circuit1_demo.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "66fb0078",
   "metadata": {},
   "outputs": [],
   "source": [
    "import sympy as sym\n",
    "from sym_helper import makesubs, printout"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "10b55e0f",
   "metadata": {},
   "outputs": [],
   "source": [
    "sym.init_printing()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "3c71c521",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Declare symbols (unknowns in first group, knowns in second)\n",
    "unks = sym.var('v1, v2, va, i1, i2, ib')\n",
    "knowns = sym.var('vb, ia, R1, R2')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "a954b97c",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Element equations\n",
    "OhmR1 = sym.Eq(v1, i1*R1)\n",
    "OhmR2 = sym.Eq(v2, i2*R2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "935cf524",
   "metadata": {},
   "outputs": [],
   "source": [
    "# KCL equations\n",
    "KCLna = -ia+i1+i2 \n",
    "KCLnb = -i2+ib "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "054e3ce7",
   "metadata": {},
   "outputs": [],
   "source": [
    "# KVL equations\n",
    "KVLl1 = -va+v1\n",
    "KVLl2 = -v1+v2+vb"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "f467db12",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Collect equations\n",
    "eqns = [OhmR1, OhmR2, KCLna, KCLnb, KVLl1, KVLl2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "4487120f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "v₁\n",
      "R₁⋅R₂⋅ia + R₁⋅vb\n",
      "────────────────\n",
      "    R₁ + R₂     \n",
      "v₂\n",
      "R₁⋅R₂⋅ia - R₂⋅vb\n",
      "────────────────\n",
      "    R₁ + R₂     \n",
      "va\n",
      "R₁⋅R₂⋅ia + R₁⋅vb\n",
      "────────────────\n",
      "    R₁ + R₂     \n",
      "i₁\n",
      "R₂⋅ia + vb\n",
      "──────────\n",
      " R₁ + R₂  \n",
      "i₂\n",
      "R₁⋅ia - vb\n",
      "──────────\n",
      " R₁ + R₂  \n",
      "ib\n",
      "R₁⋅ia - vb\n",
      "──────────\n",
      " R₁ + R₂  \n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Solve and display\n",
    "sol = sym.solve(eqns, unks)\n",
    "printout(sol, unks)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "4c749a0f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "v₁\n",
      "7.188\n",
      "v₂\n",
      "-4.813\n",
      "va\n",
      "7.188\n",
      "i₁\n",
      "0.007187\n",
      "i₂\n",
      "-0.002187\n",
      "ib\n",
      "-0.002187\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Define substitions\n",
    "subvar = [R1, R2, ia, vb]\n",
    "subval = [1000, 2200, 5/1000, 12]\n",
    "subsol = makesubs(sol, subvar, subval)\n",
    "printout(subsol, unks, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "13fe9d77",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Aux equations\n",
    "aunks = sym.var('pdelia, pdelvb, pabsR1, pabsR2')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "81d44079",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Aux equations\n",
    "aunks = sym.var('pdelia, pdelvb, pabsR1, pabsR2')\n",
    "\n",
    "ae = []\n",
    "ae.append(sym.Eq(pdelia, va*ia))\n",
    "ae.append(sym.Eq(pdelvb, -vb*ib))\n",
    "ae.append(sym.Eq(pabsR1, v1*i1))\n",
    "ae.append(sym.Eq(pabsR2, v2*i2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "1263644f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "pdelia\n",
      "ia⋅va\n",
      "pdelvb\n",
      "-ib⋅vb\n",
      "pabsR₁\n",
      "i₁⋅v₁\n",
      "pabsR₂\n",
      "i₂⋅v₂\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Show as functions of all variables\n",
    "asol = sym.solve(ae, aunks)\n",
    "printout(asol, aunks)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "62b8934b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "pdelia\n",
      "ia⋅(R₁⋅R₂⋅ia + R₁⋅vb)\n",
      "─────────────────────\n",
      "       R₁ + R₂       \n",
      "pdelvb\n",
      "-vb⋅(R₁⋅ia - vb) \n",
      "─────────────────\n",
      "     R₁ + R₂     \n",
      "pabsR₁\n",
      "(R₂⋅ia + vb)⋅(R₁⋅R₂⋅ia + R₁⋅vb)\n",
      "───────────────────────────────\n",
      "                    2          \n",
      "           (R₁ + R₂)           \n",
      "pabsR₂\n",
      "(R₁⋅ia - vb)⋅(R₁⋅R₂⋅ia - R₂⋅vb)\n",
      "───────────────────────────────\n",
      "                    2          \n",
      "           (R₁ + R₂)           \n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Show as functions of known variables\n",
    "subasol1 = makesubs(asol, sol.keys(), sol.values())\n",
    "printout(subasol1, aunks)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "683a386e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "pdelia\n",
      "0.03594\n",
      "pdelvb\n",
      "0.02625\n",
      "pabsR₁\n",
      "0.05166\n",
      "pabsR₂\n",
      "0.01053\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Show with all substitutions\n",
    "subasol2 = makesubs(asol, subsol.keys(), subsol.values())\n",
    "subasol2 = makesubs(subasol2, subvar, subval)\n",
    "printout(subasol2, aunks, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6c934df2",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "421f0d21",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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