{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "e5ecb852",
   "metadata": {},
   "source": [
    "# The exemplars from *The Internal Logic of Symbulator*\n",
    "\n",
    "The monograph [*The Internal Logic of Symbulator*](https://learn.symbulator.com/monograph.pdf) closes with seven exemplar circuits, chosen because each shows one thing the simulator is for. This notebook runs all of them, as the eight entries the app's Built-in Examples menu lists under *The Monograph* -- the circuits below are read from that same file, not retyped.\n",
    "\n",
    "Each section gives the problem as the monograph poses it, draws the circuit, solves it, and reads the answer the text discusses. Run the cells in order; nothing here takes more than a few seconds.\n",
    "\n",
    "If you are on Colab, run the first cell."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "f2599e74",
   "metadata": {},
   "outputs": [],
   "source": [
    "# !pip install symbulator matplotlib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "a052029e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'0.5.30'"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import sympy as sp\n",
    "from symbulator import dc, ac, fd, tr, th, draw, polar, bode_samples, t, s\n",
    "import symbulator\n",
    "symbulator.__version__"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "04c872ff",
   "metadata": {},
   "source": [
    "## 1. The two-stage amplifier of 1999\n",
    "\n",
    "The circuit that closed the 1999 paper and the thesis's Problem 87: a two-stage amplifier whose gain Bode diagram Prof. Yee asked for. An FD solve returns every node voltage in s, and the gain is the Evaluate line, v4/v5. For the Bode plot itself, set vg to 1 (so v_4 is the transfer function) and plot v_4 between 1.6e3 and 1.6e12 Hz. Three minutes on the TI-89 in 2001; under a second here.\n",
    "\n",
    "The analysis is in the s-domain, so `fd()`: every node voltage comes back as a function of `s`. A bare `a` would show all of them; the output node is enough here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "966d1f30",
   "metadata": {},
   "outputs": [
    {
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      ],
      "text/plain": [
       "<IPython.core.display.SVG object>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "amp = '''\n",
    "e1,5,0,vg\n",
    "r1,5,1,150\n",
    "r2,1,0,1'k\n",
    "cc1,1,0,100'p\n",
    "cc2,1,2,3'p\n",
    "jd1,2,0,0.05*v_1\n",
    "r3,2,0,2'k\n",
    "r4,2,3,100\n",
    "r5,3,0,1'k\n",
    "cc3,3,0,100'p\n",
    "cc4,3,4,3'p\n",
    "jd2,4,0,0.05*v_3\n",
    "r6,4,0,2'k\n",
    "'''\n",
    "draw(amp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "e66dfc82",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{vg \\left(1.8 \\cdot 10^{17} s^{2} - 6.0 \\cdot 10^{27} s + 5.0 \\cdot 10^{37}\\right)}{27.0 s^{4} + 134010000000.0 s^{3} + 8.6724075 \\cdot 10^{19} s^{2} + 5.4981 \\cdot 10^{27} s + 1.7825 \\cdot 10^{34}}$"
      ],
      "text/plain": [
       "vg*(1.8e+17*s**2 - 6.0e+27*s + 5.0e+37)/(27.0*s**4 + 134010000000.0*s**3 + 8.6724075e+19*s**2 + 5.4981e+27*s + 1.7825e+34)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = fd(amp)\n",
    "a[\"v4\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "abc7a9a4",
   "metadata": {},
   "source": [
    "The gain is the ratio of two of those answers. The source is the symbol `vg`, and it cancels:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "2a2c80af",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{1.8 \\cdot 10^{17} s^{2} - 6.0 \\cdot 10^{27} s + 5.0 \\cdot 10^{37}}{27.0 s^{4} + 134010000000.0 s^{3} + 8.6724075 \\cdot 10^{19} s^{2} + 5.4981 \\cdot 10^{27} s + 1.7825 \\cdot 10^{34}}$"
      ],
      "text/plain": [
       "(1.8e+17*s**2 - 6.0e+27*s + 5.0e+37)/(27.0*s**4 + 134010000000.0*s**3 + 8.6724075e+19*s**2 + 5.4981e+27*s + 1.7825e+34)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gain = sp.simplify(a[\"v4\"] / a[\"v5\"])\n",
    "gain"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c5fe80ec",
   "metadata": {},
   "source": [
    "For the Bode diagram Prof. Yee asked for, `bode_samples()` sweeps the frequency and returns arrays ready for Matplotlib. With `vg` set to 1 by a condition, `v_4` *is* the transfer function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "a7a531b4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 650x450 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "freq, mag_db, phase = bode_samples(amp, \"v_4\", 1.6e3, 1.6e12, n=400, conditions=[\"vg = 1\"])\n",
    "fig, (a1, a2) = plt.subplots(2, 1, sharex=True, figsize=(6.5, 4.5))\n",
    "a1.semilogx(freq, mag_db); a1.set_ylabel(\"gain, dB\"); a1.grid(True, which=\"both\")\n",
    "a2.semilogx(freq, phase);  a2.set_ylabel(\"phase, degrees\"); a2.set_xlabel(\"Hz\"); a2.grid(True, which=\"both\")\n",
    "a1.set_title(\"The 1999 amplifier: v4 / vg\")\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "20eefc03",
   "metadata": {},
   "source": [
    "## 2. One of each: the 2013 showcase\n",
    "\n",
    "Composed in 2013 to show off: one dependent source of each species, woven through seven resistors. Find positive values of Es and Js such that the VCCS delivers 80 W and the CCVS dissipates 0 W. The two power constraints are quadratic, so four solutions exist; the conditions pick the one meant: Es = 17.61 V and Js = 0.3973 A. And ir5 comes out exactly 0 -- the constraint drove its own controlling current to zero, which is how the CCVS dissipates nothing.\n",
    "\n",
    "This is Expert Mode: two equations about *power*, two unknowns that are the sources' own values, and two conditions that choose among the roots. Inside an equation the names are written the way the app writes them, `pjd1` for the power in `jd1`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "ba84f769",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<svg xmlns=\"http://www.w3.org/2000/svg\" viewBox=\"10 -9.50998 928.018 642.56\" width=\"928.018\" height=\"642.56\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"1.7\" stroke-linecap=\"round\" stroke-linejoin=\"round\" class=\"symbulator-schematic\"><style>.symbulator-schematic .lbl{font:13px/1 ui-sans-serif,system-ui,sans-serif;fill:currentColor;stroke:none}.symbulator-schematic .sub{font-size:0.72em}</style><g transform=\"translate(58,419.8)\"><path d=\"M0 0 L46.1 0 Q47.6 0 48.1878 1.38004 L50.0789 5.81996 Q50.6667 7.2 51.2545 5.81996 L56.2122 -5.81996 Q56.8 -7.2 57.3878 -5.81996 L62.3455 5.81996 Q62.9333 7.2 63.5211 5.81996 L68.4789 -5.81996 Q69.0667 -7.2 69.6545 -5.81996 L74.6122 5.81996 Q75.2 7.2 75.7878 5.81996 L80.7455 -5.81996 Q81.3333 -7.2 81.9211 -5.81996 L83.8122 -1.38004 Q84.4 0 85.9 0 L132 0\"/></g><text class=\"lbl\" x=\"124\" y=\"405.19\" text-anchor=\"middle\"><tspan dy=\"0\">10Ω</tspan></text><text class=\"lbl\" x=\"124\" y=\"388.29\" text-anchor=\"middle\"><tspan dy=\"0\">R</tspan><tspan class=\"sub\" dy=\"3.4\">1</tspan></text><path d=\"M105.6 436.01 L142.4 436.01\"/><path d=\"M135.9 440.01 L142.4 436.01 L135.9 432.01\" fill=\"currentColor\"/><text class=\"lbl\" x=\"124\" y=\"454.86\" text-anchor=\"middle\"><tspan font-style=\"italic\" dy=\"0\">i</tspan><tspan class=\"sub\" dy=\"3.4\">R1</tspan></text><g transform=\"translate(454,299.2) rotate(180)\"><path d=\"M0 0 L178.1 0 Q179.6 0 180.188 1.38004 L182.079 5.81996 Q182.667 7.2 183.254 5.81996 L188.212 -5.81996 Q188.8 -7.2 189.388 -5.81996 L194.346 5.81996 Q194.933 7.2 195.521 5.81996 L200.479 -5.81996 Q201.067 -7.2 201.654 -5.81996 L206.612 5.81996 Q207.2 7.2 207.788 5.81996 L212.746 -5.81996 Q213.333 -7.2 213.921 -5.81996 L215.812 -1.38004 Q216.4 0 217.9 0 L396 0\"/></g><text class=\"lbl\" x=\"256\" y=\"284.59\" text-anchor=\"middle\"><tspan dy=\"0\">20Ω</tspan></text><text class=\"lbl\" x=\"256\" y=\"267.69\" text-anchor=\"middle\"><tspan dy=\"0\">R</tspan><tspan class=\"sub\" dy=\"3.4\">2</tspan></text><g transform=\"translate(322,419.8) rotate(180)\"><path d=\"M0 0 L46.1 0 Q47.6 0 48.1878 1.38004 L50.0789 5.81996 Q50.6667 7.2 51.2545 5.81996 L56.2122 -5.81996 Q56.8 -7.2 57.3878 -5.81996 L62.3455 5.81996 Q62.9333 7.2 63.5211 5.81996 L68.4789 -5.81996 Q69.0667 -7.2 69.6545 -5.81996 L74.6122 5.81996 Q75.2 7.2 75.7878 5.81996 L80.7455 -5.81996 Q81.3333 -7.2 81.9211 -5.81996 L83.8122 -1.38004 Q84.4 0 85.9 0 L132 0\"/></g><text class=\"lbl\" x=\"256\" y=\"405.19\" text-anchor=\"middle\"><tspan dy=\"0\">40Ω</tspan></text><text class=\"lbl\" x=\"256\" y=\"388.29\" text-anchor=\"middle\"><tspan dy=\"0\">R</tspan><tspan class=\"sub\" dy=\"3.4\">4</tspan></text><g transform=\"translate(850,58) rotate(180)\"><path d=\"M0 0 L310.1 0 Q311.6 0 312.188 1.38004 L314.079 5.81996 Q314.667 7.2 315.254 5.81996 L320.212 -5.81996 Q320.8 -7.2 321.388 -5.81996 L326.346 5.81996 Q326.933 7.2 327.521 5.81996 L332.479 -5.81996 Q333.067 -7.2 333.654 -5.81996 L338.612 5.81996 Q339.2 7.2 339.788 5.81996 L344.746 -5.81996 Q345.333 -7.2 345.921 -5.81996 L347.812 -1.38004 Q348.4 0 349.9 0 L660 0\"/></g><text class=\"lbl\" x=\"520\" y=\"43.39\" text-anchor=\"middle\"><tspan dy=\"0\">50Ω</tspan></text><text class=\"lbl\" x=\"520\" y=\"26.49\" text-anchor=\"middle\"><tspan dy=\"0\">R</tspan><tspan class=\"sub\" dy=\"3.4\">5</tspan></text><path d=\"M538.4 74.21 L501.6 74.21\"/><path d=\"M508.1 70.21 L501.6 74.21 L508.1 78.21\" fill=\"currentColor\"/><text class=\"lbl\" x=\"520\" y=\"93.06\" text-anchor=\"middle\"><tspan font-style=\"italic\" dy=\"0\">i</tspan><tspan class=\"sub\" dy=\"3.4\">R5</tspan></text><g transform=\"translate(586,419.8)\"><path d=\"M0 0 L46.1 0 Q47.6 0 48.1878 1.38004 L50.0789 5.81996 Q50.6667 7.2 51.2545 5.81996 L56.2122 -5.81996 Q56.8 -7.2 57.3878 -5.81996 L62.3455 5.81996 Q62.9333 7.2 63.5211 5.81996 L68.4789 -5.81996 Q69.0667 -7.2 69.6545 -5.81996 L74.6122 5.81996 Q75.2 7.2 75.7878 5.81996 L80.7455 -5.81996 Q81.3333 -7.2 81.9211 -5.81996 L83.8122 -1.38004 Q84.4 0 85.9 0 L132 0\"/></g><text class=\"lbl\" x=\"652\" y=\"405.19\" text-anchor=\"middle\"><tspan dy=\"0\">60Ω</tspan></text><text class=\"lbl\" x=\"652\" y=\"388.29\" text-anchor=\"middle\"><tspan dy=\"0\">R</tspan><tspan class=\"sub\" dy=\"3.4\">6</tspan></text><path d=\"M621.1 429.8 L628.1 429.8 M624.6 426.3 L624.6 433.3\"/><path d=\"M675.9 429.8 L682.9 429.8\"/><g transform=\"translate(850,419.8) rotate(180)\"><path d=\"M0 0 L46.1 0 Q47.6 0 48.1878 1.38004 L50.0789 5.81996 Q50.6667 7.2 51.2545 5.81996 L56.2122 -5.81996 Q56.8 -7.2 57.3878 -5.81996 L62.3455 5.81996 Q62.9333 7.2 63.5211 5.81996 L68.4789 -5.81996 Q69.0667 -7.2 69.6545 -5.81996 L74.6122 5.81996 Q75.2 7.2 75.7878 5.81996 L80.7455 -5.81996 Q81.3333 -7.2 81.9211 -5.81996 L83.8122 -1.38004 Q84.4 0 85.9 0 L132 0\"/></g><text class=\"lbl\" x=\"784\" y=\"405.19\" text-anchor=\"middle\"><tspan dy=\"0\">70Ω</tspan></text><text class=\"lbl\" x=\"784\" y=\"388.29\" text-anchor=\"middle\"><tspan dy=\"0\">R</tspan><tspan class=\"sub\" dy=\"3.4\">7</tspan></text><path d=\"M807.9 429.8 L814.9 429.8 M811.4 426.3 L811.4 433.3\"/><path d=\"M753.1 429.8 L760.1 429.8\"/><g transform=\"translate(454,419.8) rotate(180)\"><path d=\"M0 0 L49.5 0 M82.5 0 L132 0\"/><path d=\"M49.5 0 L66 -16.5 L82.5 0 L66 16.5 Z\" fill=\"none\" stroke-linejoin=\"miter\"/><path d=\"M57 0 L75 0\"/><path d=\"M69 -4 L75 0 L69 4\" fill=\"currentColor\"/></g><text class=\"lbl\" x=\"388\" y=\"393.55\" text-anchor=\"middle\"><tspan dy=\"0\">J</tspan><tspan class=\"sub\" dy=\"3.4\">D1</tspan></text><text class=\"lbl\" x=\"388\" y=\"451.15\" text-anchor=\"middle\"><tspan dy=\"0\">0.2</tspan><tspan font-style=\"italic\" dy=\"0\">v</tspan><tspan class=\"sub\" dy=\"3.4\">R7</tspan></text><g transform=\"translate(586,178.6) rotate(180)\"><path d=\"M0 0 L115.5 0 M148.5 0 L264 0\"/><path d=\"M115.5 0 L132 -16.5 L148.5 0 L132 16.5 Z\" fill=\"none\" stroke-linejoin=\"miter\"/></g><text class=\"lbl\" x=\"454\" y=\"152.35\" text-anchor=\"middle\"><tspan dy=\"0\">E</tspan><tspan class=\"sub\" dy=\"3.4\">D2</tspan></text><text class=\"lbl\" x=\"454\" y=\"209.95\" text-anchor=\"middle\"><tspan dy=\"0\">0.1</tspan><tspan font-style=\"italic\" dy=\"0\">i</tspan><tspan class=\"sub\" dy=\"3.4\">R5</tspan></text><path d=\"M457.5 178.6 L464.5 178.6 M461 175.1 L461 182.1\"/><path d=\"M443.5 178.6 L450.5 178.6\"/><g transform=\"translate(850,299.2) rotate(180)\"><path d=\"M0 0 L115.5 0 M148.5 0 L264 0\"/><path d=\"M115.5 0 L132 -16.5 L148.5 0 L132 16.5 Z\" fill=\"none\" stroke-linejoin=\"miter\"/><path d=\"M123 0 L141 0\"/><path d=\"M135 -4 L141 0 L135 4\" fill=\"currentColor\"/></g><text class=\"lbl\" x=\"718\" y=\"272.95\" text-anchor=\"middle\"><tspan dy=\"0\">J</tspan><tspan class=\"sub\" dy=\"3.4\">D3</tspan></text><text class=\"lbl\" x=\"718\" y=\"330.55\" text-anchor=\"middle\"><tspan dy=\"0\">2</tspan><tspan font-style=\"italic\" dy=\"0\">i</tspan><tspan class=\"sub\" dy=\"3.4\">R1</tspan></text><g transform=\"translate(58,419.8) rotate(90)\"><path d=\"M0 0 L60 0 M90 0 L150 0\"/><circle cx=\"75\" cy=\"0\" r=\"15\" fill=\"none\"/></g><text class=\"lbl\" x=\"79.35\" y=\"488.8\" text-anchor=\"start\"><tspan dy=\"0\">E</tspan><tspan class=\"sub\" dy=\"3.4\">S</tspan></text><text class=\"lbl\" x=\"79.35\" y=\"507.8\" text-anchor=\"start\"><tspan dy=\"0\">es</tspan></text><path d=\"M54.5 487.8 L61.5 487.8 M58 484.3 L58 491.3\"/><path d=\"M54.5 501.8 L61.5 501.8\"/><g transform=\"translate(718,569.8) rotate(-90)\"><path d=\"M0 0 L60 0 M90 0 L150 0\"/><circle cx=\"75\" cy=\"0\" r=\"15\" fill=\"none\"/><path d=\"M66 0 L84 0\"/><path d=\"M78 -4 L84 0 L78 4\" fill=\"currentColor\"/></g><text class=\"lbl\" x=\"739.35\" y=\"488.8\" text-anchor=\"start\"><tspan dy=\"0\">J</tspan><tspan class=\"sub\" dy=\"3.4\">S</tspan></text><text class=\"lbl\" x=\"739.35\" y=\"507.8\" text-anchor=\"start\"><tspan dy=\"0\">js</tspan></text><g transform=\"translate(190,419.8) rotate(90)\"><path d=\"M0 0 L55.1 0 Q56.6 0 57.1878 1.38004 L59.0789 5.81996 Q59.6667 7.2 60.2545 5.81996 L65.2122 -5.81996 Q65.8 -7.2 66.3878 -5.81996 L71.3455 5.81996 Q71.9333 7.2 72.5211 5.81996 L77.4789 -5.81996 Q78.0667 -7.2 78.6545 -5.81996 L83.6122 5.81996 Q84.2 7.2 84.7878 5.81996 L89.7455 -5.81996 Q90.3333 -7.2 90.9211 -5.81996 L92.8122 -1.38004 Q93.4 0 94.9 0 L150 0\"/></g><text class=\"lbl\" x=\"202.86\" y=\"488.8\" text-anchor=\"start\"><tspan dy=\"0\">R</tspan><tspan class=\"sub\" dy=\"3.4\">3</tspan></text><text class=\"lbl\" x=\"202.86\" y=\"507.8\" text-anchor=\"start\"><tspan dy=\"0\">30Ω</tspan></text><g transform=\"translate(850,569.8) rotate(-90)\"><path d=\"M0 0 L58.5 0 M91.5 0 L150 0\"/><path d=\"M58.5 0 L75 -16.5 L91.5 0 L75 16.5 Z\" fill=\"none\" stroke-linejoin=\"miter\"/></g><text class=\"lbl\" x=\"872.85\" y=\"488.8\" text-anchor=\"start\"><tspan dy=\"0\">E</tspan><tspan class=\"sub\" dy=\"3.4\">D4</tspan></text><text class=\"lbl\" x=\"872.85\" y=\"507.8\" 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text-anchor=\"start\"><tspan dy=\"0\">d</tspan></text><text class=\"lbl\" x=\"856\" y=\"411.7\" text-anchor=\"start\"><tspan dy=\"0\">n</tspan></text><line x1=\"58\" y1=\"569.8\" x2=\"850\" y2=\"569.8\"/><line x1=\"58\" y1=\"299.2\" x2=\"58\" y2=\"419.8\"/><path d=\"M190 58 L190 294.2 A5 5 0 0 0 190 304.2 L190 419.8\"/><path d=\"M322 178.6 L322 294.2 A5 5 0 0 0 322 304.2 L322 419.8\"/><line x1=\"454\" y1=\"299.2\" x2=\"454\" y2=\"419.8\"/><line x1=\"586\" y1=\"178.6\" x2=\"586\" y2=\"419.8\"/><line x1=\"850\" y1=\"58\" x2=\"850\" y2=\"419.8\"/><circle cx=\"190\" cy=\"569.8\" r=\"3.4\" fill=\"currentColor\" stroke=\"none\"/><circle cx=\"718\" cy=\"569.8\" r=\"3.4\" fill=\"currentColor\" stroke=\"none\"/><circle cx=\"58\" cy=\"419.8\" r=\"3.4\" fill=\"currentColor\" stroke=\"none\"/><circle cx=\"718\" cy=\"419.8\" r=\"3.4\" fill=\"currentColor\" stroke=\"none\"/><circle cx=\"190\" cy=\"419.8\" r=\"3.4\" fill=\"currentColor\" stroke=\"none\"/><circle cx=\"322\" cy=\"419.8\" r=\"3.4\" fill=\"currentColor\" stroke=\"none\"/><circle cx=\"850\" cy=\"419.8\" r=\"3.4\" fill=\"currentColor\" stroke=\"none\"/><circle cx=\"586\" cy=\"419.8\" r=\"3.4\" fill=\"currentColor\" stroke=\"none\"/><circle cx=\"586\" cy=\"299.2\" r=\"3.4\" fill=\"currentColor\" stroke=\"none\"/><circle cx=\"850\" cy=\"299.2\" r=\"3.4\" fill=\"currentColor\" stroke=\"none\"/></svg>"
      ],
      "text/plain": [
       "<IPython.core.display.SVG object>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "showcase = '''\n",
    "es,e,0,es\n",
    "js,0,d,js\n",
    "r1,e,m,10\n",
    "r2,a,e,20\n",
    "r3,m,0,30\n",
    "r4,b,m,40\n",
    "r5,n,m,50\n",
    "r6,c,d,60\n",
    "r7,n,d,70\n",
    "jd1,a,b,0.2vr7\n",
    "ed2,c,b,0.1ir5\n",
    "jd3,n,c,2ir1\n",
    "ed4,0,n,0.7vr6\n",
    "'''\n",
    "draw(showcase)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "b020e0ac",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\begin{gathered}\\text{dc analysis} \\\\ \\begin{aligned}es &= 17.61 \\\\ i_{ed2} &= 1.469 \\\\ i_{ed4} &= 1.071 \\\\ i_{es} &= 1.08 \\\\ i_{jd1} &= -1.676 \\\\ i_{jd3} &= 1.191 \\\\ i_{js} &= 0.3973 \\\\ i_{r1} &= 0.5955 \\\\ i_{r2} &= 1.676 \\\\ i_{r3} &= 0.3886 \\\\ i_{r4} &= -0.2069 \\\\ i_{r5} &= 0 \\\\ i_{r6} &= -0.2776 \\\\ i_{r7} &= -0.1197 \\\\ js &= 0.3973 \\\\ p_{ed2} &= 0 \\\\ p_{ed4} &= -12.49 \\\\ p_{es} &= 19.02 \\\\ p_{jd1} &= -80.0 \\\\ p_{jd3} &= 9.859 \\\\ p_{js} &= -7.96 \\\\ p_{r1} &= 3.547 \\\\ p_{r2} &= 56.15 \\\\ p_{r3} &= 4.531 \\\\ p_{r4} &= 1.713 \\\\ p_{r5} &= 0 \\\\ p_{r6} &= 4.623 \\\\ p_{r7} &= 1.003 \\\\ r_{ed2} &= 0 \\\\ r_{ed4} &= 10.88 \\\\ r_{es} &= -16.31 \\\\ r_{jd1} &= 28.49 \\\\ r_{jd3} &= -6.949 \\\\ r_{js} &= 50.44 \\\\ v_{a} &= 51.13 \\\\ v_{b} &= 3.381 \\\\ v_{c} &= 3.381 \\\\ v_{d} &= 20.04 \\\\ v_{e} &= 17.61 \\\\ v_{ed2} &= 0 \\\\ v_{ed4} &= -11.66 \\\\ v_{es} &= 17.61 \\\\ v_{jd1} &= 47.74 \\\\ v_{jd3} &= 8.277 \\\\ v_{js} &= -20.04 \\\\ v_{m} &= 11.66 \\\\ v_{n} &= 11.66 \\\\ v_{r1} &= 5.955 \\\\ v_{r2} &= 33.51 \\\\ v_{r3} &= 11.66 \\\\ v_{r4} &= -8.277 \\\\ v_{r5} &= 0 \\\\ v_{r6} &= -16.65 \\\\ v_{r7} &= -8.378\\end{aligned}\\end{gathered}$"
      ],
      "text/plain": [
       "Result(domain='dc')\n",
       "  es = 17.61\n",
       "  i_ed2 = 1.469\n",
       "  i_ed4 = 1.071\n",
       "  i_es = 1.080\n",
       "  i_jd1 = -1.676\n",
       "  i_jd3 = 1.191\n",
       "  i_js = 0.3973\n",
       "  i_r1 = 0.5955\n",
       "  i_r2 = 1.676\n",
       "  i_r3 = 0.3886\n",
       "  i_r4 = -0.2069\n",
       "  i_r5 = 0\n",
       "  i_r6 = -0.2776\n",
       "  i_r7 = -0.1197\n",
       "  js = 0.3973\n",
       "  p_ed2 = 0\n",
       "  p_ed4 = -12.49\n",
       "  p_es = 19.02\n",
       "  p_jd1 = -80.00\n",
       "  p_jd3 = 9.859\n",
       "  p_js = -7.960\n",
       "  p_r1 = 3.547\n",
       "  p_r2 = 56.15\n",
       "  p_r3 = 4.531\n",
       "  p_r4 = 1.713\n",
       "  p_r5 = 0\n",
       "  p_r6 = 4.623\n",
       "  p_r7 = 1.003\n",
       "  r_ed2 = 0\n",
       "  r_ed4 = 10.88\n",
       "  r_es = -16.31\n",
       "  r_jd1 = 28.49\n",
       "  r_jd3 = -6.949\n",
       "  r_js = 50.44\n",
       "  v_a = 51.13\n",
       "  v_b = 3.381\n",
       "  v_c = 3.381\n",
       "  v_d = 20.04\n",
       "  v_e = 17.61\n",
       "  v_ed2 = 0\n",
       "  v_ed4 = -11.66\n",
       "  v_es = 17.61\n",
       "  v_jd1 = 47.74\n",
       "  v_jd3 = 8.277\n",
       "  v_js = -20.04\n",
       "  v_m = 11.66\n",
       "  v_n = 11.66\n",
       "  v_r1 = 5.955\n",
       "  v_r2 = 33.51\n",
       "  v_r3 = 11.66\n",
       "  v_r4 = -8.277\n",
       "  v_r5 = 0\n",
       "  v_r6 = -16.65\n",
       "  v_r7 = -8.378"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sc = dc(showcase,\n",
    "        unknowns=[\"es\", \"js\"],\n",
    "        equations=[\"pjd1 = -80\", \"ped2 = 0\"],\n",
    "        conditions=[\"es > 0\", \"js > 0\"])\n",
    "sc.rounded(4)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d3f64c21",
   "metadata": {},
   "source": [
    "The three answers the text names, and the current the constraint drove to zero:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "27e50635",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(17.61, 0.3973, 0.0)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sc.rounded(4)[\"es\"], sc.rounded(4)[\"js\"], sc[\"ir5\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9d4c3530",
   "metadata": {},
   "source": [
    "Without the two conditions the system has more than one solution. `Result.solutions` holds all of them; `.values` is the first."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "a9242d68",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4, [(17.61, 0.3973), (-19.79, 3.495), (19.79, -3.495), (-17.61, -0.3973)])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "every = dc(showcase, unknowns=[\"es\", \"js\"], equations=[\"pjd1 = -80\", \"ped2 = 0\"])\n",
    "len(every.solutions), [ (sp.N(sol[\"es\"], 4), sp.N(sol[\"js\"], 4)) for sol in every.solutions ]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8753a1ec",
   "metadata": {},
   "source": [
    "## 3. Prof. Boulet's switching transient\n",
    "\n",
    "Prof. Eliane Boulet's exam problem, the thesis's closing Problem 88, first interval: for t < 0 the 18 V source feeds the ladder and the capacitors sit open. DC gives their voltages -- va = 9 V and vb = 9/4 V -- the initial conditions the next entry carries.\n",
    "\n",
    "Two entries, two analyses. First the DC state before the switch."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "3033be55",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<svg xmlns=\"http://www.w3.org/2000/svg\" viewBox=\"10 -9.50998 642.95 368.76\" width=\"642.95\" height=\"368.76\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"1.7\" stroke-linecap=\"round\" stroke-linejoin=\"round\" class=\"symbulator-schematic\"><style>.symbulator-schematic .lbl{font:13px/1 ui-sans-serif,system-ui,sans-serif;fill:currentColor;stroke:none}.symbulator-schematic .sub{font-size:0.72em}</style><g transform=\"translate(58,146)\"><path d=\"M0 0 L46.1 0 Q47.6 0 48.1878 1.38004 L50.0789 5.81996 Q50.6667 7.2 51.2545 5.81996 L56.2122 -5.81996 Q56.8 -7.2 57.3878 -5.81996 L62.3455 5.81996 Q62.9333 7.2 63.5211 5.81996 L68.4789 -5.81996 Q69.0667 -7.2 69.6545 -5.81996 L74.6122 5.81996 Q75.2 7.2 75.7878 5.81996 L80.7455 -5.81996 Q81.3333 -7.2 81.9211 -5.81996 L83.8122 -1.38004 Q84.4 0 85.9 0 L132 0\"/></g><text class=\"lbl\" x=\"124\" y=\"131.39\" text-anchor=\"middle\"><tspan dy=\"0\">8Ω</tspan></text><text class=\"lbl\" x=\"124\" y=\"114.49\" text-anchor=\"middle\"><tspan dy=\"0\">R</tspan><tspan class=\"sub\" dy=\"3.4\">8</tspan></text><g transform=\"translate(190,58)\"><path d=\"M0 0 L112.1 0 Q113.6 0 114.188 1.38004 L116.079 5.81996 Q116.667 7.2 117.254 5.81996 L122.212 -5.81996 Q122.8 -7.2 123.388 -5.81996 L128.346 5.81996 Q128.933 7.2 129.521 5.81996 L134.479 -5.81996 Q135.067 -7.2 135.654 -5.81996 L140.612 5.81996 Q141.2 7.2 141.788 5.81996 L146.746 -5.81996 Q147.333 -7.2 147.921 -5.81996 L149.812 -1.38004 Q150.4 0 151.9 0 L264 0\"/></g><text class=\"lbl\" x=\"322\" y=\"43.39\" text-anchor=\"middle\"><tspan dy=\"0\">18Ω</tspan></text><text class=\"lbl\" x=\"322\" y=\"26.49\" text-anchor=\"middle\"><tspan dy=\"0\">R</tspan><tspan class=\"sub\" dy=\"3.4\">18</tspan></text><g transform=\"translate(58,146) rotate(90)\"><path d=\"M0 0 L60 0 M90 0 L150 0\"/><circle cx=\"75\" cy=\"0\" r=\"15\" fill=\"none\"/></g><text class=\"lbl\" x=\"79.35\" y=\"215\" text-anchor=\"start\"><tspan dy=\"0\">E</tspan></text><text class=\"lbl\" x=\"79.35\" y=\"234\" text-anchor=\"start\"><tspan dy=\"0\">18V</tspan></text><path d=\"M54.5 214 L61.5 214 M58 210.5 L58 217.5\"/><path d=\"M54.5 228 L61.5 228\"/><g transform=\"translate(190,146) rotate(90)\"><path d=\"M0 0 L69.5 0 M80.5 0 L150 0\"/><path d=\"M69.5 -13 L69.5 13\"/><path d=\"M80.5 -13 L80.5 13\"/></g><text class=\"lbl\" x=\"209.35\" y=\"215\" text-anchor=\"start\"><tspan dy=\"0\">C</tspan><tspan class=\"sub\" dy=\"3.4\">1</tspan></text><text class=\"lbl\" x=\"209.35\" y=\"234\" text-anchor=\"start\"><tspan dy=\"0\">1/6</tspan></text><g transform=\"translate(322,146) rotate(90)\"><path d=\"M0 0 L55.1 0 Q56.6 0 57.1878 1.38004 L59.0789 5.81996 Q59.6667 7.2 60.2545 5.81996 L65.2122 -5.81996 Q65.8 -7.2 66.3878 -5.81996 L71.3455 5.81996 Q71.9333 7.2 72.5211 5.81996 L77.4789 -5.81996 Q78.0667 -7.2 78.6545 -5.81996 L83.6122 5.81996 Q84.2 7.2 84.7878 5.81996 L89.7455 -5.81996 Q90.3333 -7.2 90.9211 -5.81996 L92.8122 -1.38004 Q93.4 0 94.9 0 L150 0\"/></g><text class=\"lbl\" x=\"334.86\" y=\"215\" text-anchor=\"start\"><tspan dy=\"0\">R</tspan><tspan class=\"sub\" dy=\"3.4\">12</tspan></text><text class=\"lbl\" x=\"334.86\" y=\"234\" text-anchor=\"start\"><tspan dy=\"0\">12Ω</tspan></text><g transform=\"translate(454,146) rotate(90)\"><path d=\"M0 0 L55.1 0 Q56.6 0 57.1878 1.38004 L59.0789 5.81996 Q59.6667 7.2 60.2545 5.81996 L65.2122 -5.81996 Q65.8 -7.2 66.3878 -5.81996 L71.3455 5.81996 Q71.9333 7.2 72.5211 5.81996 L77.4789 -5.81996 Q78.0667 -7.2 78.6545 -5.81996 L83.6122 5.81996 Q84.2 7.2 84.7878 5.81996 L89.7455 -5.81996 Q90.3333 -7.2 90.9211 -5.81996 L92.8122 -1.38004 Q93.4 0 94.9 0 L150 0\"/></g><text class=\"lbl\" x=\"466.86\" y=\"215\" text-anchor=\"start\"><tspan dy=\"0\">R</tspan><tspan class=\"sub\" dy=\"3.4\">6</tspan></text><text class=\"lbl\" x=\"466.86\" y=\"234\" text-anchor=\"start\"><tspan dy=\"0\">6Ω</tspan></text><g transform=\"translate(586,146) rotate(90)\"><path d=\"M0 0 L69.5 0 M80.5 0 L150 0\"/><path d=\"M69.5 -13 L69.5 13\"/><path d=\"M80.5 -13 L80.5 13\"/></g><text class=\"lbl\" x=\"605.35\" y=\"215\" text-anchor=\"start\"><tspan dy=\"0\">C</tspan><tspan class=\"sub\" dy=\"3.4\">2</tspan></text><text class=\"lbl\" x=\"605.35\" y=\"234\" text-anchor=\"start\"><tspan dy=\"0\">1/3</tspan></text><path d=\"M58 296 L58 308\"/><path d=\"M47 308 L69 308\"/><path d=\"M51 312 L65 312\"/><path d=\"M55 316 L61 316\"/><text class=\"lbl\" x=\"58\" y=\"330\" text-anchor=\"middle\"><tspan dy=\"0\">0</tspan></text><text class=\"lbl\" x=\"64\" y=\"137.9\" text-anchor=\"start\"><tspan dy=\"0\">s</tspan></text><text class=\"lbl\" x=\"196\" y=\"137.9\" text-anchor=\"start\"><tspan dy=\"0\">a</tspan></text><text class=\"lbl\" x=\"460\" y=\"137.9\" text-anchor=\"start\"><tspan dy=\"0\">b</tspan></text><line x1=\"190\" y1=\"146\" x2=\"322\" y2=\"146\"/><line x1=\"454\" y1=\"146\" x2=\"586\" y2=\"146\"/><line x1=\"58\" y1=\"296\" x2=\"586\" y2=\"296\"/><line x1=\"190\" y1=\"58\" x2=\"190\" y2=\"146\"/><line x1=\"454\" y1=\"58\" x2=\"454\" y2=\"146\"/><circle cx=\"190\" cy=\"296\" r=\"3.4\" fill=\"currentColor\" stroke=\"none\"/><circle cx=\"322\" cy=\"296\" r=\"3.4\" fill=\"currentColor\" stroke=\"none\"/><circle cx=\"454\" cy=\"296\" r=\"3.4\" fill=\"currentColor\" stroke=\"none\"/><circle cx=\"190\" cy=\"146\" r=\"3.4\" fill=\"currentColor\" stroke=\"none\"/><circle cx=\"454\" cy=\"146\" r=\"3.4\" fill=\"currentColor\" stroke=\"none\"/></svg>"
      ],
      "text/plain": [
       "<IPython.core.display.SVG object>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "before = '''\n",
    "e,s,0,18\n",
    "r8,s,a,8\n",
    "c1,a,0,1/6\n",
    "r12,a,0,12\n",
    "r18,a,b,18\n",
    "r6,b,0,6\n",
    "c2,b,0,1/3\n",
    "'''\n",
    "draw(before)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "71801aea",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(9, 9/4)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b0 = dc(before)\n",
    "b0[\"va\"], b0[\"vb\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d5a0fcb6",
   "metadata": {},
   "source": [
    "The t > 0 half: the DC source gone, the waveform source connected, the capacitors starting from 9 and 9/4. Find the problem's v1 -- node a here, so the limited results ask for just va. The answer's two natural modes and the forced response are legible at a glance, va(0) checks out at exactly 9 V, and the 2001 calculator's printout agrees with this solve on every digit it displayed.\n",
    "\n",
    "The circuit after the switch carries those two voltages as the capacitors' initial conditions, the fifth field on each `c` line. This one uses the cell magic: after `%load_ext symbulator`, a cell headed `%%tr` is a circuit, drawn and solved, with the options on the first line."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "ffa9cee5",
   "metadata": {},
   "outputs": [],
   "source": [
    "%load_ext symbulator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "c5bd29ca",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<svg xmlns=\"http://www.w3.org/2000/svg\" viewBox=\"10 -9.50998 635.734 399.66\" width=\"635.734\" height=\"399.66\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"1.7\" stroke-linecap=\"round\" stroke-linejoin=\"round\" class=\"symbulator-schematic\"><style>.symbulator-schematic .lbl{font:13px/1 ui-sans-serif,system-ui,sans-serif;fill:currentColor;stroke:none}.symbulator-schematic .sub{font-size:0.72em}</style><g transform=\"translate(58,58)\"><path d=\"M0 0 L112.1 0 Q113.6 0 114.188 1.38004 L116.079 5.81996 Q116.667 7.2 117.254 5.81996 L122.212 -5.81996 Q122.8 -7.2 123.388 -5.81996 L128.346 5.81996 Q128.933 7.2 129.521 5.81996 L134.479 -5.81996 Q135.067 -7.2 135.654 -5.81996 L140.612 5.81996 Q141.2 7.2 141.788 5.81996 L146.746 -5.81996 Q147.333 -7.2 147.921 -5.81996 L149.812 -1.38004 Q150.4 0 151.9 0 L264 0\"/></g><text class=\"lbl\" x=\"190\" y=\"43.39\" text-anchor=\"middle\"><tspan dy=\"0\">18Ω</tspan></text><text class=\"lbl\" x=\"190\" y=\"26.49\" text-anchor=\"middle\"><tspan dy=\"0\">R</tspan><tspan class=\"sub\" dy=\"3.4\">18</tspan></text><g transform=\"translate(58,146) rotate(90)\"><path d=\"M0 0 L69.5 0 M80.5 0 L150 0\"/><path d=\"M69.5 -13 L69.5 13\"/><path d=\"M80.5 -13 L80.5 13\"/></g><text class=\"lbl\" x=\"77.35\" y=\"215\" text-anchor=\"start\"><tspan dy=\"0\">C</tspan><tspan class=\"sub\" dy=\"3.4\">1</tspan></text><text class=\"lbl\" x=\"77.35\" y=\"234\" text-anchor=\"start\"><tspan dy=\"0\">1/6</tspan></text><g transform=\"translate(190,146) rotate(90)\"><path d=\"M0 0 L55.1 0 Q56.6 0 57.1878 1.38004 L59.0789 5.81996 Q59.6667 7.2 60.2545 5.81996 L65.2122 -5.81996 Q65.8 -7.2 66.3878 -5.81996 L71.3455 5.81996 Q71.9333 7.2 72.5211 5.81996 L77.4789 -5.81996 Q78.0667 -7.2 78.6545 -5.81996 L83.6122 5.81996 Q84.2 7.2 84.7878 5.81996 L89.7455 -5.81996 Q90.3333 -7.2 90.9211 -5.81996 L92.8122 -1.38004 Q93.4 0 94.9 0 L150 0\"/></g><text class=\"lbl\" x=\"202.86\" y=\"215\" text-anchor=\"start\"><tspan dy=\"0\">R</tspan><tspan class=\"sub\" dy=\"3.4\">12</tspan></text><text class=\"lbl\" x=\"202.86\" y=\"234\" text-anchor=\"start\"><tspan dy=\"0\">12Ω</tspan></text><g transform=\"translate(322,146) rotate(90)\"><path d=\"M0 0 L55.1 0 Q56.6 0 57.1878 1.38004 L59.0789 5.81996 Q59.6667 7.2 60.2545 5.81996 L65.2122 -5.81996 Q65.8 -7.2 66.3878 -5.81996 L71.3455 5.81996 Q71.9333 7.2 72.5211 5.81996 L77.4789 -5.81996 Q78.0667 -7.2 78.6545 -5.81996 L83.6122 5.81996 Q84.2 7.2 84.7878 5.81996 L89.7455 -5.81996 Q90.3333 -7.2 90.9211 -5.81996 L92.8122 -1.38004 Q93.4 0 94.9 0 L150 0\"/></g><text class=\"lbl\" x=\"334.86\" y=\"215\" text-anchor=\"start\"><tspan dy=\"0\">R</tspan><tspan class=\"sub\" dy=\"3.4\">6</tspan></text><text class=\"lbl\" x=\"334.86\" y=\"234\" text-anchor=\"start\"><tspan dy=\"0\">6Ω</tspan></text><g transform=\"translate(454,146) rotate(90)\"><path d=\"M0 0 L69.5 0 M80.5 0 L150 0\"/><path d=\"M69.5 -13 L69.5 13\"/><path d=\"M80.5 -13 L80.5 13\"/></g><text class=\"lbl\" x=\"473.35\" y=\"215\" text-anchor=\"start\"><tspan dy=\"0\">C</tspan><tspan class=\"sub\" dy=\"3.4\">2</tspan></text><text class=\"lbl\" x=\"473.35\" y=\"234\" text-anchor=\"start\"><tspan dy=\"0\">1/3</tspan></text><g transform=\"translate(586,296) rotate(-90)\"><path d=\"M0 0 L60 0 M90 0 L150 0\"/><circle cx=\"75\" cy=\"0\" r=\"15\" fill=\"none\"/><path d=\"M66 0 L84 0\"/><path d=\"M78 -4 L84 0 L78 4\" fill=\"currentColor\"/></g><text class=\"lbl\" x=\"607.35\" y=\"215\" text-anchor=\"start\"><tspan dy=\"0\">J</tspan><tspan class=\"sub\" dy=\"3.4\">S</tspan></text><path d=\"M58 296 L58 308\"/><path d=\"M47 308 L69 308\"/><path d=\"M51 312 L65 312\"/><path d=\"M55 316 L61 316\"/><text class=\"lbl\" x=\"58\" y=\"330\" text-anchor=\"middle\"><tspan dy=\"0\">0</tspan></text><text class=\"lbl\" x=\"64\" y=\"137.9\" text-anchor=\"start\"><tspan dy=\"0\">a</tspan></text><text class=\"lbl\" x=\"328\" y=\"137.9\" text-anchor=\"start\"><tspan dy=\"0\">b</tspan></text><text class=\"lbl\" x=\"36\" y=\"359.25\" text-anchor=\"start\"><tspan dy=\"0\">J</tspan><tspan class=\"sub\" dy=\"3.4\">S</tspan><tspan dy=\"-3.4\"> = </tspan><tspan dy=\"0\">10e^(-t)sin(2t+30°)</tspan></text><line x1=\"58\" y1=\"146\" x2=\"190\" y2=\"146\"/><line x1=\"322\" y1=\"146\" x2=\"586\" y2=\"146\"/><line x1=\"58\" y1=\"296\" x2=\"586\" y2=\"296\"/><line x1=\"58\" y1=\"58\" x2=\"58\" y2=\"146\"/><line x1=\"322\" y1=\"58\" x2=\"322\" y2=\"146\"/><circle cx=\"190\" cy=\"296\" r=\"3.4\" fill=\"currentColor\" stroke=\"none\"/><circle cx=\"322\" cy=\"296\" r=\"3.4\" fill=\"currentColor\" stroke=\"none\"/><circle cx=\"454\" cy=\"296\" r=\"3.4\" fill=\"currentColor\" stroke=\"none\"/><circle cx=\"58\" cy=\"146\" r=\"3.4\" fill=\"currentColor\" stroke=\"none\"/><circle cx=\"322\" cy=\"146\" r=\"3.4\" fill=\"currentColor\" stroke=\"none\"/><circle cx=\"454\" cy=\"146\" r=\"3.4\" fill=\"currentColor\" stroke=\"none\"/></svg>"
      ],
      "text/plain": [
       "<IPython.core.display.SVG object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\begin{gathered}\\text{tr analysis} \\\\ \\begin{aligned}v_{a} &= \\frac{\\left(\\left(- 80 \\sin{\\left(2 t + \\frac{\\pi}{6} \\right)} + 20 \\cos{\\left(2 t + \\frac{\\pi}{6} \\right)} - 170 \\sqrt{3} + 153\\right) e^{\\frac{t}{2}} + \\left(193 + 160 \\sqrt{3}\\right) e^{t}\\right) e^{- \\frac{3 t}{2}}}{34}\\end{aligned}\\end{gathered}$"
      ],
      "text/plain": [
       "Result(domain='tr')\n",
       "  v_a = ((-80*sin(2*t + pi/6) + 20*cos(2*t + pi/6) - 170*sqrt(3) + 153)*exp(t/2) + (193 + 160*sqrt(3))*exp(t))*exp(-3*t/2)/34"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%%tr variables=v_a into=after\n",
    "c1,a,0,1/6,9\n",
    "r12,a,0,12\n",
    "r18,a,b,18\n",
    "r6,b,0,6\n",
    "c2,b,0,1/3,9/4\n",
    "js,0,b,10*e^(-t)*sin(2*t+30*pi/180)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b839dba7",
   "metadata": {},
   "source": [
    "The initial value checks out, and the response is easy to plot with the package's own `t`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "0d0d4709",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 9$"
      ],
      "text/plain": [
       "9"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "after.at(\"va\", t=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "2725800a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sp.plot(after[\"va\"], (t, 0, 10), xlabel=\"t (s)\", ylabel=\"va (V)\", title=\"Prof. Boulet's problem: v1(t) for t > 0\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a22cb5f6",
   "metadata": {},
   "source": [
    "## 4. Three-phase wye-delta with line impedances\n",
    "\n",
    "Alexander and Sadiku's Example 12.11, the balanced wye-delta with line impedances (Lesson 9 solves it too), the sources typed the way the book prints them. One AC call: aa(iraa) reads 2.350 at -36.20 degrees, and the Evaluate line's load line voltage 169.94 at 30.81 degrees. The exemplary part is what is absent: no wye-delta transformation, no single-phase equivalent.\n",
    "\n",
    "An AC solve at a symbolic `omega` (the impedances are given as numbers already, so the frequency never enters). `polar()` is the app's `aa` mini-tool."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "aa498d6f",
   "metadata": {},
   "outputs": [
    {
     "data": {
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text-anchor=\"middle\"><tspan dy=\"0\">0</tspan></text><text class=\"lbl\" x=\"64\" y=\"225.9\" text-anchor=\"start\"><tspan dy=\"0\">na1</tspan></text><text class=\"lbl\" x=\"196\" y=\"225.9\" text-anchor=\"start\"><tspan dy=\"0\">na2</tspan></text><text class=\"lbl\" x=\"328\" y=\"225.9\" text-anchor=\"start\"><tspan dy=\"0\">nc2</tspan></text><text class=\"lbl\" x=\"460\" y=\"225.9\" text-anchor=\"start\"><tspan dy=\"0\">nc1</tspan></text><text class=\"lbl\" x=\"592\" y=\"225.9\" text-anchor=\"start\"><tspan dy=\"0\">nb2</tspan></text><text class=\"lbl\" x=\"724\" y=\"225.9\" text-anchor=\"start\"><tspan dy=\"0\">nb1</tspan></text><line x1=\"58\" y1=\"384\" x2=\"718\" y2=\"384\"/><line x1=\"190\" y1=\"58\" x2=\"190\" y2=\"234\"/><line x1=\"322\" y1=\"146\" x2=\"322\" y2=\"234\"/><line x1=\"586\" y1=\"58\" x2=\"586\" y2=\"234\"/><circle cx=\"454\" cy=\"384\" r=\"3.4\" fill=\"currentColor\" stroke=\"none\"/><circle cx=\"190\" cy=\"234\" r=\"3.4\" fill=\"currentColor\" stroke=\"none\"/><circle cx=\"586\" cy=\"234\" r=\"3.4\" fill=\"currentColor\" stroke=\"none\"/><circle cx=\"322\" cy=\"234\" r=\"3.4\" fill=\"currentColor\" stroke=\"none\"/><circle cx=\"586\" cy=\"146\" r=\"3.4\" fill=\"currentColor\" stroke=\"none\"/></svg>"
      ],
      "text/plain": [
       "<IPython.core.display.SVG object>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wye_delta = '''\n",
    "ea1,na1,0,100\n",
    "eb1,nb1,0,(100∠-120°)\n",
    "ec1,nc1,0,(100∠120°)\n",
    "raa,na1,na2,1\n",
    "rbb,nb1,nb2,1\n",
    "rcc,nc1,nc2,1\n",
    "rac,na2,nc2,100+24*pi*j\n",
    "rcb,nc2,nb2,100+24*pi*j\n",
    "rba,nb2,na2,100+24*pi*j\n",
    "'''\n",
    "draw(wye_delta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "f791edb2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\begin{gathered}\\text{ac analysis} \\\\ \\begin{aligned}ap_{ea1} &= -94.82 \\\\ ap_{eb1} &= -94.82 \\\\ ap_{ec1} &= -94.82 \\\\ ap_{raa} &= 2.762 \\\\ ap_{rac} &= 92.06 \\\\ ap_{rba} &= 92.06 \\\\ ap_{rbb} &= 2.762 \\\\ ap_{rcb} &= 92.06 \\\\ ap_{rcc} &= 2.762 \\\\ i_{ea1} &= -1.896 + 1.388 j \\\\ i_{eb1} &= 2.15 + 0.9482 j \\\\ i_{ec1} &= -0.254 - 2.336 j \\\\ i_{raa} &= 1.896 - 1.388 j \\\\ i_{rac} &= 0.5475 - 1.242 j \\\\ i_{rba} &= -1.349 + 0.1467 j \\\\ i_{rbb} &= -2.15 - 0.9482 j \\\\ i_{rcb} &= 0.8015 + 1.095 j \\\\ i_{rcc} &= 0.254 + 2.336 j \\\\ s_{ea1} &= -94.82 - 69.41 j \\\\ s_{eb1} &= -94.82 - 69.41 j \\\\ s_{ec1} &= -94.82 - 69.41 j \\\\ s_{raa} &= 2.762 \\\\ s_{rac} &= 92.06 + 69.41 j \\\\ s_{rba} &= 92.06 + 69.41 j \\\\ s_{rbb} &= 2.762 \\\\ s_{rcb} &= 92.06 + 69.41 j \\\\ s_{rcc} &= 2.762 \\\\ v_{ea1} &= 100.0 \\\\ v_{eb1} &= -50.0 - 86.6 j \\\\ v_{ec1} &= -50.0 + 86.6 j \\\\ v_{na1} &= 100.0 \\\\ v_{na2} &= 98.1 + 1.388 j \\\\ v_{nb1} &= -50.0 - 86.6 j \\\\ v_{nb2} &= -47.85 - 85.65 j \\\\ v_{nc1} &= -50.0 + 86.6 j \\\\ v_{nc2} &= -50.25 + 84.27 j \\\\ v_{raa} &= 1.896 - 1.388 j \\\\ v_{rac} &= 148.4 - 82.88 j \\\\ v_{rba} &= -146.0 - 87.04 j \\\\ v_{rbb} &= -2.15 - 0.9482 j \\\\ v_{rcb} &= -2.404 + 169.9 j \\\\ v_{rcc} &= 0.254 + 2.336 j \\\\ z_{ea1} &= 34.33 + 25.13 j \\\\ z_{eb1} &= 34.33 + 25.13 j \\\\ z_{ec1} &= 34.33 + 25.13 j\\end{aligned}\\end{gathered}$"
      ],
      "text/plain": [
       "Result(domain='ac')\n",
       "  ap_ea1 = -94.82\n",
       "  ap_eb1 = -94.82\n",
       "  ap_ec1 = -94.82\n",
       "  ap_raa = 2.762\n",
       "  ap_rac = 92.06\n",
       "  ap_rba = 92.06\n",
       "  ap_rbb = 2.762\n",
       "  ap_rcb = 92.06\n",
       "  ap_rcc = 2.762\n",
       "  i_ea1 = -1.896 + 1.388*I\n",
       "  i_eb1 = 2.15 + 0.9482*I\n",
       "  i_ec1 = -0.254 - 2.336*I\n",
       "  i_raa = 1.896 - 1.388*I\n",
       "  i_rac = 0.5475 - 1.242*I\n",
       "  i_rba = -1.349 + 0.1467*I\n",
       "  i_rbb = -2.15 - 0.9482*I\n",
       "  i_rcb = 0.8015 + 1.095*I\n",
       "  i_rcc = 0.254 + 2.336*I\n",
       "  s_ea1 = -94.82 - 69.41*I\n",
       "  s_eb1 = -94.82 - 69.41*I\n",
       "  s_ec1 = -94.82 - 69.41*I\n",
       "  s_raa = 2.762\n",
       "  s_rac = 92.06 + 69.41*I\n",
       "  s_rba = 92.06 + 69.41*I\n",
       "  s_rbb = 2.762\n",
       "  s_rcb = 92.06 + 69.41*I\n",
       "  s_rcc = 2.762\n",
       "  v_ea1 = 100.0\n",
       "  v_eb1 = -50.0 - 86.6*I\n",
       "  v_ec1 = -50.0 + 86.6*I\n",
       "  v_na1 = 100.0\n",
       "  v_na2 = 98.1 + 1.388*I\n",
       "  v_nb1 = -50.0 - 86.6*I\n",
       "  v_nb2 = -47.85 - 85.65*I\n",
       "  v_nc1 = -50.0 + 86.6*I\n",
       "  v_nc2 = -50.25 + 84.27*I\n",
       "  v_raa = 1.896 - 1.388*I\n",
       "  v_rac = 148.4 - 82.88*I\n",
       "  v_rba = -146.0 - 87.04*I\n",
       "  v_rbb = -2.15 - 0.9482*I\n",
       "  v_rcb = -2.404 + 169.9*I\n",
       "  v_rcc = 0.254 + 2.336*I\n",
       "  z_ea1 = 34.33 + 25.13*I\n",
       "  z_eb1 = 34.33 + 25.13*I\n",
       "  z_ec1 = 34.33 + 25.13*I"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tp = ac(wye_delta, omega=\"omega\")\n",
    "tp.rounded(4)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a2693f5d",
   "metadata": {},
   "source": [
    "The line current the text reads, and the load's line voltage from two node voltages:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "4d64e439",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 2.35 \\angle -36.2^\\circ$"
      ],
      "text/plain": [
       "2.350∠-36.20°"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "polar(tp[\"iraa\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "6321bc5a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 169.94 \\angle 30.811^\\circ$"
      ],
      "text/plain": [
       "169.94∠30.811°"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "polar(tp[\"vna2\"] - tp[\"vnb2\"], digits=5)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ce36c5f0",
   "metadata": {},
   "source": [
    "## 5. The ideal transformer, symbolically\n",
    "\n",
    "From the teaching corpus, after AS7's Figure 13.33 (Lesson 10 has it too): everything in the description is a name. The Thevenin equivalent at the primary derives the referred-source and referred-impedance identities every machines course teaches -- vth = vs2/n and req = z2/n^2. When the answer to a symbolic question is the textbook's own theorem, the simulator has produced knowledge in the form the student is supposed to carry away.\n",
    "\n",
    "`th()` takes the circuit and the two nodes of the port."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "4815eb49",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<svg xmlns=\"http://www.w3.org/2000/svg\" viewBox=\"32 -9.50998 490.95 280.76\" width=\"490.95\" height=\"280.76\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"1.7\" stroke-linecap=\"round\" stroke-linejoin=\"round\" class=\"symbulator-schematic\"><style>.symbulator-schematic .lbl{font:13px/1 ui-sans-serif,system-ui,sans-serif;fill:currentColor;stroke:none}.symbulator-schematic .sub{font-size:0.72em}</style><g transform=\"translate(171,58) rotate(90) scale(1,-1)\"><path d=\"M0 0 L52 0 C52.4429 2.87979 53.3598 5.74185 54.617 7.77817 C55.8741 9.8145 57.4614 11 59.0558 11 C60.6503 11 62.2376 9.8145 63.4947 7.77817 C64.7519 5.74185 65.6688 2.87979 66.1117 2.02067e-15 C66.5546 -2.87979 66.5234 -5.74185 66.1521 -7.77817 C65.7807 -9.8145 65.0792 -11 64.3706 -11 C63.6619 -11 62.9604 -9.8145 62.589 -7.77817 C62.2177 -5.74185 62.1865 -2.87979 62.6294 -3.36778e-15 C63.0723 2.87979 63.9893 5.74185 65.2464 7.77817 C66.5035 9.8145 68.0909 11 69.6853 11 C71.2797 11 72.867 9.8145 74.1242 7.77817 C75.3813 5.74185 76.2982 2.87979 76.7411 4.71489e-15 C77.184 -2.87979 77.1529 -5.74185 76.7815 -7.77817 C76.4102 -9.8145 75.7086 -11 75 -11 C74.2914 -11 73.5898 -9.8145 73.2185 -7.77817 C72.8471 -5.74185 72.816 -2.87979 73.2589 -6.062e-15 C73.7018 2.87979 74.6187 5.74185 75.8758 7.77817 C77.133 9.8145 78.7203 11 80.3147 11 C81.9091 11 83.4965 9.8145 84.7536 7.77817 C86.0107 5.74185 86.9277 2.87979 87.3706 2.6949e-14 C87.8135 -2.87979 87.7823 -5.74185 87.411 -7.77817 C87.0396 -9.8145 86.3381 -11 85.6294 -11 C84.9208 -11 84.2193 -9.8145 83.8479 -7.77817 C83.4766 -5.74185 83.4454 -2.87979 83.8883 1.07837e-14 C84.3312 2.87979 85.2481 5.74185 86.5053 7.77817 C87.7624 9.8145 89.3497 11 90.9442 11 C92.5386 11 94.1259 9.8145 95.383 7.77817 C96.6402 5.74185 97.5571 2.87979 98 2.96433e-14 L150 0\"/></g><g transform=\"translate(209,58) rotate(90)\"><path d=\"M0 0 L52 0 C52.4429 2.87979 53.3598 5.74185 54.617 7.77817 C55.8741 9.8145 57.4614 11 59.0558 11 C60.6503 11 62.2376 9.8145 63.4947 7.77817 C64.7519 5.74185 65.6688 2.87979 66.1117 2.02067e-15 C66.5546 -2.87979 66.5234 -5.74185 66.1521 -7.77817 C65.7807 -9.8145 65.0792 -11 64.3706 -11 C63.6619 -11 62.9604 -9.8145 62.589 -7.77817 C62.2177 -5.74185 62.1865 -2.87979 62.6294 -3.36778e-15 C63.0723 2.87979 63.9893 5.74185 65.2464 7.77817 C66.5035 9.8145 68.0909 11 69.6853 11 C71.2797 11 72.867 9.8145 74.1242 7.77817 C75.3813 5.74185 76.2982 2.87979 76.7411 4.71489e-15 C77.184 -2.87979 77.1529 -5.74185 76.7815 -7.77817 C76.4102 -9.8145 75.7086 -11 75 -11 C74.2914 -11 73.5898 -9.8145 73.2185 -7.77817 C72.8471 -5.74185 72.816 -2.87979 73.2589 -6.062e-15 C73.7018 2.87979 74.6187 5.74185 75.8758 7.77817 C77.133 9.8145 78.7203 11 80.3147 11 C81.9091 11 83.4965 9.8145 84.7536 7.77817 C86.0107 5.74185 86.9277 2.87979 87.3706 2.6949e-14 C87.8135 -2.87979 87.7823 -5.74185 87.411 -7.77817 C87.0396 -9.8145 86.3381 -11 85.6294 -11 C84.9208 -11 84.2193 -9.8145 83.8479 -7.77817 C83.4766 -5.74185 83.4454 -2.87979 83.8883 1.07837e-14 C84.3312 2.87979 85.2481 5.74185 86.5053 7.77817 C87.7624 9.8145 89.3497 11 90.9442 11 C92.5386 11 94.1259 9.8145 95.383 7.77817 C96.6402 5.74185 97.5571 2.87979 98 2.96433e-14 L150 0\"/></g><path d=\"M187.5 107 L187.5 159\"/><path d=\"M192.5 107 L192.5 159\"/><text class=\"lbl\" x=\"190\" y=\"101\" text-anchor=\"middle\"><tspan dy=\"0\">1 : n</tspan></text><text class=\"lbl\" x=\"190\" y=\"84.1\" text-anchor=\"middle\"><tspan dy=\"0\">T</tspan></text><g transform=\"translate(322,58)\"><path d=\"M0 0 L46.1 0 Q47.6 0 48.1878 1.38004 L50.0789 5.81996 Q50.6667 7.2 51.2545 5.81996 L56.2122 -5.81996 Q56.8 -7.2 57.3878 -5.81996 L62.3455 5.81996 Q62.9333 7.2 63.5211 5.81996 L68.4789 -5.81996 Q69.0667 -7.2 69.6545 -5.81996 L74.6122 5.81996 Q75.2 7.2 75.7878 5.81996 L80.7455 -5.81996 Q81.3333 -7.2 81.9211 -5.81996 L83.8122 -1.38004 Q84.4 0 85.9 0 L132 0\"/></g><text class=\"lbl\" x=\"388\" y=\"43.39\" text-anchor=\"middle\"><tspan dy=\"0\">z2</tspan></text><text class=\"lbl\" x=\"388\" y=\"26.49\" text-anchor=\"middle\"><tspan dy=\"0\">R</tspan><tspan class=\"sub\" dy=\"3.4\">2</tspan></text><g transform=\"translate(454,58) rotate(90)\"><path d=\"M0 0 L60 0 M90 0 L150 0\"/><circle cx=\"75\" cy=\"0\" r=\"15\" fill=\"none\"/></g><text class=\"lbl\" x=\"475.35\" y=\"127\" text-anchor=\"start\"><tspan dy=\"0\">E</tspan><tspan class=\"sub\" dy=\"3.4\">2</tspan></text><text class=\"lbl\" x=\"475.35\" y=\"146\" text-anchor=\"start\"><tspan dy=\"0\">vs2</tspan></text><path d=\"M450.5 126 L457.5 126 M454 122.5 L454 129.5\"/><path d=\"M450.5 140 L457.5 140\"/><path d=\"M190 208 L190 220\"/><path d=\"M179 220 L201 220\"/><path d=\"M183 224 L197 224\"/><path d=\"M187 228 L193 228\"/><text class=\"lbl\" x=\"190\" y=\"242\" text-anchor=\"middle\"><tspan dy=\"0\">0</tspan></text><text class=\"lbl\" x=\"64\" y=\"49.9\" text-anchor=\"start\"><tspan dy=\"0\">2</tspan></text><text class=\"lbl\" x=\"328\" y=\"49.9\" text-anchor=\"start\"><tspan dy=\"0\">3</tspan></text><text class=\"lbl\" x=\"460\" y=\"49.9\" text-anchor=\"start\"><tspan dy=\"0\">4</tspan></text><line x1=\"58\" y1=\"58\" x2=\"171\" y2=\"58\"/><line x1=\"209\" y1=\"58\" x2=\"322\" y2=\"58\"/><line x1=\"171\" y1=\"208\" x2=\"454\" y2=\"208\"/><circle cx=\"162\" cy=\"113\" r=\"3.4\" fill=\"currentColor\" stroke=\"none\"/><circle cx=\"218\" cy=\"113\" r=\"3.4\" fill=\"currentColor\" stroke=\"none\"/><circle cx=\"209\" cy=\"208\" r=\"3.4\" fill=\"currentColor\" stroke=\"none\"/></svg>"
      ],
      "text/plain": [
       "<IPython.core.display.SVG object>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xfmr = '''\n",
    "t,2,3,1,n\n",
    "r2,3,4,z2\n",
    "e2,4,0,vs2\n",
    "'''\n",
    "draw(xfmr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "fa5c6bbc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\begin{gathered}\\text{Thevenin / Norton equivalent, dc} \\\\ \\begin{aligned}vth &= \\frac{vs_{2}}{n} \\\\ ino &= \\frac{n vs_{2}}{z_{2}} \\\\ req &= \\frac{z_{2}}{n^{2}} \\\\ pmax &= \\frac{vs_{2}^{2}}{4 z_{2}}\\end{aligned}\\end{gathered}$"
      ],
      "text/plain": [
       "TheveninResult(domain='dc', vth=vs2/n, ino=n*vs2/z2, req=z2/n**2, pmax=vs2**2/(4*z2))"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "th(xfmr, \"2\", \"0\", domain=\"dc\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0c67c236",
   "metadata": {},
   "source": [
    "## 6. Coupled coils with initial conditions\n",
    "\n",
    "Composed for the monograph: two identical coupled coils, each closed on its own resistor, no sources anywhere -- the primary carries 1 A at t = 0 and the secondary is at rest. One TR call: il1 = (e^-t + e^-3t)/2 and il2 = (e^-t - e^-3t)/2, the circuit's common and differential modes in plain sight. Energy handed across the coupling and returned to heat, the whole story in two exponentials.\n",
    "\n",
    "The `m` line couples the two inductors; the fourth field on `l1` is its initial current."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "43528d70",
   "metadata": {},
   "outputs": [
    {
     "data": {
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      ],
      "text/plain": [
       "<IPython.core.display.SVG object>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coils = '''\n",
    "l1,1,0,2,1\n",
    "r1,1,0,3\n",
    "l2,2,0,2\n",
    "r2,2,0,3\n",
    "m,l1,l2,1\n",
    "'''\n",
    "draw(coils)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "09206ccd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\begin{gathered}\\text{tr analysis} \\\\ \\begin{aligned}i_{l1} &= \\frac{\\left(e^{2 t} + 1\\right) e^{- 3 t}}{2} \\\\ i_{l2} &= \\frac{\\left(e^{2 t} - 1\\right) e^{- 3 t}}{2} \\\\ i_{r1} &= - \\frac{\\left(e^{2 t} + 1\\right) e^{- 3 t}}{2} \\\\ i_{r2} &= \\frac{\\left(1 - e^{2 t}\\right) e^{- 3 t}}{2} \\\\ v_{1} &= - \\frac{\\left(3 e^{2 t} + 3\\right) e^{- 3 t}}{2} \\\\ v_{2} &= \\frac{3 \\left(1 - e^{2 t}\\right) e^{- 3 t}}{2}\\end{aligned}\\end{gathered}$"
      ],
      "text/plain": [
       "Result(domain='tr')\n",
       "  i_l1 = (exp(2*t) + 1)*exp(-3*t)/2\n",
       "  i_l2 = (exp(2*t) - 1)*exp(-3*t)/2\n",
       "  i_r1 = -(exp(2*t) + 1)*exp(-3*t)/2\n",
       "  i_r2 = (1 - exp(2*t))*exp(-3*t)/2\n",
       "  v_1 = -(3*exp(2*t) + 3)*exp(-3*t)/2\n",
       "  v_2 = 3*(1 - exp(2*t))*exp(-3*t)/2"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cc = tr(coils)\n",
    "cc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "4ece052e",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sp.plot(cc[\"il1\"], cc[\"il2\"], (t, 0, 5), xlabel=\"t (s)\", ylabel=\"A\", legend=True,\n",
    "        title=\"il1: the sum of the modes; il2: their difference\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b3f87901",
   "metadata": {},
   "source": [
    "## 7. Two op-amps, all symbols\n",
    "\n",
    "After Bobrow's Example 3.3 (Lesson 5 solves it too): a two-op-amp summing cascade in which every conductance is a symbol. The Evaluate line reads the gain, vo/vs = (g1-g2)/(g3-g4) -- a difference of conductances over a difference of conductances, so the circuit's structure is read directly off the expression. The single most persuasive demonstration of what Symbulator is for.\n",
    "\n",
    "The resistors are written as reciprocals of conductances, so the gain comes out in the conductances. `vs` is the source's *value*, a symbol, not an answer, so the gain divides by the symbol itself."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "1d9ddde5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
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r=\"3.4\" fill=\"currentColor\" stroke=\"none\"/><circle cx=\"190\" cy=\"234\" r=\"3.4\" fill=\"currentColor\" stroke=\"none\"/><circle cx=\"454\" cy=\"234\" r=\"3.4\" fill=\"currentColor\" stroke=\"none\"/><circle cx=\"322\" cy=\"234\" r=\"3.4\" fill=\"currentColor\" stroke=\"none\"/><circle cx=\"586\" cy=\"234\" r=\"3.4\" fill=\"currentColor\" stroke=\"none\"/></svg>"
      ],
      "text/plain": [
       "<IPython.core.display.SVG object>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "opamps = '''\n",
    "e,1,0,vs\n",
    "r12,1,2,1/g1\n",
    "r14,1,4,1/g2\n",
    "r23,2,3,1/g\n",
    "r34,3,4,1/g\n",
    "r2o,2,o,1/g4\n",
    "r4o,4,o,1/g3\n",
    "o1,0,2,3\n",
    "o2,0,4,o\n",
    "'''\n",
    "draw(opamps)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "ea9dcc3d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{g_{1} - g_{2}}{g_{3} - g_{4}}$"
      ],
      "text/plain": [
       "(g1 - g2)/(g3 - g4)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "oa = dc(opamps)\n",
    "vs = sp.Symbol(\"vs\")\n",
    "sp.simplify(oa[\"vo\"] / vs)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "80f744a9",
   "metadata": {},
   "source": [
    "## Where next\n",
    "\n",
    "* The monograph itself: https://learn.symbulator.com/monograph.pdf\n",
    "* The same eight entries in the app, under *Built-in Examples › The Monograph*: https://symbulator.pythonanywhere.com/?input=monograph\n",
    "* The package's quick start for notebooks, `quickstart.ipynb`, beside this file, and the README's *In a notebook* section."
   ]
  }
 ],
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