qguv/electronics_lab04.ipynb

## electronics_lab04.ipynb
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  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Hey Shen. Here's the code from\n",
      "\n",
      "# Lab 4: Passive Analog Signal Processing\n",
      "\n",
      "_Shen Ge and Quint Guvernator_\n",
      "\n",
      "2015-02-19 in Small Hall 230\n",
      "\n",
      "<hr />"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import sys\n",
      "from math import sqrt, log10\n",
      "\n",
      "def G_lowpass(freq: \"input frequency, in Hz\", f3db: \"cut-off frequency, in Hz\") -> \"v_out / v_in, in V\":\n",
      "    '''The function 'G' for low-pass filters.'''\n",
      "    return 1 / sqrt(1 + (freq / f3db)**2)\n",
      "\n",
      "def G_highpass(freq: \"input frequency, in Hz\", f3db: \"cut-off frequency, in Hz\") -> \"v_out / v_in, in V\":\n",
      "    '''The function 'G' for high-pass filters.'''\n",
      "    numerator = freq / f3db\n",
      "    return numerator / sqrt(1 + numerator**2)\n",
      "\n",
      "def our_G(freq: \"input frequency, in Hz\") -> \"v_out / v_in, in V\":\n",
      "    '''The function 'G' for our multi-stage band-pass filter.'''\n",
      "    highpass_cutoff =   495 # Hz\n",
      "    lowpass_cutoff  = 78899 # Hz\n",
      "    return G_highpass(freq, highpass_cutoff) * G_lowpass(freq, lowpass_cutoff)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# The frequencies at which to test, given by the lab 4 manual, problem 7.\n",
      "test_frequencies = [50, 100, 1e3, 5e3, 10e3, 20e3, 50e3, 100e3, 1e6]\n",
      "\n",
      "# Apply our combined 'G' function to each test frequency\n",
      "ratios = list(map(our_G, test_frequencies)) # unitless, ratio\n",
      "\n",
      "gains        = [ 20 * log10(ratio) for ratio in ratios ] # dB\n",
      "raw_voltages = [ 7.68 * ratio      for ratio in ratios ] # V\n",
      "loaded100k   = [ voltage * 10/11   for voltage in raw_voltages ] # V\n",
      "loaded1k     = [ voltage *  1/11   for voltage in raw_voltages ] # V"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Our observations\n",
      "obs_loaded100k = [720e-3, 1.42, 6.24, 6.92, 6.92, 6.70, 5.82, 4.33, 504e-3] # V\n",
      "obs_loaded1k   = [0.10, 0.16, 1.30, 3.17, 3.42, 3.49, 3.34, 2.96, 0.49]     # V"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from re import sub\n",
      "\n",
      "# Header\n",
      "column = \"{:>11}\"\n",
      "centered = \"{:>22}\"\n",
      "first = (column * 2 + 2 * centered).format(\"\", \"\", \"calc'd load voltage\", \"obsv'd load voltage\")\n",
      "second = (column * 6).format(\"FREQ\", \"CALC. GAIN\", \"100 kOhm\", \"1 kOhm\", \"100 kOhm\", \"1 kOhm\")\n",
      "underlines = sub(r\"\\S.\", '\u2014\u2014', second)\n",
      "print(first, second, underlines, sep='\\n')\n",
      "\n",
      "# Table Rows\n",
      "voltage = \"{:9.3} V\"\n",
      "for row in zip(test_frequencies, gains, loaded100k, loaded1k, obs_loaded100k, obs_loaded1k):\n",
      "    print((\"{:8.4g} Hz{:8.3} dB\" + voltage * 4).format(*row))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "                         calc'd load voltage   obsv'd load voltage\n",
        "       FREQ CALC. GAIN   100 kOhm     1 kOhm   100 kOhm     1 kOhm\n",
        "       \u2014\u2014\u2014\u2014 \u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014   \u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014     \u2014\u2014\u2014\u2014\u2014\u2014   \u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014     \u2014\u2014\u2014\u2014\u2014\u2014\n",
        "      50 Hz   -20.0 dB    0.702 V   0.0702 V     0.72 V      0.1 V\n",
        "     100 Hz   -14.1 dB     1.38 V    0.138 V     1.42 V     0.16 V\n",
        "    1000 Hz  -0.952 dB     6.26 V    0.626 V     6.24 V      1.3 V\n",
        "    5000 Hz -0.0598 dB     6.93 V    0.693 V     6.92 V     3.17 V\n",
        "   1e+04 Hz -0.0798 dB     6.92 V    0.692 V     6.92 V     3.42 V\n",
        "   2e+04 Hz  -0.273 dB     6.77 V    0.677 V      6.7 V     3.49 V\n",
        "   5e+04 Hz   -1.47 dB      5.9 V     0.59 V     5.82 V     3.34 V\n",
        "   1e+05 Hz   -4.16 dB     4.32 V    0.432 V     4.33 V     2.96 V\n",
        "   1e+06 Hz   -22.1 dB    0.549 V   0.0549 V    0.504 V     0.49 V\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import matplotlib.pyplot as plt\n",
      "from pylab import rcParams\n",
      "%matplotlib inline\n",
      "\n",
      "# Some basic styling and scaling to make defaults bearable\n",
      "plt.style.use('ggplot')\n",
      "rcParams[\"figure.figsize\"] = 12, 7\n",
      "rcParams[\"lines.markersize\"] = 12\n",
      "\n",
      "plt.title(\"Calculated Gain Through Band-pass Filter\")\n",
      "plt.ylabel(\"Gain (dB)\")\n",
      "plt.xlabel(\"Frequency (Hz)\")\n",
      "plt.semilogx(test_frequencies, gains, '.k', basex=10)\n",
      "plt.show()\n",
      "\n",
      "plt.title(\"Voltage Through Loaded (100k\u03a9) Band-pass Filter\")\n",
      "plt.ylabel(\"Voltage through Load (V)\")\n",
      "plt.xlabel(\"Frequency (Hz)\")\n",
      "plt.semilogx(test_frequencies, loaded100k, '+k', label=\"Calculated\")\n",
      "plt.semilogx(test_frequencies, obs_loaded100k, '.g', label=\"Observed\")\n",
      "plt.legend(loc=\"best\")\n",
      "plt.show()\n",
      "\n",
      "plt.title(\"Voltage Through Loaded (1k\u03a9) Band-pass Filter\")\n",
      "plt.ylabel(\"Voltage through Load (V)\")\n",
      "plt.xlabel(\"Frequency (Hz)\")\n",
      "plt.semilogx(test_frequencies, loaded1k, '+k', label=\"Calculated\")\n",
      "plt.semilogx(test_frequencies, obs_loaded1k, '.g', label=\"Observed\")\n",
      "plt.legend(loc=\"best\")\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
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avn27Ro0apUaNGjmNdWUwiIqK0pgxY/TYY49p1apVOnLkiHbv3q1FixY5tomLi9Mbb7yh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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10b285d30>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ZMGCA7es///nPiomJ0enTp1WjRg1J9lNEfv75Z2VmZurJJ5+UJDVu3Fj33nuv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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10cbcea20>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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LRTcAADAdNySq2Pz9/fWXv/xF06dP1xdffKGMjAzl5OToq6++0pw5c3T58mX5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\nHnI9pNrm2v07/pJqmmokieANAABMxfQSDBpFPxX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       "text": [
        "<matplotlib.figure.Figure at 0x10c7f5160>"
       ]
      }
     ],
     "prompt_number": 5
    }
   ],
   "metadata": {}
  }
 ]
}