EIS_2020_04_12.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Electrochemical Impedance Spectroscopy\n",
    "\n",
    "Electrochemical Impedance Spectroscopy, or EIS for short, is an analytical technique for probing the inner workings of an electrochemical system like a battery or fuel cell. In principle, it could also be used for any unknown electrical circuit. It works by introducing unit impulses to the circuit at a range of frequencies and measuring the impedance.\n",
    "\n",
    "Gamry, a manufacturer of potentiostats that can be used to perform EIS measurements, [has a good primer on the subject](https://www.gamry.com/application-notes/EIS/basics-of-electrochemical-impedance-spectroscopy/).\n",
    "\n",
    "I'm also familiar with the math behind EIS by a background in [Control Theory](https://en.wikipedia.org/wiki/Control_theory) and didn't learn it as an electrochemist might. So the wording may make more sense to an electrical engineer or chemical engineer than it might an electrochemist (who is more likely to use it).\n",
    "\n",
    "The short explanation is an equivalent circuit is set up with several individual circuit elements and the liberal application of [Ohm's Law](https://en.wikipedia.org/wiki/Ohm%27s_law) and worked up using either Laplace Transformations (as I do here) or Fourier Transformations (a special case of Laplace Transformations and how most EIS literature does it). The impedance response is a complex number.\n",
    "\n",
    "The advantage to doing it in the frequency domain is all the math is algebra and all the complicated dynamics of the differential equations are removed by the transform. Working with the data as Laplace Transforms also allows (usually) convenient conversion between frequency and time domains.\n",
    "\n",
    "A [Gamry Interface 1010E Potentiostat](https://www.gamry.com/potentiostats/interface-1010e-potentiostat/) (the machine I'm most familiar with) has a range of 2 MHz to 10 μHz. Low frequencies take a long time to run in practice, but may be necessary to probe things like diffusion. \n",
    "\n",
    "Here I'm going to: \n",
    "* Set up Python classes for common circuit elements\n",
    "* Set up a Python class for an Equivalent Circuit made of of those individual elements\n",
    "* Plot Nyquist and Bode diagrams for example data\n",
    "* Return those data as a pandas dataframe"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First we need to import a couple libraries:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next let's define the frequency range from 10 μHz to 0.1 MHz:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.00000000e+05, 7.94328235e+04, 6.30957344e+04, 5.01187234e+04,\n",
       "       3.98107171e+04, 3.16227766e+04, 2.51188643e+04, 1.99526231e+04,\n",
       "       1.58489319e+04, 1.25892541e+04, 1.00000000e+04, 7.94328235e+03,\n",
       "       6.30957344e+03, 5.01187234e+03, 3.98107171e+03, 3.16227766e+03,\n",
       "       2.51188643e+03, 1.99526231e+03, 1.58489319e+03, 1.25892541e+03,\n",
       "       1.00000000e+03, 7.94328235e+02, 6.30957344e+02, 5.01187234e+02,\n",
       "       3.98107171e+02, 3.16227766e+02, 2.51188643e+02, 1.99526231e+02,\n",
       "       1.58489319e+02, 1.25892541e+02, 1.00000000e+02, 7.94328235e+01,\n",
       "       6.30957344e+01, 5.01187234e+01, 3.98107171e+01, 3.16227766e+01,\n",
       "       2.51188643e+01, 1.99526231e+01, 1.58489319e+01, 1.25892541e+01,\n",
       "       1.00000000e+01, 7.94328235e+00, 6.30957344e+00, 5.01187234e+00,\n",
       "       3.98107171e+00, 3.16227766e+00, 2.51188643e+00, 1.99526231e+00,\n",
       "       1.58489319e+00, 1.25892541e+00, 1.00000000e+00, 7.94328235e-01,\n",
       "       6.30957344e-01, 5.01187234e-01, 3.98107171e-01, 3.16227766e-01,\n",
       "       2.51188643e-01, 1.99526231e-01, 1.58489319e-01, 1.25892541e-01,\n",
       "       1.00000000e-01, 7.94328235e-02, 6.30957344e-02, 5.01187234e-02,\n",
       "       3.98107171e-02, 3.16227766e-02, 2.51188643e-02, 1.99526231e-02,\n",
       "       1.58489319e-02, 1.25892541e-02, 1.00000000e-02, 7.94328235e-03,\n",
       "       6.30957344e-03, 5.01187234e-03, 3.98107171e-03, 3.16227766e-03,\n",
       "       2.51188643e-03, 1.99526231e-03, 1.58489319e-03, 1.25892541e-03,\n",
       "       1.00000000e-03, 7.94328235e-04, 6.30957344e-04, 5.01187234e-04,\n",
       "       3.98107171e-04, 3.16227766e-04, 2.51188643e-04, 1.99526231e-04,\n",
       "       1.58489319e-04, 1.25892541e-04, 1.00000000e-04, 7.94328235e-05,\n",
       "       6.30957344e-05, 5.01187234e-05, 3.98107171e-05, 3.16227766e-05,\n",
       "       2.51188643e-05, 1.99526231e-05, 1.58489319e-05, 1.25892541e-05,\n",
       "       1.00000000e-05])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "myFrequencies = np.logspace(5,-5,num=101)\n",
    "myFrequencies"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now classes for the following circuit elements:\n",
    "* Resistors\n",
    "* Capacitors\n",
    "* Inductors\n",
    "* Resistor-Capacity (RC) units\n",
    "* Warburg elements (diffusion)\n",
    "* Constant Phase Elements (diffusion at an interface)\n",
    "\n",
    "For each class, there are 3 methods:\n",
    "* A constructor, where the physical characteristics are assigned (like resistance or capacitance)\n",
    "* An impulse, as if we ran that element through a range of frequencies and measured the impedance\n",
    "* The voltage change response that element would have in voltage to a step-change in current\n",
    "\n",
    "I'm not going to demonstrate the current step here, but it's available."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Resistor:\n",
    "    def __init__(self, R):\n",
    "        self.ImpulseSet = False\n",
    "        self.R = R\n",
    "        \n",
    "    def impulse(self, Frequencies):\n",
    "        self.ImpulseSet = True\n",
    "        s = np.array(Frequencies)\n",
    "        numFrequencies = len(Frequencies)\n",
    "        self.Z = self.R * np.ones(numFrequencies)\n",
    "        \n",
    "    def CurrentStep(self, i, t):\n",
    "        self.I = i\n",
    "        self.t = t\n",
    "        self.V = i * self.R * np.ones(len(t))\n",
    "    \n",
    "class Capacitor:\n",
    "    def __init__(self, C):\n",
    "        self.ImpulseSet = False\n",
    "        self.C = C\n",
    "        \n",
    "    def impulse(self, Frequencies):\n",
    "        self.ImpulseSet = True\n",
    "        s = np.array(Frequencies)\n",
    "        numFrequencies = len(Frequencies)\n",
    "        self.Z = (1/(s*self.C))\n",
    "        \n",
    "    def CurrentStep(self, i, t):\n",
    "        self.I = i\n",
    "        self.t = t\n",
    "        self.V = i * t / self.C\n",
    "        \n",
    "class Inductor:\n",
    "    def __init__(self, L):\n",
    "        self.ImpulseSet = False\n",
    "        self.L = L\n",
    "        \n",
    "    def impulse(self, Frequencies):\n",
    "        self.ImpulseSet = True\n",
    "        s = np.array(Frequencies)\n",
    "        numFrequencies = len(Frequencies)\n",
    "        self.Z = s*self.L\n",
    "        \n",
    "    def CurrentStep(self, i, t):\n",
    "        self.I = i\n",
    "        self.t = t\n",
    "        self.V = i * self.L * t\n",
    "    \n",
    "class RC:\n",
    "    def __init__(self, R, C):\n",
    "        self.ImpulseSet = False\n",
    "        self.R = R\n",
    "        self.C = C\n",
    "        self.Tau = R*C\n",
    "        \n",
    "    def impulse(self, Frequencies):\n",
    "        self.ImpulseSet = True\n",
    "        s = np.array(Frequencies)\n",
    "        numFrequencies = len(Frequencies)\n",
    "        self.Z = self.R / (self.Tau*s+1)\n",
    "        \n",
    "    def CurrentStep(self, i, t):\n",
    "        self.I = i\n",
    "        self.t = t\n",
    "        self.V = i*self.R - i*self.R*np.exp(-t/self.Tau)\n",
    "        \n",
    "class Warburg:\n",
    "    def __init__(self, W):\n",
    "        self.ImpulseSet = False\n",
    "        self.W = W\n",
    "    \n",
    "    def impulse(self, Frequencies):\n",
    "        self.ImpulseSet = True\n",
    "        s = np.array(Frequencies)\n",
    "        numFrequencies = len(Frequencies)\n",
    "        self.Z = self.W / np.sqrt(s)\n",
    "        \n",
    "    def CurrentStep(self, i, t):\n",
    "        self.I = i\n",
    "        self.t = t\n",
    "        self.V = 2*i*self.W*np.sqrt(t)/np.sqrt(np.pi)\n",
    "        \n",
    "class ConstantPhaseElement:\n",
    "    def __init__(self, A, alpha):\n",
    "        self.ImpulseSet = False\n",
    "        self.A = A\n",
    "        self.alpha = alpha\n",
    "    \n",
    "    def impulse(self, Frequencies):\n",
    "        self.ImpulseSet = True\n",
    "        s = np.array(Frequencies)\n",
    "        numFrequencies = len(Frequencies)\n",
    "        self.Z = 1/(self.A*(s**(self.alpha)))\n",
    "        \n",
    "    def CurrentStep(self, i, t):\n",
    "        self.I = i\n",
    "        self.t = t\n",
    "        self.V = i*(t**self.alpha)/(self.A*scipy.special.gamma(self.alpha+1))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Equivalent Circuit class then has the following methods:\n",
    "* A contructor\n",
    "* A way to set the impulse frequencies for the entire equivalent circuit\n",
    "* A way to add elements in both series and parallel\n",
    "* A way to plot Nyquist Diagrams, Bode Diagrams, or both\n",
    "* A way to return the data as a pandas dataframe, for further data manipulation "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "class EquivalentCircuit():\n",
    "    def __init__(self):\n",
    "        self.ElementTypes = (Resistor, Capacitor, RC, Warburg, ConstantPhaseElement)\n",
    "        self.PlotWidth = 10\n",
    "        self.Z = 0j\n",
    "        \n",
    "    def setImpulseFrequencies(self, Frequencies):\n",
    "        self.Frequencies = Frequencies\n",
    "\n",
    "    def addSeriesElement(self, *elements):\n",
    "        for element in elements:\n",
    "            if isinstance(element, self.ElementTypes):\n",
    "                element.impulse(self.Frequencies * 1j)\n",
    "                self.Z += element.Z\n",
    "            elif isinstance(element, EquivalentCircuit):\n",
    "                self.Z += elementZ\n",
    "            else:\n",
    "                raise ValueError(f'{element} is not a circuit element')\n",
    "        self.__BodeTerms__()\n",
    "                \n",
    "    def addParallelElement(self, *elements):\n",
    "        invZ = 0\n",
    "        for element in elements:\n",
    "            if isinstance(element, self.ElementTypes):\n",
    "                element.impulse(self.Frequencies * 1j)\n",
    "                invZ += 1/element.Z\n",
    "            elif isinstance(element, EquivalentCircuit):\n",
    "                invZ += 1/element.Z\n",
    "            else:\n",
    "                raise ValueError(f'{element} is not a circuit element')\n",
    "        self.Z =  1 / invZ\n",
    "    \n",
    "    def __BodeTerms__(self):\n",
    "        self.magnitude = 20*np.log10(np.sqrt(np.real(self.Z)**2 + np.imag(self.Z)**2))\n",
    "        self.phase = np.arctan(np.imag(self.Z)/np.real(self.Z))*180/np.pi\n",
    "        \n",
    "    def plotNyquist(self):\n",
    "        plt.figure(figsize=(self.PlotWidth, self.PlotWidth))\n",
    "        plt.plot(np.real(self.Z), -np.imag(self.Z))\n",
    "        maxValue = 1.05 * np.maximum(np.max(np.abs(np.real(self.Z))), np.max(np.abs(np.imag(self.Z))))\n",
    "        plt.xlabel('Z real')\n",
    "        plt.ylabel('-Z imag')\n",
    "        plt.xlim(0, maxValue)\n",
    "        plt.ylim(0, maxValue)\n",
    "        plt.grid()\n",
    "        plt.title('Nyquist Diagram')\n",
    "        plt.show()\n",
    "        \n",
    "    def plotBode(self):\n",
    "        f, (BodeMagnitudePlot, BodePhasePlot) = plt.subplots(2, 1)\n",
    "        f.set_size_inches((self.PlotWidth, self.PlotWidth))\n",
    "        BodeMagnitudePlot.set_title('Bode Diagram')\n",
    "        BodeMagnitudePlot.semilogx(self.Frequencies, self.magnitude)\n",
    "        BodeMagnitudePlot.set_xlabel('Frequency (Hz)')\n",
    "        BodeMagnitudePlot.set_ylabel('Magnitude (dB)')\n",
    "        BodeMagnitudePlot.set_ylim(0,1.05*np.max(someEquivalentCircuit.magnitude))\n",
    "        BodeMagnitudePlot.grid()\n",
    "\n",
    "        BodePhasePlot.semilogx(self.Frequencies, -self.phase)\n",
    "        BodePhasePlot.set_xlabel('Frequency (Hz)')\n",
    "        BodePhasePlot.set_ylabel('-Phase (degrees)')\n",
    "        BodePhasePlot.set_ylim(-90,90)\n",
    "        BodePhasePlot.grid()\n",
    "        BodePhasePlot.set_yticks(np.linspace(-90, 90, 13))\n",
    "        plt.show()\n",
    "        \n",
    "    def plotAll(self):\n",
    "        self.plotNyquist()\n",
    "        self.plotBode()\n",
    "        \n",
    "    def to_dataframe(self):\n",
    "        cols = ['Frequency (Hz)', 'Z (Ohms)', 'Zreal', 'Zimag', 'Radius (Ohms)', 'Magnitude (dB)', 'Phase (degrees)']\n",
    "        df = pd.DataFrame(columns=cols)\n",
    "        df['Frequency (Hz)'] = self.Frequencies\n",
    "        df['Z (Ohms)'] = self.Z\n",
    "        df['Zreal'] = np.real(self.Z)\n",
    "        df['Zimag'] = np.imag(self.Z)\n",
    "        df['Radius (Ohms)'] = np.sqrt(np.real(self.Z)**2 + np.imag(self.Z)**2)\n",
    "        df['Magnitude (dB)'] = 20*np.log10(np.sqrt(np.real(self.Z)**2 + np.imag(self.Z)**2))\n",
    "        df['Phase (degrees)'] = np.arctan(np.imag(self.Z)/np.real(self.Z))*180/np.pi\n",
    "        self.df = df\n",
    "        return df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To demonstrate how this works, let's set up an equivalent circuit containing 4 elements:\n",
    "* A resistor with a resistance of 40 ohms\n",
    "* A Resistor-Capacitor element with a resistor of 90 ohms and capacitance of 500 μF\n",
    "* A second Resistor-Capacitor element with a resistor of 200 ohms and capacitance of 30 μF\n",
    "* A warburg element with a value of 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "someR = Resistor(40)\n",
    "someRC1 = RC(90,.005)\n",
    "someRC2 = RC(200,.00003)\n",
    "someWarburg = Warburg(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "someEquivalentCircuit = EquivalentCircuit()\n",
    "someEquivalentCircuit.setImpulseFrequencies(myFrequencies)\n",
    "someEquivalentCircuit.addSeriesElement(someR, someRC1, someRC2, someWarburg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plots for the Nyquist and Bode digrams:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "someEquivalentCircuit.plotAll()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Returning the equivalent circuit values as a pandas dataframe:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Frequency (Hz)</th>\n",
       "      <th>Z (Ohms)</th>\n",
       "      <th>Zreal</th>\n",
       "      <th>Zimag</th>\n",
       "      <th>Radius (Ohms)</th>\n",
       "      <th>Magnitude (dB)</th>\n",
       "      <th>Phase (degrees)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>100000.000000</td>\n",
       "      <td>(40.00279166643429-0.3375684753864916j)</td>\n",
       "      <td>40.002792</td>\n",
       "      <td>-0.337568</td>\n",
       "      <td>40.004216</td>\n",
       "      <td>32.042115</td>\n",
       "      <td>-0.483486</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>79432.823472</td>\n",
       "      <td>(40.00338947231721-0.4246667168318618j)</td>\n",
       "      <td>40.003389</td>\n",
       "      <td>-0.424667</td>\n",
       "      <td>40.005643</td>\n",
       "      <td>32.042425</td>\n",
       "      <td>-0.608216</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>63095.734448</td>\n",
       "      <td>(40.004210637163794-0.5342788738489503j)</td>\n",
       "      <td>40.004211</td>\n",
       "      <td>-0.534279</td>\n",
       "      <td>40.007778</td>\n",
       "      <td>32.042889</td>\n",
       "      <td>-0.765172</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>50118.723363</td>\n",
       "      <td>(40.00537038895218-0.6722291381058704j)</td>\n",
       "      <td>40.005370</td>\n",
       "      <td>-0.672229</td>\n",
       "      <td>40.011018</td>\n",
       "      <td>32.043592</td>\n",
       "      <td>-0.962677</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>39810.717055</td>\n",
       "      <td>(40.00704946648614-0.8458485042528762j)</td>\n",
       "      <td>40.007049</td>\n",
       "      <td>-0.845849</td>\n",
       "      <td>40.015990</td>\n",
       "      <td>32.044671</td>\n",
       "      <td>-1.211195</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>31622.776602</td>\n",
       "      <td>(40.00953219932713-1.0643641827870147j)</td>\n",
       "      <td>40.009532</td>\n",
       "      <td>-1.064364</td>\n",
       "      <td>40.023687</td>\n",
       "      <td>32.046342</td>\n",
       "      <td>-1.523867</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>25118.864315</td>\n",
       "      <td>(40.01326682112679-1.3393891679585193j)</td>\n",
       "      <td>40.013267</td>\n",
       "      <td>-1.339389</td>\n",
       "      <td>40.035678</td>\n",
       "      <td>32.048944</td>\n",
       "      <td>-1.917182</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>19952.623150</td>\n",
       "      <td>(40.01896100003028-1.685537230252724j)</td>\n",
       "      <td>40.018961</td>\n",
       "      <td>-1.685537</td>\n",
       "      <td>40.054441</td>\n",
       "      <td>32.053014</td>\n",
       "      <td>-2.411785</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>15848.931925</td>\n",
       "      <td>(40.02773313765615-2.1211944873617696j)</td>\n",
       "      <td>40.027733</td>\n",
       "      <td>-2.121194</td>\n",
       "      <td>40.083898</td>\n",
       "      <td>32.059399</td>\n",
       "      <td>-3.033445</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>12589.254118</td>\n",
       "      <td>(40.04135194332757-2.6694854615013828j)</td>\n",
       "      <td>40.041352</td>\n",
       "      <td>-2.669485</td>\n",
       "      <td>40.130238</td>\n",
       "      <td>32.069435</td>\n",
       "      <td>-3.814163</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>10000.000000</td>\n",
       "      <td>(40.062615639998384-3.3594787313618397j)</td>\n",
       "      <td>40.062616</td>\n",
       "      <td>-3.359479</td>\n",
       "      <td>40.203225</td>\n",
       "      <td>32.085218</td>\n",
       "      <td>-4.793363</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>7943.282347</td>\n",
       "      <td>(40.09595178772775-4.227683762034331j)</td>\n",
       "      <td>40.095952</td>\n",
       "      <td>-4.227684</td>\n",
       "      <td>40.318217</td>\n",
       "      <td>32.110026</td>\n",
       "      <td>-6.018980</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>6309.573445</td>\n",
       "      <td>(40.14836505502175-5.319893507795863j)</td>\n",
       "      <td>40.148365</td>\n",
       "      <td>-5.319894</td>\n",
       "      <td>40.499290</td>\n",
       "      <td>32.148948</td>\n",
       "      <td>-7.548056</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>5011.872336</td>\n",
       "      <td>(40.23093218061143-6.693421003832081j)</td>\n",
       "      <td>40.230932</td>\n",
       "      <td>-6.693421</td>\n",
       "      <td>40.783940</td>\n",
       "      <td>32.209784</td>\n",
       "      <td>-9.446061</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>3981.071706</td>\n",
       "      <td>(40.36115349979036-8.419750110111554j)</td>\n",
       "      <td>40.361153</td>\n",
       "      <td>-8.419750</td>\n",
       "      <td>41.230024</td>\n",
       "      <td>32.304272</td>\n",
       "      <td>-11.783494</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>3162.277660</td>\n",
       "      <td>(40.566635399217944-10.587546150456358j)</td>\n",
       "      <td>40.566635</td>\n",
       "      <td>-10.587546</td>\n",
       "      <td>41.925506</td>\n",
       "      <td>32.449566</td>\n",
       "      <td>-14.627414</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>2511.886432</td>\n",
       "      <td>(40.890815915692784-13.305803123318627j)</td>\n",
       "      <td>40.890816</td>\n",
       "      <td>-13.305803</td>\n",
       "      <td>43.001200</td>\n",
       "      <td>32.669612</td>\n",
       "      <td>-18.024801</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>1995.262315</td>\n",
       "      <td>(41.401764722896374-16.706549131792872j)</td>\n",
       "      <td>41.401765</td>\n",
       "      <td>-16.706549</td>\n",
       "      <td>44.645435</td>\n",
       "      <td>32.995541</td>\n",
       "      <td>-21.975191</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>1584.893192</td>\n",
       "      <td>(42.205454444064166-20.94582623061118j)</td>\n",
       "      <td>42.205454</td>\n",
       "      <td>-20.945826</td>\n",
       "      <td>47.117173</td>\n",
       "      <td>33.463585</td>\n",
       "      <td>-26.394398</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>1258.925412</td>\n",
       "      <td>(43.46514991198426-26.200333033837637j)</td>\n",
       "      <td>43.465150</td>\n",
       "      <td>-26.200333</td>\n",
       "      <td>50.751125</td>\n",
       "      <td>34.108914</td>\n",
       "      <td>-31.081129</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>1000.000000</td>\n",
       "      <td>(45.42821052743007-32.654792124557986j)</td>\n",
       "      <td>45.428211</td>\n",
       "      <td>-32.654792</td>\n",
       "      <td>55.946919</td>\n",
       "      <td>34.955524</td>\n",
       "      <td>-35.709407</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>794.328235</td>\n",
       "      <td>(48.459464878915156-40.47149206187026j)</td>\n",
       "      <td>48.459465</td>\n",
       "      <td>-40.471492</td>\n",
       "      <td>63.136847</td>\n",
       "      <td>36.005658</td>\n",
       "      <td>-39.867342</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>630.957344</td>\n",
       "      <td>(53.07400008014952-49.729146723262865j)</td>\n",
       "      <td>53.074000</td>\n",
       "      <td>-49.729147</td>\n",
       "      <td>72.731269</td>\n",
       "      <td>37.234423</td>\n",
       "      <td>-43.136454</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>501.187234</td>\n",
       "      <td>(59.948136979411316-60.31683796120883j)</td>\n",
       "      <td>59.948137</td>\n",
       "      <td>-60.316838</td>\n",
       "      <td>85.040579</td>\n",
       "      <td>38.592524</td>\n",
       "      <td>-45.175653</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>398.107171</td>\n",
       "      <td>(69.86399177355301-71.78086655518706j)</td>\n",
       "      <td>69.863992</td>\n",
       "      <td>-71.780867</td>\n",
       "      <td>100.167211</td>\n",
       "      <td>40.014512</td>\n",
       "      <td>-45.775334</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>316.227766</td>\n",
       "      <td>(83.52246863098011-83.1663876681218j)</td>\n",
       "      <td>83.522469</td>\n",
       "      <td>-83.166388</td>\n",
       "      <td>117.867090</td>\n",
       "      <td>41.427851</td>\n",
       "      <td>-44.877605</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>251.188643</td>\n",
       "      <td>(101.18669609670077-92.97932979560281j)</td>\n",
       "      <td>101.186696</td>\n",
       "      <td>-92.979330</td>\n",
       "      <td>137.418715</td>\n",
       "      <td>42.760918</td>\n",
       "      <td>-42.579558</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>199.526231</td>\n",
       "      <td>(122.25798583184859-99.45477278432047j)</td>\n",
       "      <td>122.257986</td>\n",
       "      <td>-99.454773</td>\n",
       "      <td>157.601608</td>\n",
       "      <td>43.951213</td>\n",
       "      <td>-39.127762</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>158.489319</td>\n",
       "      <td>(145.10047817637712-101.19141966624632j)</td>\n",
       "      <td>145.100478</td>\n",
       "      <td>-101.191420</td>\n",
       "      <td>176.900685</td>\n",
       "      <td>44.954590</td>\n",
       "      <td>-34.891479</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>125.892541</td>\n",
       "      <td>(167.4340424383373-97.84037649429646j)</td>\n",
       "      <td>167.434042</td>\n",
       "      <td>-97.840376</td>\n",
       "      <td>193.924980</td>\n",
       "      <td>45.752675</td>\n",
       "      <td>-30.299955</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>71</th>\n",
       "      <td>0.007943</td>\n",
       "      <td>(337.9327182171763-8.265099340082763j)</td>\n",
       "      <td>337.932718</td>\n",
       "      <td>-8.265099</td>\n",
       "      <td>338.033776</td>\n",
       "      <td>50.579202</td>\n",
       "      <td>-1.401051</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>72</th>\n",
       "      <td>0.006310</td>\n",
       "      <td>(338.90122112577086-9.165054109470361j)</td>\n",
       "      <td>338.901221</td>\n",
       "      <td>-9.165054</td>\n",
       "      <td>339.025126</td>\n",
       "      <td>50.604638</td>\n",
       "      <td>-1.549097</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>73</th>\n",
       "      <td>0.005012</td>\n",
       "      <td>(339.9876907950041-10.19714280877964j)</td>\n",
       "      <td>339.987691</td>\n",
       "      <td>-10.197143</td>\n",
       "      <td>340.140576</td>\n",
       "      <td>50.633169</td>\n",
       "      <td>-1.717939</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>74</th>\n",
       "      <td>0.003981</td>\n",
       "      <td>(341.20659827848687-11.372897411112348j)</td>\n",
       "      <td>341.206598</td>\n",
       "      <td>-11.372897</td>\n",
       "      <td>341.396083</td>\n",
       "      <td>50.665171</td>\n",
       "      <td>-1.909042</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75</th>\n",
       "      <td>0.003162</td>\n",
       "      <td>(342.5741519751984-12.706201015911235j)</td>\n",
       "      <td>342.574152</td>\n",
       "      <td>-12.706201</td>\n",
       "      <td>342.809710</td>\n",
       "      <td>50.701062</td>\n",
       "      <td>-2.124148</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>76</th>\n",
       "      <td>0.002512</td>\n",
       "      <td>(344.1085200943466-14.213380665817024j)</td>\n",
       "      <td>344.108520</td>\n",
       "      <td>-14.213381</td>\n",
       "      <td>344.401936</td>\n",
       "      <td>50.741312</td>\n",
       "      <td>-2.365254</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>77</th>\n",
       "      <td>0.001995</td>\n",
       "      <td>(345.8300763990363-15.913351356062485j)</td>\n",
       "      <td>345.830076</td>\n",
       "      <td>-15.913351</td>\n",
       "      <td>346.196009</td>\n",
       "      <td>50.786441</td>\n",
       "      <td>-2.634604</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>78</th>\n",
       "      <td>0.001585</td>\n",
       "      <td>(347.76167349571654-17.827809306384747j)</td>\n",
       "      <td>347.761673</td>\n",
       "      <td>-17.827809</td>\n",
       "      <td>348.218340</td>\n",
       "      <td>50.837033</td>\n",
       "      <td>-2.934667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>79</th>\n",
       "      <td>0.001259</td>\n",
       "      <td>(349.9289479306948-19.981474000083242j)</td>\n",
       "      <td>349.928948</td>\n",
       "      <td>-19.981474</td>\n",
       "      <td>350.498970</td>\n",
       "      <td>50.893735</td>\n",
       "      <td>-3.268127</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>80</th>\n",
       "      <td>0.001000</td>\n",
       "      <td>(352.36066154280155-22.402379766796606j)</td>\n",
       "      <td>352.360662</td>\n",
       "      <td>-22.402380</td>\n",
       "      <td>353.072092</td>\n",
       "      <td>50.957268</td>\n",
       "      <td>-3.637854</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>81</th>\n",
       "      <td>0.000794</td>\n",
       "      <td>(355.08908385454527-25.122218841561928j)</td>\n",
       "      <td>355.089084</td>\n",
       "      <td>-25.122219</td>\n",
       "      <td>355.976661</td>\n",
       "      <td>51.028431</td>\n",
       "      <td>-4.046879</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>82</th>\n",
       "      <td>0.000631</td>\n",
       "      <td>(358.1504207353678-28.176738912941524j)</td>\n",
       "      <td>358.150421</td>\n",
       "      <td>-28.176739</td>\n",
       "      <td>359.257084</td>\n",
       "      <td>51.108107</td>\n",
       "      <td>-4.498361</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>83</th>\n",
       "      <td>0.000501</td>\n",
       "      <td>(361.5852951257499-31.606199212081016j)</td>\n",
       "      <td>361.585295</td>\n",
       "      <td>-31.606199</td>\n",
       "      <td>362.964017</td>\n",
       "      <td>51.197271</td>\n",
       "      <td>-4.995532</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>84</th>\n",
       "      <td>0.000398</td>\n",
       "      <td>(365.4392862645882-35.45589022269169j)</td>\n",
       "      <td>365.439286</td>\n",
       "      <td>-35.455890</td>\n",
       "      <td>367.155270</td>\n",
       "      <td>51.296995</td>\n",
       "      <td>-5.541644</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>85</th>\n",
       "      <td>0.000316</td>\n",
       "      <td>(369.7635346151326-39.77672313593609j)</td>\n",
       "      <td>369.763535</td>\n",
       "      <td>-39.776723</td>\n",
       "      <td>371.896840</td>\n",
       "      <td>51.408450</td>\n",
       "      <td>-6.139891</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>86</th>\n",
       "      <td>0.000251</td>\n",
       "      <td>(374.61542054176607-44.6258962584295j)</td>\n",
       "      <td>374.615421</td>\n",
       "      <td>-44.625896</td>\n",
       "      <td>377.264077</td>\n",
       "      <td>51.532909</td>\n",
       "      <td>-6.793321</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>87</th>\n",
       "      <td>0.000200</td>\n",
       "      <td>(380.0593257592085-50.06764672883367j)</td>\n",
       "      <td>380.059326</td>\n",
       "      <td>-50.067647</td>\n",
       "      <td>383.343006</td>\n",
       "      <td>51.671751</td>\n",
       "      <td>-7.504725</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>88</th>\n",
       "      <td>0.000158</td>\n",
       "      <td>(386.16748766817574-56.174097130727866j)</td>\n",
       "      <td>386.167488</td>\n",
       "      <td>-56.174097</td>\n",
       "      <td>390.231800</td>\n",
       "      <td>51.826453</td>\n",
       "      <td>-8.276515</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>89</th>\n",
       "      <td>0.000126</td>\n",
       "      <td>(393.02095792036346-63.02620792827521j)</td>\n",
       "      <td>393.020958</td>\n",
       "      <td>-63.026208</td>\n",
       "      <td>398.042430</td>\n",
       "      <td>51.998587</td>\n",
       "      <td>-9.110582</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>90</th>\n",
       "      <td>0.000100</td>\n",
       "      <td>(400.7106779363328-70.71484811864656j)</td>\n",
       "      <td>400.710678</td>\n",
       "      <td>-70.714848</td>\n",
       "      <td>406.902491</td>\n",
       "      <td>52.189807</td>\n",
       "      <td>-10.008146</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>91</th>\n",
       "      <td>0.000079</td>\n",
       "      <td>(409.3386856502992-79.34199811407133j)</td>\n",
       "      <td>409.338686</td>\n",
       "      <td>-79.341998</td>\n",
       "      <td>416.957207</td>\n",
       "      <td>52.401830</td>\n",
       "      <td>-10.969598</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>92</th>\n",
       "      <td>0.000063</td>\n",
       "      <td>(419.01946949618866-89.02210066089677j)</td>\n",
       "      <td>419.019469</td>\n",
       "      <td>-89.022101</td>\n",
       "      <td>428.371626</td>\n",
       "      <td>52.636414</td>\n",
       "      <td>-11.994343</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>93</th>\n",
       "      <td>0.000050</td>\n",
       "      <td>(429.8814876025374-99.88357759909778j)</td>\n",
       "      <td>429.881488</td>\n",
       "      <td>-99.883578</td>\n",
       "      <td>441.333006</td>\n",
       "      <td>52.895328</td>\n",
       "      <td>-13.080657</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>94</th>\n",
       "      <td>0.000040</td>\n",
       "      <td>(442.0688723556688-112.07053249146567j)</td>\n",
       "      <td>442.068872</td>\n",
       "      <td>-112.070532</td>\n",
       "      <td>456.053387</td>\n",
       "      <td>53.180314</td>\n",
       "      <td>-14.225566</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>95</th>\n",
       "      <td>0.000032</td>\n",
       "      <td>(455.74334295006133-125.74466163807756j)</td>\n",
       "      <td>455.743343</td>\n",
       "      <td>-125.744662</td>\n",
       "      <td>472.772371</td>\n",
       "      <td>53.493042</td>\n",
       "      <td>-15.424774</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>96</th>\n",
       "      <td>0.000025</td>\n",
       "      <td>(471.08635130454286-141.0873987726884j)</td>\n",
       "      <td>471.086351</td>\n",
       "      <td>-141.087399</td>\n",
       "      <td>491.760109</td>\n",
       "      <td>53.835066</td>\n",
       "      <td>-16.672627</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>97</th>\n",
       "      <td>0.000020</td>\n",
       "      <td>(488.30148981947593-158.30232185111964j)</td>\n",
       "      <td>488.301490</td>\n",
       "      <td>-158.302322</td>\n",
       "      <td>513.320533</td>\n",
       "      <td>54.207773</td>\n",
       "      <td>-17.962161</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>98</th>\n",
       "      <td>0.000016</td>\n",
       "      <td>(507.6171929245106-177.61785382955162j)</td>\n",
       "      <td>507.617193</td>\n",
       "      <td>-177.617854</td>\n",
       "      <td>537.794865</td>\n",
       "      <td>54.612333</td>\n",
       "      <td>-19.285203</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99</th>\n",
       "      <td>0.000013</td>\n",
       "      <td>(529.2897682648619-199.29029323964826j)</td>\n",
       "      <td>529.289768</td>\n",
       "      <td>-199.290293</td>\n",
       "      <td>565.565451</td>\n",
       "      <td>55.049657</td>\n",
       "      <td>-20.632560</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>100</th>\n",
       "      <td>0.000010</td>\n",
       "      <td>(553.6067977481557-223.60721474997894j)</td>\n",
       "      <td>553.606798</td>\n",
       "      <td>-223.607215</td>\n",
       "      <td>597.060025</td>\n",
       "      <td>55.520360</td>\n",
       "      <td>-21.994265</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>101 rows × 7 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     Frequency (Hz)                                  Z (Ohms)       Zreal  \\\n",
       "0     100000.000000   (40.00279166643429-0.3375684753864916j)   40.002792   \n",
       "1      79432.823472   (40.00338947231721-0.4246667168318618j)   40.003389   \n",
       "2      63095.734448  (40.004210637163794-0.5342788738489503j)   40.004211   \n",
       "3      50118.723363   (40.00537038895218-0.6722291381058704j)   40.005370   \n",
       "4      39810.717055   (40.00704946648614-0.8458485042528762j)   40.007049   \n",
       "5      31622.776602   (40.00953219932713-1.0643641827870147j)   40.009532   \n",
       "6      25118.864315   (40.01326682112679-1.3393891679585193j)   40.013267   \n",
       "7      19952.623150    (40.01896100003028-1.685537230252724j)   40.018961   \n",
       "8      15848.931925   (40.02773313765615-2.1211944873617696j)   40.027733   \n",
       "9      12589.254118   (40.04135194332757-2.6694854615013828j)   40.041352   \n",
       "10     10000.000000  (40.062615639998384-3.3594787313618397j)   40.062616   \n",
       "11      7943.282347    (40.09595178772775-4.227683762034331j)   40.095952   \n",
       "12      6309.573445    (40.14836505502175-5.319893507795863j)   40.148365   \n",
       "13      5011.872336    (40.23093218061143-6.693421003832081j)   40.230932   \n",
       "14      3981.071706    (40.36115349979036-8.419750110111554j)   40.361153   \n",
       "15      3162.277660  (40.566635399217944-10.587546150456358j)   40.566635   \n",
       "16      2511.886432  (40.890815915692784-13.305803123318627j)   40.890816   \n",
       "17      1995.262315  (41.401764722896374-16.706549131792872j)   41.401765   \n",
       "18      1584.893192   (42.205454444064166-20.94582623061118j)   42.205454   \n",
       "19      1258.925412   (43.46514991198426-26.200333033837637j)   43.465150   \n",
       "20      1000.000000   (45.42821052743007-32.654792124557986j)   45.428211   \n",
       "21       794.328235   (48.459464878915156-40.47149206187026j)   48.459465   \n",
       "22       630.957344   (53.07400008014952-49.729146723262865j)   53.074000   \n",
       "23       501.187234   (59.948136979411316-60.31683796120883j)   59.948137   \n",
       "24       398.107171    (69.86399177355301-71.78086655518706j)   69.863992   \n",
       "25       316.227766     (83.52246863098011-83.1663876681218j)   83.522469   \n",
       "26       251.188643   (101.18669609670077-92.97932979560281j)  101.186696   \n",
       "27       199.526231   (122.25798583184859-99.45477278432047j)  122.257986   \n",
       "28       158.489319  (145.10047817637712-101.19141966624632j)  145.100478   \n",
       "29       125.892541    (167.4340424383373-97.84037649429646j)  167.434042   \n",
       "..              ...                                       ...         ...   \n",
       "71         0.007943    (337.9327182171763-8.265099340082763j)  337.932718   \n",
       "72         0.006310   (338.90122112577086-9.165054109470361j)  338.901221   \n",
       "73         0.005012    (339.9876907950041-10.19714280877964j)  339.987691   \n",
       "74         0.003981  (341.20659827848687-11.372897411112348j)  341.206598   \n",
       "75         0.003162   (342.5741519751984-12.706201015911235j)  342.574152   \n",
       "76         0.002512   (344.1085200943466-14.213380665817024j)  344.108520   \n",
       "77         0.001995   (345.8300763990363-15.913351356062485j)  345.830076   \n",
       "78         0.001585  (347.76167349571654-17.827809306384747j)  347.761673   \n",
       "79         0.001259   (349.9289479306948-19.981474000083242j)  349.928948   \n",
       "80         0.001000  (352.36066154280155-22.402379766796606j)  352.360662   \n",
       "81         0.000794  (355.08908385454527-25.122218841561928j)  355.089084   \n",
       "82         0.000631   (358.1504207353678-28.176738912941524j)  358.150421   \n",
       "83         0.000501   (361.5852951257499-31.606199212081016j)  361.585295   \n",
       "84         0.000398    (365.4392862645882-35.45589022269169j)  365.439286   \n",
       "85         0.000316    (369.7635346151326-39.77672313593609j)  369.763535   \n",
       "86         0.000251    (374.61542054176607-44.6258962584295j)  374.615421   \n",
       "87         0.000200    (380.0593257592085-50.06764672883367j)  380.059326   \n",
       "88         0.000158  (386.16748766817574-56.174097130727866j)  386.167488   \n",
       "89         0.000126   (393.02095792036346-63.02620792827521j)  393.020958   \n",
       "90         0.000100    (400.7106779363328-70.71484811864656j)  400.710678   \n",
       "91         0.000079    (409.3386856502992-79.34199811407133j)  409.338686   \n",
       "92         0.000063   (419.01946949618866-89.02210066089677j)  419.019469   \n",
       "93         0.000050    (429.8814876025374-99.88357759909778j)  429.881488   \n",
       "94         0.000040   (442.0688723556688-112.07053249146567j)  442.068872   \n",
       "95         0.000032  (455.74334295006133-125.74466163807756j)  455.743343   \n",
       "96         0.000025   (471.08635130454286-141.0873987726884j)  471.086351   \n",
       "97         0.000020  (488.30148981947593-158.30232185111964j)  488.301490   \n",
       "98         0.000016   (507.6171929245106-177.61785382955162j)  507.617193   \n",
       "99         0.000013   (529.2897682648619-199.29029323964826j)  529.289768   \n",
       "100        0.000010   (553.6067977481557-223.60721474997894j)  553.606798   \n",
       "\n",
       "          Zimag  Radius (Ohms)  Magnitude (dB)  Phase (degrees)  \n",
       "0     -0.337568      40.004216       32.042115        -0.483486  \n",
       "1     -0.424667      40.005643       32.042425        -0.608216  \n",
       "2     -0.534279      40.007778       32.042889        -0.765172  \n",
       "3     -0.672229      40.011018       32.043592        -0.962677  \n",
       "4     -0.845849      40.015990       32.044671        -1.211195  \n",
       "5     -1.064364      40.023687       32.046342        -1.523867  \n",
       "6     -1.339389      40.035678       32.048944        -1.917182  \n",
       "7     -1.685537      40.054441       32.053014        -2.411785  \n",
       "8     -2.121194      40.083898       32.059399        -3.033445  \n",
       "9     -2.669485      40.130238       32.069435        -3.814163  \n",
       "10    -3.359479      40.203225       32.085218        -4.793363  \n",
       "11    -4.227684      40.318217       32.110026        -6.018980  \n",
       "12    -5.319894      40.499290       32.148948        -7.548056  \n",
       "13    -6.693421      40.783940       32.209784        -9.446061  \n",
       "14    -8.419750      41.230024       32.304272       -11.783494  \n",
       "15   -10.587546      41.925506       32.449566       -14.627414  \n",
       "16   -13.305803      43.001200       32.669612       -18.024801  \n",
       "17   -16.706549      44.645435       32.995541       -21.975191  \n",
       "18   -20.945826      47.117173       33.463585       -26.394398  \n",
       "19   -26.200333      50.751125       34.108914       -31.081129  \n",
       "20   -32.654792      55.946919       34.955524       -35.709407  \n",
       "21   -40.471492      63.136847       36.005658       -39.867342  \n",
       "22   -49.729147      72.731269       37.234423       -43.136454  \n",
       "23   -60.316838      85.040579       38.592524       -45.175653  \n",
       "24   -71.780867     100.167211       40.014512       -45.775334  \n",
       "25   -83.166388     117.867090       41.427851       -44.877605  \n",
       "26   -92.979330     137.418715       42.760918       -42.579558  \n",
       "27   -99.454773     157.601608       43.951213       -39.127762  \n",
       "28  -101.191420     176.900685       44.954590       -34.891479  \n",
       "29   -97.840376     193.924980       45.752675       -30.299955  \n",
       "..          ...            ...             ...              ...  \n",
       "71    -8.265099     338.033776       50.579202        -1.401051  \n",
       "72    -9.165054     339.025126       50.604638        -1.549097  \n",
       "73   -10.197143     340.140576       50.633169        -1.717939  \n",
       "74   -11.372897     341.396083       50.665171        -1.909042  \n",
       "75   -12.706201     342.809710       50.701062        -2.124148  \n",
       "76   -14.213381     344.401936       50.741312        -2.365254  \n",
       "77   -15.913351     346.196009       50.786441        -2.634604  \n",
       "78   -17.827809     348.218340       50.837033        -2.934667  \n",
       "79   -19.981474     350.498970       50.893735        -3.268127  \n",
       "80   -22.402380     353.072092       50.957268        -3.637854  \n",
       "81   -25.122219     355.976661       51.028431        -4.046879  \n",
       "82   -28.176739     359.257084       51.108107        -4.498361  \n",
       "83   -31.606199     362.964017       51.197271        -4.995532  \n",
       "84   -35.455890     367.155270       51.296995        -5.541644  \n",
       "85   -39.776723     371.896840       51.408450        -6.139891  \n",
       "86   -44.625896     377.264077       51.532909        -6.793321  \n",
       "87   -50.067647     383.343006       51.671751        -7.504725  \n",
       "88   -56.174097     390.231800       51.826453        -8.276515  \n",
       "89   -63.026208     398.042430       51.998587        -9.110582  \n",
       "90   -70.714848     406.902491       52.189807       -10.008146  \n",
       "91   -79.341998     416.957207       52.401830       -10.969598  \n",
       "92   -89.022101     428.371626       52.636414       -11.994343  \n",
       "93   -99.883578     441.333006       52.895328       -13.080657  \n",
       "94  -112.070532     456.053387       53.180314       -14.225566  \n",
       "95  -125.744662     472.772371       53.493042       -15.424774  \n",
       "96  -141.087399     491.760109       53.835066       -16.672627  \n",
       "97  -158.302322     513.320533       54.207773       -17.962161  \n",
       "98  -177.617854     537.794865       54.612333       -19.285203  \n",
       "99  -199.290293     565.565451       55.049657       -20.632560  \n",
       "100 -223.607215     597.060025       55.520360       -21.994265  \n",
       "\n",
       "[101 rows x 7 columns]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "myShinyNewDataframe = someEquivalentCircuit.to_dataframe()\n",
    "display(myShinyNewDataframe)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
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   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
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   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.0"
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