{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "a38fac8e",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import numpy as np \n",
    "import matplotlib.pyplot as plt\n",
    "from math import exp   \n",
    "from scipy.integrate import solve_ivp\n",
    "from scipy.interpolate import interp1d\n",
    "from scipy.stats import linregress\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "a5b7ec98",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy import symbols, exp as sexp, diff, Derivative, Eq"
   ]
  },
  {
   "attachments": {
    "bc547-pulse.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "9a5dc2ed",
   "metadata": {},
   "source": [
    "![bc547-pulse.png](attachment:bc547-pulse.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ae0f8575",
   "metadata": {},
   "source": [
    "The object was to measure the voltage at the base of the transmitter (and later on at the base of R2) to determine the characteristics of the transistor.  Specifically to estimate the thermal coefficient $V_T$ and the scale current $I_{ES}$. The capacitor was to produce a comparatively slowly changing transistor base voltage with hopefully enough time for me to make measurements using an Arduino.  (This has since become slightly more complicated because the Arduino analog inputs have a time lag of 100 $\\mu S$ which may add some measurement bias)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "17ce4b69",
   "metadata": {},
   "outputs": [],
   "source": [
    "r1, r2, c, issym, vt, vin, vout, vbe, vc, t = symbols(\"R1 R2 C I_{ES} V_T V_{in} V_{out} V_{BE} V_C t\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "771d4afc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - C \\frac{d}{d t} V_{C} - I_{ES} \\left(e^{\\frac{V_{C}}{V_{T}}} - 1\\right) + \\frac{- V_{C} + V_{in}}{R_{1}} = 0$"
      ],
      "text/plain": [
       "Eq(-C*Derivative(V_C, t) - I_{ES}*(exp(V_C/V_T) - 1) + (-V_C + V_{in})/R1, 0)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    " Eq((vin - vc)/r1 - c * Derivative(vc,t) - issym*(sexp(vc/vt)-1),0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "09b9a562",
   "metadata": {},
   "source": [
    "The above is a differential equation for the R1, C and base-emitter junction.  $V_C$ is the voltage across the capacitor.  Vin is a choice of 0 or 5 Volts as it is connected to one of the outputs of the Arduino digital pins.  By turning it on or off I was hoping to sweep through a range of voltages controlled by the time constand of R1 $\\times$ C.  In my case R1 = 6K8 and C = $100 \\mu F$.  I think R2 is about 5K.\n",
    "\n",
    "It's basically a non linear differential equation which is impossible to solve using analytical methods.  Hence the attempt to solve it below using numerical methods."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "29143ef7",
   "metadata": {},
   "source": [
    "Now I try to build my theoretical model using the equation above and some scientific libraries to integrate the equation to find what the solution would look like over time.\n",
    "I am basically plotting the voltage across the capacitor as function of time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "3ddce293-9367-492a-bef1-70f908de1302",
   "metadata": {},
   "outputs": [],
   "source": [
    "r1val = 6800\n",
    "r2val = 5000\n",
    "cval = 100e-6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "4e3423e0",
   "metadata": {},
   "outputs": [],
   "source": [
    "def model(t, y, vin):\n",
    "    vcc=vin\n",
    "    vt =  0.0321850033399526\n",
    "    isval = 1.602564611659814e-12\n",
    "    r=r1val\n",
    "    c=cval\n",
    "    \n",
    "    vc = y\n",
    "    try:\n",
    "        vcp =  (vcc-vc)/(r*c) - isval * (exp(vc/vt)-1) /(c)\n",
    "    except OverflowError:\n",
    "        print (vc)\n",
    "        return np.inf\n",
    "    #print (vcp)\n",
    "    return vcp\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "6b52e0bf",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[56.81583729]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/conda/lib/python3.9/site-packages/scipy/integrate/_ivp/rk.py:109: RuntimeWarning: invalid value encountered in true_divide\n",
      "  return norm(self._estimate_error(K, h) / scale)\n"
     ]
    }
   ],
   "source": [
    "teval = np.linspace(0, .4,100)\n",
    "res = solve_ivp(model, (0,.4), (0,),args=(5,), t_eval = teval, first_step=0.001)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "c446244e",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = res.t\n",
    "y = res.y[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "013ad3eb-5890-4d92-a3e2-59b98d6ae5f5",
   "metadata": {},
   "outputs": [],
   "source": [
    "max60idx = np.argmax(res.y > .61)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "04001485",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Charging of $V_C$ over time(t)')"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "ax.plot(x,y)\n",
    "ax.grid()\n",
    "ax.set_xlabel(\"x (secs)\")\n",
    "ax.set_ylabel(\"Vc (cap)\")\n",
    "ax.set_title(\"Charging of $V_C$ over time(t)\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "13fc3ea0-b3d6-44a9-998f-032e82536dab",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LinregressResult(slope=6.835735444182808, intercept=0.00793245148483196, rvalue=0.9996269961182904, pvalue=2.504751927081888e-34, stderr=0.0407538642126952, intercept_stderr=0.002115122684005686)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "ax.plot(x[:max60idx],y[:max60idx])\n",
    "ax.grid()\n",
    "ax.set_xlabel(\"x (secs)\")\n",
    "ax.set_ylabel(\"Vc (cap)\")\n",
    "ax.set_title(\"Charging of $V_C$ over time(t)\")\n",
    "res = linregress(x[:max60idx],y[:max60idx])\n",
    "vcslope = res.slope\n",
    "print (res)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "ca4f45a4-8841-4674-86b1-b921486165cc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0006835735444182809"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "capcurrent = vcslope*cval\n",
    "capcurrent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "5b459d43",
   "metadata": {},
   "outputs": [],
   "source": [
    "teval = np.linspace(0, 1,100)\n",
    "res = solve_ivp(model, (0,1), (.7,),args=(0,), t_eval = teval, first_step=0.001)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "a829b00b",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = res.t\n",
    "y = res.y[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "c46ad600",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Discharging of C over time(t)')"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "ax.plot(x,y)\n",
    "ax.grid()\n",
    "ax.set_xlabel(\"x (secs)\")\n",
    "ax.set_ylabel(\"Vc (cap)\")\n",
    "ax.set_title(\"Discharging of C over time(t)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7fae56b9",
   "metadata": {},
   "source": [
    "The results are unsurprising as the capacitor charges up to ( or discharges from ) 0.7 volts approximately.  Anything higher and the transistor conducts so the results are at least realistic."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "551150e0",
   "metadata": {},
   "source": [
    "Now I look at the results obtained from direct measurement via the Arduino analog input pin."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "ea25cc0b",
   "metadata": {},
   "outputs": [],
   "source": [
    "measurements = np.array([\n",
    "    [ 0, 0.00, 4.98], \n",
    "    [ 4, 0.03, 4.97], \n",
    "    [ 8, 0.07, 4.98], \n",
    "    [ 12, 0.09, 4.98], \n",
    "    [ 16, 0.13, 4.97], \n",
    "    [ 20, 0.15, 4.98], \n",
    "    [ 24, 0.18, 4.97], \n",
    "    [ 28, 0.21, 4.97], \n",
    "    [ 32, 0.23, 4.98], \n",
    "    [ 36, 0.26, 4.98], \n",
    "    [ 40, 0.28, 4.97], \n",
    "    [ 44, 0.31, 4.98], \n",
    "    [ 48, 0.34, 4.98], \n",
    "    [ 52, 0.37, 4.98], \n",
    "    [ 56, 0.40, 4.97], \n",
    "    [ 60, 0.42, 4.98], \n",
    "    [ 64, 0.45, 4.97], \n",
    "    [ 68, 0.47, 4.97], \n",
    "    [ 72, 0.50, 4.96], \n",
    "    [ 76, 0.52, 4.95], \n",
    "    [ 80, 0.55, 4.90], \n",
    "    [ 84, 0.57, 4.81], \n",
    "    [ 88, 0.60, 4.54], \n",
    "    [ 92, 0.62, 3.82], \n",
    "    [ 96, 0.64, 2.05], \n",
    "    [ 100, 0.67, 0.06], \n",
    "    [ 104, 0.70, 0.04], \n",
    "    [ 108, 0.71, 0.03], \n",
    "    [ 112, 0.72, 0.02], \n",
    "    [ 116, 0.73, 0.02], \n",
    "    [ 120, 0.73, 0.02], \n",
    "    [ 125, 0.74, 0.02], \n",
    "    [ 129, 0.74, 0.02], \n",
    "    [ 133, 0.74, 0.02], \n",
    "    [ 137, 0.74, 0.02], \n",
    "\n",
    " ])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "c3d98428",
   "metadata": {},
   "outputs": [],
   "source": [
    "dfmeasure =  pd.DataFrame(measurements)\n",
    "dfmeasure.columns = ['time', 'v1', 'v2']\n",
    "# ADC is the measure obtained from Arduino analogRead which returns a value from 0 to 1023.\n",
    "# I divide that by  and multiply by 5 to get a voltage."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "79933ebd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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PCSecwFNPPcVTTz2FiPDzzz/TuXPnGsdlTFhFcbNStj9AZk4e6c2TKvwymO0PkFdQRLY/UKZMQQH8+CN89Gkh/3nNx841x6K7nGR48X/LO9p+7g+1UqbJwBU0H7yMMVMyOKJzyxp/oQ3W4JNDanICD5/VgzFTMvDFxFBQXMzDZ/WolZN80EEH8corr3DVVVfRpUsXrr76anJycujevTsdO3akf//+ABQVFTFixAi2bduGqnLTTTfRrFkz7rrrLm688UZ69OiBqtKxY0fefPPNGsdlTFhFaXKYOj+LsaX+70t/+y4pc/1BBdz00Jfcf3IPWgfa8dVX8PXXMGsW7NwJEEdCy0Y0PngdvpZ+RJSEuBgu+XNH0ps3AiAzZyevzFpFoHDPl9GalolP2wbUXmtHsAafHABO7dWOIzq33Oc3iKro2LEjixcvLrP+/vvv5/777y+z/ttvvy2zLikpieeff36vddasZDwnCpNDtj/AmMkZbF+TQsGWZACuythM1smtSU50vvn78wu494PNFBTtx7SFSaz6sSXnPNAMLXJuaNejB1xxBRx9NBzSJ8Dp478hv2DPh3qiL4ZbbjyA1OSSx4zlvcDqOilTW60dwSw5uFKTE2o16xpjXBHqkC6vySgvD778El5+A1ZOG0KhP3Gvfa7Z6w4zPqAnAJ+K4kvbRov+a7jrylZcdEYyLVoEl913C0QorRS1VaY2WHIwxtStCHRIBzcZ5eXG8ZdmfVg7vzmffOI0AzVOjiex/QYSDviDhP22gtsM9PZVh9G8sfMhm7MjwDnPzyFQWMyN/XfyzArnW/yIc9vSIrnsY4bSAhHOMjVlycEYU7fC3KyU7Q9w0wsryFnSkbwVaQSymvOkCm3bKZdeKpx6KgweLHyypJgxU9bv9e27X4/gD9kEHv9rZ8ZMyaBxoyISfb59fkMPpQUinGVqwpKDMaZu1UFyKN1kVFQEc+bA1KnwzrtxrPrtaAB8rbfR9M+/0vLgzUy+82B67d9s9zGq8g39h9nf8t2pgxpU07MlB2NM3arl5FDSZBRb6GPrb83pFuhGxqzGbN7stGANOkrY2WURvk4biGvijCOK88XQvkXZDttQv6En+WIbVGKAMCcHERkGPIFzD+kXVfXBUttvBS4Miu0goJWqbglnnMaYWlTS51ALHdKLVgS46o4cti/rQ/7qlmhhLBsSCzjztCLOPjOWE06Apk1jmDa/GWOmrMEXE1dnHbb1XdiSg4jEAs8AxwGZwFwRmaaqu6/3VNVHgEfc8qcANzWExHDPPfeQnJzMLbfcwqWXXsrJJ5/M8OHDq3SMVatWMWvWLC644II6itKYaqpizSG4yahF4wQWLXKai6ZNgx9+SAAOJa7pTpJ7rqFRlz9oecB27rxqAD3bN9t9jHB02NZ34aw5DABWqOpKABGZBJwGlB0M4DgfsBFfIVq1ahVvvPFGlZJDYWHh7nmcjKkzVUgOU+dnMWZyBgVrU9m6tDXxWen8keXsP2AA3HF3IRM3zKa42XZKZqcplJhyr/G3y9NrJpwT77UD1gYtZ7rryhCRRsAwYEoY4nJs2gRz5zq/a8mrr75Kjx496NmzJxdddBGrV69m6NCh9OjRg6FDh7JmzZpK9//xxx85+uij6du3LyeccALr168HYMWKFRx77LH07NmTPn368Ntvv3HbbbfxzTff0KtXL/773/+Sn5/PZZddRvfu3enduzczZswAYMKECZx99tmccsopHH/88bX2XI2pUIjJIdsfYMw7Gaz78GB+f3UAOT+2x99oC489WcC6dfD993D/P+N44uo/kRQfQ0pCHIm+GGsyqiPh/NpY3g2KtYKypwDfVdSkJCIjgZEAaWlpzJw5c6/tTZs2DWkkcVFREbm5ucS98w6Jo0c7baMFBeQ/8wyFVWzWKW3JkiXcd999fPbZZ6SmprJlyxZGjRrF2WefzYUXXshrr73GNddcw5tvvkkgEMDn85Gbm0tBQQF5eXls2bKFa665hkmTJtGyZUumTJnCmDFjeOqppzjvvPO4+eabOeWUU8jPz6e4uJi7776bJ598knfeeQeAxx57jIKCAmbNmsXy5cs5/fTT+emnn8jPz2fWrFnMmjWLFi1alDlP+fn5Zc5nTfj9/lo9Xjh4LeZoj1eKijga+H35cla7cZYX8/YdxTT+vCf++W0ZevKvDDt9GY2SiunUqjHLlsWybJlTrgnwzJBEdhUVEx8bQ+zWX5k589c6fQ7Rfo5Lq414w5kcMoH2QcvpwLoKyp5HJU1KqvoC8AJAv379dPDgwXttX7JkCSkpKfsMKDc3l5T8fBg92hk6mZcHQNK118LJJ0OrVvs8RkW+//57zjnnHDp27AhASkoKc+fOZdq0afh8Pv76179y9913k5KSQkJCAgkJCaSkpODz+UhKSmLdunUsWbKEM844A3AS2X777cfOnTvZsGHD7uajkufZqFEj4uLidi/PnTuX6667jpSUFPr27UvHjh1Zv349iYmJHH/88XTo0KHcuBMTE+ndu3e1n3dpM2fOpPTrE+28FnPUx+ve0KpT+/Z0cuMsHXNuLpx8ajE//xBD8yGLWXHI7zz9q5Do80XFJaRRf45LqY14w5kc5gJdRKQTkIWTAMo0kItIU+BoYERYolq1CuLjdycGwKlBrFpVo+SgqmWm7C6tsu2qyiGHHMLs2bP3Wp+VFdqNiEruMFeexo0bh3QMY2qFiNO0VEGz0qZNcNJJ8PPPMdxw7xY+3rXarjKKAmHrc1DVQmA08AmwBHhbVReJyCgRGRVU9AzgU1UNzy3POnaEXbv2XldQ4KyvgaFDh/L222+TnZ0NwJYtW/jzn//MpEmTAJg4cSKDBg2qcP+uXbuyadOm3cmhoKCARYsW0aRJE9LT03n//fcBCAQC7Ny5k5SUlL2aiI466igmTpwIwPLly1mzZs1e94UwJqwqSA5r1sCRR8LChfDee/D4XS34buwxvH7lQL4be0yt36PAhC6sl6qo6nRgeql140otTwAmhC2oVq3gpZec6RXdPgdeeqlGtQaAQw45hDvuuIOjjz6a2NhYevfuzZNPPsnll1/OI488QqtWrXj55Zcr3D8+Pp7Jkydz/fXXs23bNgoLC7nxxhvZf//9ee2117jqqqu4++678fl8vPPOO/To0YO4uDh69uzJpZdeyjXXXMOoUaPo3r07cXFxTJgwgYQE+wZmIqSc5LB4MRx/PPj98NlnUPJdya4yihKq6umfvn37ammLFy8us64827dv37OwcaPqDz84v6PYXjHXgVDPXahmzJhRq8cLB6/F7Il4mzVTve46VVXdnJuvjz3xgzZvXqxt2qj+8kuEYwuBJ85xkFDiBeZpJZ+tdpF7iVatalxbMMZUwOeDwkKmzs9i9MPr2Phub7TRTh78Xy49erSJdHSmHOEc52CMaaji4sjPC3D1vZvIfKsvrdJ2kHbBbB77/mey/YFIR2fKUW+Tg1ZytY4pn50zU2fi4liYUcD693qS0C6H6+/8ltjkwO7bW5roUy+TQ2JiItnZ2fZhVwWqSnZ2NomJifsubEwVqEJObhyLf4LkAzfS+uwfSGrkdE7Xxe0tTe2ol30O6enpZGZmsmkfU2Hk5+d77sOwLmNOTEwkPT29To5tGqaiIrj+erhhaxxdOxXw6sRCbp8KsSI29UWUq5fJwefz0alTp32WmzlzZq2OBg4HL8ZsGqZdu+Dii+Gtt+CuVB9d+hYi/dpxVLeGefMcr6mXzUrGmMjy+50ZaN56Cx5+GNq0i0PccQ4N9eY5XmPJwRhTa7L9AWb+so2jhxTzxRcwfjzceiuVTp9holO9bFYyxoTf1PlZ3Dx+OVlv9mdXjnL7o9lcdlmqs9GSg+dYzcEYU2PZ/gDXPrCB1S8fxq7tCbQ+5wembPlhzxiGuLhauU2oCR9LDsaYGlm9GoafGUPW232JSSykzQVzSNx/y95jGNwR0sY7rFnJGFMtu3bBY4/BvfeCSBythi4lqfdKJNYZX7TXGIa4OMjPj2C0pqqs5mCMCUm2P8Ava7c6nc4zoVcvuP12GDYMliwRXnw0haREKf/2ndbn4DlWczDG7NPU+VmMnZKB7Exk3WcHsn1BOzp1gg8+gL/8xSmz//7tOKJzSzJz8khvnrT3paqWHDzHkoMxplLZ/gBj3slg87x0tn7VjeKCWFIHreCrKe1p33rvsQoV3ouh5F4pxjMsORhjKvXpV7tYO+HP5K1rSmKHzbQ4biEt2gbYEmhJe0IcyGY1B8+x5GCMKde2bXDnnfDss8lIowAtT/mZRgetQwQKimOqNmGeJQfPsQ5pY8xeVOGNN6BrV3j2Wbj2WuG16VtI7bmBJonldDaHwpKD54S15iAiw4AngFjgRVV9sJwyg4HHAR+wWVWPDmOIxjRI2f4AmTl55G1qxJ1j4vniC+jfHz78EPr2BWjL8b1Ty+9sDoUNgvOcsCUHEYkFngGOAzKBuSIyTVUXB5VpBjwLDFPVNSLSOlzxGdNQTZ2fxa2TFrL1u85smtWExo2Lee65GP76V4iN3VOuws7mUNggOM8JZ81hALBCVVcCiMgk4DRgcVCZC4B3VXUNgKpuDGN8xjQ42f4AN49fzto3/kxBdgqND8mkzXHLOHvEIGJja3HWVGtW8hwJ193SRGQ4To3gSnf5ImCgqo4OKvM4TnPSIUAK8ISqvlrOsUYCIwHS0tL6Tpo0qVox+f1+kpOTq7VvpHgtZq/FC96LuSbxLvstgdvG9CI/L47Lr59Lt+6biBWhU6vGJPli932AEHV+8knSPv+c76ZNq3HMkVAf4x0yZMiPqtqvwgKqGpYf4GycfoaS5YuAp0qVeRqYAzQGWgK/AgdWdty+fftqdc2YMaPa+0aK12L2Wryq3ou5uvF+/71qixbFGts4X/e77CvtMPYD7TD2A+1653TdnJtfu0HedJNqSsruxYZyjiMllHiBeVrJZ2s4r1bKBNoHLacD68op87Gq7lDVzcDXQM8wxWdMg/HZZ3DMMdCsmfDMmzk0abej/Gkvaot1SHtOOPsc5gJdRKQTkAWch9PHEGwq8LSIxAHxwEDgv2GM0Zh67+23YcQIOOgg+Phj2G+/Ngwfckz1r0QKhXVIe07YkoOqForIaOATnEtZx6vqIhEZ5W4fp6pLRORjIAMoxmmGWhiuGI2p7557Dq69FgYNgmnToFkzZ32NrkQKRUmHtCqI1N3jmFoT1nEOqjodmF5q3bhSy48Aj4QzLmPqs2x/gLVb8pj0QjIP/SuOU05x7u2cVIUBzjUW537UFBfvfX2siVo2fYYx9djU+VmMmZzB5k8PZsvcZhxzyg7efbfx7s/qsCl5wMJCSw4eYdNnGFNP7R7DMKkPW+Z2oEn/lWT2+Jpt+YHwB1OSHKxT2jOs5mBMPVRQAPc/UMzv444EFZoPXUSTfquIj40jMyevbvsXyuPzOb+tU9ozLDkYU8988w1cfTUsWpRE8oF/0PSYRcQ1de7lvNetO8MpuFnJeII1KxnjYdn+AHkFRWT7A2zaBJddBkcdBX4/TJ0KE98qJLlloG7HMITCkoPnWM3BGI8quXXn6K4FXHbur+z49mACeTHcfjvccQc0bgxQya07w8mSg+dYcjDGg7L9AcZOyWD7+kb8Z1J3/ljRgqQO2Xz1RQqH94vfq2ydj2EIhXVIe44lB2M8KDMnj11rW7BhUh8aJxSTevJ82vT+g0ZpA3EmF4gy1iHtOdbnYIwHLZzdmFUT+xHbOMAt935F8iFZFGqEOptDYc1KnmM1B2M85pVX4IorfHTutoviE+bQqlU+iZt9ketsDoUlB8+x5GCMh/znP3DLLTB0KLz3Xjy75Eh+mP0t3506KHoTA1hy8CBLDsZ4gCrcfjs89BAMHw6vvw4JCQAJJPliozsxwJ4+B+uQ9gxLDsZEqWx/gMycPNqkJHHHLQm89BKMGgVPP+3B6Yms5uA5lhyMiUIlYxhii+NYM6U7/mVtuOsu+Oc/PTrjtSUHz7HkYEyUKRnDsDM3ho3v9SGwJpXWxy/mhjEHIBLlzUcVseTgOZYcjIkya7fksXNJW9Z90pWinfG0POVnWvfeSGZO2+jvW6iIJQfPseRgTBRZvhxuuroJa7/sSXybrbQ6cx4J+22joDgmescwhMI6pD3HkoMxUSAvDx54wLkaKTExhpG3bWVmzGzi42IoKI7ghHm1xWoOnhPW5CAiw4AncO4h/aKqPlhq+2BgKvC7u+pdVb03nDEaEw4lVyKlN09i7rcJjB4Nv/0GF14Ijz4Kbdo0I9t/TOQnzKstlhw8J2zJQURigWeA44BMYK6ITFPVxaWKfqOqJ4crLmPCreRKJPxJZH3cDf/SNnTtCl98Acccs6dcVEyYV1ssOXhOOGsOA4AVqroSQEQmAacBpZODMfVWyZVI2Qtak/1RTygWWg5expeTO9I2tZ4kgvLYrKyeE87k0A5YG7ScCQwsp9zhIvILsA64RVUXlS4gIiOBkQBpaWnMnDmzWgH5/f5q7xspXovZa/FC3cacV1BE73VteWtaDzp23sLFV/9E67Q8fvkpk+W+6o1s88I5TtywgcOApQsXsmHmTE/EHKxBxquqYfkBzsbpZyhZvgh4qlSZJkCy+/dJwK/7Om7fvn21umbMmFHtfSPFazF7LV7Vuou5uFj19rsKFFSTDtig7W+erh3GfqBd75yum3Pzq31cT5zjtWtVQfV//1NVj8QcpD7GC8zTSj5bwzlldybQPmg5Had2sJuqbldVv/v3dMAnIi3DF6IxdaO4GG68ER64L44hJ++k/Tk/0zQ5JrK37gwn63PwnCo3K4nIA8BdqlooIjE43/S3h7DrXKCLiHQCsoDzgAtKHbsN8IeqqogMwLnfRHZVYzQmmhQUOPd2njgRbr4ZHnmkETk7h9SfK5FCYcnBc6rT55CsqoUAqlosIv8FrtjXTm4yGQ18gnMp63hVXSQio9zt44DhwNUiUgjkAee51R9jPGnHDjj7bPjoI2ccw9ixztxI9epKpFBYh7TnVCc5FJdazg11R7epaHqpdeOC/n4aeLoaMRkTNUrGMDTWJC4+L4Hvv4f//Q+uvDLSkUWQ3SbUc6qTHL4TkUeBx4EioHWtRmSMhwWPYfh9Yl+Kt8bzzjvCmWdGOrIIs2Ylz9lnchCRbqq6tGRZVd8WkTXAnUACcH8dxmeMZ5SMYdj6e1M2/18vivN9pJ/7A0cf3wvnX6UBs+TgOaHUHKaLyEzgHlVdA6Cqc4A5dRmYMV6z4Ld8/vigO1vnpxObkkfa+XNo2mEnmTl5Dat/oTwx7oWRlhw8I5RLWbsBPwNficjjItKqjmMyxlOKi+Gll+DMIU3YmtGWJgN+o+2VX5HQZjsFxcXenk21tog4tQfrkPaMfSYHVd2lqk8BB+GMVfheRO4VkZQ6j86YKJTtD/DL2q1k+wNkZMCRRzqdzYceKjz51ib2O345TVOk4YxhCJXPZzUHDwm5Q1pV84FHReQ54AbgJxF5XlUfrbPojIkyJR3OMQU+Nsw8gG3zOtKiuTBhAlx8MYikccGwejSbam2Ki7Pk4CEhJwcR6YjTxNQV2B/nEtZ/A5YcTIOwe9K8ha3J+fxgivyJNO2zltnvpdF5/z1JoMGNYQiVJQdPCeVqpQycqS7WAEuBJcCXONNvL6vT6IyJImu35JE9oyubv/sTvtbbaHX6T7T8k58d0oQGfzVSKCw5eEooNYczgJU2Utk0ZEVF8Ng/Utj8XTOSe66hxfELkRj1/u07w8nnsw5pD9lnclDV38IRiDHRKj/fuUPbu+/GMvyKXDLaLCI+NpaC4mLrcK4Kqzl4it1D2phKbN8Op58OM2bAf/8LN96YUr9u3xlOlhw8xZKDMRXYuBFOPBEyMuC112DECGe9dThXkyUHTwn5fg7iGCEid7vL+7vTahtT76xaBYMGwZIlMHXqnsRgasCSg6dU5WY/zwKHA+e7y7k4VywZU29k+wMsWZ7I4X9WNm2Czz6Dk06KdFT1hHVIe0pVmpUGqmofEfkZQFVzRCS+juIyJuymzs/i+sfXsHlyXwIS4LHx2zjiiLRIh1V/WM3BU6pScygQkVhAAdw5lkrf28EYT8raHOCKG3ay5vUBNE7eRZsRs3g24yey/YFIh1Z/WHLwlKokhyeB94DWIvIv4FucEdLGeNpnn8Hh/ePI/roLjbr8wY13f0Nc0zx8MTFk5uRFOrz6w5KDp1RlbqWJIvIjMBQQ4HRVXVJnkRlTx9atg5tugrffhj8dIKRf8AOx7TeR0rQQiLMZVWubzcrqKVWpOaCqS1X1GVV9ujqJQUSGicgyEVkhIrdVUq6/iBSJyPCqPoYxFSmZTfWPrQEefxy6dXOuRPrnP2HRwhieubUdib4YYsVmVK0TNiurp1Rl4r2by1m9DfhRVeeHsH8sztVNx+FM/T1XRKap6uJyyj0EfBJqbMbsS8lsqgXrmpP14cEE/khg2DB4+mk44ACnzKm92nFE55b8MPtbvjt1kCWG2mbNSp5SlZpDP2AU0M79GQkMBv4nImNC2H8AsEJVV6rqLmAScFo55a4DpgAbqxCbMRXK9gcY8/YC1k0/iJXjD6Nwh4+2Z/3Ea28HdieGEqnJCST5Yi0x1AVLDp5SlUtZU4E+quoHEJF/AJOBo4AfgYf3sX87YG3QciYwMLiAiLTDmejvGKB/RQcSkZE4yYm0tDRmzpxZhaexh9/vr/a+keK1mKMh3pxcJf6jXuTOb8PRJ/zGX4YvpXGjIubOySHJF1umfDTEXBVeifeQrVtJ2rqVeTNneibmEg0x3qokh/2BXUHLBUAHVc0TkVCu95Ny1pWe6fVxYKyqFomUV9zdSfUF4AWAfv366eDBg0N4+LJmzpxJdfeNFK/FHOl4c3LgxJOKWThfaHHCAlb1WsMzKyDR56uw6SjSMVeVZ+Jt0waysxk8eLB3YnY1xHirkhzeAOaIyFR3+RTgTRFpDCyueLfdMoH2QcvpwLpSZfoBk9zE0BI4SUQKVfX9KsRpDOBcjXTCCbB8eQxjHs5m6vZMfDFxNptqpFiHtKdU5VLW+0RkOjAIpxYwSlXnuZsvDOEQc4EuItIJyALOAy4o9RidSv4WkQnAB5YYTHX8+iscfzxs3gzTp8PQoamMsdlUI8v6HDylqrOyrgRigUSgkYgcpapfh7KjqhaKyGicq5BigfGqukhERrnbx1UxFmPK9fPPMGwYFBc7U2336+est9lUI8ySg6dU5VLWK4EbcJqD5gOHAbNxOo9DoqrTgeml1pWbFFT10lCPa0y2P0BmTh6rFjbionPjad4cPv0UunaNdGRmN0sOnlKVmsMNOFcQzVHVISLSDfhn3YRlTOhKxjDkLW/D2ik9SO9QwHdf+UhPj3RkZi82QtpTqjLOIV9V8wFEJEFVlwL2vcxEVLY/wNgpGWz+sS1r3umFL207Cad/RVIzmzAv6liHtKdUpeaQKSLNgPeBz0Qkh7JXGxkTVmu35LF19gFkf3EgiZ020ur0n0hMFjJz8qx/IdpYs5KnVOVqpTPcP+8RkRlAU+CjOonKmBAUF8P/Hk3mjy+a0eigLFr+5RckVikojrEJ86KRJQdPqcptQh8q+VtVv1LVacD9dRKVMftQUACXXw7PPhXHX871k35mBk0axdqEedHMkoOnVKVZ6ThgbKl1J5azzpg6lZcH55wDH3zgzKh6113JbNlhYxiiXkmfg5aeGMFEo30mBxG5GrgGOEBEMtgzDUYK8F0dxmZMGVu3wqmnwrffwrPPwtVXO+ttDIMHxLkfN0VFkY3DhCSUmsNEnLEJDwC34SQHBXJVNacOYzMG2DOGwbcriQvOSmDxYpg0yak9GA8pSQ7WtOQJoSSHLJxkIMDJQetFRFRVm9RJZMawZwxD8dbGrHq9H7GBYj78MIbjjot0ZKbKLDl4yj6Tg6qmhCMQY0orGcOwPasxf7w9AIpj2O+8OfQ5vC9gTUieY8nBU6p0m1BjwikzJ49da1uw4Y3DkRilzQWzadI+l8ycvEiHZqrD53N+2yhpT6jSxHsi0hM40l38RlV/qf2QjHEsnN2YVRP7Edskj7RzvyeuSb6NYfAyqzl4SlXGOdyA0znd2v15XUSuq6vATMM2YQJccoGPzt2K6HDpHJq3KrQxDF5nycFTqlJzuAIYqKo7YPeguNnAU3URmGm4Hn0Ubr0VjjsO3n03ngBH2hiG+sCSg6dUJTkIEHyBchHl3/rTmGpRhbFj4ZFHnMtUX30VEhIgGRvDUC9YcvCUqiSH8cD3IvIeTlI4DXipTqIyDU5hIYwcCS+/7Axse+opiI2NdFSmVlmHtKdU9U5wo4HeOMnhMlX9ufZDMg1Jtj/AivV5/POmFD76MJZ//AP+8Q8Qq5PWP1Zz8JSqJIcmwDhgCzAJm67b1NDU+VncMnEx697uy841MYwcu5V77mkW6bBMXbHk4CkhX62kqv9U1UOAa4G2wFci8nlVHkxEhonIMhFZISK3lbP9NBHJEJH5IjJPRAZV5fjGO7L9Af72ylJWvzqAnZnNaHnKfL7yzSbbbzfpqbcsOXhKdQbBbQQ2ANk4l7SGRERigWdwZnI9GDhfRA4uVewLoKeq9gIuB16sRnzGA+bMD7D2lcMpzGlM67Pm0vjgdfhiYmyAW31Wkhysz8ETqjLO4WoRmYnzAd4S+Kuq9qjCYw0AVqjqSlXdhdM0dVpwAVX1q+6ez7cxzpxOpp7JyIDLh6dQmB9H2rnfk/SnzQAUFBfbALf6rKRD2moOniAa4tzqIvIgMElV51frgUSGA8NU9Up3+SKccROjS5U7A2cG2NbAX1R1djnHGgmMBEhLS+s7adKk6oSE3+8nOTm5WvtGitdiLh3vggVNuf327iQlFfGP+39EUjbvnuY3vXkSTZN8EYu1hNfPcbRqmpFB7xtuYP6jj5LZtasnYi7hlXNcIpR4hwwZ8qOq9quwgKqG5Qc4G3gxaPki4KlKyh8FfL6v4/bt21era8aMGdXeN1K8FnNwvP/3f6qJiaoHHqi6apWzbnNuvs5fk6Obc/MjE2A5vHyOo9qsWaqg+vHH3onZVR/jBeZpJZ+t4Zx4LxNoH7ScTiVXPKnq1zg3GGpZ14GZuvfqq3D66XDooc6Nejp0cNanJifQs30zG+TWEFiHtKeEMznMBbqISCcRiQfOA6YFFxCRziLOFe4i0geIx+n4Nh6U7Q+QV1DEfQ8UcsklMHgwfPkltGoV6chMRFiHtKdUdRBctalqoYiMBj4BYoHxqrpIREa528cBZwEXi0gBkAec61Z/jMdMnZ/FmMkZdMzozKf/F8efj83jww+SSLAKQsNlHdKeErbkAKCq03FuORq8blzQ3w8BD4UzJlP7sv0BbnrxV9Z/1JflK1uT3Gs1mwcsxl9wDAmWHRoua1bylLAmB1P/BQJw9z3FrHr+SIhRzhyxgHlt1xAfF0dmTp71LTRklhw8xZKDqTWffw7XXgvLlyeRctB6mgxezOAj/Py4IM7GMBhLDh5jtwk11ZLtD/DL2q1k+wOsXw/nn+/cf6GoCD76CF5/o5jk1F3EithNeozDZmX1FKs5mCqbOj+LsVMyiCOWTXPT8X/XjcJdMfzjH879GJKSANpxROeW/DD7W747dZAlBmM1B4+x5GCqJNsfYOyUDHL/SGLztN7s+qMpjTpt5pt3mzCgV/xeZVOTE0jyxVpiMA5LDp5iycFUSWZOHoUbmrFhYh8AWp76E2k9N5GQOhBnWIoxFbDk4CmWHEyVrPylEStf7U9M0i7SzvkeX4udFGqMdTabfbPk4CmWHEzIJk+GCy+MZ//9C4j7yxySmhZQUGydzSZE1iHtKZYcTEheeAFGjYLDD4cPPvBR7DuCzJw80psnWWIwobGag6dYcjCVUoV//xvuvBNOOgneeQcaNQJIsKRgqiYmxrk5uCUHT7DkYMqV7Q+wJjuP5x9O5vln4xgxAsaP39MyYEy1xMVZcvAISw6mjKnzsxjz9gL++KAH2xY045QL/bzySjIxNmTS1JQlB8+wf3ezl2x/gFteX8zat/qwbUFbmh21lGUdvyFnZyDSoZn6wOezDmmPsJqD2U0VnvtfIb8/dxRFefG0OCGDlF5riY+1SfNMLbGag2dYcjAALFoE11wDX3/dmMR2ObQ+5wfi07YD2KR5pvZYcvAMa1Zq4HbsgNtug169YMEC55LVN6ftpEm6n5SEOJs0z9QuSw6eYTWHBijbHyAzJ4+M7xpz51gfa9bAZZfBQw+V3MKzHUce2NLGMZjaFxdnfQ4eYcmhgZk6P4ubX/qVTZ8eTO7yZnToXMA33/gYNGjvcqnJNo7B1AGfz2oOHhHWZiURGSYiy0RkhYjcVs72C0Ukw/2ZJSI9wxlffZftD3DtQ+v5/flB+H9vQbPBS0g4+wsO6mVXIpkwsWYlzwhbzUFEYoFngOOATGCuiExT1cVBxX4HjlbVHBE5EXgBGBiuGOu7518qJOutPsS3zqXVmfOIa5JPvM+uRDJhZMnBM8LZrDQAWKGqKwFEZBJwGrA7OajqrKDyc4D0MMZXrz3xBNxxY2Madcgm9Yx5xCQ4/6B2JZIJK0sOniGqGp4HEhkODFPVK93li4CBqjq6gvK3AN1KypfaNhIYCZCWltZ30qRJ1YrJ7/eTnJxcrX0jpaoxq8L48Z14/fUOHHnkJq77WwYbd+xAAAXSmyfRNKnu5sRoCOc40rwUb9+rrmJX8+bMvvNOz8QM3jrHEFq8Q4YM+VFV+1VYQFXD8gOcDbwYtHwR8FQFZYcAS4DUfR23b9++Wl0zZsyo9r6RUpWYCwtVr7pKFVSvvNJZVlXdnJuv89fk6Obc/LoJMkh9P8fRwFPxHnaY6vHHeytm9dg51tDiBeZpJZ+t4WxWygTaBy2nA+tKFxKRHsCLwImqmh2m2OqdQABGjHDuwXD77fCvfzkTYoJdiWQiyJqVPCOcVyvNBbqISCcRiQfOA6YFFxCR/YF3gYtUdXkYY6s3sv0BZi3ZynEnFDN5Mjz2mDPldkliMCaiLDl4RthqDqpaKCKjgU+AWGC8qi4SkVHu9nHA3UAq8Kw4n2aFWlmbmNnL1PlZ/O3VpWRN6kf+Brjh3i3cdFOLSIdlzB5xcbBzZ6SjMCEI6yA4VZ0OTC+1blzQ31cCZTqgzb5l+wPc/NJy1rwxkKLtSbQ680c+3rWZbP8x1oRkoofNyuoZNrdSPTFzToA1rxxO0Y4EWp/7PY06b8QXE0NmTl6kQzNmD2tW8gybPqMemDMHrjwnBdUAbS6YTXzrXMDGMJgoZMnBM6zm4HEffwxDh0JqC+G5SVtp0m6HzaZqopclB8+wmoOHvfkmXHwxHHqokyTS0tpw5tHH2GyqJnpZcvAMSw4e9fTTcP31cNRRMHUqNG3qrLcxDCaqWYe0Z1izkodk+wPs3FXErbcXct11cOqpTo2hJDEYE/Ws5uAZVnPwiKnzsxjzTgZpP3Tjm8/jOPa0HUye3Jg4ewWNl1hy8Az7aPGAbH+Av72ylHUf9mb5r21oMvA31hy6nG35NobBeIwlB8+w5BDliorgP08U8ftzR1FcGMMZIxbwU7s1xMfafRiMB1ly8AxLDlFs3jy4+mqYN68RjTpuptmxCxkyeBs/LYizMQzGm6xD2jOsQzpKZPsD/LJ2K9n+AFu3wujRMGAAZGY6l6y+8W6AlDZ5xIrYGAbjXVZz8AyrOUSBqfOzGDslgziJYUtGG/K+PZTtObGMHg333VdyNVI7BnVpyQ+zv+W7UwdZYjDeZMnBMyw5RFi2P8DYKRnk/pHElk8PJX91SxLbbuWzrxpxzKD4vcqmJieQ5Iu1xGC8Ky7O6UgL0x0oTfVZcoiwzJw8dHsjNrx+GBTH0OKEBezXfx2pHQYC8fvc3xhPca+9luLiCAdi9sWSQ4Q1j09i9Vu90eIY9rvoO3ypOygkxjqbTf3kc+5XLta0FPUsOUSQKvxtdAIFm+Jpd+48mrUNUFBsnc2mHiupORQVRTgQsy+WHCLo/vudezw/8ohw2ageNmGeqf8sOXiGJYcIef99uPtuGDEC/vY3ELEJ80wDYMnBM8I6zkFEhonIMhFZISK3lbO9m4jMFpGAiNwSztjCaeFCuOgi6N8fXngBnNtlG9MAlCQH63OIemGrOYhILPAMcByQCcwVkWmqujio2BbgeuD0cMUVbtnZzmyqKSnw3nuQZP3OpiEp6ZC2mkPUC2fNYQCwQlVXquouYBJwWnABVd2oqnOBejm+vqAAzj4b1q1zEkO7dpGOyJgws2YlzwhncmgHrA1aznTX1XslU2Ncc10RM2Y4TUkDB0Y6KmMiwJKDZ4SzQ7q8lvVqDZMUkZHASIC0tDRmzpxZrYD8fn+19w3VtrwCMnPymDVjf954sRennrGa/ff/neo+bDhirk1eixe8F7OX4m21bBmHAHm5uZ6JGbx1jqF24g1ncsgE2gctpwPrqnMgVX0BeAGgX79+Onjw4GoFNHPmTKq7byiy/QGOeOhLtq5ozR9v9yCx00aWHrSE7v2GVPvKpLqOubZ5LV7wXsyeijcnB4DG8fH090rMeOwcUzvxhrNZaS7QRUQ6iUg8cB4wLYyPH3aLV+Wz6ZND+GPSQOKa7aTlqT8THydk5uRFOjRjIsOalTwjbDUHVS0UkdHAJ0AsMF5VF4nIKHf7OBFpA8wDmgDFInIjcLCqbg9XnLVBFd54A26+uQlbNjUhpe8qmh25nJiEQgqKbWoM04BZcvCMsA6CU9XpwPRS68YF/b0Bp7nJs5YsgWuvhRkzYMAA4bbHN/L84qX4YmJsagxjLDl4ho2QrqFsf4DMnDxaJCTx3OMJPPooNG4M48bBlVdCbGxrLvYfY1NjGAOWHDzEkkMNlNykJ29FGus/6kbBNrjkEnj4YWjdek+51GSbGsMYYPcguBhLDlHPbhNaTSU36Vn/6YGsmdQH4opof9Ec/vN0YK/EYIwJUlJz2LEDNm2KcDCmMpYcqikzJw9/RjrbfziA5J6r2e+yb2jaaZtdiWRMZb74AgBZuxY6dHBukG6ikiWHalq/vBHrPjyExA6baXH8IiRWKSgutiuRjKnIpk3OTdFxJ97Ly4MrrrAaRJSy5FANmZlw2Yh40vYrJv2s+TRJiiXRZ1ciGVOpVasg3rn1bcdPPnHW+XzOehN1rEO6ivLy4PTTwe+HOXPiaNPhSLsSyZhQdOwI7lTdcTt3Out27IAmTSIXk6mQ1RyqQNW5PPWnn2DiRDjkEOdKpJ7tm1liMGZfWrWCl16CpCTm3n670zmtCkccAePHQ3FxpCM0QSw5VMEjjzgjn++7z7kngzGmis4/H1avpqh7d2fu+vnzoVs3p+/hqKNgwQKnD2LuXOuLiDBLDiGaPh1uuw3OOQf+/vdIR2OMh7VqBY0aOb+7d4evv3ZqDkuXQq9e0LYtHHusXc0UYZYcQrBkifOFp1cv5z1st/U0phbFxMBll8F33zn/XIWFsH2708F36aWwYUOkI2yQLDlUItsf4JsF2zj5lGISE+H9952pMYwxdWD7dkhO3nvdrl1Os9Oll8K77zpXgoA1PYWBJYcKTJ2fxZ8fmMFJZxSw8ne46cFN7L9/pKMyph7r2NFJBsHi4+G442DaNDjrLGjZEnr3du6xO3SoNT3VIUsO5cj2Bxjz9gKyph6K/7eWtDhuIRNWziPbH4h0aMbUX0FXM9GkifN7wgR45x344w9nquNLL4VffnFuyJ6b6zQ9XXwxzJzpXPkULJTaRahldu4MrZZSm49ZG2VqwJJDOX5dl8f6yX3YsSidpkcuI6XXWnwxMTY1hjF1zb2aic8/d36ff76z3ueDwYOdq5pSUvbep7AQhgyBP/0JbrjBmaLjtdecWsVxx1Vcu3jzzdDLLF++71pKVY4XjjI1ZIPgSsnJgRsvaULur0KL4xeQ0nsNgE2NYUy4tGrl/JSnY0en1hAsMRH+/W/48kt44QV48sk92/LcL3SXXOLUPkoSS24ujBnjHCuEMm1mzXLKlS5ToorHq/UyV1zhXOFV0XmrBksOQdatg2HDYOnSGMY8nM3U7Zn4YuIoKC62qTGMiQYlTU9XXOHUJgoKnOXzz4ebbnJGXD/3nHO9eXASKShwtlemkjLd3nkn9OPU0mNWqUzJNCSWHGrfihVODW3TJmdMw7HHpjLGbtJjTPQ5/3znW/KqVU5NIvgDsXFj55v23XfvnRwSEmDOHEhNdZazs+GwwyAQCKnM7Dvv5PD77y9bpkQVj1frZQoKnHNRiyw5AD//7NQYioudPq/+/Z31dpMeY6JUZU1PFdUuevXaU6Z9e3j55ZDLBFJTnQ7y0mWqebw6KVOLtQYIc3IQkWHAE0As8KKqPlhqu7jbTwJ2Apeq6k91EUu2P0BeQRHTPt7FRefG07QpfPqpc0m1McbjKqtdVKfM3LlOB3llH8C1/Zg1LVNDYUsOIhILPAMcB2QCc0VkmqouDip2ItDF/RkIPOf+rlUlt/c8ekcq/3sylnb7FzDrax/p6bX9SMaYiKmsdlHVMiXTfYTzMWujTA2E81LWAcAKVV2pqruAScBppcqcBryqjjlAMxHZrzaDKLm955aFrfnf4/3xtd5O4hlfkdTMxjAYY0yJcDYrtQPWBi1nUrZWUF6ZdsD64EIiMhIY6S76RWRZqEGIL6lRXPP9DpSYmNiYlG2gTVn9enFRq6fWL9eCvJ2hHieCWgKbIx1EFXgtXvBezF6LF7wXc32Mt0NlG8OZHMqbrk6rUQZVfQF4ocYBicwr3LaxX02PE04iMk9VPROz1+IF78XstXjBezE3xHjD2ayUCbQPWk4H1lWjjDHGmDoWzuQwF+giIp1EJB44D5hWqsw04GJxHAZsU9X1pQ9kjDGmboWtWUlVC0VkNPAJzqWs41V1kYiMcrePA6bjXMa6AudS1svqOKwaN01FgNdi9lq84L2YvRYveC/mBhevaOmZDI0xxjR4NiurMcaYMiw5GGOMKaPBJgcRGSYiy0RkhYjcFul4ShOR9iIyQ0SWiMgiEbnBXd9CRD4TkV/d380jHWswEYkVkZ9F5AN3OdrjbSYik0VkqXuuD4/mmEXkJvf9sFBE3hSRxGiLV0TGi8hGEVkYtK7CGEXkdvf/cJmInBBFMT/ivi8yROQ9EWkWLTGXF2/QtltEREWkZdC6KsfbIJND0FQeJwIHA+eLyMGRjaqMQuBvqnoQcBhwrRvjbcAXqtoF+MJdjiY3AEuClqM93ieAj1W1G9ATJ/aojFlE2gHXA/1U9VCcCzvOI/rinQAMK7Wu3Bjd9/R5wCHuPs+6/5/hNoGyMX8GHKqqPYDlwO0QNTFPoGy8iEh7nCmK1gStq1a8DTI5ENpUHhGlqutLJh1U1VycD612OHG+4hZ7BTg9IgGWQ0TSgb8ALwatjuZ4mwBHAS8BqOouVd1KFMeMc4VhkojEAY1wxgFFVbyq+jWwpdTqimI8DZikqgFV/R3nSsUB4YgzWHkxq+qnqlroLs7BGXcFURBzBecY4L/AGPYePFyteBtqcqhomo6oJCIdgd7A90BaydgP93frCIZW2uM4b8zioHXRHO+fgE3Ay25T2Isi0pgojVlVs4BHcb4VrscZB/QpURpvKRXF6JX/xcuBj9y/ozJmETkVyFLVX0ptqla8DTU5hDRNRzQQkWRgCnCjqm6PdDwVEZGTgY2q+mOkY6mCOKAP8Jyq9gZ2EPkmmQq57fSnAZ2AtkBjERkR2ahqLOr/F0XkDpxm3oklq8opFtGYRaQRcAdwd3mby1m3z3gbanLwxDQdIuLDSQwTVfVdd/UfJTPVur83Riq+Uo4AThWRVTjNdMeIyOtEb7zgvA8yVfV7d3kyTrKI1piPBX5X1U2qWgC8C/yZ6I03WEUxRvX/oohcApwMXKh7BoVFY8wH4Hxp+MX9H0wHfhKRNlQz3oaaHEKZyiOiRERw2sKXqOpjQZumAZe4f18CTA13bOVR1dtVNV1VO+Kczy9VdQRRGi+Aqm4A1opIV3fVUGAx0RvzGuAwEWnkvj+G4vRFRWu8wSqKcRpwnogkiEgnnHu5/BCB+MoQ5+ZkY4FTVTV4xuaoi1lVF6hqa1Xt6P4PZgJ93Pd49eJV1Qb5gzNNx3LgN+COSMdTTnyDcKp+GcB89+ckIBXnao9f3d8tIh1rObEPBj5w/47qeIFewDz3PL8PNI/mmIF/AkuBhcBrQEK0xQu8idMnUuB+SF1RWYw4zSG/AcuAE6Mo5hU4bfUl/3/joiXm8uIttX0V0LIm8dr0GcYYY8poqM1KxhhjKmHJwRhjTBmWHIwxxpRhycEYY0wZlhyMMcaUYcnB1Gsikioi892fDSKS5f7tF5Fn6+gxbxSRi6u4zx3ubKsZbnwDq/G4rUTk46ruZ0x5wnabUGMiQVWzccYyICL3AH5VfbSuHs+dEO9ynJHWoe5zOM4o3D6qGnCnWo6v6mOr6iYRWS8iR6jqd1Xd35hgVnMwDZKIDJY995y4R0ReEZFPRWSViJwpIg+LyAIR+didxgQR6SsiX4nIjyLyScl0EKUcA/yk7myeIjJTRP4rIl+Lc7+I/iLyrjj3Nbjf3Wc/YLOqBgBUdbOqrqvsMUWks4h8LiK/iMhPInKAe6z3gQvr6LSZBsSSgzGOA3CmGz8NeB2YoardgTzgL26CeAoYrqp9gfHAv8o5zhFA6ckHd6nqUcA4nGkjrgUOBS4VkVTgU6C9iCwXkWdF5GjYPbdWRY85EXhGVXvizK+03l0/DziyZqfCGGtWMqbER6paICILcG6iU9J2vwDoCHTF+UD/zJnWiFj2fCAH24+9b3YEe+btWgAsUnfqahFZCbRX1fki0hfnQ30I8JY4dyecV95jikgK0E5V3wNQ1fygx9qIM2OrMTViycEYR0mTTrGIFOieeWWKcf5PBOeD/fB9HCcPSCzv2O6xAkHrS46NqhYBM4GZboK6BKcGUuYx3ZsUVSTRjcGYGrFmJWNCswxo5XYeIyI+ETmknHJLgM5VObCIdBWRLkGregGrK3pMde7rkSkip7vrE9z5/AEOxJmUz5gaseRgTAjUuZ3scOAhEfkFZ5bOP5dT9COcW49WRTLwiogsFpEMnPua37OPx7wIuN4tPwto464fAnxYxcc3pgybldWYWiYi7wFjVPXXCDz218BpqpoT7sc29YslB2NqmXvzoDR1bgIfzsdtBRyhqu+H83FN/WTJwRhjTBnW52CMMaYMSw7GGGPKsORgjDGmDEsOxhhjyrDkYIwxpoz/B+vSjAB04lmeAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "ax.set_title('Arduino measure response transistor base')\n",
    "\n",
    "x=dfmeasure['time']\n",
    "\n",
    "f1=interp1d(dfmeasure['time'], dfmeasure['v1'])\n",
    "f2=interp1d(dfmeasure['time'], dfmeasure['v2'])\n",
    "\n",
    "ax1 = dfmeasure.plot('time', 'v1', kind='scatter', ax=ax, label='base')\n",
    "ax1 = dfmeasure.plot('time', 'v2', kind='scatter', ax=ax, color='r', label='collector')\n",
    "ax1.plot(x, f1(x),'b')\n",
    "ax1.plot(x, f2(x), 'r')\n",
    "ax1.set_xlabel('Time (mSec)')\n",
    "ax1.set_ylabel('voltage $V_C$')\n",
    "ax1.set_ylim(0,.8)\n",
    "ax1.legend()\n",
    "ax1.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "1540f085-7bd3-4d8a-b58b-aaf4e468d8ad",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "ax.set_title('Arduino measure transistor base response')\n",
    "\n",
    "ax1 = dfmeasure.plot('time', 'v1', kind='scatter', ax=ax, label='base')\n",
    "ax1 = dfmeasure.plot('time', 'v2', kind='scatter', ax=ax, color='r', label='collector')\n",
    "ax1.plot(x, f1(x),'b')\n",
    "ax1.plot(x, f2(x), 'r')   \n",
    "ax1.set_xlabel('Time (mSec)')\n",
    "ax1.set_ylabel('voltage $V_C$')\n",
    "ax1.legend()\n",
    "ax1.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "fa1bfc4e-6e46-4250-935f-3272f831434a",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "ax.set_title('Source Current')\n",
    "x = np.linspace(0,130,200)\n",
    "ax.plot(x, 1000*(5 - f1(x))/r1val,'b')\n",
    " \n",
    "ax.set_xlabel('Time (mSec)')\n",
    "ax.set_ylabel('Current $I_b$ (mA)')\n",
    "\n",
    "ax.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "9548f86f-81b0-4e83-bb3b-b6458256e688",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6.657692307692306 0.0006657692307692306\n",
      "0.67 mA going into capacitor per second\n",
      "or 665.8 μA per mSec\n"
     ]
    }
   ],
   "source": [
    "df = dfmeasure[dfmeasure['time']<100]\n",
    "res = linregress(df['time']/1000, df['v1'])\n",
    "capcurrent = res.slope*cval\n",
    "print (res.slope, capcurrent)\n",
    "print (\"{:.2f} mA going into capacitor per second\".format(capcurrent*1000))\n",
    "print (\"or {:3.1f} \\N{greek small letter mu}A per mSec\".format(capcurrent*1e6))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "baaa9f83-1ed8-418b-b3f6-95c3b495c181",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "ax.set_title('Base Current')\n",
    "x = np.linspace(0,130,200)\n",
    "ax.plot(x, 1000*(5 - f1(x))/r1val-capcurrent/1000,'b')\n",
    " \n",
    "ax.set_xlabel('Time (mSec)')\n",
    "ax.set_ylabel('Current $I_b$ (mA)')\n",
    "\n",
    "ax.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "280bd7cc-5a6e-4aa2-8df9-9850caec75be",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "ax.set_title('Collector Current')\n",
    "x = np.linspace(0,130,200)\n",
    "ax.plot(x, 1000*(5 - f2(x))/r2val,'b')\n",
    " \n",
    "ax.set_xlabel('Time (mSec)')\n",
    "ax.set_ylabel('Current $I_b$ (mA)')\n",
    "\n",
    "ax.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "b946f07b-1e0d-4df1-b8bc-d6aa3b99d0e7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "ax.set_title('Arduino measure transistor base-collector response')\n",
    "\n",
    "df=dfmeasure.drop_duplicates('v1') \n",
    "xi = np.linspace(.5,.7,100)\n",
    "f3=interp1d( df['v1'], df['v2'], kind='quadratic')\n",
    "\n",
    "ax1 = dfmeasure.plot('v1', 'v2', kind='scatter', ax=ax, label='5K')\n",
    "ax1.plot(xi, f3(xi),'b')\n",
    "\n",
    "ax1.set_xlim(.5,.7)\n",
    "ax1.set_xlabel('voltage $V_B$')\n",
    "ax1.set_ylabel('voltage $V_C$')\n",
    "ax1.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "0bbcde3e-495e-4171-8644-6145f7ae7d9c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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bN27k/PPP58Ybb+QXv/gFTU1NLF68mIcffpiDD+783ohLly5l+/bt+3136qmnPufus/sSUz5dB9LZqQKdbuXdfS4wF2D27NnemxueLVq1jVse/xs7W9p6/JuKkiRrNpTQuHwE7U/X7N/TUlRMW8eYM5bwre+cyMjKty9omxtb2HXka6x/YCbfemAM5ZM3UlbcxlPXvrvblshAv5mb6lfYBkv9Xn31Vaqqqnr0m2XbtlGcTOyXQIqTCba1JpnYw2F0JR1DVVUVF154IS+//DLFxcV84hOfoKGhgY9+9KPMnz+/01jLyso45phj+jT+zuRTAmkAMrfO1cCa/h5J9YhyWlOpAxfM0J5yRp+7iOFtTmpPktbNlWBOUWULiYoWLAEVpUU0bG3uNCE0bG1mxDvWs+HR3ex4dhLlkzdSnEh0WV5EClNn25fWVIrqEeV9Gm5TUxOpVIqqqiqampp45JFH+MY3vsHLL78MwJe+9CXWrl3LBRdcwLx58ygp6Vtrp6fy6TTeB4FPWuBdwPZcHP8YWVnKDRfOoKw4QVVpEWXFCT55woRuu2/88Axu/PBMyooTDKsyhtbsZMi4HSQrg+QB3S8k1SPKabd2qmYtZ/eKg9mzsbJfFioRyS+dbV9uuHBGn/8orl+/npNPPpmZM2dy3HHHcc4553Dmmfufk3T99ddTU1PDJZdcQqqXf5KzFeVpvHcBdcAoM2sAvgkUA7j7LcA8glN4lxKcxpuzc9HOO3r83gPg6QPaXzx9WrfdwH6/eWrpJq7pcKCsq4UkvVB9uek1tj1+OK3Lx3DDVZVqfYgMQJ1tX/rq0EMPZdGiRW/7/o477tivO8prQCDas7A+foD+DnwhonAYWVm634w9UHfH73q7kKTLH/u/7UwpnsJ5Ryf7sTYikk86234MRPl0DKTg9HYhGVlZyntPDU7zTaUgkU87EEVEekmbsIidcgps2wbhsS8RkYKlBBKxU04J3p98Mt44RKTnorxerr/lMnYlkIhNnAjV1fDEE3FHIiI9UVZWxubNmwsyiaSfB1JWVpaT4esYSMTMglZIfX1whXoB3yVaZFCorq6moaGBjRs3xh1KVtJPJMwFJZAYnHIK3HUXLFsGkyfHHY2IdKe4uDgnT/MbCLQLKwY6DiIiA4ESSAymT4cRI5RARKSwKYHEIJGAk09WAhGRwqYEEpNTToE33oB16+KOREQkO0ogMTnppOD9mWfijUNEJFtKIDE58sjg/dVX441DRCRbSiAxGTYMxo2DV16JOxIRkewogcRo+nQlEBEpXEogMZo+PdiFFdGzX0RE+pUSSIymT4emJmhoiDsSEZHeUwKJ0fTpwbt2Y4lIIVICiZESiIgUMiWQGI0cCQcfrAQiIoVJCSRmOhNLRAqVEkjM0mdiFeCzakRkkFMCidn06cEz0nVPLBEpNEogMdOBdBEpVEogMTviiOBdCURECo0SSMzGjIHhw5VARKTwKIHEzGzfgXQRkUKiBJIHdCqviBQiJZA8MH06bNwYvERECoUSSB44/PDgfcmSeOMQEekNJZA8MGVK8P7mm/HGISLSG5EmEDM708yWmNlSM/tqJ/2Hmdn/mtkiM1tsZpdFGV9cJk6EREIJREQKS2QJxMySwM3AWcB04ONmNr1DsS8Ar7j7TKAO+C8zK4kqxriUlEBNjRKIiBSWKFsgxwFL3X2Zu+8B7gbO71DGgSozM6AS2AK0RRhjbCZPhmXL4o5CRKTniiIc13hgVUZ3A3B8hzI/Ah4E1gBVwMfc/W0PfDWzOcAcgNGjR1NfX5+LeCNVXj6N558fRX3903u/a2xsHBB164rqV9hUP4kygVgn33W8B+0ZwELgNGAy8Ecze9Ldd+z3I/e5wFyA2bNne11dXb8HG7W//Q0eeghmzaqjqir4rr6+noFQt66ofoVN9ZMod2E1ADUZ3dUELY1MlwH3e2Ap8BZweETxxWry5OBdx0FEpFBEmUCeBaaa2aTwwPhFBLurMq0ETgcws9HAYcCgODJw6KHBuxKIiBSKyHZhuXubmV0JPAwkgdvcfbGZXRH2vwX4FnCHmb1EsMvrWnffFFWMcUq3QHQgXUQKRZTHQHD3ecC8Dt/dkvF5DfD+KGPKF8OGBc9IVwtERAqFrkTPI5MnK4GISOFQAskjSiAiUkiUQPLI5MmwciW0tsYdiYjIgSmB5JFDD4X29iCJiIjkOyWQPKJrQUSkkCiB5BElEBEpJEogeWTsWCgrUwIRkcKgBJJHEongOIguJhSRQqAEkmd0Kq+IFAolkDxz6KFBAvGO9ykWEckzSiB5ZvJkaGqCDRvijkREpHtKIHkmfVfe5ctjDUNE5ICUQPJMbW3wrgQiIvlOCSTPTJwYvCuBiEi+UwLJM5WVwW3dV6yIOxIRke4pgeShiRPVAhGR/KcEkodqa5VARCT/KYHkodraYBeWrgURkXymBJKHJk6EXbtg+/biuEMREemSEkgeSp/Ku25dWaxxiIh0RwkkDymBiEghUALJQ+lrQdavVwIRkfylBJKHhg2D4cPVAhGR/KYEkqcmTlQCEZH8pgSSp2prYf360rjDEBHpkhJInqqtDVoguhZERPKVEkiemjgRmpuL2LIl7khERDqnBJKn0qfy6qaKIpKvlEDylJ4LIiL5TgkkT+m5ICKS7yJNIGZ2ppktMbOlZvbVLsrUmdlCM1tsZo9HGV8+GTECKiralEBEJG8VRTUiM0sCNwPvAxqAZ83sQXd/JaPMcODHwJnuvtLMDokqvnxjBmPG7GbFisq4QxER6VSULZDjgKXuvszd9wB3A+d3KHMxcL+7rwRw9w0Rxpd3DjlkN6+90c7mxpa4QxEReZvIWiDAeGBVRncDcHyHMtOAYjOrB6qAH7r7nR0HZGZzgDkAo0ePpr6+Phfxxmp7cyvDR0xm4aJh3P3gw1SPKGdY+cC6vXtjY+OAnHdpql9hG+j16w9RJhDr5LuOl8kVAbOA04Fy4C9m9ld3f32/H7nPBeYCzJ492+vq6vo/2hhtbmzhpOsf4/Dhu9jdXMz3nillSFUbT137bkZWDpyr0+vr6xlo8y6T6lfYBnr9+kOUu7AagJqM7mpgTSdl/s/dm9x9E/AEMDOi+PJGw9ZmihMJRoxsBqB9RznFiQQNW5tjjkxEZJ8oE8izwFQzm2RmJcBFwIMdyjwAnGJmRWZWQbCL69UIY8wL1SPKaU2l9iaQtp1Bd/WI8pgjExHZJ7IE4u5twJXAwwRJ4R53X2xmV5jZFWGZV4H/A14EngF+5u4vRxVjvhhZWcoNF87goJG7AUg0lXPDhTMG1O4rESl8UR4Dwd3nAfM6fHdLh+4bgRujjCsfnXf0eMo2vk4y6Vx85OGcd3Sks0pE5IB0JXoeKyk2xo0zNq1X8hCR/NOnBBJe+Cc5VFMDq1YduJyISNR69NfWzIYAR4avd4TvRwEVwIicRSfU1MCCBXFHISLydgdsgZjZcuB14DvAO4E3gRnAMe6u5JFjEyZAQwN6sJSI5J2e7ML6PbAF+Km7X+XuPwZaBvttRqJSUwMtLbBxY9yRiIjs74AJxN2vBM4FzjGzBWZ2Fm+/glxypCa89FLHQUQk3/ToILq7L3f3TwGfIrgH1Rgzq8thXBJSAhGRfNXbs7Bed/cLgDrga2b2RP+HJJmUQEQkX/X4AgMz+xnwITNrIriH1UvAolwFJoGDD4bSUiUQEck/vblC7RRgtLu3mtl4gpscHpWbsCTNDKqrlUBEJP/0JoH8leCajw3uvhpYTYfbkkhu1NTAypVxRyEisr/eHAOZCzxuZv9oZqeY2bBcBSX709XoIpKPepNAfgncQ9Bq+XvgaTN7MydRyX5qamDNGmhvjzsSEZF9erMLq8Hdv5n5hZnp/uIRqKkJksfatcHxEBGRfNCbFshCM/ti5hfu3tLP8UgnJkwI3rUbS0TySW8SyGjgCjNbY2a/N7PvmNlHchWY7KNrQUQkH/V4F5a7fxT27rZK3433OODe3IQmaUogIpKPev2konC31fPhSyIwbBhUViqBiEh+6fUDpczsu2ZWFH42Mxva/2FJJjOdyisi+SebJxJWunsbgLs78IP+DUk6owQiIvkmmwSS6tC9sz8Cke4pgYhIvskmgTxlZv9pZtVmNhY4pL+DkrerqYF162DPnrgjEREJHPAgupn9mODOuy8CL7n7PWa2EvgaUAp8O7chCuw7E2vNGqitjTUUERGgZ2dhLSR4BvpFwDvMbCf7J5RXcheepKWvQF+1SglERPLDAROIu8/N7DazaoKEchRwDnB3bkKTTOkWSENDvHGIiKRlcx1IA9CAbuUeqcwWiIhIPsjmILrEoKoquKBQLRARyRdKIAVETyYUkXyiBFJAamrUAhGR/BFpAjGzM81siZktNbOvdlPuWDNrN7MPRxlfvlMLRETySWQJxMySwM3AWcB04ONmNr2LctcDD0cVW6GoqYH163UxoYjkhyhbIMcBS919mbvvITj99/xOyl0F/BbYEGFsBSF9JtaaNfHGISIC0SaQ8UDmDpiG8Lu9zGw8cAFwS4RxFQydyisi+aTX14H0gXXynXfovgm41t3bzTorHg7IbA4wB2D06NHU19f3U4j5pbGxcb+6rV1bARzHI4+8Qnt74TfQOtZvoFH9CttAr19/iDKBNAA1Gd3VQMedMbOBu8PkMQo428za3P13mYXCq+PnAsyePdvr6upyFHK86uvryazbzp1w6aVQVTWdurq3HT4qOB3rN9CofoVtoNevP0SZQJ4FpprZJGA1wb21Ls4s4O6T0p/N7A7g9x2Tx2CmiwlFJJ9ElkDcvc3MriQ4uyoJ3Obui83sirC/jnv0gE7lFZF8EWULBHefR4d7aHWVONz90ihiKjS6mFBE8oWuRC8waoGISL5QAikwuphQRPKFEkiBSV8Lsnp1vHGIiCiBFJh0AtFxEBGJmxJIgUk/mVDHQUQkbkogBUYtEBHJF0ogBSZ9MaFaICISNyWQAlRdrRaIiMRPCaQA1dSoBSIi8VMCKUC6mFBE8oESSAGqrYUNG6CpKe5IRGQwUwIpQFOnBu9Ll8Ybh4gMbkogBWjatOD9jTfijUNEBjclkAI0ZUrw/vrr8cYhIoObEkgBqqyEsWPVAhGReCmBFKhp05RARCReSiAFaupU7cISkXgpgRSoqVNh40bYvj3uSERksFICKVDpU3m1G0tE4qIEUqDSp/JqN5aIxEUJpEBNngxmaoGISHyUQApUWVlwU0UlEBGJixJIAdOpvCISJyWQApY+ldc97khEZDBSAilgU6fCtm3w+Ivb2dzYEnc4IjLIKIEUsC1FmwD4zA9f5aTrH+PBhatjjkhEBhMlkAK1ubGFX726GIDt68vY3Zrimt++qJaIiERGCaRANWxtpuKgFrAUrVuHAFCcSNCwtTnmyERksFACKVDVI8pps3aKhjXTFiaQ1lSK6hHlMUcmIoOFEkiBGllZyg0XzqB0ZBOpbZWUFSe44cIZjKwsjTs0ERkkIk0gZnammS0xs6Vm9tVO+v+dmb0Yvp42s5lRxldozjt6PJ86+yBSW6uYf/VpnHf0+LhDEpFBJLIEYmZJ4GbgLGA68HEzm96h2FvAe9x9BvAtYG5U8RWqU99dxJ4WY9VStTxEJFpRtkCOA5a6+zJ33wPcDZyfWcDdn3b3rWHnX4HqCOMrSCecELz/5S/xxiEig0+UCWQ8sCqjuyH8riufAf6Q04gGgPHjg3tiKYGISNSKIhyXdfJdpzfhMLNTCRLIyV30nwPMARg9ejT19fX9FGJ+aWxs7FHdJk+eTn39UOrr/5r7oPpRT+tXqFS/wjbQ69cfokwgDUBNRnc1sKZjITObAfwMOMvdN3c2IHefS3h8ZPbs2V5XV9fvweaD+vp6elK3hQuhvh6mTatj3LhcR9V/elq/QqX6FbaBXr/+EOUurGeBqWY2ycxKgIuABzMLmNkE4H7gEnfXo5J6SMdBRCQOkSUQd28DrgQeBl4F7nH3xWZ2hZldERb7BjAS+LGZLTSzBVHFV8iOOQZKS5VARCRaUe7Cwt3nAfM6fHdLxufPAp+NMqaBoKQEZs1SAhGRaOlK9AHihBPguedgz564IxGRwUIJZIA44QRoaYEXXog7EhEZLJRABggdSBeRqCmBDBDjxsGECUogIhIdJZAB5JRT4NFHdRxERKKhBDKAXHwxbN4MDz0UdyQiMhgogQwg738/jB0Lt98edyQiMhgogQwgRUVwySUwbx6sXx93NCIy0CmBDDCXXgrt7fDLX8YdiYgMdEogA8wRR8Dxxwe7sbzTex2LiPQPJZAB6LLLYPHi4Mp0EZFcUQIZgD72MSgrg9tuizsSERnIlEAGoOHDgyTy85/rYLqI5I4SyAD1r/8a3Bvrm99qY9GqbWxubIk7JBEZYCK9nbtEZ+pUeM85Tcy9pYz6koUwpJkbLpzBeUd39xh6EZGeUwtkgNrc2MJbNc/ibqx5vJbdrSmu+e2LaomISL9RAhmgGrY2M2RkC5VHrWLnohradpRRnEjQsLU57tBEZIBQAhmgqkeU05pKMezEpQBse/IwWlMpqkeUxxyZiAwUSiAD1MjKUm64cAaVI/dw8InLaXq5mjNLjmdkZWncoYnIAKEEMoCdd/R4nrr2NP7w85GcdEqKud89iJdeijsqERkolEAGuJGVpcyaNJz77kkwbBh8+MOwc2fcUYnIQKAEMkiMGQN33w1Ll8JZZ8GyZXFHJCKFTglkEHnPe+BXv4KXXoIZM2DuXN1wUUSypwQyyFx0UZBAjj8ePvc5OPlk+NOf9iWSzY0tunJdRHpEV6IPQhMmwB//CLfeCv/+7/C+9wXPU3/v323iV6uepSSZoDWV0pXrItIttUAGqUQCLr88OCbyox/BG0udb14xihW3v4sNr4ygeY+uXBeR7imBDHKlpfCFL8ADj29n7Nmv0NZYyob7jmPtHSfT9Mo4lm/Ulesi0jklEAFg8thyhr5zBePn1DPyrEV4W5KG+2dy4WnDuOkm2L49KKdjJCKSpgQiwL4r18vLjLHHruPQzz/JP39/M+PHGVdfDePHw1kfaeSdVz7P3/30b5x0/WM8uHB13GGLSIx0EF32Ou/o8Zw0ZRQNW5upHlEe3Pbk6uDRuN+/qZ277irH208gWdlMxWHr+PySdRx2/SgOm9T97VE2N7bsP8xe9heR/BRpAjGzM4EfAkngZ+7+vQ79Lex/NrALuNTdn48yxsFuZGXp2zbis2bBNf+xkxfGPceGVw5i15KxNC6awM7nJnH4vcGzR444InifPBmqq2HcuODixb+sWc3XHnyR4kTnZ3Y9sHA11/626/6dyUVC6u9hbm5sobm1nc2NLf0WQxTl+3uYuZgXUcQQ9TiimE65EFkCMbMkcDPwPqABeNbMHnT3VzKKnQVMDV/HAz8J3yVm1SPKSZXsofLINVQeuQZvS+CbhnPZocfy0sIiXn8dHnkEdu/u+MvxWMkhJMpbSZS2ctHP2znpiHaGD02yffthPLtlD6nEYVhxO1bczuXPbGfZuYdwyEHFVFRARUXwfPfS0uD15Jvr+f6fllCcNNo8xbVnHMZpR4zBHVIp+NMr6/n+n16juMhoo51vfvBwLjh2LBUVkEx2Xreukph7UJ97nl7Lvz/wGklP0tYO1541jTNnjKGkBKqqYMgQMHv78P7hiFauvv6xHiXF3ibSA5VvawtuWbNrV/D5D4vWccPD4XSzdv7tgsP56IljKSnJPobtza2cdP1jnZZvbYV7/rKGb9y3hGSqiNZWuPLdh3HS5ENobw/mlVnwSiSgqCh4Pfnmem6a/xolJU57oo3vfewIPnTs+P2mb0+nw5498Jun1nLd/7wWxNAGV58+jdOOGI0ZlJQEy1Z5eTAPy8rodDwHmi49nW7uwVNC06/WVmhvhz+8uI7r/7CEokSwTP/z2Ydz9swxFBXtW+5LS4PplO28yhXziC5FNrMTgOvc/Yyw+58B3P27GWX+G6h397vC7iVAnbuv7Wq4s2fP9gULFuQ09rjU19dTV1cXdxh7PbhwNdd0s9CmUrBuHaxZE7yeXbyLuY+spnlnEandxaRaiki0ljBx6FC8rYjNW5rZvDNJqjWBtyaBLrYS/aSiAoYOhWHDgo1GWRkkilK8sHIrqRSQSpBqTUJrEcOKytmxw9iz58DDNYPKyuBVXpFidWMjnmhnwrB2GpqdRBJOnHIQJUVJ3Nmb7NIb0j1tKZ5fsZVUxqqYSMDs2hGUlSRIJPZtbM2gpTXFX5ZuIZUiSOTtCWhLMrqikuZdRmNjZ4m8c6WlwTSprHLWNO2E4jYs2Y4Vp0gWOe898mCGlAWZNx17Wxs07mpn5epNLN2SxNuSwfxrLWJospydO3s23XoqmXQqK42qqn0Ju7gYLJli4aqttLcTzLu2RDDvkhU0NlqPp8G+8QTzsKIiWD7cG6kaVsHrG7fjiRSYBwkv6Rw/aSTFyQR72lI8s2wL7e0GKcNThnmCSSOqaN2ToKUlmBe7dgWvvigrC+Mb4jRNXErlCa/v61ec4KlrT+tVS8TMnnP32X2JKcpdWOOBVRndDby9ddFZmfFAlwlEotPpMZIMiUSw62rcuKD7pNOS3LtrKeWtqb1lyooTPHHtaYysLOLRx/7KF+bvZndrKtg4tSUotWLuv/wUSiiluRmamoIVsKUFlqxu4gcPv0HzHsc9SDblRQk+XzeZ2oOHsHJLEzfPXxoML2V4e4JSK+Jjx0xieEk5O3aw99XcHAx3y44UZgaJFJZsp2hICyVlKU6dmWRydSm7vJl7X3yLFm/Dkiks4ZQmk1x+8hRGD6lg5072vpqaYNWGNja+upvWVnASeGsR3mqsWeuUl+xLAslkML0SCdjdmsIwYF8GMTd2NqVo25OgvX3fxtsdWtpT+J4inBRWlCJR2kZxiTPzyFImjC5hyBD2bmwrKmDtzl389M9L2d2WCjZy7UYpxXxoRi1DrJzt22Hl+lY2Ld7NnpYg5vbmBClPsnAhJMKw0rEXF0M7sHt3KaRSJErasHC6nX5MkkljS2lMNfPbF5ezx1qxonYsmaKizLjm7GlMHVO59990KrUvmb6+tokf/N8b7NodJsa2JMWpYs49cgJDEmX7TefWVtjamIJUAhLtWFEbReUpSsrbqZtZRO3YUppp5v6XltNirVhRCkukKC9JcNVpU5k4cgitrcFykF7OGhv3tdqam2HlymaspJSiHe20toYJwg1vS7B5a4qKkgS79qSgPQnhvLBEiuJiGF9bzugRJZSVBRv+dFIqL9/XoiguhrU7dvHTP7/J7rb2fetIMsmnT5zMmKoKWluD5bS5OYirsRFWrW/lhbb9s2P6YXFR78qKsgXyEeAMd/9s2H0JcJy7X5VR5iHgu+7+57D7UeAad3+uw7DmAHMARo8ePevuu++OpA5Ra2xspLKyMu4w+mR7cysNW5v3bh6rR5QzrLwYCOrXniztsn9H7SnntXU7SWUsswkzDh9TRTJhB+wfxTAzy48uh/XNfY8hivLZDHPLth2sy7hMKNfzorfls4khU2NjI+UVQ3I6jiimU1dOPfXUgmqBNAA1Gd3VwJosyuDuc4G5EOzCyqfdPP0p33ZhZaurg33p+vXmYGBTJ7vRTs/YjXag/lEMM13+H45o5ebXivslhijK93aYD/zhj9z8Qluk86K35bOJIS29fOZyHNn+vq/j7DfuHsmLIFktAyYBJcAi4MgOZc4B/kCwM/xdwDMHGu6sWbN8oJo/f37cIeRUtvXbtHO3L1y51Tft3J1V/yiGuWnnbp/3yJ/6NYYoyvdmmPPnz49lXvS2fDYxuO+/fOZqHH35fV/HCSzwPm7XI2uBuHubmV0JPExwGu9t7r7YzK4I+98CzCM4hXcpwWm8l0UVnxSOzk417k3/KIY5srKU8uJkr38Td/n+HmYu5kUUMUQ9jiimUy5Eeh2Iu88jSBKZ392S8dmBL0QZk4iIZEe3MhERkawogYiISFaUQEREJCtKICIikpXILiTMFTPbCKyIO44cGQVsijuIHFL9CpvqV9gOc/eqvgyg4G/n7u4Hxx1DrpjZAu/jlaL5TPUrbKpfYTOzPt9EULuwREQkK0ogIiKSFSWQ/DY37gByTPUrbKpfYetz/Qr+ILqIiMRDLRAREcmKEoiIiGRFCSQGZnammS0xs6Vm9tUuytSZ2UIzW2xmj3folzSzF8zs99FE3Dt9qZ+ZDTez+8zsNTN7NXwUcl7pY/2uDr972czuMrOy6CLvmQPVz8z+KazbwrAe7WZ2UE9+mw+yrZ+Z1ZjZ/HC5XGxmX4wj/gPpy/wL+/d8+9LX+8Hr1evnoiSBN4FD2fdclOkdygwHXgEmhN2HdOj/ZeDXwO/jrk9/1w/4OfDZ8HMJMDzuOvVX/Qgez/wWUB523wNcGnedelu/DuXPBR7L5rcFWL+xwDvDz1XA6wOpfhnf9Xj7ohZI9I4Dlrr7MnffA9wNnN+hzMXA/e6+EsDdN6R7mFk1wYO3fhZRvL2Vdf3MbCjwbuDW8Ps97r4tqsB7qE/zj+Di3XIzKwIq6OSJmzHrSf0yfRy4K8vfxiHr+rn7Wnd/Pvy8E3iV4E9BPunL/Ov19kUJJHrjgVUZ3Q28fSGcBowws3oze87MPpnR7ybgGiCV0yiz15f6HQpsBG4Pm9A/M7MhuQ+5V7Kun7uvBv4TWAmsBba7+yMRxNwbPakfAGZWAZwJ/La3v41RX+qX2a8WOAb4W/+H2Cd9rd9N9GL7ogQSvc6eet/xXOoiYBbBP4EzgK+b2TQz+wCwwd2fy3GMfZF1/cLv3wn8xN2PAZqAfNuP3pf5N4Lg3+AkYBwwxMw+kctgs9CT+qWdCzzl7luy+G1c+lK/YABmlQQb3S+5+45+jq+vsq5fNtuXgr8XVgFqAGoyuqt5+26MBmCTuzcBTWb2BDCTYON6npmdDZQBQ83sl+6eTxuhvtTvSaDB3dP/6u4j/xJIX+oH8Ja7bwQws/uBE4Ff5jbkXulJ/dIuImP3Ry9/G5e+1A8zKyZIHr9y9/tzEmHf9KV+J9Hb7UvcB30G24sgaS8j+BeaPsh1ZIcyRwCPhmUrgJeBd3QoU0d+HkTvU/0Ikshh4efrgBvjrlN/1Q84HlgcfmcEJwxcFXedelu/sNwwYAswpLe/LeD6GXAncFPc9chF/Tr079H2RS2QiLl7m5ldCTxMcMbEbe6+2MyuCPvf4u6vmtn/AS8S7Iv8mbu/HF/UPdcP9bsK+JWZlRCsCJdFX4uu9bV+ZnYf8DzQBrxAnt0uoyf1C4teADziQSur299GW4Pu9aV+BP/QLwFeMrOF4Xf/4u7zoon+wPpYv17TrUxERCQrOoguIiJZUQIREZGsKIGIiEhWlEBERCQrSiAiIpIVJRAREcmKEohIL5jZ58zslgOX7NGwfmRmK/pjWCJxUAIR6Z0ZwEt9HYiZTSK42rfEzKr6OjyROCiBiPTOUQRXmHfKzO4NWxZ/NrMVZnaymd1pZq+b2a0ZRf8N+DbBc0OOzHHMIjmhBCLSO++g+xbIUcAydz+Z4F5XtwLXhr/7kJmVmtmRYfdvCJ4poQQiBUkJRKSHzKwGaHT3bWa2wMxuNrPHw4RA+Hja4QTPVABoBm714EFEe4BdwB7gO8DXPbiP0KsEyUSk4CiBiPTcDIIb6dUAz7j7F4AHCG6ZDUFL4nl3Tz+MZybhA4fCJ72tIXhi3BnAzWa2HPg6aoFIgdLdeEV6Ln38YxYwzcxuI3je+fcz+i/KKD+DfcdLZoaf/wP4gLs/CmBmownuyitScNQCEem5owiOf8wCvuLunwZaMh67exSwEPbuzip3961hv3QyKU0nDwB3X0/wZMKDoqmCSP/R7dxFesnM5gErCJ71sdXdvxZzSCKxUAIREZGsaBeWiIhkRQlERESyogQiIiJZUQIREZGsKIGIiEhWlEBERCQrSiAiIpIVJRAREcmKEoiIiGTl/wdhfo+4KRWwNwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "ax.set_title('Arduino measure transistor base-collector response')\n",
    "\n",
    "\n",
    "df=dfmeasure.drop_duplicates('v1').copy() \n",
    "df.loc[:,'bcurrent'] = ((5 - df['v1'])/r1val-capcurrent/1000)*1000 # (convert to milliamps)\n",
    "df.loc[:,'ccurrent'] = 1000*(5 - df['v2'])/r2val # 1000 * (convert to milliAmps)\n",
    "xi = np.linspace(.63, .734,100)\n",
    "f3=interp1d( df['bcurrent'], df['ccurrent'], kind='quadratic')\n",
    "#f2=interp1d(dfmeasure['time'], dfmeasure['v2'])\n",
    "\n",
    "ax1 = df.plot('bcurrent', 'ccurrent', kind='scatter', ax=ax, label='5K')\n",
    "#ax1 = dfmeasure.plot('time', 'v2', kind='scatter', ax=ax, color='r', label='collector')\n",
    "ax1.plot(xi, f3(xi),'b')\n",
    "#ax1.plot(x, f2(x), 'r')\n",
    "#ax1.set_xlim(.5,.7)\n",
    "ax1.set_xlabel('$I_B mA$')\n",
    "ax1.set_ylabel('$I_C mA$')\n",
    "ax1.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "5cb596cb-9200-4aae-8165-3035e5f30e40",
   "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>time</th>\n",
       "      <th>v1</th>\n",
       "      <th>v2</th>\n",
       "      <th>bcurrent</th>\n",
       "      <th>ccurrent</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>4.98</td>\n",
       "      <td>0.734628</td>\n",
       "      <td>0.004</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.0</td>\n",
       "      <td>0.03</td>\n",
       "      <td>4.97</td>\n",
       "      <td>0.730217</td>\n",
       "      <td>0.006</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>8.0</td>\n",
       "      <td>0.07</td>\n",
       "      <td>4.98</td>\n",
       "      <td>0.724334</td>\n",
       "      <td>0.004</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>12.0</td>\n",
       "      <td>0.09</td>\n",
       "      <td>4.98</td>\n",
       "      <td>0.721393</td>\n",
       "      <td>0.004</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>16.0</td>\n",
       "      <td>0.13</td>\n",
       "      <td>4.97</td>\n",
       "      <td>0.715511</td>\n",
       "      <td>0.006</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>20.0</td>\n",
       "      <td>0.15</td>\n",
       "      <td>4.98</td>\n",
       "      <td>0.712570</td>\n",
       "      <td>0.004</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>24.0</td>\n",
       "      <td>0.18</td>\n",
       "      <td>4.97</td>\n",
       "      <td>0.708158</td>\n",
       "      <td>0.006</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>28.0</td>\n",
       "      <td>0.21</td>\n",
       "      <td>4.97</td>\n",
       "      <td>0.703746</td>\n",
       "      <td>0.006</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>32.0</td>\n",
       "      <td>0.23</td>\n",
       "      <td>4.98</td>\n",
       "      <td>0.700805</td>\n",
       "      <td>0.004</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>36.0</td>\n",
       "      <td>0.26</td>\n",
       "      <td>4.98</td>\n",
       "      <td>0.696393</td>\n",
       "      <td>0.004</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>40.0</td>\n",
       "      <td>0.28</td>\n",
       "      <td>4.97</td>\n",
       "      <td>0.693452</td>\n",
       "      <td>0.006</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>44.0</td>\n",
       "      <td>0.31</td>\n",
       "      <td>4.98</td>\n",
       "      <td>0.689040</td>\n",
       "      <td>0.004</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>48.0</td>\n",
       "      <td>0.34</td>\n",
       "      <td>4.98</td>\n",
       "      <td>0.684628</td>\n",
       "      <td>0.004</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>52.0</td>\n",
       "      <td>0.37</td>\n",
       "      <td>4.98</td>\n",
       "      <td>0.680217</td>\n",
       "      <td>0.004</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>56.0</td>\n",
       "      <td>0.40</td>\n",
       "      <td>4.97</td>\n",
       "      <td>0.675805</td>\n",
       "      <td>0.006</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>60.0</td>\n",
       "      <td>0.42</td>\n",
       "      <td>4.98</td>\n",
       "      <td>0.672864</td>\n",
       "      <td>0.004</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>64.0</td>\n",
       "      <td>0.45</td>\n",
       "      <td>4.97</td>\n",
       "      <td>0.668452</td>\n",
       "      <td>0.006</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>68.0</td>\n",
       "      <td>0.47</td>\n",
       "      <td>4.97</td>\n",
       "      <td>0.665511</td>\n",
       "      <td>0.006</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>72.0</td>\n",
       "      <td>0.50</td>\n",
       "      <td>4.96</td>\n",
       "      <td>0.661099</td>\n",
       "      <td>0.008</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>76.0</td>\n",
       "      <td>0.52</td>\n",
       "      <td>4.95</td>\n",
       "      <td>0.658158</td>\n",
       "      <td>0.010</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>80.0</td>\n",
       "      <td>0.55</td>\n",
       "      <td>4.90</td>\n",
       "      <td>0.653746</td>\n",
       "      <td>0.020</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>84.0</td>\n",
       "      <td>0.57</td>\n",
       "      <td>4.81</td>\n",
       "      <td>0.650805</td>\n",
       "      <td>0.038</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>88.0</td>\n",
       "      <td>0.60</td>\n",
       "      <td>4.54</td>\n",
       "      <td>0.646393</td>\n",
       "      <td>0.092</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>92.0</td>\n",
       "      <td>0.62</td>\n",
       "      <td>3.82</td>\n",
       "      <td>0.643452</td>\n",
       "      <td>0.236</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>96.0</td>\n",
       "      <td>0.64</td>\n",
       "      <td>2.05</td>\n",
       "      <td>0.640511</td>\n",
       "      <td>0.590</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>100.0</td>\n",
       "      <td>0.67</td>\n",
       "      <td>0.06</td>\n",
       "      <td>0.636099</td>\n",
       "      <td>0.988</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>104.0</td>\n",
       "      <td>0.70</td>\n",
       "      <td>0.04</td>\n",
       "      <td>0.631687</td>\n",
       "      <td>0.992</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>108.0</td>\n",
       "      <td>0.71</td>\n",
       "      <td>0.03</td>\n",
       "      <td>0.630217</td>\n",
       "      <td>0.994</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>112.0</td>\n",
       "      <td>0.72</td>\n",
       "      <td>0.02</td>\n",
       "      <td>0.628746</td>\n",
       "      <td>0.996</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>116.0</td>\n",
       "      <td>0.73</td>\n",
       "      <td>0.02</td>\n",
       "      <td>0.627275</td>\n",
       "      <td>0.996</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>125.0</td>\n",
       "      <td>0.74</td>\n",
       "      <td>0.02</td>\n",
       "      <td>0.625805</td>\n",
       "      <td>0.996</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     time    v1    v2  bcurrent  ccurrent\n",
       "0     0.0  0.00  4.98  0.734628     0.004\n",
       "1     4.0  0.03  4.97  0.730217     0.006\n",
       "2     8.0  0.07  4.98  0.724334     0.004\n",
       "3    12.0  0.09  4.98  0.721393     0.004\n",
       "4    16.0  0.13  4.97  0.715511     0.006\n",
       "5    20.0  0.15  4.98  0.712570     0.004\n",
       "6    24.0  0.18  4.97  0.708158     0.006\n",
       "7    28.0  0.21  4.97  0.703746     0.006\n",
       "8    32.0  0.23  4.98  0.700805     0.004\n",
       "9    36.0  0.26  4.98  0.696393     0.004\n",
       "10   40.0  0.28  4.97  0.693452     0.006\n",
       "11   44.0  0.31  4.98  0.689040     0.004\n",
       "12   48.0  0.34  4.98  0.684628     0.004\n",
       "13   52.0  0.37  4.98  0.680217     0.004\n",
       "14   56.0  0.40  4.97  0.675805     0.006\n",
       "15   60.0  0.42  4.98  0.672864     0.004\n",
       "16   64.0  0.45  4.97  0.668452     0.006\n",
       "17   68.0  0.47  4.97  0.665511     0.006\n",
       "18   72.0  0.50  4.96  0.661099     0.008\n",
       "19   76.0  0.52  4.95  0.658158     0.010\n",
       "20   80.0  0.55  4.90  0.653746     0.020\n",
       "21   84.0  0.57  4.81  0.650805     0.038\n",
       "22   88.0  0.60  4.54  0.646393     0.092\n",
       "23   92.0  0.62  3.82  0.643452     0.236\n",
       "24   96.0  0.64  2.05  0.640511     0.590\n",
       "25  100.0  0.67  0.06  0.636099     0.988\n",
       "26  104.0  0.70  0.04  0.631687     0.992\n",
       "27  108.0  0.71  0.03  0.630217     0.994\n",
       "28  112.0  0.72  0.02  0.628746     0.996\n",
       "29  116.0  0.73  0.02  0.627275     0.996\n",
       "31  125.0  0.74  0.02  0.625805     0.996"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "8c97bc44-fe91-4b4b-b018-850f8a46d06c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinregressResult(slope=-8.760011429659974, intercept=5.864425402266887, rvalue=-0.6656341317602029, pvalue=0.01814338092082274, stderr=3.105774106289957, intercept_stderr=2.0494083514807624)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1 = df[13:25]\n",
    "linregress(df1['bcurrent'], df1['ccurrent'])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ccebc7b4-2619-4eca-b5ec-4bad21b30222",
   "metadata": {},
   "source": [
    "This doesn't look like a particularly good regression so I look at the graph."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "394ae27f-e6e1-4215-86df-2c3a029e4578",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "ax.set_title('Arduino measure transistor base-collector response')\n",
    "\n",
    "\n",
    "xi = np.linspace(.64052 ,.68, 100)\n",
    "f3=interp1d( df1['bcurrent'], df1['ccurrent'], kind='quadratic')\n",
    "\n",
    "ax1 = df1.plot('bcurrent', 'ccurrent', kind='scatter', ax=ax, label='5K')\n",
    "ax1.plot(xi, f3(xi),'b')\n",
    "\n",
    "ax1.set_xlabel('$I_B mA$')\n",
    "ax1.set_ylabel('$I_C mA$')\n",
    "ax1.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "79e2c595-d3d4-4879-bbae-384c4c789c0c",
   "metadata": {},
   "outputs": [],
   "source": [
    " "
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}