\n", "c1" ] }, { "cell_type": "code", "execution_count": 33, "id": "99628c59", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle - \\frac{2 \\pi A C R f}{4 \\pi^{2} C^{2} R^{2} f^{2} + 1}$" ], "text/plain": [ " -2⋅π⋅A⋅C⋅R⋅f \n", "─────────────────\n", " 2 2 2 2 \n", "4⋅π ⋅C ⋅R ⋅f + 1" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Get cosine coefficient\n", "c2 = reduce(multiplyIt, (list(filter(lambda x:type(x) not in [cos],simpeq2.args[1].args))))\n", "c2" ] }, { "cell_type": "code", "execution_count": 34, "id": "36345ddc", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle \\frac{2 \\pi A C R f}{4 \\pi^{2} C^{2} R^{2} f^{2} + 1}$" ], "text/plain": [ " 2⋅π⋅A⋅C⋅R⋅f \n", "─────────────────\n", " 2 2 2 2 \n", "4⋅π ⋅C ⋅R ⋅f + 1" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Get third coefficient (of exponential term)\n", "reduce(multiplyIt, filter(lambda x:type(x) not in [ exp],simpeq2.args[2].args))" ] }, { "cell_type": "code", "execution_count": 35, "id": "07f2f49c", "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAGUAAAAhCAYAAADAtWW1AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuNSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/xnp5ZAAAACXBIWXMAABJ0AAASdAHeZh94AAAFAUlEQVR4nO2aW4hVVRjHf+Ml8UIXqWyCRFPLVHSc8SFJFHoQjAgVQoKkq+JDVJgWSvD3XxBpWVZEWZKD1kMZ6JMGdoHULMYaL6OEmZhi+TSIt8LM6WGtM+w5zjlnn+NxzhydPxz2Xuv71rf++3xrrW/t9e2atrY2rhbYrgWGSNpt+zbgZ+AuSWcrTK0o1FxNTsmG7T3Ag5KOVZpLMehTaQKlwPY9QDPwq6S6HDoNQO9qcwhAr0oTKBHvAm8BY2xfly20PRhYB8zvamLlQNU5xfZsAu8VQF9gTJa8H7AJeF3SD11OsAyoKqfY7g+8CSySdBL4E5iYkNcAjcC3ktZXgmM5UG0x5SVgu6TmWN4P1CXk9wFzgL22Z8a6uZL2dRnDMqBqnGJ7GPAsMCFR3QJMyhQkbafKZn9nqJotse2NwEzgv0R1DXAauElSdTxIClTFTLE9HZgGNADnE6LRwAZgOHC4AtSuCLq9U2z3Bd4BVkr6JUt2NN5O5CpySjWsv88BtxDeTTpA0ingBB2DfdWjamLKtYRqmCnXHHqc0g3R45RuiD4AtnsCSzeBpJqyBXrbdwDrgVuBC8CrkjZUwk4pNsrFvxwo5/J1AXhe0hhgOrDK9sAK2SnFRrn4Xzau2Ja4XFm/ctjJZcP2PGAJMBT4RNL8Qm26Ap2+0dteArwGvC/pmWKN5sv62a4DFhOOTW4G/gJ2ASskNRWyY/sb4P5YvAAciW0/LoaL7dHAB8DDwI+EM7SC/EuF7anAIsJR0e3AE5IaO9O9xCm27yVk7PaW2Hkm6zevE9njwJoonwMcA4bF/hYATSns1ANLgbVAP+BpYLXtXYkj/YJcgIeAFkkbi2jT2fM2AkckLSugOohwqr0u/nKig1Ns3wB8BjwJKEu2n6wsX1IsaVm+rJ/tyQSHLJb0dkJ0FPg+/hkZ3U7t2B4B3Ah8JelErFsNvAyMJeTt89qIsoPAqHjfBmySNOtKZi0lbQY2xz4b8+lmB/qPgC8lfdeJ7qx4fQCoJUzBc8BTwPIUWb+VwE9ZDkmSbo2E89lpAE4Be6JuLSETeRFoP6xMwWUKcJDgzFrgse6UtWyfKTHojQQezaE7BGgDtkk6Y3skMICQCfzb9hRyZP1sjwImA4+k4JQve9hAWAZO2e4F9Ccc5b8g6UBKGxAceyewIzHjcvJPwbmsyLw83k0I7FMk/ZtDdwJwWNKZWK4jzJRDUDDrVx+vuwoRSmFnDfAGcH3kfEjSqiJsAIwjPPvuItoAYHspIaZl0A9os70oUTdD0rZCtnIhM1MmE3ZC+21nZL2BqbYXAAOB8XQM/nWEQHkxRT8D4vVMXq3CqAc+lXQIIHI7bHt1kSO6DvgjfnxRLD4EvkiUlwPH6ZhaOF6C3XZknLKJS0fxWuA3wmg8T3DKloS8jri2p0BLvE4DPs8W2h4g6Vw+A7aHA4OB9j9f0hHbzcBc4MWUXCBw312Efjti7GtN8DoNtGYGSjnQJ3Z0EjiZFNg+Gztriev3OMKoyGAEsDNNJ5KabG8B3oufCe0gxKd6wtbTwPYCZhoIAf1AVv1WYDbFO+XrIvQvG7YHEWI2hGVyaHxna5V0NKmb9phlBGEJSy5f+4CFtmektDGLsFNaSBilTYRPhnaSItYQnPK7pH+y6rcCo2yPTUMi7rLGU+JMuQxMImzZmwkbFMf7V7IVezKP3RA9+ZRuiB6ndEP8D4b5MjWJKv6PAAAAAElFTkSuQmCC", "text/latex": [ "$\\displaystyle \\frac{A^{2}}{4 \\pi^{2} C^{2} R^{2} f^{2} + 1}$" ], "text/plain": [ " 2 \n", " A \n", "─────────────────\n", " 2 2 2 2 \n", "4⋅π ⋅C ⋅R ⋅f + 1" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Compute c3^2 using pythagoras theorem\n", "c3_2 = simplify(c1**2 + c2**2)\n", "c3_2" ] }, { "cell_type": "code", "execution_count": 36, "id": "907ce05a", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle \\frac{A}{\\sqrt{4 \\pi^{2} C^{2} R^{2} f^{2} + 1}}$" ], "text/plain": [ " A \n", "──────────────────────\n", " ___________________\n", " ╱ 2 2 2 2 \n", "╲╱ 4⋅π ⋅C ⋅R ⋅f + 1 " ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# find c3 by taking square root\n", "c3 = sqrt(c3_2) \n", "c3\n" ] }, { "cell_type": "code", "execution_count": 37, "id": "56dcb8dc", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle - \\frac{1}{2 \\pi C R f}$" ], "text/plain": [ " -1 \n", "─────────\n", "2⋅π⋅C⋅R⋅f" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Compute the phase\n", "c1/c2" ] }, { "cell_type": "markdown", "id": "4b24e8dd", "metadata": {}, "source": [ "The tan function can be equated to the fraction of $ \\frac{\\sin( \\theta )}{\\cos (\\theta )}$ " ] }, { "cell_type": "code", "execution_count": 38, "id": "05abad5c", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle - \\operatorname{atan}{\\left(\\frac{1}{2 \\pi C R f} \\right)}$" ], "text/plain": [ " ⎛ 1 ⎞\n", "-atan⎜─────────⎟\n", " ⎝2⋅π⋅C⋅R⋅f⎠" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "simplify(atan(c1/c2))" ] }, { "cell_type": "markdown", "id": "61093af9", "metadata": {}, "source": [ "I wish to compare this with the complex analysis of the circuit" ] }, { "cell_type": "code", "execution_count": 39, "id": "3bfdd494", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle \\frac{C R \\omega - i}{C \\omega}$" ], "text/plain": [ "C⋅R⋅ω - ⅈ\n", "─────────\n", " C⋅ω " ] }, "execution_count": 39, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Z = R - I / (w*C)\n", "zc = cancel(Z) # express as fraction\n", "zc" ] }, { "cell_type": "code", "execution_count": 40, "id": "f3db2138", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle - \\frac{i}{C R \\omega - i}$" ], "text/plain": [ " -ⅈ \n", "─────────\n", "C⋅R⋅ω - ⅈ" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Now we try and work out Vout as R/Z\n", "rzc = (-I/(w*C))/zc\n", "rzc" ] }, { "cell_type": "code", "execution_count": 41, "id": "01ccfae6", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle \\frac{1}{C^{2} R^{2} \\omega^{2} + 1}$" ], "text/plain": [ " 1 \n", "────────────\n", " 2 2 2 \n", "C ⋅R ⋅ω + 1" ] }, "execution_count": 41, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sympy.re(rzc)" ] }, { "cell_type": "code", "execution_count": 42, "id": "b5d08d9b", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle - \\frac{C R \\omega}{C^{2} R^{2} \\omega^{2} + 1}$" ], "text/plain": [ " -C⋅R⋅ω \n", "────────────\n", " 2 2 2 \n", "C ⋅R ⋅ω + 1" ] }, "execution_count": 42, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sympy.im(rzc)" ] }, { "cell_type": "code", "execution_count": 43, "id": "18c46477", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle \\frac{C^{2} R^{2} \\omega^{2}}{\\left(C^{2} R^{2} \\omega^{2} + 1\\right)^{2}} + \\frac{1}{\\left(C^{2} R^{2} \\omega^{2} + 1\\right)^{2}}$" ], "text/plain": [ " 2 2 2 \n", " C ⋅R ⋅ω 1 \n", "─────────────── + ───────────────\n", " 2 2\n", "⎛ 2 2 2 ⎞ ⎛ 2 2 2 ⎞ \n", "⎝C ⋅R ⋅ω + 1⎠ ⎝C ⋅R ⋅ω + 1⎠ " ] }, "execution_count": 43, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sympy.re(rzc)**2 + sympy.im(rzc)**2" ] }, { "cell_type": "code", "execution_count": 44, "id": "0436eb4f", "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle \\frac{1}{C^{2} R^{2} \\omega^{2} + 1}$" ], "text/plain": [ " 1 \n", "────────────\n", " 2 2 2 \n", "C ⋅R ⋅ω + 1" ] }, "execution_count": 44, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# This is the square of the magnitude of voltage dividing impedance across R\n", "c3_2 = cancel(_)\n", "c3_2" ] }, { "cell_type": "code", "execution_count": 45, "id": "225bcd4b", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle - \\operatorname{atan}{\\left(C R \\omega \\right)}$" ], "text/plain": [ "-atan(C⋅R⋅ω)" ] }, "execution_count": 45, "metadata": {}, "output_type": "execute_result" } ], "source": [ "phase = atan(sympy.im(rzc)/sympy.re(rzc))\n", "phase" ] }, { "cell_type": "code", "execution_count": 46, "id": "26cdf8e7", "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle \\frac{1}{\\sqrt{\\omega^{2} + 1}}$" ], "text/plain": [ " 1 \n", "───────────\n", " ________\n", " ╱ 2 \n", "╲╱ ω + 1 " ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" } ], "source": [ "u = sqrt(c3_2).subs([(A,1), (C,1), (R,1)])\n", "u" ] }, { "cell_type": "code", "execution_count": 47, "id": "75116894", "metadata": {}, "outputs": [], "source": [ "f1 = lambdify(w, u)" ] }, { "cell_type": "code", "execution_count": 48, "id": "25585a9d", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, (ax1, ax2) = plt.subplots(1, 2)\n", "fig.set_figwidth(13)\n", "\n", "f1 = lambdify(w, u)\n", "t1 = np.linspace(0, 4, 8000)\n", "y = f1(t1)\n", "y2 = 1 - y\n", "\n", "ax1.title.set_text(\"frequency vs phase $V_c$\")\n", "ax1.set_xlabel(\"Frequency ($ \\omega $)\")\n", "ax1.set_ylabel(\"cos(Phase)\")\n", "ax1.plot(t1, y)\n", "ax1.grid()\n", "\n", "\n", "ax2.title.set_text(\"frequency vs phase $V_R$\")\n", "ax2.set_xlabel(\"Frequency ($ \\omega $)\")\n", "ax2.set_ylabel(\"cos(phase)\")\n", "ax2.plot(t1, y2)\n", "ax2.grid()\n", "\n", "plt.show()\n" ] }, { "cell_type": "code", "execution_count": 49, "id": "f30ac994", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle \\frac{2 \\pi e^{- t}}{1 + 4 \\pi^{2}}$" ], "text/plain": [ " -t \n", "2⋅π⋅ℯ \n", "────────\n", " 2\n", "1 + 4⋅π " ] }, "execution_count": 49, "metadata": {}, "output_type": "execute_result" } ], "source": [ "expdropoff = simpeq2.args[2].subs([(C*R, 1), (A,1), (f,1)])\n", "expdropoff" ] }, { "cell_type": "code", "execution_count": 50, "id": "cc21b169", "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle \\frac{\\sin{\\left(2 \\pi t \\right)}}{1 + 4 \\pi^{2}} - \\frac{2 \\pi \\cos{\\left(2 \\pi t \\right)}}{1 + 4 \\pi^{2}} + \\frac{2 \\pi e^{- t}}{1 + 4 \\pi^{2}}$" ], "text/plain": [ " -t \n", "sin(2⋅π⋅t) 2⋅π⋅cos(2⋅π⋅t) 2⋅π⋅ℯ \n", "────────── - ────────────── + ────────\n", " 2 2 2\n", " 1 + 4⋅π 1 + 4⋅π 1 + 4⋅π " ] }, "execution_count": 50, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fn = simpeq2.subs([(C*R, 1), (A,1), (f,1)])\n", "fn" ] }, { "cell_type": "code", "execution_count": 51, "id": "1aa54e9c", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([ 184, 588, 989, 1389, 1789, 2189, 2589, 2989, 3389, 3789])" ] }, "execution_count": 51, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f1 = lambdify(t, fn)\n", "f3 = lambdify(t, expdropoff)\n", "t1 = np.linspace(0, 10, 4000)\n", "y2 = np.sin(2*np.pi*t1)\n", "y = f1(t1)\n", "pks = find_peaks(y)[0]\n", "pks" ] }, { "cell_type": "code", "execution_count": 52, "id": "e12e53d3", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/latex": [ "$\\displaystyle \\left[ \\left( 0.460115028757189, \\ 0.254479337914674\\right), \\ \\left( 1.47036759189797, \\ 0.192790174277999\\right), \\ \\left( 2.47311827956989, \\ 0.170255738060344\\right), \\ \\left( 3.47336834208552, \\ 0.161983472100571\\right), \\ \\left( 4.47361840460115, \\ 0.15894225432955\\right), \\ \\left( 5.47386846711678, \\ 0.157824705183785\\right), \\ \\left( 6.47411852963241, \\ 0.157414411932577\\right), \\ \\left( 7.47436859214804, \\ 0.157263993225821\\right), \\ \\left( 8.47461865466367, \\ 0.157208907812005\\right), \\ \\left( 9.47486871717929, \\ 0.157188639481615\\right)\\right]$" ], "text/plain": [ "[(0.4601150287571893, 0.25447933791467403), (1.4703675918979744, 0.19279017427 ↪\n", "\n", "↪ 799905), (2.4731182795698925, 0.17025573806034372), (3.4733683420855215, 0.1 ↪\n", "\n", "↪ 6198347210057146), (4.47361840460115, 0.15894225432954986), (5.4738684671167 ↪\n", "\n", "↪ 79, 0.1578247051837846), (6.474118529632408, 0.15741441193257652), (7.474368 ↪\n", "\n", "↪ 5921480365, 0.15726399322582088), (8.474618654663665, 0.15720890781200475), ↪\n", "\n", "↪ (9.474868717179294, 0.15718863948161516)]" ] }, "execution_count": 52, "metadata": {}, "output_type": "execute_result" } ], "source": [ "[(t1[ii],y[ii]) for ii in pks]" ] }, { "cell_type": "code", "execution_count": 53, "id": "2bd80ab4", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, (ax1, ax3) = plt.subplots(1,2)\n", "fig.set_figwidth(12)\n", "\n", "f1 = lambdify(t, fn)\n", "f3 = lambdify(t, expdropoff)\n", "t1 = np.linspace(0, 10, 4000)\n", "y2 = np.sin(2*np.pi*t1)\n", "y = f1(t1)\n", "\n", "ax1.title.set_text(\"Amplitude vs time from $ V_C $ formula\")\n", "ax1.set_xlabel(\"Time (RC units)\")\n", "ax1.set_ylabel(\"Relative Amplitude\")\n", "ax1.plot(t1, y)\n", "ax1.grid()\n", "\n", "\n", "t1 = np.linspace(0, 10, 4000)\n", "y = f3(t1)\n", "\n", "ax3.title.set_text(\"Exponential drop off component\")\n", "ax3.set_xlabel(\"Time (RC units)\")\n", "ax3.set_ylabel(\"Relative Amplitude\")\n", "ax3.plot(t1, y)\n", "ax3.grid()\n", "plt.show()\n" ] }, { "cell_type": "code", "execution_count": 54, "id": "eadcb521", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(array([], dtype=int64), {})" ] }, "execution_count": 54, "metadata": {}, "output_type": "execute_result" } ], "source": [ "find_peaks(y)" ] }, { "cell_type": "code", "execution_count": 55, "id": "c42e81ff", "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 55, "metadata": {}, "output_type": "execute_result" } ], "source": [ "\n", "Image(url='https://images.kiwiheretic.xyz/RC-filter1.jpg', width=400)" ] }, { "cell_type": "markdown", "id": "c3e5d823", "metadata": {}, "source": [ "I am assuming that the voltage in the direction of conventional current produces a positive voltage above ground.\n", "That means $ R_1 ( i_2 - i_1) $ is considered to be a positive voltage above ground because the current is flowing to ground. However the same must be true of $ R_2 i_2 $ if we look at $ R_1 ( i_2 - i_1) $ being the voltage source of the last stage.\n", "\n", "There are two equations:\n", "\n", "$$ V_{in} = V_{C1} + R_1 (i_1 - i_2) $$\n", "$$ R_1 ( i_2 - i_1) = V_{C2} + R_2 i_2 $$\n", "\n", "These can be rearranged so that all the i's are on the right and everything else on the left.\n", "\n", "$$ V_{in} - V_{C1} = R_1 i_1 - R_1 i_2) $$\n", "$$ V_{C2} = R_1 ( i_2 - i_1) - R_2 i_2 = (R_1 - R_2) i_2 - R_1 i_1 $$\n" ] }, { "cell_type": "markdown", "id": "c914fb13", "metadata": {}, "source": [ "In matrix form this looks like:\n", "\n", "$$ \\begin{pmatrix}\n", "V_{in} - V_{C1} \\\\ V_{C2}\n", "\\end{pmatrix} \n", "=\n", "\\begin{pmatrix}\n", "R_1 & -R_1 \\\\\n", "-R_1 & R_1 - R_2 \\\\\n", "\\end{pmatrix}\n", "\\begin{pmatrix}\n", "i_1 \\\\ i_2\n", "\\end{pmatrix} $$" ] }, { "cell_type": "code", "execution_count": 56, "id": "e91de147", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(R_1, R_2, V_{in}, Vc1, Vc2, C_1, C_2)" ] }, "execution_count": 56, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A_0, A_1, A_2, B_1, B_2, R1, R2, R3, Vin, C1, C2 = symbols(\"A_0 A_1 A_2 B_1 B_2 R_1 R_2 R_3 V_{in} C_1 C_2\")\n", "Vc1 = Function('Vc1')\n", "Vc2 = Function('Vc2')\n", "Vc3 = Function('Vc3')\n", "R1,R2, Vin, Vc1, Vc2, C1,C2" ] }, { "cell_type": "code", "execution_count": 57, "id": "14c67acf", "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left[\\begin{matrix}R_{1} & - R_{1}\\\\- R_{1} & R_{1} - R_{2}\\end{matrix}\\right]$" ], "text/plain": [ "⎡R₁ -R₁ ⎤\n", "⎢ ⎥\n", "⎣-R₁ R₁ - R₂⎦" ] }, "execution_count": 57, "metadata": {}, "output_type": "execute_result" } ], "source": [ "m = Matrix([[R1, -R1], [-R1, R1-R2]]); m" ] }, { "cell_type": "code", "execution_count": 58, "id": "34ec4cdb", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left[\\begin{matrix}V_{in} - \\operatorname{Vc}_{1}{\\left(t \\right)}\\\\\\operatorname{Vc}_{2}{\\left(t \\right)}\\end{matrix}\\right]$" ], "text/plain": [ "⎡V_{in} - Vc₁(t)⎤\n", "⎢ ⎥\n", "⎣ Vc₂(t) ⎦" ] }, "execution_count": 58, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v = Matrix([Vin-Vc1(t), Vc2(t)]);v" ] }, { "cell_type": "code", "execution_count": 59, "id": "a6128b46", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left[\\begin{matrix}\\frac{- R_{1} + R_{2}}{R_{1} R_{2}} & - \\frac{1}{R_{2}}\\\\- \\frac{1}{R_{2}} & - \\frac{1}{R_{2}}\\end{matrix}\\right]$" ], "text/plain": [ "⎡-R₁ + R₂ -1 ⎤\n", "⎢──────── ───⎥\n", "⎢ R₁⋅R₂ R₂ ⎥\n", "⎢ ⎥\n", "⎢ -1 -1 ⎥\n", "⎢ ─── ───⎥\n", "⎣ R₂ R₂ ⎦" ] }, "execution_count": 59, "metadata": {}, "output_type": "execute_result" } ], "source": [ "m.inv()" ] }, { "cell_type": "code", "execution_count": 60, "id": "eb0fd76f", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left[\\begin{matrix}- \\frac{\\operatorname{Vc}_{2}{\\left(t \\right)}}{R_{2}} + \\frac{\\left(- R_{1} + R_{2}\\right) \\left(V_{in} - \\operatorname{Vc}_{1}{\\left(t \\right)}\\right)}{R_{1} R_{2}}\\\\- \\frac{V_{in} - \\operatorname{Vc}_{1}{\\left(t \\right)}}{R_{2}} - \\frac{\\operatorname{Vc}_{2}{\\left(t \\right)}}{R_{2}}\\end{matrix}\\right]$" ], "text/plain": [ "⎡ Vc₂(t) (-R₁ + R₂)⋅(V_{in} - Vc₁(t))⎤\n", "⎢- ────── + ────────────────────────────⎥\n", "⎢ R₂ R₁⋅R₂ ⎥\n", "⎢ ⎥\n", "⎢ V_{in} - Vc₁(t) Vc₂(t) ⎥\n", "⎢ - ─────────────── - ────── ⎥\n", "⎣ R₂ R₂ ⎦" ] }, "execution_count": 60, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mtmp = m.inv()*v\n", "mtmp" ] }, { "cell_type": "code", "execution_count": 61, "id": "7f06d9c5", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle \\frac{d}{d t} \\operatorname{Vc}_{1}{\\left(t \\right)} = - \\frac{\\operatorname{Vc}_{2}{\\left(t \\right)}}{C R}$" ], "text/plain": [ "d -Vc₂(t) \n", "──(Vc₁(t)) = ────────\n", "dt C⋅R " ] }, "execution_count": 61, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eqn_1 = Eq(C1 * Vc1(t).diff()/C, mtmp[0]/C)\n", "eqn1 = eqn_1.subs([(R1, R), (R2, R), (C1,C)])\n", "eqn1" ] }, { "cell_type": "code", "execution_count": 62, "id": "1fdca3e2", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle \\frac{d}{d t} \\operatorname{Vc}_{2}{\\left(t \\right)}$" ], "text/plain": [ "d \n", "──(Vc₂(t))\n", "dt " ] }, "execution_count": 62, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Vc2(t).diff()" ] }, { "cell_type": "code", "execution_count": 63, "id": "8e3d540c", "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle \\frac{d}{d t} \\operatorname{Vc}_{2}{\\left(t \\right)} = \\frac{- V_{in} + \\operatorname{Vc}_{1}{\\left(t \\right)} - \\operatorname{Vc}_{2}{\\left(t \\right)}}{C R}$" ], "text/plain": [ "d -V_{in} + Vc₁(t) - Vc₂(t)\n", "──(Vc₂(t)) = ─────────────────────────\n", "dt C⋅R " ] }, "execution_count": 63, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eqn_2 = Eq(Vc2(t).diff(), simplify(mtmp[1]/C))\n", "eqn2 = eqn_2.subs([(R1, R), (R2, R)])\n", "eqn2" ] }, { "cell_type": "code", "execution_count": 64, "id": "8ae391f1", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle \\frac{d}{d t} \\operatorname{Vc}_{1}{\\left(t \\right)} = - \\frac{\\operatorname{Vc}_{2}{\\left(t \\right)}}{C R}$" ], "text/plain": [ "d -Vc₂(t) \n", "──(Vc₁(t)) = ────────\n", "dt C⋅R " ] }, "execution_count": 64, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eqn1" ] }, { "cell_type": "code", "execution_count": 65, "id": "03271341", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "sympy.core.mul.Mul" ] }, "execution_count": 65, "metadata": {}, "output_type": "execute_result" } ], "source": [ "type(eqn2.rhs)" ] }, { "cell_type": "code", "execution_count": 66, "id": "c7d7558d", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "sympy.core.add.Add" ] }, "execution_count": 66, "metadata": {}, "output_type": "execute_result" } ], "source": [ "type(expand(eqn2.rhs))" ] }, { "cell_type": "code", "execution_count": 67, "id": "68e3840e", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 67, "metadata": {}, "output_type": "execute_result" } ], "source": [ "isinstance(eqn1, sympy.Equality)" ] }, { "cell_type": "code", "execution_count": 68, "id": "13085f87", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "sympy.core.function.Derivative" ] }, "execution_count": 68, "metadata": {}, "output_type": "execute_result" } ], "source": [ "type(eqn1.lhs)" ] }, { "cell_type": "code", "execution_count": 69, "id": "428b07d4", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 69, "metadata": {}, "output_type": "execute_result" } ], "source": [ "isinstance(eqn1.lhs.args[0], sympy.Function)" ] }, { "cell_type": "code", "execution_count": 70, "id": "15a87aec", "metadata": {}, "outputs": [], "source": [ "def fn1(t, y, R, C, f):\n", " \"\"\" y is an array of size 2\"\"\"\n", " #print (t,y,R,C,f)\n", " yp1 = (-y[1]) / (C*R)\n", " yp2 = (y[0] - y[1] - math.sin(2 * math.pi * f * t))/(C*R)\n", " return [ yp1, yp2 ]\n" ] }, { "cell_type": "code", "execution_count": 71, "id": "716f1667", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle 0.01$" ], "text/plain": [ "0.01" ] }, "execution_count": 71, "metadata": {}, "output_type": "execute_result" } ], "source": [ "1000*0.00001 " ] }, { "cell_type": "code", "execution_count": 72, "id": "93d7f0da", "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle \\left[ 0.0, \\ -0.0628318489376257\\right]$" ], "text/plain": [ "[0.0, -0.06283184893762572]" ] }, "execution_count": 72, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fn1(0.0001, [0,0], 1000, 0.00001, 1)" ] }, { "cell_type": "code", "execution_count": 73, "id": "8217b134", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, axs = plt.subplots(2,3)\n", "fig.set_figwidth(14)\n", "fig.set_figheight(10)\n", "\n", "farr = [1,5]\n", "\n", "start_idx = 8\n", "for ax1, ax2, ax3 in axs:\n", " freq = farr.pop(0)\n", " res = solve_ivp(fn1, [0,5], [0,0], 'RK45', args = (1000,0.00001,freq), first_step=0.0001)\n", " ax1.title.set_text(\"$V_{{C1}} $ freq = {} Hz\".format(freq))\n", " ax1.set_ylabel(\"$V_{C1}$\")\n", " ax1.set_xlabel(\"Time\")\n", " ax1.plot(res.t[start_idx:]/(math.pi*2), res.y[0][start_idx:])\n", " ax1.grid()\n", "\n", " ax2.title.set_text(\"$V_{{C2}} $ freq = {} Hz\".format(freq))\n", " ax2.set_ylabel(\"$V_{C2}$\")\n", " ax2.set_xlabel(\"Time\")\n", " ax2.plot(res.t[start_idx:]/(math.pi*2), res.y[1][start_idx:])\n", " ax2.grid()\n", " \n", " vr1 = np.sin(2 * math.pi * freq * res.t) - res.y[0] - res.y[1]\n", " ax3.title.set_text(\"$V_{{out}} $ freq = {} Hz\".format(freq))\n", " ax3.set_ylabel(\"$V_{out}$\")\n", " ax3.set_xlabel(\"Time\")\n", " ax3.plot(res.t[start_idx:]/(math.pi*2), vr1[start_idx:])\n", " ax3.grid()\n", "\n", "plt.show()\n" ] }, { "cell_type": "code", "execution_count": 74, "id": "1db9ef88", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle \\frac{d}{d t} \\operatorname{Vc}_{1}{\\left(t \\right)} = - \\frac{\\operatorname{Vc}_{2}{\\left(t \\right)}}{C R}$" ], "text/plain": [ "d -Vc₂(t) \n", "──(Vc₁(t)) = ────────\n", "dt C⋅R " ] }, "execution_count": 74, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eqn1" ] }, { "cell_type": "code", "execution_count": 75, "id": "d8c3b4e9", "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXAAAAAcCAYAAAB4WOSqAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuNSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/xnp5ZAAAACXBIWXMAABJ0AAASdAHeZh94AAAMXklEQVR4nO2debAUxR3HPw9NIkoiJSZeqETFqxQeoIhBjBovYjSgRoMRAgKJoiYEtCJR6usvlEq8wEQhJVaEJGpCPDARTzxiJfEiCiLigUe8UIyICsYDffmje3jz5s3OzL63s+y+mk/VVu9290z/pvvX1697ehuamprIipmdCkyU1DPzRQUFBQUFudCpzPiNwKLKi1FQUFBQUC5tacCfyEGOgoKCgoIy2bhUgJk1AtOAAcByYDSwN/DLqkhWUFBQUJBIbANuZj2BvwMzgbHAbsBcYFPq2IRiZnOAwcDXJa3NeE0/YCEwVtI1ecqXQZay5S+oPcotx1rSwVolj7pdD/neELeIaWZ3Ae9IOinkNws4RtJWMfGvA04CTpc0IylBM7sbOAw4VtIt7ZQ/M2a2L/AIcJaky2PCfwZcDvxA0vWRsFtwM5GektZUQ94Y+RLlb+e9hwHXAzMljUuJOxM4FbhU0tmVlKO91Lse1qoO1nq+5lm3s+S7mW0FvAHMkHRmTHhP4BTgcGAHoCuwGlgM3AzMlvRhKH6Qh2HeBp4DrpD0l8CzlQ3czLb3CU2LBH1K6dH3LO+OKREe3LsHcCiwAvhbUtwcuAB4HzeriKOfd/8dE3YRsDXwkxzkykqa/O1hsXf3SopkZn2AHwGvA5aDHO2l3vWwVnWw1vM1z7qdJd+/i2tLbw57mlmDmU0BlgLnAB8BNwKXAQuAPsBVwF0x8jbhzNWGe74HcR3JXN8hAfGLmH2Az2iu1AF9KdGAS3oA1zv0MbO+CQ86GmgArpW0LiFeRTGzXXGKNVfS/0pE6weswT1HCyQ9CjwD/NjMyl34bTcZ5W8Pz+KUa++UeL/B6czEPEeBZjbSzJrM7KByrusAeliTOljL+Zp33c6Y70OBd3CNbJjfAecBzwONkgZKOk3SOZKGAd19+PLQ8+wEbAE8J8f5ks6TdDxwho/20yB+nA28CdgI+BLwib/pIGA/YHqJBwDXS1+Cs5mfFg00s42AUf7+cfam/sBE4ABgS2AVsAS4RtLchHSzcApOsf4ck+5U4Ochr8/N1g8uR0j6g//+J+B83NQm2mPmTUn5K4Gkz8xsKdDPzLpLei0ax8xOBgYC90rKRY4KUXd6WCc62OZ87QB1u2S4mX0FOAS4XtJnIf8JwEhgGTBA0gfRm/oO5wIz6xzy3se7cbOFO737tcAjrkdZCHwMXGpmO5vZUcAffdiimPgBc3AN/jAz2zQmfDCwHbBA0kvhADMbC/wLGOLdy4D5XtBEm2xGDsXNKh6OCXvcy45P20KfB0Lx/undqG2qGiTJXymCGVerUbiZdQF+hTOjnRENrzHqUQ/rQQfblK8dpG4nhX8H+CKw3t5vZtvgzB7rgBPiGu8wkZlDUgO+i3eXBR6tRuCSVpjZKGAqMAK373s2cBYxU5DQdW+b2TzgBP+ZHYky1rtXhz3NbE9gBs6GNUjS0kh491JpZsHMNsPtX18Wtzotaa6ZdQV+CMyRdHU0jucx7x6Ykt543CJFVhZJmpdwv0T5K0i4Ab8jEjYZ2Ba4WNIzOcrQbupRDyutg3nQlnztQHU7KXwosBa4O+Q3HtgEtzj5VMIjxBE04AvDnma2JXCp/zk18I/dRijpBuCGqHeGxK/GFe4YQgXse6RvAyuBWyPXnOblmBItYC9Lq+l8mWyHMwmtSIgT2PUeLxVB0ntm9hFuFTmJ8cCOZcg3B5iXEJ5F/koQu5DpbYzjgdeIvANgZlcB20oamrNs5VKPelhJHcyLcvN1Q+cpVCBfS4Wb2SbAkcAdkj4KBQ3x7u8TpY9gZg0heY8xs0Nwz7cjcAzOYjIuvAul5Is8beQ+4AVgoJntISkY6o/yac2W9GnkmgHejY76WmFmk4BjcfvSP8ZNmyal9HLdvPtuQpy+OPPAkhQRVgGttlGGkdQj5R7lkiq/mb1MeZ3GdZJOjvg96d2oCWU6boo4IWaUcx4u39pMiuz3h2yWAXMkjUy5bd56eCBuRtoPNzMZJWl2ymVp5VgxHfQyvkz7dSJKufnakep2XPhhQBdamk+6ALvi1gIeSUkzSk9gc/99YiRsLXC8pDvDnhVdzZYUXsAYA+t7ldG4B5oVc1lX776eIYmDcFOyb+AWDtYBC8xsi4RrAvvSJnGBZrYxrtF6WtLHKel3Dt2vWiTK73kBt5Mk6+eN6A0kvQu8Cuzh8wQzOxpn27wn3OuHr6nAbpTptLRNGs2juDkxYfPSblgFPewCPIXbDZBVH0qWY0462G6diNKGfO3q3Y5Qt+PCj8WtC8wP+X3Vu++H93ZnJDCfXCupQVIDrpOaAGwG3OBNQusJKmr2Iwlj8AkFXIubao/wveogYCfgPknLYy5f7d3tcNt1ktI5IvzbzIYD7+F2R5Tad7rSu91KhO+JU4CSUyyfViecQr6UEm88FbSBky4/kr5VRnpJLMYtyvQ0sxdx7wJ8AsS9nNAd3+BLeib0ewhu6jwIeBMYI+n+BNmnx9x7JG5v7Wy/ha0t5KmHtwO3e1lnZ5QnqRwrqoNexkrpRJRy8nW1d+u6bseF+103R+Oe+71Q9GCW2tnMNgrvTMlAK/u3pFXANDPbH/geMBy3nRfwDXikAW4Xkt4ys78Cx+Eqc2AfLbWA8LAXfDAphRzDl3GziKQp1ArcW0y7lQhv9G7aIV274bYrLUqJN57K2sDT5K8kQQO+N250sTMwVdKzMXF7Ax/SvLDd27sTgCm43SqX4d6A65OjzLFUWQ+zkFSOjd6tlA7mRpn52lHqdlz4gbiOo8XbppJWmtl/cG3AQcC9pRI1s06SPg95Je1AuQbXgA8j1ICnmlDM7FQzez4tXoRgKjURV8D/JfKgIWbipkuT/ap1NP2kleorcJn6UKkIftr3ILClme0SEyXovd9PSAea7XklR5M+vR7B9CfjZ2TK/dLkryTBQuZg4Be4EfWUEnEbgSUhBWzE5eGJkhb40diNNE8pNwTV0sNUUsqxojpYBbLma0ep23HhQ4HPab0YDs1vsc8ws92jgebe0ByM218e+HXCDXTW0folyiDt1cAAM9s28MyyiNmI73nM7BKgV3S6E8PdwMtAf//7SkmfxEWU9LSZjQN+CzxhZrfi3lzqBuyLy/yDo9eZ2eW4FwMOyDBNuQk3YjiC0FtPnqC3u8DM9sJNgZbG2HwPx+03jSuwvEmSv5IEijPSuyMS7Hi9aTki6Q3Ml/RmyG8X8pU3jdz1sExKlWM96GCYTPnagep2i3Bv9x8CPCTprZj4vwZ64V4yWmLubJPncIup2/tn6447fyhgd9zayuLIjhYAJH1qZrfjzqQZinsFP9MiZiPNU5D+wKNpF0QWOyB+0SgcfxbuoW7DTTvOxm2beTsQNIyZTcNNJQ6R9GKaPLhCXonb1x5N+0GcjXetd0Xz1CtIb3Ncgd0m6dUM6VWakvJXmOU4swjAXZJuSojbSMsGvJHWo6U+bNjpfq562AZiy7FOdHA95eRrvdftEuH74Brim6PxfbpNkkYDR+GeuxE4Hbfw2wtXT0bS8nyVJPNJQDDLOS7waHEaocWfAX4/LkNvBL4QutkySa2mRXljZlcAJwIHh7YxZbluEnAh0FdSWX9KYWZn4nrVQZL+Uc61laI98ucgy2a40dNASQ+Hfn8znD9m9iowOcMWu7rFzNYAZ2R9xraWYy3oYN7UYt2OCzezC4FJwE6KvM1bbdabUCz5DPCFwP7e3Q94BbdXs6r4F0eG43rEd81sax+0JsN2tmm4Y1B/iVs9zppmZ1xh3bSBK06b5M+JXt59MvJ7URDBzLrhponr/ToKfq9vYHPtBOzgBz+rJL2ScnnZ5VhDOpgbtVi3E8KH4kwdG7TxhpYmlCtxNsxzJC2XNB+4B1gp6Q1gG+AD4DFJb/p9w9VmHG51+l7cCnTwOSvtQm9XGg4s9CPGrPTArbCnppEn7ZA/D3oDz4fs48HvcEXrg7P5PV1t4arAPjiz4hO4/cHmv6f+W1Uby7EHNaCDOVOLdTs2XNIekhrLSCc3GpqamoIzwF8B+ksK3vvHzGYAO0s6wswmA4dLGrShhC0oKCgoaCYYgWc5A7yR4g+NCwoKCmqGoAEPnwEOtDgDPGi0e9Ns8ywoKCgo2MAEi5jhM8Avxu1JDP77blEo7u5+E/mHklZXUc6CgoKCggidwJ0BjjtR7EjcIT3n4o6LDL8qfS7wfdyxohdVW9CCgoKCgpbE/it9QUFBQUHt83/059PqjYN3uAAAAABJRU5ErkJggg==", "text/latex": [ "$\\displaystyle \\frac{d}{d t} \\operatorname{Vc}_{2}{\\left(t \\right)} = \\frac{- V_{in} + \\operatorname{Vc}_{1}{\\left(t \\right)} - \\operatorname{Vc}_{2}{\\left(t \\right)}}{C R}$" ], "text/plain": [ "d -V_{in} + Vc₁(t) - Vc₂(t)\n", "──(Vc₂(t)) = ─────────────────────────\n", "dt C⋅R " ] }, "execution_count": 75, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eqn2" ] }, { "cell_type": "code", "execution_count": 76, "id": "184ca226", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[(a_2*omega, -a_1*omega), (a_3/(C*R), a_4/(C*R))]\n", "[(a_4*omega, -a_3*omega), (-a_1/(C*R), -a_2/(C*R)), (a_5/(C*R), a_6/(C*R)), (a_3/(C*R), a_4/(C*R))]\n", "[a_1, a_2, a_3, a_4, a_5, a_6]\n" ] } ], "source": [ "sysEqns = systemEqns()\n", "\n", "res1 = sysEqns.extractCoeffsFromDiffEqn(eqn1)\n", "print (res1)\n", "res2 = sysEqns.extractCoeffsFromDiffEqn(eqn2)\n", "print (res2)\n", "print (sysEqns.symbols_used)\n" ] }, { "cell_type": "code", "execution_count": 77, "id": "71203e92", "metadata": { "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "a_2*omega -a_1*omega\n", "a_3/(C*R) a_4/(C*R)\n", "a_4*omega -a_3*omega\n", "-a_1/(C*R) -a_2/(C*R)\n", "a_5/(C*R) a_6/(C*R)\n", "a_3/(C*R) a_4/(C*R)\n" ] }, { "data": { "text/latex": [ "$\\displaystyle \\left[\\begin{matrix}- \\omega & 0 & 0 & \\frac{1}{C R} & 0 & 0\\\\0 & \\omega & \\frac{1}{C R} & 0 & 0 & 0\\\\0 & - \\frac{1}{C R} & - \\omega & \\frac{1}{C R} & 0 & \\frac{1}{C R}\\\\- \\frac{1}{C R} & 0 & \\frac{1}{C R} & \\omega & \\frac{1}{C R} & 0\\end{matrix}\\right]$" ], "text/plain": [ "⎡ 1 ⎤\n", "⎢-ω 0 0 ─── 0 0 ⎥\n", "⎢ C⋅R ⎥\n", "⎢ ⎥\n", "⎢ 1 ⎥\n", "⎢ 0 ω ─── 0 0 0 ⎥\n", "⎢ C⋅R ⎥\n", "⎢ ⎥\n", "⎢ -1 1 1 ⎥\n", "⎢ 0 ─── -ω ─── 0 ───⎥\n", "⎢ C⋅R C⋅R C⋅R⎥\n", "⎢ ⎥\n", "⎢-1 1 1 ⎥\n", "⎢─── 0 ─── ω ─── 0 ⎥\n", "⎣C⋅R C⋅R C⋅R ⎦" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "M, syms_used = sysEqns.orderedMatrix([res1, res2])\n", "display(M)" ] }, { "cell_type": "code", "execution_count": 78, "id": "eed5dd94", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle \\left[ a_{1}, \\ a_{2}, \\ a_{3}, \\ a_{4}, \\ a_{5}, \\ a_{6}\\right]$" ], "text/plain": [ "[a₁, a₂, a₃, a₄, a₅, a₆]" ] }, "execution_count": 78, "metadata": {}, "output_type": "execute_result" } ], "source": [ "syms_used" ] }, { "cell_type": "markdown", "id": "cbb4a6e8", "metadata": {}, "source": [ "The rows of M1 are in order of a1, a2, a3, a4" ] }, { "cell_type": "code", "execution_count": 79, "id": "9c052a4c", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left[\\begin{matrix}- \\omega & 0 & 0 & \\frac{1}{C R}\\\\0 & \\omega & \\frac{1}{C R} & 0\\\\0 & - \\frac{1}{C R} & - \\omega & \\frac{1}{C R}\\\\- \\frac{1}{C R} & 0 & \\frac{1}{C R} & \\omega\\end{matrix}\\right]$" ], "text/plain": [ "⎡ 1 ⎤\n", "⎢-ω 0 0 ───⎥\n", "⎢ C⋅R⎥\n", "⎢ ⎥\n", "⎢ 1 ⎥\n", "⎢ 0 ω ─── 0 ⎥\n", "⎢ C⋅R ⎥\n", "⎢ ⎥\n", "⎢ -1 1 ⎥\n", "⎢ 0 ─── -ω ───⎥\n", "⎢ C⋅R C⋅R⎥\n", "⎢ ⎥\n", "⎢-1 1 ⎥\n", "⎢─── 0 ─── ω ⎥\n", "⎣C⋅R C⋅R ⎦" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "M1 = M[:4,:4]\n", "display(M1)" ] }, { "cell_type": "code", "execution_count": 80, "id": "798afa00", "metadata": {}, "outputs": [], "source": [ "A,B,D,E,F,G,H, w = symbols('A B D E F G H \\omega')" ] }, { "cell_type": "code", "execution_count": 81, "id": "82281ff1", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left[\\begin{matrix}0\\\\0\\\\0\\\\- \\frac{A}{C R}\\end{matrix}\\right]$" ], "text/plain": [ "⎡ 0 ⎤\n", "⎢ ⎥\n", "⎢ 0 ⎥\n", "⎢ ⎥\n", "⎢ 0 ⎥\n", "⎢ ⎥\n", "⎢-A ⎥\n", "⎢───⎥\n", "⎣C⋅R⎦" ] }, "execution_count": 81, "metadata": {}, "output_type": "execute_result" } ], "source": [ "amat = Matrix([0,0, 0,-A/(C*R)])\n", "amat" ] }, { "cell_type": "code", "execution_count": 82, "id": "1be85e38", "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left[\\begin{matrix}- \\frac{A \\left(C^{3} R^{3} \\omega^{2} - C R\\right)}{C R \\left(C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1\\right)}\\\\\\frac{A C R \\omega}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}\\\\- \\frac{A C^{2} R^{2} \\omega^{2}}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}\\\\- \\frac{A \\left(C^{4} R^{4} \\omega^{3} - C^{2} R^{2} \\omega\\right)}{C R \\left(C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1\\right)}\\end{matrix}\\right]$" ], "text/plain": [ "⎡ ⎛ 3 3 2 ⎞ ⎤\n", "⎢ -A⋅⎝C ⋅R ⋅ω - C⋅R⎠ ⎥\n", "⎢─────────────────────────────⎥\n", "⎢ ⎛ 4 4 4 2 2 2 ⎞⎥\n", "⎢C⋅R⋅⎝C ⋅R ⋅ω - C ⋅R ⋅ω + 1⎠⎥\n", "⎢ ⎥\n", "⎢ A⋅C⋅R⋅ω ⎥\n", "⎢ ─────────────────────── ⎥\n", "⎢ 4 4 4 2 2 2 ⎥\n", "⎢ C ⋅R ⋅ω - C ⋅R ⋅ω + 1 ⎥\n", "⎢ ⎥\n", "⎢ 2 2 2 ⎥\n", "⎢ -A⋅C ⋅R ⋅ω ⎥\n", "⎢ ─────────────────────── ⎥\n", "⎢ 4 4 4 2 2 2 ⎥\n", "⎢ C ⋅R ⋅ω - C ⋅R ⋅ω + 1 ⎥\n", "⎢ ⎥\n", "⎢ ⎛ 4 4 3 2 2 ⎞ ⎥\n", "⎢ -A⋅⎝C ⋅R ⋅ω - C ⋅R ⋅ω⎠ ⎥\n", "⎢─────────────────────────────⎥\n", "⎢ ⎛ 4 4 4 2 2 2 ⎞⎥\n", "⎣C⋅R⋅⎝C ⋅R ⋅ω - C ⋅R ⋅ω + 1⎠⎦" ] }, "execution_count": 82, "metadata": {}, "output_type": "execute_result" } ], "source": [ "coeffs = M1**-1 * amat\n", "coeffs" ] }, { "cell_type": "code", "execution_count": 83, "id": "08cf3dfa", "metadata": {}, "outputs": [], "source": [ "d,b,f,e = coeffs" ] }, { "cell_type": "code", "execution_count": 84, "id": "c2603919", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle \\frac{A C R \\omega \\left(\\omega - \\omega\\right)}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}$" ], "text/plain": [ " A⋅C⋅R⋅ω⋅(\\omega - ω) \n", "───────────────────────\n", " 4 4 4 2 2 2 \n", "C ⋅R ⋅ω - C ⋅R ⋅ω + 1" ] }, "execution_count": 84, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Do a sanity check - should equal zero\n", "simplify(b*w+f/(C*R))" ] }, { "cell_type": "code", "execution_count": 85, "id": "60c8e5ae", "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAJsAAAAjCAYAAACD+HiUAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuNSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/xnp5ZAAAACXBIWXMAABJ0AAASdAHeZh94AAAG80lEQVR4nO2baaweUxjHfy1Fa4mdijXUUkV7r1hTW6JBJJbYo1EJIoQ2FLEkfw9irxYhGiQNX0g/EJLaYq+tiy7WSFtNhbaWhtqpXh/OmWvuuTPvLO/aml9yc98575n/eZ5nzpxzZt7nDOjp6aGiHGY2FNhB0nwz2xGYC+wt6ddWajRDqxkMKNPZzGwr4HPgCEmLG25VEzCz6cD7kiYF5Q3zxcwWACdL+qqdGs3QKtBmYpwBNkw5YT9gHvC5pJEJVW4AZqwrHc1zC/CmmT0m6adYeaovZjYSuAY4GtgWWA7MAe6WNDuo2w1sEL+wZvYqcJw/XAMs9ec+mmRgkkZZGqkV6B4FTAS6gZ2ACyVNi1VJizMDUzQfAO4DhpvZRkFjQ4CLgMcbY35rkPQRsAQ4Pyqr5YuZjcN1rD+Bs4G9gQv88aVB3a2BJ4BLApkuXGceCuwFPAVMNbNRCe2laRSmkVoJbAZ8DIwHfg+/TIpzRL+RzcxOx3XCu4HrgeHA/FiVk4Ae4J3gvMnAaOAQSWuD7+YAMyVNyO9TNiXafA44F3jIH6f5cjjwGHCNpMmxr5YBb/mLGdXdGHgWuFPSu7HyPYEtgRclrfBlU4GbgP1xM0dNjTI+1tJqBJJmADN8W9NSqoVxBoKRzcwGA/cCEyX9CHwDhHfhaGCupJ7YefsAV+Auzlr681mCTl2UbHMWcIj3ExJ88UwCPgg6Wi+SVnkbBgDTgNckPRlU6wZWAwt83aG42K4FPoz5kapR1McMe1pJGGeg/8h2He5Oie66T4CRQZ3dcJ0wzkRggaTXUxpfBRxa1OIMyrT5DTAIt9ZYTIIvZjYMOBx3Z2ZxJG6KXWhmp/qysX4q6cZNOavNbCAwGPgLuFrSpzk1ivpYS6uVhHEGYp3NzHYHrgQOip30MXBwIDQYWBk7byBwBm7ajcomA0skPeiLNgcSH7/N7Dbgxgzjj5X0RgPajNYYg2P/VwZ1uvz/ORk2IWkm6eveLtxUfA+wBXA7sEjSlDwaZXzMsCeuXTjmBQnjDPQ1bDKwFfClma0xszW4ReCBfniO+N7Xi9gDtzaJ3z1nAb/Fjg8C4ndznCnAfhl/s4JzyrYZrbW+S/EFYIj//0uKvXnpAt6VtEjSh7iHisvM7ICc59cb11pMoXjMixDGGfAjm5mNwT3ed+OG+oh9gek4x5f4snnAuFid6GL94rWOwQ2ff/njYbip+I4kqyR9j7voRSjb5gjga0nRaBb6Am40BxePp8OGzWyIpN/C8qDOHriA93YUSUvNbB4wFri21vmeuuJai5IxL0IYZwA2NLNBwP3AJH8H9mJmy/zHUfzX2V4C7jKzbST9gHtCWwucZ2Y/4l6bPA+c7F8qPgwsBJ5poDNl2xzt7Y8IfUHSbDN7AXjQL3DfwT2xdgEXAwbMzLCv29sXjjqvAKeTr7O1I66ZmNlmuNc44GbGXf37yFWSov4Sxrm38nhgO5wzfZC0GlhB7CHBLzZnAef4429xr0jOBF4GpuIWtqOA94EfgJMk/VOfm33sKtymmW0CnAY8GtPp40uM03BPjlfhXvvMxj08vUeOtRyusy2W9EdQ/gowzMz2b4aPLeJg3IwwD7cmM//5FkiOc0TZn6tOwI2Gw9vgbCnM7HLgFEljgvJ1zpdOJi3OkOPJJQlJL+Je2O1cp22t5G/cO6s+rKO+dDKJcYaSI1tFRRlKjWwVFWWoOltFy6g6W0XLiF7qVgu3iqZT1wOCzwf7DJguaWK7NJqhVYcNuwBPAtvjEiZvlTS91RrN0KqXeqfRG3EvGNut0QytsqwBJkgaDowBppjZpm3QaIZWXZTubP63uX2BF9qp0QytepC0XNJ8/3kF7jfIrWue1ASNZmjVS9oehJFk597f6+sckaKRJ/++pkZBGqmVSrUvIVE3a18CkJxHNY6M3HszOwX4QtIXNWyomX+fUyMXjdTKaGcc/5N9CWY2zcxuzilfc19CRJ+RrUDu/WHAOWZ2pm9okJmtlhT9GJsn/76mhj8nb/59pla9dNK+BP997r0JHbIvod80miv3XtL1uIyE6G4fEVzYzPz7LI1Y/v3xWfn3OexpBB2xL8F/nzs2HbQvoU9aeJHc+yzy5t/Xoh37GhLpsH0JUCw2nbIvoc/Iljv3Pk7SQpCc+fdpGvXsa0ixJ65dJv++I/YlQPHYFNiXcANuLRmxMdBjZvH3lSdKejtLK424EY3KvYf1L/++U/YlQPNi8wguSTb6ey6hrNBAFBIf2erOvff11sf8+07ZlwBNio1fc66K2fszLtV7URGdWvR2tgbl3sN6mH/fQfsSoMNiA7n3JfSby+vNvYf1N/++7fsSoGNjU3NfQkSVqVvRMqp8toqWUXW2ipbxL4GdE8r1qpCeAAAAAElFTkSuQmCC", "text/latex": [ "$\\displaystyle \\frac{A \\left(\\omega - \\omega\\right) \\left(C^{2} R^{2} \\omega^{2} - 1\\right)}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}$" ], "text/plain": [ " ⎛ 2 2 2 ⎞\n", "A⋅(\\omega - ω)⋅⎝C ⋅R ⋅ω - 1⎠\n", "─────────────────────────────\n", " 4 4 4 2 2 2 \n", " C ⋅R ⋅ω - C ⋅R ⋅ω + 1 " ] }, "execution_count": 85, "metadata": {}, "output_type": "execute_result" } ], "source": [ "simplify(e/(C*R)-d*w)" ] }, { "cell_type": "code", "execution_count": 86, "id": "6f02f484", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle \\frac{A \\left(- C^{4} R^{4} \\omega \\omega^{3} + C^{2} R^{2} \\omega \\omega - 1\\right)}{C R \\left(C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1\\right)}$" ], "text/plain": [ " ⎛ 4 4 3 2 2 ⎞\n", "A⋅⎝- C ⋅R ⋅\\omega⋅ω + C ⋅R ⋅\\omega⋅ω - 1⎠\n", "──────────────────────────────────────────\n", " ⎛ 4 4 4 2 2 2 ⎞ \n", " C⋅R⋅⎝C ⋅R ⋅ω - C ⋅R ⋅ω + 1⎠ " ] }, "execution_count": 86, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# This reduces to -A/(C*R) but simplify doesn't do much of a job of reducing it\n", "simplify(e*w-(d-f)/(C*R))" ] }, { "cell_type": "code", "execution_count": 87, "id": "69e5d7b8", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle \\frac{A C^{2} R^{2} \\omega^{2} \\left(\\omega - \\omega\\right)}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}$" ], "text/plain": [ " 2 2 2 \n", "A⋅C ⋅R ⋅ω ⋅(\\omega - ω)\n", "───────────────────────\n", " 4 4 4 2 2 2 \n", "C ⋅R ⋅ω - C ⋅R ⋅ω + 1" ] }, "execution_count": 87, "metadata": {}, "output_type": "execute_result" } ], "source": [ "simplify((e-b)/(C*R)-f*w)" ] }, { "cell_type": "markdown", "id": "919c4009", "metadata": {}, "source": [ "This is a little bit at variance with the results downstairs but not by much. It indicates that I may have a sign issue somewhere." ] }, { "cell_type": "code", "execution_count": 88, "id": "bcaecaa0", "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle E \\sin{\\left(\\omega t \\right)} + F \\cos{\\left(\\omega t \\right)}$" ], "text/plain": [ "E⋅sin(\\omega⋅t) + F⋅cos(\\omega⋅t)" ] }, "execution_count": 88, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vc2 = E*sin(w*t)+F*cos(w*t)\n", "vc2" ] }, { "cell_type": "code", "execution_count": 89, "id": "58abd6f0", "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle B \\sin{\\left(\\omega t \\right)} + D \\cos{\\left(\\omega t \\right)}$" ], "text/plain": [ "B⋅sin(\\omega⋅t) + D⋅cos(\\omega⋅t)" ] }, "execution_count": 89, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vc1 = B*sin(w*t)+D*cos(w*t)\n", "vc1" ] }, { "cell_type": "code", "execution_count": 90, "id": "eabd944b", "metadata": {}, "outputs": [ { "data": { "image/png": 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Bds96sesEW5Y5zGwy/ra5I/BN/PChHSRtNj+O80V8KqvZzo+luEf2ZTyy9M3AoI3J/Iz0U4ArawPRVrpSpsNM3rWtaBPDTG+qpitlmFN+BL4kMWiOBIRljhDMcjke5b0vfrrVh4Fk/WU/vLNNt5CG9ZWjgTvNjycd8gzymMbjQakndbjdNzVdLNNmZW8qalvRVsYzTPSmarpYhpnlkvaSNKmqjhVlRE9PT7Kj4jpg+xBcMQY/Zevjkq4wsyuBJyUtaHq3mpqampqammFHEoC5M75XNwlOmYVvoUm2gu4LrKampqampqamJkUSM3E/sKv5PzMZje+TtejcgFHAxLCn9JWsw4Nqampqampqhh8jASStxbeq3IHvmV0q6Zyo3r8CnwCeoP+BKjU1NTU1NTXDmMytoTU1NTU1NTU1Rfh/BKTtSA449+EAAAAASUVORK5CYII=", "text/latex": [ "$\\displaystyle \\frac{\\partial}{\\partial t} \\left(B \\sin{\\left(\\omega t \\right)} + D \\cos{\\left(\\omega t \\right)}\\right) = - \\frac{E \\sin{\\left(\\omega t \\right)} + F \\cos{\\left(\\omega t \\right)}}{C R}$" ], "text/plain": [ "∂ -(E⋅sin(\\omega⋅t) + F⋅cos(\\omega⋅t)) \n", "──(B⋅sin(\\omega⋅t) + D⋅cos(\\omega⋅t)) = ─────────────────────────────────────\n", "∂t C⋅R " ] }, "execution_count": 90, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eq1 = eqn1.subs([(Vc1(t), vc1), (Vc2(t), vc2)])\n", "eq1" ] }, { "cell_type": "code", "execution_count": 91, "id": "ee42ac89", "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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", "text/latex": [ "$\\displaystyle \\frac{\\partial}{\\partial t} \\left(E \\sin{\\left(\\omega t \\right)} + F \\cos{\\left(\\omega t \\right)}\\right) = \\frac{- A \\sin{\\left(\\omega t \\right)} + B \\sin{\\left(\\omega t \\right)} + D \\cos{\\left(\\omega t \\right)} - E \\sin{\\left(\\omega t \\right)} - F \\cos{\\left(\\omega t \\right)}}{C R}$" ], "text/plain": [ "∂ -A⋅sin(\\omega⋅t) + B⋅sin(\\omega⋅t) + D ↪\n", "──(E⋅sin(\\omega⋅t) + F⋅cos(\\omega⋅t)) = ────────────────────────────────────── ↪\n", "∂t ↪\n", "\n", "↪ ⋅cos(\\omega⋅t) - E⋅sin(\\omega⋅t) - F⋅cos(\\omega⋅t)\n", "↪ ──────────────────────────────────────────────────\n", "↪ C⋅R " ] }, "execution_count": 91, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eq2 = eqn2.subs([(Vc1(t), vc1), (Vc2(t), vc2), (Vin, A*sin(w*t))])\n", "eq2" ] }, { "cell_type": "code", "execution_count": 92, "id": "22a2f62d", "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle B \\omega \\cos{\\left(\\omega t \\right)} - D \\omega \\sin{\\left(\\omega t \\right)}$" ], "text/plain": [ "B⋅\\omega⋅cos(\\omega⋅t) - D⋅\\omega⋅sin(\\omega⋅t)" ] }, "execution_count": 92, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eq1.lhs.doit()" ] }, { "cell_type": "code", "execution_count": 93, "id": "8781faf8", "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle E \\omega \\cos{\\left(\\omega t \\right)} - F \\omega \\sin{\\left(\\omega t \\right)}$" ], "text/plain": [ "E⋅\\omega⋅cos(\\omega⋅t) - F⋅\\omega⋅sin(\\omega⋅t)" ] }, "execution_count": 93, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eq2.lhs.doit()" ] }, { "cell_type": "code", "execution_count": 94, "id": "86a4b00e", "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle \\left( B \\sin{\\left(\\omega t \\right)}, \\ D \\cos{\\left(\\omega t \\right)}, \\ - A \\sin{\\left(\\omega t \\right)}, \\ - E \\sin{\\left(\\omega t \\right)}, \\ - F \\cos{\\left(\\omega t \\right)}\\right)$" ], "text/plain": [ "(B⋅sin(\\omega⋅t), D⋅cos(\\omega⋅t), -A⋅sin(\\omega⋅t), -E⋅sin(\\omega⋅t), -F⋅cos( ↪\n", "\n", "↪ \\omega⋅t))" ] }, "execution_count": 94, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eq2.rhs.args[2].args" ] }, { "cell_type": "markdown", "id": "e3e1066b", "metadata": {}, "source": [ "Afte cancelling for sines and cosines we end up with the following equations:\n", "\n", "$$ F + B \\omega C R = 0 $$\n", "$$ E - D \\omega C R = 0 $$\n", "$$ E \\omega C R - D + F = 0 $$\n", "$$ E - B - F \\omega C R = -A $$" ] }, { "cell_type": "code", "execution_count": 95, "id": "2a239e00", "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle \\frac{d}{d t} \\operatorname{Vc}_{1}{\\left(t \\right)} = - \\frac{\\operatorname{Vc}_{2}{\\left(t \\right)}}{C R}$" ], "text/plain": [ "d -Vc₂(t) \n", "──(Vc₁(t)) = ────────\n", "dt C⋅R " ] }, "execution_count": 95, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eqn1" ] }, { "cell_type": "code", "execution_count": 96, "id": "a16c4a3f", "metadata": {}, "outputs": [], "source": [ "from IPython.display import display\n", "from sympy import Function, Equality, Mul, Add" ] }, { "cell_type": "code", "execution_count": 97, "id": "e75ca38a", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 97, "metadata": {}, "output_type": "execute_result" } ], "source": [ "isinstance(eqn1, Equality)" ] }, { "cell_type": "code", "execution_count": 98, "id": "31d5305e", "metadata": {}, "outputs": [], "source": [ "if isinstance(eqn1, Equality):\n", " eq = eqn1.lhs - eqn1.rhs\n", "else:\n", " eq = eqn1\n", "\n" ] }, { "cell_type": "code", "execution_count": 99, "id": "6521fde3", "metadata": {}, "outputs": [], "source": [ "ii = 1\n", "for eqn in [eqn1, eqn2]:\n", " sym1, sym2 = symbols('a_{} a_{}'.format(ii, ii+1))\n", " vc = sym1*cos(w * t) + sym2 * sin(w*t)\n", " eq = eqn.subs([])\n", " \n", " #display ([sym1, sym2])\n", " ii += 2\n", " " ] }, { "cell_type": "code", "execution_count": 100, "id": "c170de0f", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left[\\begin{matrix}C R \\omega & 0 & 0 & 1\\\\0 & - C R \\omega & 1 & 0\\\\0 & -1 & C R \\omega & 1\\\\-1 & 0 & 1 & - C R \\omega\\end{matrix}\\right]$" ], "text/plain": [ "⎡C⋅R⋅\\omega 0 0 1 ⎤\n", "⎢ ⎥\n", "⎢ 0 -C⋅R⋅\\omega 1 0 ⎥\n", "⎢ ⎥\n", "⎢ 0 -1 C⋅R⋅\\omega 1 ⎥\n", "⎢ ⎥\n", "⎣ -1 0 1 -C⋅R⋅\\omega⎦" ] }, "execution_count": 100, "metadata": {}, "output_type": "execute_result" } ], "source": [ "m = Matrix([[w*C*R, 0, 0, 1], [0, -w*C*R, 1, 0], [0, -1, w*C*R, 1], [-1,0, 1, -w*C*R]])\n", "m" ] }, { "cell_type": "code", "execution_count": 101, "id": "e8cd9971", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left[\\begin{matrix}\\frac{C^{3} R^{3} \\omega^{3}}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1} & \\frac{1}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1} & - \\frac{C R \\omega}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1} & \\frac{C^{2} R^{2} \\omega^{2} - 1}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}\\\\\\frac{1}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1} & - \\frac{C^{3} R^{3} \\omega^{3}}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1} & \\frac{C^{2} R^{2} \\omega^{2} - 1}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1} & \\frac{C R \\omega}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}\\\\\\frac{C R \\omega}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1} & \\frac{- C^{2} R^{2} \\omega^{2} + 1}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1} & \\frac{C^{3} R^{3} \\omega^{3} - C R \\omega}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1} & \\frac{C^{2} R^{2} \\omega^{2}}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}\\\\\\frac{- C^{2} R^{2} \\omega^{2} + 1}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1} & - \\frac{C R \\omega}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1} & \\frac{C^{2} R^{2} \\omega^{2}}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1} & \\frac{- C^{3} R^{3} \\omega^{3} + C R \\omega}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}\\end{matrix}\\right]$" ], "text/plain": [ "⎡ 3 3 3 ↪\n", "⎢ C ⋅R ⋅\\omega 1 ↪\n", "⎢───────────────────────────────── ───────────────────────────────── ─────── ↪\n", "⎢ 4 4 4 2 2 2 4 4 4 2 2 2 4 4 ↪\n", "⎢C ⋅R ⋅\\omega - C ⋅R ⋅\\omega + 1 C ⋅R ⋅\\omega - C ⋅R ⋅\\omega + 1 C ⋅R ⋅\\ ↪\n", "⎢ ↪\n", "⎢ 3 3 3 ↪\n", "⎢ 1 -C ⋅R ⋅\\omega ↪\n", "⎢───────────────────────────────── ───────────────────────────────── ─────── ↪\n", "⎢ 4 4 4 2 2 2 4 4 4 2 2 2 4 4 ↪\n", "⎢C ⋅R ⋅\\omega - C ⋅R ⋅\\omega + 1 C ⋅R ⋅\\omega - C ⋅R ⋅\\omega + 1 C ⋅R ⋅\\ ↪\n", "⎢ ↪\n", "⎢ 2 2 2 3 ↪\n", "⎢ C⋅R⋅\\omega - C ⋅R ⋅\\omega + 1 C ⋅R ↪\n", "⎢───────────────────────────────── ───────────────────────────────── ─────── ↪\n", "⎢ 4 4 4 2 2 2 4 4 4 2 2 2 4 4 ↪\n", "⎢C ⋅R ⋅\\omega - C ⋅R ⋅\\omega + 1 C ⋅R ⋅\\omega - C ⋅R ⋅\\omega + 1 C ⋅R ⋅\\ ↪\n", "⎢ ↪\n", "⎢ 2 2 2 ↪\n", "⎢ - C ⋅R ⋅\\omega + 1 -C⋅R⋅\\omega ↪\n", "⎢───────────────────────────────── ───────────────────────────────── ─────── ↪\n", "⎢ 4 4 4 2 2 2 4 4 4 2 2 2 4 4 ↪\n", "⎣C ⋅R ⋅\\omega - C ⋅R ⋅\\omega + 1 C ⋅R ⋅\\omega - C ⋅R ⋅\\omega + 1 C ⋅R ⋅\\ ↪\n", "\n", "↪ 2 2 2 ⎤\n", "↪ -C⋅R⋅\\omega C ⋅R ⋅\\omega - 1 ⎥\n", "↪ ────────────────────────── ─────────────────────────────────⎥\n", "↪ 4 2 2 2 4 4 4 2 2 2 ⎥\n", "↪ omega - C ⋅R ⋅\\omega + 1 C ⋅R ⋅\\omega - C ⋅R ⋅\\omega + 1⎥\n", "↪ ⎥\n", "↪ 2 2 2 ⎥\n", "↪ C ⋅R ⋅\\omega - 1 C⋅R⋅\\omega ⎥\n", "↪ ────────────────────────── ─────────────────────────────────⎥\n", "↪ 4 2 2 2 4 4 4 2 2 2 ⎥\n", "↪ omega - C ⋅R ⋅\\omega + 1 C ⋅R ⋅\\omega - C ⋅R ⋅\\omega + 1⎥\n", "↪ ⎥\n", "↪ 3 3 2 2 2 ⎥\n", "↪ ⋅\\omega - C⋅R⋅\\omega C ⋅R ⋅\\omega ⎥\n", "↪ ────────────────────────── ─────────────────────────────────⎥\n", "↪ 4 2 2 2 4 4 4 2 2 2 ⎥\n", "↪ omega - C ⋅R ⋅\\omega + 1 C ⋅R ⋅\\omega - C ⋅R ⋅\\omega + 1⎥\n", "↪ ⎥\n", "↪ 2 2 2 3 3 3 ⎥\n", "↪ C ⋅R ⋅\\omega - C ⋅R ⋅\\omega + C⋅R⋅\\omega ⎥\n", "↪ ────────────────────────── ─────────────────────────────────⎥\n", "↪ 4 2 2 2 4 4 4 2 2 2 ⎥\n", "↪ omega - C ⋅R ⋅\\omega + 1 C ⋅R ⋅\\omega - C ⋅R ⋅\\omega + 1⎦" ] }, "execution_count": 101, "metadata": {}, "output_type": "execute_result" } ], "source": [ "minv = m**-1\n", "minv" ] }, { "cell_type": "code", "execution_count": 102, "id": "2c252f1a", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left[\\begin{matrix}0\\\\0\\\\0\\\\- A\\end{matrix}\\right]$" ], "text/plain": [ "⎡0 ⎤\n", "⎢ ⎥\n", "⎢0 ⎥\n", "⎢ ⎥\n", "⎢0 ⎥\n", "⎢ ⎥\n", "⎣-A⎦" ] }, "execution_count": 102, "metadata": {}, "output_type": "execute_result" } ], "source": [ "amat = Matrix([0,0,0,-A])\n", "amat" ] }, { "cell_type": "code", "execution_count": 103, "id": "4a5efba9", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left[\\begin{matrix}- \\frac{A \\left(C^{2} R^{2} \\omega^{2} - 1\\right)}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}\\\\- \\frac{A C R \\omega}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}\\\\- \\frac{A C^{2} R^{2} \\omega^{2}}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}\\\\- \\frac{A \\left(- C^{3} R^{3} \\omega^{3} + C R \\omega\\right)}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}\\end{matrix}\\right]$" ], "text/plain": [ "⎡ ⎛ 2 2 2 ⎞ ⎤\n", "⎢ -A⋅⎝C ⋅R ⋅\\omega - 1⎠ ⎥\n", "⎢───────────────────────────────── ⎥\n", "⎢ 4 4 4 2 2 2 ⎥\n", "⎢C ⋅R ⋅\\omega - C ⋅R ⋅\\omega + 1 ⎥\n", "⎢ ⎥\n", "⎢ -A⋅C⋅R⋅\\omega ⎥\n", "⎢───────────────────────────────── ⎥\n", "⎢ 4 4 4 2 2 2 ⎥\n", "⎢C ⋅R ⋅\\omega - C ⋅R ⋅\\omega + 1 ⎥\n", "⎢ ⎥\n", "⎢ 2 2 2 ⎥\n", "⎢ -A⋅C ⋅R ⋅\\omega ⎥\n", "⎢───────────────────────────────── ⎥\n", "⎢ 4 4 4 2 2 2 ⎥\n", "⎢C ⋅R ⋅\\omega - C ⋅R ⋅\\omega + 1 ⎥\n", "⎢ ⎥\n", "⎢ ⎛ 3 3 3 ⎞ ⎥\n", "⎢-A⋅⎝- C ⋅R ⋅\\omega + C⋅R⋅\\omega⎠ ⎥\n", "⎢──────────────────────────────────⎥\n", "⎢ 4 4 4 2 2 2 ⎥\n", "⎣C ⋅R ⋅\\omega - C ⋅R ⋅\\omega + 1 ⎦" ] }, "execution_count": 103, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Find the coefficients of B,D,E and F.\n", "coeffs = minv*amat\n", "coeffs" ] }, { "cell_type": "code", "execution_count": 104, "id": "7edafd6a", "metadata": {}, "outputs": [ { "data": { "image/png": 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L7oP2511KbNwHfcR90J4KscnhgzKdqrFxL1RgwHwAA+QF90E9mNl0wg3K17Qr07KBIOmHZvYgcApwfcY6zYyvK6p8SK1vuJhJGHK6BNiT0KhZK2lBikY8QU4B5jUtmw+sk7QwLtqDFk+Xa1OfZu0LCFN+deJtkn7c9D45NpKW0fr+kYZOaVw6aVSNTUl9mnXPJVz/12BXYNTMmudMfrekn5ZpDQGVvZDDB0WdXnzQoU4NnX76oKHVMTb98EHUcS8Ecv0mDJsPIDE2OXzQSaeb2PhvQmUGwgdQX27kPmhPn3wwh3CD9lPtCnSq+BzgbDPbJWOFJsfXJzNozQTulLRW0r2Em1T+1szekPj5qYTr0Zpbcu8HmoN1BFCl1d1gAXBYyd/dhc/kik2vcYH6YvMVYEbT3/daLKv0BTmBGZTjPaw+gMGOjXsh4D5o7QPYMWLjPggMyrGG+o73AtwH7RhXH1h4gNvRhGPSlnaXGCFprZldSbgz+tJM9VoTX48HvlVcaWaTO7VmmspNJcwl++KBkvSIma0EZgFnJ9Rl7/j6ZNR8K2GKqGfj+2mEg/LFBK3tkLSRMN9tFXqOTaa4QE2xiddQbmqq71Zgk6S1VXSGhEE53kPng1hu0GPjXgi4D9qzI8TGfRAYlGMN9f3+uw/a0AcfzAP+StJznQq1bSAASPpnM7vYzGYoPuyhFyQtN7ObgIVmthtwBzBKaNl9DDBgWYLUCOHGkmJL7RbgZNIO9vqocbqZbQa+BNwIvMfCsyCuAu4DvpOg1TOZYpMjLjBgsQEws90J05JBGPl6tYU5kTdJWj9e9cjFAB3vgTrW/h3RGfdBS4byWHts2uM+aMlQ/v4PUGwGKi4NqnrBzP4a+Lak1WXaKdfLfoa8T357H2FE4pPAKmA58GngZ6QPoYwAD0v6XWH5LcA0Mzu8TEDSbwh33p8K/ABYRLgB5UjC48KfAE6U9HxinXLQa2x6jgsMbGyOIkxDtpJwc5HF/3PPljCe9P14D+ix9u+I9rgPxjKsxxo8Nu1wH4xlmH//+x6bAY0LVPfCekk3pAhPGh0dzVJDx3Ecx3Ecx3EmPkkzbjiO4ziO4ziOs2PgDQTHcRzHcRzHcV7k/wG5C7ipZPc1CwAAAABJRU5ErkJggg==", "text/latex": [ "$\\displaystyle \\left( - \\frac{A \\left(C^{2} R^{2} \\omega^{2} - 1\\right)}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}, \\ - \\frac{A C^{2} R^{2} \\omega^{2}}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}, \\ - \\frac{A C R \\omega}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}, \\ - \\frac{A \\left(- C^{3} R^{3} \\omega^{3} + C R \\omega\\right)}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}\\right)$" ], "text/plain": [ "⎛ ⎛ 2 2 2 ⎞ 2 2 2 ↪\n", "⎜ -A⋅⎝C ⋅R ⋅\\omega - 1⎠ -A⋅C ⋅R ⋅\\omega ↪\n", "⎜─────────────────────────────────, ─────────────────────────────────, ─────── ↪\n", "⎜ 4 4 4 2 2 2 4 4 4 2 2 2 4 4 ↪\n", "⎝C ⋅R ⋅\\omega - C ⋅R ⋅\\omega + 1 C ⋅R ⋅\\omega - C ⋅R ⋅\\omega + 1 C ⋅R ⋅\\ ↪\n", "\n", "↪ ⎛ 3 3 3 ⎞ ⎞\n", "↪ -A⋅C⋅R⋅\\omega -A⋅⎝- C ⋅R ⋅\\omega + C⋅R⋅\\omega⎠ ⎟\n", "↪ ──────────────────────────, ──────────────────────────────────⎟\n", "↪ 4 2 2 2 4 4 4 2 2 2 ⎟\n", "↪ omega - C ⋅R ⋅\\omega + 1 C ⋅R ⋅\\omega - C ⋅R ⋅\\omega + 1 ⎠" ] }, "execution_count": 104, "metadata": {}, "output_type": "execute_result" } ], "source": [ "b = coeffs[0]\n", "d = coeffs[1]\n", "e = coeffs[2]\n", "f = coeffs[3]\n", "b, e, d, f" ] }, { "cell_type": "code", "execution_count": 105, "id": "15bfbe9d", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle 0$" ], "text/plain": [ "0" ] }, "execution_count": 105, "metadata": {}, "output_type": "execute_result" } ], "source": [ "simplify(f + b * w* C* R)" ] }, { "cell_type": "code", "execution_count": 106, "id": "2274eae6", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle 0$" ], "text/plain": [ "0" ] }, "execution_count": 106, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eq = eq1.subs([(B,b), (D,d), (E,e), (F,f)]).doit()\n", "simplify(eq.lhs - eq.rhs)" ] }, { "cell_type": "code", "execution_count": 107, "id": "47d3a7eb", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle 0$" ], "text/plain": [ "0" ] }, "execution_count": 107, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eq = eq2.subs([(B,b), (D,d), (E,e), (F,f)]).doit()\n", "simplify(eq.lhs - eq.rhs)" ] }, { "cell_type": "code", "execution_count": 108, "id": "1e658941", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle - \\frac{A C R \\omega \\cos{\\left(\\omega t \\right)}}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1} - \\frac{A \\left(C^{2} R^{2} \\omega^{2} - 1\\right) \\sin{\\left(\\omega t \\right)}}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}$" ], "text/plain": [ " ⎛ 2 2 2 ⎞ \n", " A⋅C⋅R⋅\\omega⋅cos(\\omega⋅t) A⋅⎝C ⋅R ⋅\\omega - 1⎠⋅sin(\\omega⋅t)\n", "- ───────────────────────────────── - ───────────────────────────────────\n", " 4 4 4 2 2 2 4 4 4 2 2 2 \n", " C ⋅R ⋅\\omega - C ⋅R ⋅\\omega + 1 C ⋅R ⋅\\omega - C ⋅R ⋅\\omega + 1 " ] }, "execution_count": 108, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vc1.subs([(B,b),(D,d)])" ] }, { "cell_type": "code", "execution_count": 109, "id": "21799d72", "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle - \\frac{A C^{2} R^{2} \\omega^{2} \\sin{\\left(\\omega t \\right)}}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1} - \\frac{A \\left(- C^{3} R^{3} \\omega^{3} + C R \\omega\\right) \\cos{\\left(\\omega t \\right)}}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}$" ], "text/plain": [ " 2 2 2 ⎛ 3 3 3 ⎞ ↪\n", " A⋅C ⋅R ⋅\\omega ⋅sin(\\omega⋅t) A⋅⎝- C ⋅R ⋅\\omega + C⋅R⋅\\omega⎠⋅cos(\\om ↪\n", "- ───────────────────────────────── - ──────────────────────────────────────── ↪\n", " 4 4 4 2 2 2 4 4 4 2 2 2 ↪\n", " C ⋅R ⋅\\omega - C ⋅R ⋅\\omega + 1 C ⋅R ⋅\\omega - C ⋅R ⋅\\omega + 1 ↪\n", "\n", "↪ \n", "↪ ega⋅t)\n", "↪ ──────\n", "↪ \n", "↪ " ] }, "execution_count": 109, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vc2.subs([(E,e), (F,f)])" ] }, { "cell_type": "code", "execution_count": 110, "id": "8d622a8f", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle \\frac{A^{2}}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}$" ], "text/plain": [ " 2 \n", " A \n", "─────────────────────────────────\n", " 4 4 4 2 2 2 \n", "C ⋅R ⋅\\omega - C ⋅R ⋅\\omega + 1" ] }, "execution_count": 110, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Compute the magnitude of Vc1\n", "simplify(b**2+d**2)" ] }, { "cell_type": "code", "execution_count": 111, "id": "37d264fc", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle \\frac{A^{2} C^{2} R^{2} \\omega^{2}}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}$" ], "text/plain": [ " 2 2 2 2 \n", " A ⋅C ⋅R ⋅\\omega \n", "─────────────────────────────────\n", " 4 4 4 2 2 2 \n", "C ⋅R ⋅\\omega - C ⋅R ⋅\\omega + 1" ] }, "execution_count": 111, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Compute the magnitude of Vc2\n", "(simplify(e**2+f**2))" ] }, { "cell_type": "code", "execution_count": 112, "id": "096e59a0", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/latex": [ "$\\displaystyle \\phi = \\operatorname{acos}{\\left(C R \\sqrt{\\frac{\\omega^{2}}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}} \\right)}$" ], "text/plain": [ " ⎛ ___________________________________⎞\n", " ⎜ ╱ 2 ⎟\n", " ⎜ ╱ \\omega ⎟\n", "φ = acos⎜C⋅R⋅ ╱ ───────────────────────────────── ⎟\n", " ⎜ ╱ 4 4 4 2 2 2 ⎟\n", " ⎝ ╲╱ C ⋅R ⋅\\omega - C ⋅R ⋅\\omega + 1 ⎠" ] }, "execution_count": 112, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Now compute phase of Vc1\n", "Eq(phi, acos(sqrt(simplify(d**2/(b**2+d**2)))))" ] }, { "cell_type": "code", "execution_count": 113, "id": "bc3d128f", "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle \\phi = \\operatorname{acos}{\\left(\\sqrt{\\frac{\\left(C^{2} R^{2} \\omega^{2} - 1\\right)^{2}}{C^{2} R^{2} \\omega^{2} + \\left(C^{2} R^{2} \\omega^{2} - 1\\right)^{2}}} \\right)}$" ], "text/plain": [ " ⎛ ______________________________________⎞\n", " ⎜ ╱ 2 ⎟\n", " ⎜ ╱ ⎛ 2 2 2 ⎞ ⎟\n", " ⎜ ╱ ⎝C ⋅R ⋅\\omega - 1⎠ ⎟\n", "φ = acos⎜ ╱ ──────────────────────────────────── ⎟\n", " ⎜ ╱ 2 ⎟\n", " ⎜ ╱ 2 2 2 ⎛ 2 2 2 ⎞ ⎟\n", " ⎝╲╱ C ⋅R ⋅\\omega + ⎝C ⋅R ⋅\\omega - 1⎠ ⎠" ] }, "execution_count": 113, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Now compute phase of Vc2\n", "Eq(phi, acos(sqrt(simplify(f**2/(e**2+f**2)))))" ] }, { "cell_type": "code", "execution_count": 114, "id": "5f98d6e5", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle \\frac{C R \\omega}{C^{2} R^{2} \\omega^{2} - 1}$" ], "text/plain": [ " C⋅R⋅\\omega \n", "─────────────────\n", " 2 2 2 \n", "C ⋅R ⋅\\omega - 1" ] }, "execution_count": 114, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# I am have a bit of a guess here at computing tan (phi)\n", "d/b" ] }, { "cell_type": "markdown", "id": "9952df1c", "metadata": {}, "source": [ "## Larger RC Network x 3 ##\n", "Now try the same thing with three lots of RC components\n", "\n", "There are three equations:\n", "\n", "$$ A \\sin ( \\omega t ) - V_{C1} - R_1 (i_1 - i_2) = 0 $$\n", "$$ R_1 ( i_2 - i_1) - V_{C2} - R_2 (i_2 - i_3) = 0 $$\n", "$$ R_2 ( i_3 - i_2) - V_{C3} - R_3 i_3 = 0 $$\n", "//\n", "These can be rearranged so that all the i's are on the right and everything else on the left.\n", "\n", "$$ A \\sin ( \\omega t ) - V_{C1} = R_1 i_1 - R_1 i_2 $$\n", "$$ V_{C2} = R_1 ( i_2 - i_1) - R_2 (i_2 - i_3) = (R_1 - R_2) i_2 - R_1 i_1 - R_2 i_3 $$\n", "$$ V_{C3} = R_2 ( i_3 - i_2) - R_3 i_3 = (R_2 - R_3) i_3 - R_2 i_2 $$\n", "\n", "However if R1 = R2 = R3 the above simplifies to :\n", "\n", "$$ A \\sin ( \\omega t ) - V_{C1} = R i_1 - R i_2 $$\n", "$$ V_{C2} = - R i_1 - R i_3 $$\n", "$$ V_{C3} = - R i_2 $$\n", "\n" ] }, { "cell_type": "code", "execution_count": 115, "id": "be3953e6", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left[\\begin{matrix}R & - R & 0\\\\- R & 0 & - R\\\\0 & - R & 0\\end{matrix}\\right]$" ], "text/plain": [ "⎡R -R 0 ⎤\n", "⎢ ⎥\n", "⎢-R 0 -R⎥\n", "⎢ ⎥\n", "⎣0 -R 0 ⎦" ] }, "execution_count": 115, "metadata": {}, "output_type": "execute_result" } ], "source": [ "m = Matrix([[R, -R, 0], [-R, 0, -R], [0, -R, 0]]); m" ] }, { "cell_type": "code", "execution_count": 116, "id": "989e65a5", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle - R^{3}$" ], "text/plain": [ " 3\n", "-R " ] }, "execution_count": 116, "metadata": {}, "output_type": "execute_result" } ], "source": [ "m.det()" ] }, { "cell_type": "code", "execution_count": 117, "id": "8e0a402b", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left[\\begin{matrix}A \\sin{\\left(\\omega t \\right)} - \\operatorname{Vc}_{1}{\\left(t \\right)}\\\\\\operatorname{Vc}_{2}{\\left(t \\right)}\\\\\\operatorname{Vc}_{3}{\\left(t \\right)}\\end{matrix}\\right]$" ], "text/plain": [ "⎡A⋅sin(\\omega⋅t) - Vc₁(t)⎤\n", "⎢ ⎥\n", "⎢ Vc₂(t) ⎥\n", "⎢ ⎥\n", "⎣ Vc₃(t) ⎦" ] }, "execution_count": 117, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v = Matrix([A*sin(w*t)-Vc1(t), Vc2(t), Vc3(t)]);v" ] }, { "cell_type": "code", "execution_count": 118, "id": "d94e3e61", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left[\\begin{matrix}\\frac{1}{R} & 0 & - \\frac{1}{R}\\\\0 & 0 & - \\frac{1}{R}\\\\- \\frac{1}{R} & - \\frac{1}{R} & \\frac{1}{R}\\end{matrix}\\right]$" ], "text/plain": [ "⎡ 1 -1 ⎤\n", "⎢ ─ 0 ───⎥\n", "⎢ R R ⎥\n", "⎢ ⎥\n", "⎢ -1 ⎥\n", "⎢ 0 0 ───⎥\n", "⎢ R ⎥\n", "⎢ ⎥\n", "⎢-1 -1 1 ⎥\n", "⎢─── ─── ─ ⎥\n", "⎣ R R R ⎦" ] }, "execution_count": 118, "metadata": {}, "output_type": "execute_result" } ], "source": [ "m.inv()" ] }, { "cell_type": "code", "execution_count": 119, "id": "bbeeee6b", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left[\\begin{matrix}\\frac{A \\sin{\\left(\\omega t \\right)} - \\operatorname{Vc}_{1}{\\left(t \\right)}}{R} - \\frac{\\operatorname{Vc}_{3}{\\left(t \\right)}}{R}\\\\- \\frac{\\operatorname{Vc}_{3}{\\left(t \\right)}}{R}\\\\- \\frac{A \\sin{\\left(\\omega t \\right)} - \\operatorname{Vc}_{1}{\\left(t \\right)}}{R} - \\frac{\\operatorname{Vc}_{2}{\\left(t \\right)}}{R} + \\frac{\\operatorname{Vc}_{3}{\\left(t \\right)}}{R}\\end{matrix}\\right]$" ], "text/plain": [ "⎡ A⋅sin(\\omega⋅t) - Vc₁(t) Vc₃(t) ⎤\n", "⎢ ──────────────────────── - ────── ⎥\n", "⎢ R R ⎥\n", "⎢ ⎥\n", "⎢ -Vc₃(t) ⎥\n", "⎢ ──────── ⎥\n", "⎢ R ⎥\n", "⎢ ⎥\n", "⎢ A⋅sin(\\omega⋅t) - Vc₁(t) Vc₂(t) Vc₃(t)⎥\n", "⎢- ──────────────────────── - ────── + ──────⎥\n", "⎣ R R R ⎦" ] }, "execution_count": 119, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Now to calculate the currents i1, i2, i3\n", "minvv = m.inv()*v; minvv" ] }, { "cell_type": "code", "execution_count": 120, "id": "e51811ad", "metadata": {}, "outputs": [], "source": [ "Vc1 = Function('Vc1')\n", "Vc2 = Function('Vc2')\n", "Vc3 = Function('Vc3')\n" ] }, { "cell_type": "code", "execution_count": 121, "id": "8902fcbd", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left[\\begin{matrix}C \\frac{d}{d t} \\operatorname{Vc}_{1}{\\left(t \\right)}\\\\C \\frac{d}{d t} \\operatorname{Vc}_{2}{\\left(t \\right)}\\\\C \\frac{d}{d t} \\operatorname{Vc}_{3}{\\left(t \\right)}\\end{matrix}\\right]$" ], "text/plain": [ "⎡ d ⎤\n", "⎢C⋅──(Vc₁(t))⎥\n", "⎢ dt ⎥\n", "⎢ ⎥\n", "⎢ d ⎥\n", "⎢C⋅──(Vc₂(t))⎥\n", "⎢ dt ⎥\n", "⎢ ⎥\n", "⎢ d ⎥\n", "⎢C⋅──(Vc₃(t))⎥\n", "⎣ dt ⎦" ] }, "execution_count": 121, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mm = Matrix([C*Vc1(t).diff(), C*Vc2(t).diff(), C*Vc3(t).diff()]); mm" ] }, { "cell_type": "code", "execution_count": 122, "id": "28aa249b", "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle \\frac{d}{d t} \\operatorname{Vc}_{1}{\\left(t \\right)} = \\frac{A \\sin{\\left(\\omega t \\right)} - \\operatorname{Vc}_{1}{\\left(t \\right)} - \\operatorname{Vc}_{3}{\\left(t \\right)}}{C R}$" ], "text/plain": [ "d A⋅sin(\\omega⋅t) - Vc₁(t) - Vc₃(t)\n", "──(Vc₁(t)) = ─────────────────────────────────\n", "dt C⋅R " ] }, "execution_count": 122, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eqn1 = Eq(mm[0]/C, simplify(minvv[0]/C)); eqn1" ] }, { "cell_type": "code", "execution_count": 123, "id": "717505e9", "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle \\frac{d}{d t} \\operatorname{Vc}_{1}{\\left(t \\right)} = \\frac{A \\sin{\\left(\\omega t \\right)} - \\operatorname{Vc}_{1}{\\left(t \\right)} - \\operatorname{Vc}_{3}{\\left(t \\right)}}{C R}$" ], "text/plain": [ "d A⋅sin(\\omega⋅t) - Vc₁(t) - Vc₃(t)\n", "──(Vc₁(t)) = ─────────────────────────────────\n", "dt C⋅R " ] }, "execution_count": 123, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eqn1" ] }, { "cell_type": "code", "execution_count": 124, "id": "ea323a49", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Eq(Derivative(Vc1(t), t), (A*sin(\\omega*t) - Vc1(t) - Vc3(t))/(C*R))\n" ] } ], "source": [ "print(eqn1)" ] }, { "cell_type": "code", "execution_count": 125, "id": "e74d9997", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle \\frac{d}{d t} \\operatorname{Vc}_{2}{\\left(t \\right)} = - \\frac{\\operatorname{Vc}_{3}{\\left(t \\right)}}{C R}$" ], "text/plain": [ "d -Vc₃(t) \n", "──(Vc₂(t)) = ────────\n", "dt C⋅R " ] }, "execution_count": 125, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eqn2 = Eq(mm[1]/C, simplify(minvv[1]/C)); eqn2" ] }, { "cell_type": "code", "execution_count": 126, "id": "2875b41c", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Eq(Derivative(Vc2(t), t), -Vc3(t)/(C*R))\n" ] } ], "source": [ "print(eqn2)" ] }, { "cell_type": "code", "execution_count": 127, "id": "8066a383", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/latex": [ "$\\displaystyle \\frac{d}{d t} \\operatorname{Vc}_{3}{\\left(t \\right)} = \\frac{- A \\sin{\\left(\\omega t \\right)} + \\operatorname{Vc}_{1}{\\left(t \\right)} - \\operatorname{Vc}_{2}{\\left(t \\right)} + \\operatorname{Vc}_{3}{\\left(t \\right)}}{C R}$" ], "text/plain": [ "d -A⋅sin(\\omega⋅t) + Vc₁(t) - Vc₂(t) + Vc₃(t)\n", "──(Vc₃(t)) = ───────────────────────────────────────────\n", "dt C⋅R " ] }, "execution_count": 127, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eqn3 = Eq(mm[2]/C, simplify(minvv[2]/C)); eqn3" ] }, { "cell_type": "code", "execution_count": 128, "id": "c23c9ce7", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Eq(Derivative(Vc3(t), t), (-A*sin(\\omega*t) + Vc1(t) - Vc2(t) + Vc3(t))/(C*R))\n" ] } ], "source": [ "print(eqn3)" ] }, { "cell_type": "code", "execution_count": 129, "id": "55da3b94", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[(a_2*omega, -a_1*omega), (a_1/(C*R), a_2/(C*R)), (a_3/(C*R), a_4/(C*R)), (0, -A*a_6/(C*R))]\n", "[(a_8*omega, -a_7*omega), (a_3/(C*R), a_4/(C*R))]\n", "[(a_4*omega, -a_3*omega), (-a_1/(C*R), -a_2/(C*R)), (-a_3/(C*R), -a_4/(C*R)), (a_7/(C*R), a_8/(C*R)), (0, A*a_6/(C*R))]\n", "[a_1, a_2, a_3, a_4, a_5, a_6, a_7, a_8]\n" ] } ], "source": [ "sysEqns3 = systemEqns()\n", "\n", "res1 = sysEqns3.extractCoeffsFromDiffEqn(eqn1)\n", "print (res1)\n", "res2 = sysEqns3.extractCoeffsFromDiffEqn(eqn2)\n", "print (res2)\n", "res3 = sysEqns3.extractCoeffsFromDiffEqn(eqn3)\n", "print (res3)\n", "\n", "print (sysEqns3.symbols_used)" ] }, { "cell_type": "code", "execution_count": 130, "id": "bb3c1ceb", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "a_2*omega -a_1*omega\n", "a_1/(C*R) a_2/(C*R)\n", "a_3/(C*R) a_4/(C*R)\n", "0 -A*a_6/(C*R)\n", "a_8*omega -a_7*omega\n", "a_3/(C*R) a_4/(C*R)\n", "a_4*omega -a_3*omega\n", "-a_1/(C*R) -a_2/(C*R)\n", "-a_3/(C*R) -a_4/(C*R)\n", "a_7/(C*R) a_8/(C*R)\n", "0 A*a_6/(C*R)\n" ] }, { "data": { "text/latex": [ "$\\displaystyle \\left[\\begin{matrix}- \\omega & \\frac{1}{C R} & 0 & 0 & 0 & \\frac{1}{C R} & 0 & - \\frac{A}{C R}\\\\\\frac{1}{C R} & \\omega & 0 & 0 & \\frac{1}{C R} & 0 & 0 & 0\\\\0 & 0 & - \\omega & 0 & 0 & \\frac{1}{C R} & 0 & 0\\\\0 & 0 & 0 & \\omega & \\frac{1}{C R} & 0 & 0 & 0\\\\0 & - \\frac{1}{C R} & 0 & \\frac{1}{C R} & - \\omega & - \\frac{1}{C R} & 0 & \\frac{A}{C R}\\\\- \\frac{1}{C R} & 0 & \\frac{1}{C R} & 0 & - \\frac{1}{C R} & \\omega & 0 & 0\\end{matrix}\\right]$" ], "text/plain": [ "⎡ 1 1 -A ⎤\n", "⎢-ω ─── 0 0 0 ─── 0 ───⎥\n", "⎢ C⋅R C⋅R C⋅R⎥\n", "⎢ ⎥\n", "⎢ 1 1 ⎥\n", "⎢─── ω 0 0 ─── 0 0 0 ⎥\n", "⎢C⋅R C⋅R ⎥\n", "⎢ ⎥\n", "⎢ 1 ⎥\n", "⎢ 0 0 -ω 0 0 ─── 0 0 ⎥\n", "⎢ C⋅R ⎥\n", "⎢ ⎥\n", "⎢ 1 ⎥\n", "⎢ 0 0 0 ω ─── 0 0 0 ⎥\n", "⎢ C⋅R ⎥\n", "⎢ ⎥\n", "⎢ -1 1 -1 A ⎥\n", "⎢ 0 ─── 0 ─── -ω ─── 0 ───⎥\n", "⎢ C⋅R C⋅R C⋅R C⋅R⎥\n", "⎢ ⎥\n", "⎢-1 1 -1 ⎥\n", "⎢─── 0 ─── 0 ─── ω 0 0 ⎥\n", "⎣C⋅R C⋅R C⋅R ⎦" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "M, syms_used = sysEqns3.orderedMatrix([res1, res2, res3])\n", "display(M)" ] }, { "cell_type": "code", "execution_count": 131, "id": "66d5c346", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle \\left[ a_{1}, \\ a_{2}, \\ a_{7}, \\ a_{8}, \\ a_{3}, \\ a_{4}, \\ a_{5}, \\ a_{6}\\right]$" ], "text/plain": [ "[a₁, a₂, a₇, a₈, a₃, a₄, a₅, a₆]" ] }, "execution_count": 131, "metadata": {}, "output_type": "execute_result" } ], "source": [ "syms_used" ] }, { "cell_type": "code", "execution_count": 132, "id": "9006121e", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left[\\begin{matrix}- \\omega & \\frac{1}{C R} & 0 & 0 & 0 & \\frac{1}{C R} & 0 & - \\frac{A}{C R}\\\\\\frac{1}{C R} & \\omega & 0 & 0 & \\frac{1}{C R} & 0 & 0 & 0\\\\0 & 0 & - \\omega & 0 & 0 & \\frac{1}{C R} & 0 & 0\\\\0 & 0 & 0 & \\omega & \\frac{1}{C R} & 0 & 0 & 0\\\\0 & - \\frac{1}{C R} & 0 & \\frac{1}{C R} & - \\omega & - \\frac{1}{C R} & 0 & \\frac{A}{C R}\\\\- \\frac{1}{C R} & 0 & \\frac{1}{C R} & 0 & - \\frac{1}{C R} & \\omega & 0 & 0\\end{matrix}\\right]$" ], "text/plain": [ "⎡ 1 1 -A ⎤\n", "⎢-ω ─── 0 0 0 ─── 0 ───⎥\n", "⎢ C⋅R C⋅R C⋅R⎥\n", "⎢ ⎥\n", "⎢ 1 1 ⎥\n", "⎢─── ω 0 0 ─── 0 0 0 ⎥\n", "⎢C⋅R C⋅R ⎥\n", "⎢ ⎥\n", "⎢ 1 ⎥\n", "⎢ 0 0 -ω 0 0 ─── 0 0 ⎥\n", "⎢ C⋅R ⎥\n", "⎢ ⎥\n", "⎢ 1 ⎥\n", "⎢ 0 0 0 ω ─── 0 0 0 ⎥\n", "⎢ C⋅R ⎥\n", "⎢ ⎥\n", "⎢ -1 1 -1 A ⎥\n", "⎢ 0 ─── 0 ─── -ω ─── 0 ───⎥\n", "⎢ C⋅R C⋅R C⋅R C⋅R⎥\n", "⎢ ⎥\n", "⎢-1 1 -1 ⎥\n", "⎢─── 0 ─── 0 ─── ω 0 0 ⎥\n", "⎣C⋅R C⋅R C⋅R ⎦" ] }, "execution_count": 132, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M" ] }, { "cell_type": "code", "execution_count": 133, "id": "2a72d91f", "metadata": {}, "outputs": [], "source": [ "\n", "\n", "#M_1 = M[:6,:6]**-1; M_1" ] }, { "cell_type": "code", "execution_count": 134, "id": "7eca5f0f", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle \\left( 6, \\ 8\\right)$" ], "text/plain": [ "(6, 8)" ] }, "execution_count": 134, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M.shape\n" ] }, { "cell_type": "code", "execution_count": 135, "id": "20d74c31", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left[\\begin{matrix}C R \\omega & -1 & 0 & 0 & 0 & -1 & 0 & A\\\\-1 & - C R \\omega & 0 & 0 & -1 & 0 & 0 & 0\\\\0 & 0 & - C R \\omega & 0 & 0 & 1 & 0 & 0\\\\0 & 0 & 0 & C R \\omega & 1 & 0 & 0 & 0\\\\0 & -1 & 0 & 1 & - C R \\omega & -1 & 0 & A\\\\-1 & 0 & 1 & 0 & -1 & C R \\omega & 0 & 0\\end{matrix}\\right]$" ], "text/plain": [ "⎡C⋅R⋅ω -1 0 0 0 -1 0 A⎤\n", "⎢ ⎥\n", "⎢ -1 -C⋅R⋅ω 0 0 -1 0 0 0⎥\n", "⎢ ⎥\n", "⎢ 0 0 -C⋅R⋅ω 0 0 1 0 0⎥\n", "⎢ ⎥\n", "⎢ 0 0 0 C⋅R⋅ω 1 0 0 0⎥\n", "⎢ ⎥\n", "⎢ 0 -1 0 1 -C⋅R⋅ω -1 0 A⎥\n", "⎢ ⎥\n", "⎣ -1 0 1 0 -1 C⋅R⋅ω 0 0⎦" ] }, "execution_count": 135, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Use the method row_op on the matrix to multiply the whole matrix through by a prefactor\n", "\n", "# I also did a bit of fiddling with the signs of the first two rows of the matrix by also swapping\n", "# it's signs on the basis that if I multiply any equation through by a constant it shouldn't matter. The\n", "# same principle as for the rest of the rows really.\n", "#\n", "M2 = M.copy()\n", "for ii in range(6):\n", " if ii < 2:\n", " M2.row_op(ii, lambda e, col: -e*R*C)\n", " else:\n", " M2.row_op(ii, lambda e, col: e*R*C)\n", "\n", "M2" ] }, { "cell_type": "code", "execution_count": 136, "id": "dc5fc471", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left[\\begin{matrix}C R \\omega & -1 & 0 & 0 & 0 & -1\\\\-1 & - C R \\omega & 0 & 0 & -1 & 0\\\\0 & 0 & - C R \\omega & 0 & 0 & 1\\\\0 & 0 & 0 & C R \\omega & 1 & 0\\\\0 & -1 & 0 & 1 & - C R \\omega & -1\\\\-1 & 0 & 1 & 0 & -1 & C R \\omega\\end{matrix}\\right]$" ], "text/plain": [ "⎡C⋅R⋅ω -1 0 0 0 -1 ⎤\n", "⎢ ⎥\n", "⎢ -1 -C⋅R⋅ω 0 0 -1 0 ⎥\n", "⎢ ⎥\n", "⎢ 0 0 -C⋅R⋅ω 0 0 1 ⎥\n", "⎢ ⎥\n", "⎢ 0 0 0 C⋅R⋅ω 1 0 ⎥\n", "⎢ ⎥\n", "⎢ 0 -1 0 1 -C⋅R⋅ω -1 ⎥\n", "⎢ ⎥\n", "⎣ -1 0 1 0 -1 C⋅R⋅ω⎦" ] }, "execution_count": 136, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M3 = M2[:6,:6]\n", "M3" ] }, { "cell_type": "code", "execution_count": 137, "id": "1b70eefa", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left[\\begin{matrix}\\frac{C^{5} R^{5} \\omega^{5} + 2 C^{3} R^{3} \\omega^{3}}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & \\frac{- C^{4} R^{4} \\omega^{4} - 2 C^{2} R^{2} \\omega^{2} - 1}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & \\frac{C^{3} R^{3} \\omega^{3} + C R \\omega}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & - \\frac{1}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & \\frac{C R \\omega}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & \\frac{C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2}}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}\\\\\\frac{- C^{4} R^{4} \\omega^{4} - 2 C^{2} R^{2} \\omega^{2} - 1}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & \\frac{- C^{5} R^{5} \\omega^{5} - 2 C^{3} R^{3} \\omega^{3}}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & - \\frac{1}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & \\frac{- C^{3} R^{3} \\omega^{3} - C R \\omega}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & \\frac{C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2}}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & - \\frac{C R \\omega}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}\\\\\\frac{C^{3} R^{3} \\omega^{3} + C R \\omega}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & - \\frac{1}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & \\frac{- C^{5} R^{5} \\omega^{5} - C^{3} R^{3} \\omega^{3}}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & \\frac{C^{2} R^{2} \\omega^{2}}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & - \\frac{C^{3} R^{3} \\omega^{3}}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & \\frac{C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}\\\\- \\frac{1}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & \\frac{- C^{3} R^{3} \\omega^{3} - C R \\omega}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & \\frac{C^{2} R^{2} \\omega^{2}}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & \\frac{C^{5} R^{5} \\omega^{5} + C^{3} R^{3} \\omega^{3}}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & \\frac{C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & \\frac{C^{3} R^{3} \\omega^{3}}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}\\\\\\frac{C R \\omega}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & \\frac{C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2}}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & - \\frac{C^{3} R^{3} \\omega^{3}}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & \\frac{C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & \\frac{- C^{5} R^{5} \\omega^{5} - C^{3} R^{3} \\omega^{3} - C R \\omega}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & - \\frac{C^{4} R^{4} \\omega^{4}}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}\\\\\\frac{C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2}}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & - \\frac{C R \\omega}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & \\frac{C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & \\frac{C^{3} R^{3} \\omega^{3}}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & - \\frac{C^{4} R^{4} \\omega^{4}}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & \\frac{C^{5} R^{5} \\omega^{5} + C^{3} R^{3} \\omega^{3} + C R \\omega}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}\\end{matrix}\\right]$" ], "text/plain": [ "⎡ 5 5 5 3 3 3 4 4 4 2 2 2 ↪\n", "⎢ C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω - C ⋅R ⋅ω - 2⋅C ⋅R ⋅ω - 1 ↪\n", "⎢──────────────────────────────────── ──────────────────────────────────── ─ ↪\n", "⎢ 6 6 6 4 4 4 2 2 2 6 6 6 4 4 4 2 2 2 ↪\n", "⎢C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ↪\n", "⎢ ↪\n", "⎢ 4 4 4 2 2 2 5 5 5 3 3 3 ↪\n", "⎢ - C ⋅R ⋅ω - 2⋅C ⋅R ⋅ω - 1 - C ⋅R ⋅ω - 2⋅C ⋅R ⋅ω ↪\n", "⎢──────────────────────────────────── ──────────────────────────────────── ─ ↪\n", "⎢ 6 6 6 4 4 4 2 2 2 6 6 6 4 4 4 2 2 2 ↪\n", "⎢C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ↪\n", "⎢ ↪\n", "⎢ 3 3 3 ↪\n", "⎢ C ⋅R ⋅ω + C⋅R⋅ω -1 ↪\n", "⎢──────────────────────────────────── ──────────────────────────────────── ─ ↪\n", "⎢ 6 6 6 4 4 4 2 2 2 6 6 6 4 4 4 2 2 2 ↪\n", "⎢C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ↪\n", "⎢ ↪\n", "⎢ 3 3 3 ↪\n", "⎢ -1 - C ⋅R ⋅ω - C⋅R⋅ω ↪\n", "⎢──────────────────────────────────── ──────────────────────────────────── ─ ↪\n", "⎢ 6 6 6 4 4 4 2 2 2 6 6 6 4 4 4 2 2 2 ↪\n", "⎢C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ↪\n", "⎢ ↪\n", "⎢ 4 4 4 2 2 2 ↪\n", "⎢ C⋅R⋅ω C ⋅R ⋅ω + C ⋅R ⋅ω ↪\n", "⎢──────────────────────────────────── ──────────────────────────────────── ─ ↪\n", "⎢ 6 6 6 4 4 4 2 2 2 6 6 6 4 4 4 2 2 2 ↪\n", "⎢C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ↪\n", "⎢ ↪\n", "⎢ 4 4 4 2 2 2 ↪\n", "⎢ C ⋅R ⋅ω + C ⋅R ⋅ω -C⋅R⋅ω ↪\n", "⎢──────────────────────────────────── ──────────────────────────────────── ─ ↪\n", "⎢ 6 6 6 4 4 4 2 2 2 6 6 6 4 4 4 2 2 2 ↪\n", "⎣C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ↪\n", "\n", "↪ 3 3 3 ↪\n", "↪ C ⋅R ⋅ω + C⋅R⋅ω -1 ↪\n", "↪ ─────────────────────────────────── ──────────────────────────────────── ─ ↪\n", "↪ 6 6 6 4 4 4 2 2 2 6 6 6 4 4 4 2 2 2 ↪\n", "↪ ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ↪\n", "↪ ↪\n", "↪ 3 3 3 ↪\n", "↪ -1 - C ⋅R ⋅ω - C⋅R⋅ω ↪\n", "↪ ─────────────────────────────────── ──────────────────────────────────── ─ ↪\n", "↪ 6 6 6 4 4 4 2 2 2 6 6 6 4 4 4 2 2 2 ↪\n", "↪ ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ↪\n", "↪ ↪\n", "↪ 5 5 5 3 3 3 2 2 2 ↪\n", "↪ - C ⋅R ⋅ω - C ⋅R ⋅ω C ⋅R ⋅ω ↪\n", "↪ ─────────────────────────────────── ──────────────────────────────────── ─ ↪\n", "↪ 6 6 6 4 4 4 2 2 2 6 6 6 4 4 4 2 2 2 ↪\n", "↪ ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ↪\n", "↪ ↪\n", "↪ 2 2 2 5 5 5 3 3 3 ↪\n", "↪ C ⋅R ⋅ω C ⋅R ⋅ω + C ⋅R ⋅ω ↪\n", "↪ ─────────────────────────────────── ──────────────────────────────────── ─ ↪\n", "↪ 6 6 6 4 4 4 2 2 2 6 6 6 4 4 4 2 2 2 ↪\n", "↪ ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ↪\n", "↪ ↪\n", "↪ 3 3 3 4 4 4 2 2 2 ↪\n", "↪ -C ⋅R ⋅ω C ⋅R ⋅ω + C ⋅R ⋅ω + 1 ↪\n", "↪ ─────────────────────────────────── ──────────────────────────────────── ─ ↪\n", "↪ 6 6 6 4 4 4 2 2 2 6 6 6 4 4 4 2 2 2 ↪\n", "↪ ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ↪\n", "↪ ↪\n", "↪ 4 4 4 2 2 2 3 3 3 ↪\n", "↪ C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ⋅R ⋅ω ↪\n", "↪ ─────────────────────────────────── ──────────────────────────────────── ─ ↪\n", "↪ 6 6 6 4 4 4 2 2 2 6 6 6 4 4 4 2 2 2 ↪\n", "↪ ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ↪\n", "\n", "↪ 4 4 4 2 2 2 ⎤\n", "↪ C⋅R⋅ω C ⋅R ⋅ω + C ⋅R ⋅ω ⎥\n", "↪ ─────────────────────────────────── ────────────────────────────────────⎥\n", "↪ 6 6 6 4 4 4 2 2 2 6 6 6 4 4 4 2 2 2 ⎥\n", "↪ ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1⎥\n", "↪ ⎥\n", "↪ 4 4 4 2 2 2 ⎥\n", "↪ C ⋅R ⋅ω + C ⋅R ⋅ω -C⋅R⋅ω ⎥\n", "↪ ─────────────────────────────────── ────────────────────────────────────⎥\n", "↪ 6 6 6 4 4 4 2 2 2 6 6 6 4 4 4 2 2 2 ⎥\n", "↪ ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1⎥\n", "↪ ⎥\n", "↪ 3 3 3 4 4 4 2 2 2 ⎥\n", "↪ -C ⋅R ⋅ω C ⋅R ⋅ω + C ⋅R ⋅ω + 1 ⎥\n", "↪ ─────────────────────────────────── ────────────────────────────────────⎥\n", "↪ 6 6 6 4 4 4 2 2 2 6 6 6 4 4 4 2 2 2 ⎥\n", "↪ ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1⎥\n", "↪ ⎥\n", "↪ 4 4 4 2 2 2 3 3 3 ⎥\n", "↪ C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ⋅R ⋅ω ⎥\n", "↪ ─────────────────────────────────── ────────────────────────────────────⎥\n", "↪ 6 6 6 4 4 4 2 2 2 6 6 6 4 4 4 2 2 2 ⎥\n", "↪ ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1⎥\n", "↪ ⎥\n", "↪ 5 5 5 3 3 3 4 4 4 ⎥\n", "↪ - C ⋅R ⋅ω - C ⋅R ⋅ω - C⋅R⋅ω -C ⋅R ⋅ω ⎥\n", "↪ ─────────────────────────────────── ────────────────────────────────────⎥\n", "↪ 6 6 6 4 4 4 2 2 2 6 6 6 4 4 4 2 2 2 ⎥\n", "↪ ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1⎥\n", "↪ ⎥\n", "↪ 4 4 4 5 5 5 3 3 3 ⎥\n", "↪ -C ⋅R ⋅ω C ⋅R ⋅ω + C ⋅R ⋅ω + C⋅R⋅ω ⎥\n", "↪ ─────────────────────────────────── ────────────────────────────────────⎥\n", "↪ 6 6 6 4 4 4 2 2 2 6 6 6 4 4 4 2 2 2 ⎥\n", "↪ ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1⎦" ] }, "execution_count": 137, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M3**-1" ] }, { "cell_type": "code", "execution_count": 138, "id": "2e9c93a3", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left[\\begin{matrix}A\\\\0\\\\0\\\\0\\\\A\\\\0\\end{matrix}\\right]$" ], "text/plain": [ "⎡A⎤\n", "⎢ ⎥\n", "⎢0⎥\n", "⎢ ⎥\n", "⎢0⎥\n", "⎢ ⎥\n", "⎢0⎥\n", "⎢ ⎥\n", "⎢A⎥\n", "⎢ ⎥\n", "⎣0⎦" ] }, "execution_count": 138, "metadata": {}, "output_type": "execute_result" } ], "source": [ "col = M2[:,7]\n", "col" ] }, { "cell_type": "code", "execution_count": 139, "id": "ad3c7583", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left[\\begin{matrix}\\frac{A C R \\omega}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} + \\frac{A \\left(C^{5} R^{5} \\omega^{5} + 2 C^{3} R^{3} \\omega^{3}\\right)}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}\\\\\\frac{A \\left(C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2}\\right)}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} + \\frac{A \\left(- C^{4} R^{4} \\omega^{4} - 2 C^{2} R^{2} \\omega^{2} - 1\\right)}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}\\\\- \\frac{A C^{3} R^{3} \\omega^{3}}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} + \\frac{A \\left(C^{3} R^{3} \\omega^{3} + C R \\omega\\right)}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}\\\\\\frac{A \\left(C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1\\right)}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} - \\frac{A}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}\\\\\\frac{A C R \\omega}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} + \\frac{A \\left(- C^{5} R^{5} \\omega^{5} - C^{3} R^{3} \\omega^{3} - C R \\omega\\right)}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}\\\\- \\frac{A C^{4} R^{4} \\omega^{4}}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} + \\frac{A \\left(C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2}\\right)}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}\\end{matrix}\\right]$" ], "text/plain": [ "⎡ ⎛ 5 5 5 3 3 3⎞ ⎤\n", "⎢ A⋅C⋅R⋅ω A⋅⎝C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω ⎠ ⎥\n", "⎢ ──────────────────────────────────── + ──────────────────────────────────── ⎥\n", "⎢ 6 6 6 4 4 4 2 2 2 6 6 6 4 4 4 2 2 2 ⎥\n", "⎢ C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 ⎥\n", "⎢ ⎥\n", "⎢ ⎛ 4 4 4 2 2 2⎞ ⎛ 4 4 4 2 2 2 ⎞ ⎥\n", "⎢ A⋅⎝C ⋅R ⋅ω + C ⋅R ⋅ω ⎠ A⋅⎝- C ⋅R ⋅ω - 2⋅C ⋅R ⋅ω - 1⎠ ⎥\n", "⎢ ──────────────────────────────────── + ──────────────────────────────────── ⎥\n", "⎢ 6 6 6 4 4 4 2 2 2 6 6 6 4 4 4 2 2 2 ⎥\n", "⎢ C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 ⎥\n", "⎢ ⎥\n", "⎢ 3 3 3 ⎛ 3 3 3 ⎞ ⎥\n", "⎢ A⋅C ⋅R ⋅ω A⋅⎝C ⋅R ⋅ω + C⋅R⋅ω⎠ ⎥\n", "⎢- ──────────────────────────────────── + ────────────────────────────────────⎥\n", "⎢ 6 6 6 4 4 4 2 2 2 6 6 6 4 4 4 2 2 2 ⎥\n", "⎢ C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1⎥\n", "⎢ ⎥\n", "⎢ ⎛ 4 4 4 2 2 2 ⎞ ⎥\n", "⎢ A⋅⎝C ⋅R ⋅ω + C ⋅R ⋅ω + 1⎠ A ⎥\n", "⎢ ──────────────────────────────────── - ──────────────────────────────────── ⎥\n", "⎢ 6 6 6 4 4 4 2 2 2 6 6 6 4 4 4 2 2 2 ⎥\n", "⎢ C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 ⎥\n", "⎢ ⎥\n", "⎢ ⎛ 5 5 5 3 3 3 ⎞ ⎥\n", "⎢ A⋅C⋅R⋅ω A⋅⎝- C ⋅R ⋅ω - C ⋅R ⋅ω - C⋅R⋅ω⎠ ⎥\n", "⎢ ──────────────────────────────────── + ──────────────────────────────────── ⎥\n", "⎢ 6 6 6 4 4 4 2 2 2 6 6 6 4 4 4 2 2 2 ⎥\n", "⎢ C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 ⎥\n", "⎢ ⎥\n", "⎢ 4 4 4 ⎛ 4 4 4 2 2 2⎞ ⎥\n", "⎢ A⋅C ⋅R ⋅ω A⋅⎝C ⋅R ⋅ω + C ⋅R ⋅ω ⎠ ⎥\n", "⎢- ──────────────────────────────────── + ────────────────────────────────────⎥\n", "⎢ 6 6 6 4 4 4 2 2 2 6 6 6 4 4 4 2 2 2 ⎥\n", "⎣ C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1⎦" ] }, "execution_count": 139, "metadata": {}, "output_type": "execute_result" } ], "source": [ "res = M3**-1*col\n", "res" ] }, { "cell_type": "code", "execution_count": 140, "id": "599f7599", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle \\frac{A C R \\omega \\left(C^{2} R^{2} \\omega^{2} \\left(C^{2} R^{2} \\omega^{2} + 2\\right) + 1\\right)}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}$" ], "text/plain": [ " ⎛ 2 2 2 ⎛ 2 2 2 ⎞ ⎞\n", "A⋅C⋅R⋅ω⋅⎝C ⋅R ⋅ω ⋅⎝C ⋅R ⋅ω + 2⎠ + 1⎠\n", "─────────────────────────────────────\n", " 6 6 6 4 4 4 2 2 2 \n", "C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1 " ] }, "execution_count": 140, "metadata": {}, "output_type": "execute_result" } ], "source": [ "simplify(res[0])" ] }, { "cell_type": "code", "execution_count": 141, "id": "8830a26f", "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle \\frac{A \\left(- C^{2} R^{2} \\omega^{2} - 1\\right)}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}$" ], "text/plain": [ " ⎛ 2 2 2 ⎞ \n", " A⋅⎝- C ⋅R ⋅ω - 1⎠ \n", "────────────────────────────────────\n", " 6 6 6 4 4 4 2 2 2 \n", "C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1" ] }, "execution_count": 141, "metadata": {}, "output_type": "execute_result" } ], "source": [ "simplify(res[1])" ] }, { "cell_type": "code", "execution_count": 142, "id": "3bd9f332", "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle \\frac{A C R \\omega}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}$" ], "text/plain": [ " A⋅C⋅R⋅ω \n", "────────────────────────────────────\n", " 6 6 6 4 4 4 2 2 2 \n", "C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1" ] }, "execution_count": 142, "metadata": {}, "output_type": "execute_result" } ], "source": [ "simplify(res[2])" ] }, { "cell_type": "code", "execution_count": 143, "id": "5de8a6c6", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle \\frac{A C^{2} R^{2} \\omega^{2} \\left(C^{2} R^{2} \\omega^{2} + 1\\right)}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}$" ], "text/plain": [ " 2 2 2 ⎛ 2 2 2 ⎞ \n", " A⋅C ⋅R ⋅ω ⋅⎝C ⋅R ⋅ω + 1⎠ \n", "────────────────────────────────────\n", " 6 6 6 4 4 4 2 2 2 \n", "C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1" ] }, "execution_count": 143, "metadata": {}, "output_type": "execute_result" } ], "source": [ "simplify(res[3])" ] }, { "cell_type": "code", "execution_count": 144, "id": "d393000e", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle \\frac{A C^{3} R^{3} \\omega^{3} \\left(- C^{2} R^{2} \\omega^{2} - 1\\right)}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}$" ], "text/plain": [ " 3 3 3 ⎛ 2 2 2 ⎞ \n", " A⋅C ⋅R ⋅ω ⋅⎝- C ⋅R ⋅ω - 1⎠ \n", "────────────────────────────────────\n", " 6 6 6 4 4 4 2 2 2 \n", "C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1" ] }, "execution_count": 144, "metadata": {}, "output_type": "execute_result" } ], "source": [ "simplify(res[4])" ] }, { "cell_type": "code", "execution_count": 145, "id": "2a546639", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle \\frac{A C^{2} R^{2} \\omega^{2}}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}$" ], "text/plain": [ " 2 2 2 \n", " A⋅C ⋅R ⋅ω \n", "────────────────────────────────────\n", " 6 6 6 4 4 4 2 2 2 \n", "C ⋅R ⋅ω + 2⋅C ⋅R ⋅ω + C ⋅R ⋅ω + 1" ] }, "execution_count": 145, "metadata": {}, "output_type": "execute_result" } ], "source": [ "simplify(res[5])" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.10" } }, "nbformat": 4, "nbformat_minor": 5 }