path: root/Grob's_Basic_Electronics_by_M._E._Schultz/Chapter27.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter 27 : Diodes and Diodes Applications"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example No. 27_1 Page No.  864"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Forward Resistance at Point A = 59.09 Ohms\n",
      "Approx 59.1 Ohms\n",
      "The Forward Resistance at Point B = 31.11 Ohms\n"
     ]
    }
   ],
   "source": [
    "# For the diode curve, calculate the dc resistance, RF, at points A and B.\n",
    "\n",
    "# Given data\n",
    "\n",
    "Vf1 = 0.65#         # Forward votage 1=0.65 Volts\n",
    "If1 = 11*10**-3      # Forward current 1=11 mAmps\n",
    "Vf2 = 0.7#          # Forward votage 2=0.7 Volts\n",
    "If2 = 22.5*10**-3    # Forward current 2=22.5 mAmps\n",
    "\n",
    "Rf1 = Vf1/If1#\n",
    "print 'The Forward Resistance at Point A = %0.2f Ohms'%Rf1\n",
    "print 'Approx 59.1 Ohms'\n",
    "\n",
    "Rf2 = Vf2/If2#\n",
    "print 'The Forward Resistance at Point B = %0.2f Ohms'%Rf2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example No. 27_2 Page No.  865"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Bulk Resistance = 0.40 Ohms\n"
     ]
    }
   ],
   "source": [
    "# A silicon diode has a forward voltage drop of 1.1 V for a forward diode current, If, of 1 A. Calculate the bulk resistance, Rb.\n",
    "\n",
    "# Given data\n",
    "\n",
    "Vf1 = 1.1#  # Forward votage 1=1.1 Volts\n",
    "If1 = 1.     # Forward current 1=1 Amps\n",
    "Vf2 = 0.7#  # Fwd. vltg. 2=0.7 Volts (min working vltg of diode is 0.7 V)\n",
    "If2 = 0     # Forward current=0 Amps\n",
    "\n",
    "delV = Vf1-Vf2#     # diff. between max. min. Voltages\n",
    "delI = If1-If2#     # diff. between max. min. Currents\n",
    "\n",
    "Rb = delV/delI#\n",
    "print 'The Bulk Resistance = %0.2f Ohms'%Rb"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example No. 27_3  Page No.  868"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Load Voltage of First Approximation = 10.00 Volts(dc)\n",
      "The Load Current of First Approximation = 0.10 Amps\n",
      "i.e 100 mAmps\n",
      "The Load Voltage of Second Approximation = 9.30 Volts\n",
      "The Load Current of Second Approximation = 0.09 Amps\n",
      "i.e 93 mAmps\n",
      "The Load Current of Third Approximation = 0.09 Amps\n",
      "i.e 90.73 mAmps\n",
      "The Load Voltage of Third Approximation 9.07 Volts\n"
     ]
    }
   ],
   "source": [
    "# Solve for the load voltage and current using the first, second, and third diode approximations.\n",
    "\n",
    "# Given data\n",
    "\n",
    "Rl = 100.#       # Load resistance=100 Ohms\n",
    "Rb = 2.5#       # Resistance=2.5 Ohms\n",
    "Vin = 10.#       # Input voltage=10 Volts\n",
    "Vb = 0.7#       # Voltage=0.7 Volts\n",
    "\n",
    "\n",
    "# Using first approximation\n",
    "\n",
    "Vl1 = Vin\n",
    "print 'The Load Voltage of First Approximation = %0.2f Volts(dc)'%Vl1\n",
    "\n",
    "Il1 = Vl1/Rl#\n",
    "print 'The Load Current of First Approximation = %0.2f Amps'%Il1\n",
    "print 'i.e 100 mAmps'\n",
    "\n",
    "# Using second approximation\n",
    "\n",
    "Vl2 = Vin-Vb\n",
    "print 'The Load Voltage of Second Approximation = %0.2f Volts'%Vl2\n",
    "\n",
    "Il2 = Vl2/Rl#\n",
    "print 'The Load Current of Second Approximation = %0.2f Amps'%Il2\n",
    "print 'i.e 93 mAmps'\n",
    "\n",
    "# Using third approximation\n",
    "\n",
    "Il3 = (Vin-Vb)/(Rl+Rb)#\n",
    "print 'The Load Current of Third Approximation = %0.2f Amps'%Il3\n",
    "print 'i.e 90.73 mAmps'\n",
    "\n",
    "Vl3 = Il3*Rl#\n",
    "print 'The Load Voltage of Third Approximation %0.2f Volts'%Vl3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example No. 27_4 Page No.  875"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Secondary Voltage = 40.00 Volts(ac)\n",
      "The DC Voltage = 17.76 Volts\n",
      "The Load Current = 0.18 Amps\n",
      "The DC Diode Current = 0.18 Amps\n",
      "The PIV for Diode-1 = 56.56 Volts\n",
      "The Output Frequency = 60.00 Hertz\n"
     ]
    }
   ],
   "source": [
    "# If the turns ratio Np:Ns is 3:1, calculate the following: Vs, Vdc, Il, Idiode, PIV for D1, and fout.\n",
    "\n",
    "# Given data\n",
    "\n",
    "Vp = 120.#       # Primary voltage=120 Vac\n",
    "A = 3/1.#        # Turns ratio Np:Ns=3:1\n",
    "B = 1/3.#        # Turns ratio Ns:Np=1:3\n",
    "Rl = 100.#       # Load resistance=100 Ohms\n",
    "fi = 60.#        # Input frequency=60\n",
    "\n",
    "Vs = B*Vp#\n",
    "print 'The Secondary Voltage = %0.2f Volts(ac)'%Vs\n",
    "\n",
    "Vspk = (Vs*1.414)#\n",
    "\n",
    "C = Vspk-0.7#\n",
    "\n",
    "Vdc = 0.318*C#\n",
    "print 'The DC Voltage = %0.2f Volts'%Vdc\n",
    "\n",
    "Il = Vdc/Rl#\n",
    "print 'The Load Current = %0.2f Amps'%Il\n",
    "\n",
    "Idiode = Il#\n",
    "print 'The DC Diode Current = %0.2f Amps'%Idiode\n",
    "\n",
    "PIV = Vspk#\n",
    "print 'The PIV for Diode-1 = %0.2f Volts'%PIV\n",
    "\n",
    "fo =fi#\n",
    "print 'The Output Frequency = %0.2f Hertz'%fo"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example No. 27_5 age No.  878"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The DC Voltage = 17.54 Volts\n",
      "The Load Current = 0.18 Amps\n",
      "i.e 175.4 mAmps\n",
      "The DC Diode Current = 0.09 Amps\n",
      "i.e 87.7 mAmps\n",
      "The PIV for Diode-1 = 55.86 Volts\n",
      "The Output Frequency = 120.00 Hertz\n"
     ]
    }
   ],
   "source": [
    "# If the turns ratio Np:Ns is\u0006 3:1, calculate the following: Vdc, Il, Idiode, PIV for D1, and fout.\n",
    "\n",
    "# Given data\n",
    "\n",
    "Vp = 120.       # Primary voltage=120 Vac\n",
    "A = 3/1.        # Turns ratio Np:Ns = 3:1\n",
    "B = 1/3.        # Turns ratio Ns:Np = 1:3\n",
    "Rl = 100.       # Load resistance=100 Ohms\n",
    "\n",
    "Vs = B*Vp#\n",
    "Vspk = 1.414*(Vs/2)#\n",
    "Vopk = Vspk-0.7#\n",
    "\n",
    "Vdc = 0.636*Vopk#\n",
    "print 'The DC Voltage = %0.2f Volts'%Vdc\n",
    "\n",
    "Il = Vdc/Rl#\n",
    "print 'The Load Current = %0.2f Amps'%Il\n",
    "print 'i.e 175.4 mAmps'\n",
    "\n",
    "Idiode = Il/2#\n",
    "print 'The DC Diode Current = %0.2f Amps'%Idiode\n",
    "print 'i.e 87.7 mAmps'\n",
    "\n",
    "C = (Vspk*2)-0.7#\n",
    "\n",
    "PIV = C#\n",
    "print 'The PIV for Diode-1 = %0.2f Volts'%PIV\n",
    "\n",
    "f =120#\n",
    "print 'The Output Frequency = %0.2f Hertz'%f"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example No. 27_6 Page No.  880"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The DC Voltage = 35.08 Volts\n",
      "The Load Current = 0.35 Amps\n",
      "i.e 350.8 mAmps\n",
      "The DC Diode Current = 0.1754 Amps\n",
      "i.e 175.4 mAmps\n",
      "The PIV for each Diode = 55.86 Volts\n",
      "The Output Frequency = 120.00 Hertz\n"
     ]
    }
   ],
   "source": [
    "# If the turns ratio Np:Ns is\u0006 3:1, calculate the following: Vdc, Il, Idiode, PIV for each diode, and fout.\n",
    "\n",
    "# Given data\n",
    "\n",
    "Vp = 120.#       # Primary voltage=120 Vac\n",
    "A = 3./1#        # Turns ratio Np:Ns = 3:1\n",
    "B = 1./3#        # Turns ratio Ns:Np = 1:3\n",
    "Rl = 100.#       # Load resistance=100 Ohms\n",
    "\n",
    "Vs = B*Vp#\n",
    "Vspk = 1.414*(Vs)#\n",
    "Vopk = Vspk-1.4#\n",
    "\n",
    "Vdc = 0.636*Vopk#\n",
    "print 'The DC Voltage = %0.2f Volts'%Vdc\n",
    "\n",
    "Il = Vdc/Rl#\n",
    "print 'The Load Current = %0.2f Amps'%Il\n",
    "print 'i.e 350.8 mAmps'\n",
    "\n",
    "Idiode = Il/2#\n",
    "print 'The DC Diode Current = %0.4f Amps'%Idiode\n",
    "print 'i.e 175.4 mAmps'\n",
    "\n",
    "C = Vspk-0.7#\n",
    "\n",
    "PIV = C#\n",
    "print 'The PIV for each Diode = %0.2f Volts'%PIV\n",
    "\n",
    "f =120#\n",
    "print 'The Output Frequency = %0.2f Hertz'%f"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example No. 27_7 Page No.  883"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Ripple Voltage for Turns Ratio Np:Ns=4:1 = 5.21 Volts(p-p)\n",
      "Approx 5.21 Volts(p-p)\n",
      "The DC Voltage for Turns Ratio Np:Ns=4:1 = 39.12 Volts\n",
      "Approx 39.12 Volts\n",
      "The Ripple Voltage for Turns Ratio Np:Ns=2:1 = 2.69 Volts(p-p)\n",
      "Approx 2.69 Volts(p-p)\n",
      "The DC Voltage for Turns Ratio Np:Ns=2:1 = 40.38 Volts\n",
      "Approx 40.38 Volts\n"
     ]
    }
   ],
   "source": [
    "from math import exp\n",
    "# Assume the transformer turns ratio Np:Ns = 4:1 in Fig. 27–21 a and 2:1 in Fig. 27–22a. Compare Vripple and Vdc if C =\u0006 500 uF and Rl =\u0006 250\u0007.\n",
    "    \n",
    "# Given data\n",
    "\n",
    "A1 = 4./1#           # Turns ratio Np:Ns=4:1\n",
    "B1 = 1./4#           # Turns ratio Ns:Np=1:4\n",
    "A2 = 2./1#           # Turns ratio Np:Ns=2:1\n",
    "B2 = 1./2#           # Turns ratio Ns:Np=1:2\n",
    "Vp = 120.#           # Primary voltage=120 Vac\n",
    "Vb = 0.7#           # \n",
    "t1 = 16.67*10**-3#   # Charging Time of Capacitor of Turns ratio Np:Ns=4:1=16.67 mSec\n",
    "t2 = 8.33*10**-3#    # Charging Time of Capacitor of Turns ratio Np:Ns=4:1=8.33 mSec\n",
    "Rl = 250.#           # Load resistance=250 Ohms\n",
    "C = 500.*10**-6#      # Capacitor=500 uFarad\n",
    "\n",
    "# Calculations for Turns Ratio Np:Ns=4:1\n",
    "\n",
    "Vs1 = B1*Vp#\n",
    "Vspk1 = Vs1*1.414#\n",
    "Vopk1 = Vspk1 - Vb#\n",
    "D = -t1/(Rl*C)#\n",
    "\n",
    "Vrp1 = Vopk1*(1-exp(D))#\n",
    "print 'The Ripple Voltage for Turns Ratio Np:Ns=4:1 = %0.2f Volts(p-p)'%Vrp1\n",
    "print 'Approx 5.21 Volts(p-p)'\n",
    "\n",
    "Vdc1 = Vopk1-(Vrp1/2)#\n",
    "print 'The DC Voltage for Turns Ratio Np:Ns=4:1 = %0.2f Volts'%Vdc1\n",
    "print 'Approx 39.12 Volts'\n",
    "\n",
    "# Calculations for Turns Ratio Np:Ns = 2:1\n",
    "\n",
    "Vs2 = B2*Vp#\n",
    "V2 = Vs2/2#\n",
    "V2pk2 = V2*1.414\n",
    "Vopk2 = V2pk2 - Vb#\n",
    "E = -t2/(Rl*C)#\n",
    "\n",
    "Vrp2 = Vopk2*(1-(exp(E)))\n",
    "print 'The Ripple Voltage for Turns Ratio Np:Ns=2:1 = %0.2f Volts(p-p)'%Vrp2\n",
    "print 'Approx 2.69 Volts(p-p)'\n",
    "\n",
    "Vdc2 = Vopk2-(Vrp2/2)#\n",
    "print 'The DC Voltage for Turns Ratio Np:Ns=2:1 = %0.2f Volts'%Vdc2\n",
    "print 'Approx 40.38 Volts'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example No. 27_8 Page No.  885"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The LED Current = 0.01 Amps\n",
      "i.e 10 mAmps\n"
     ]
    }
   ],
   "source": [
    "#  Calculate the LED current.\n",
    "\n",
    "# Given data\n",
    "\n",
    "Vin = 24.#       # Input voltage=24 Volts\n",
    "Vled = 2.#       # Voltage drop at LED=2 Volts\n",
    "Rs = 2.2*10**3#  # Source Resistance=2.2 kOhms\n",
    "\n",
    "Iled = (Vin-Vled)/Rs#\n",
    "print 'The LED Current = %0.2f Amps'%Iled\n",
    "print 'i.e 10 mAmps'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example No. 27_9 Page No.  888"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Resistance Rs, Required to Provide an LED Current of 25 mA = 880.00 Ohms\n"
     ]
    }
   ],
   "source": [
    "# Calculate the resistance Rs, required to provide an LED current of 25 mA.\n",
    "\n",
    "# Given data\n",
    "\n",
    "Vin = 24.#           # Input voltage=24 Volts\n",
    "Vled = 2.#           # Voltage drop at LED=2 Volts\n",
    "Iled = 25.*10**-3#    # LED Current=25 mAmps\n",
    "\n",
    "Rs = (Vin-Vled)/Iled#\n",
    "print 'The Resistance Rs, Required to Provide an LED Current of 25 mA = %0.2f Ohms'%Rs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example No. 27_10 Page No.  889"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Maximum Rated Current of Zener = 0.10 Amps\n",
      "i.e 100 mAmps\n"
     ]
    }
   ],
   "source": [
    "# Calculate the maximum rated zener current for a 1 W, 10 V zener.\n",
    "\n",
    "# Given data\n",
    "\n",
    "Pzm = 1.#        # Power rating of zener= 1 Watts\n",
    "Vz = 10.#        # Voltage rating of zener= 10 Volts\n",
    "\n",
    "Izm = Pzm/Vz#\n",
    "print 'The Maximum Rated Current of Zener = %0.2f Amps'%Izm\n",
    "print 'i.e 100 mAmps'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example No. 27_11 Page No.  890"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Zener Current = 0.01 Amps\n",
      "i.e 15 mAmps\n"
     ]
    }
   ],
   "source": [
    "# If Vz=10 V, calculate Iz.\n",
    "\n",
    "# Given data\n",
    "\n",
    "Vin = 25.#       # Input voltage=25 Volts\n",
    "Vz = 10.#        # Zener voltage=10 Volts\n",
    "Rs = 1.*10**3#    # Source Resistance=1 kOhms\n",
    "\n",
    "Iz = (Vin-Vz)/Rs#\n",
    "print 'The Zener Current = %0.2f Amps'%Iz\n",
    "print 'i.e 15 mAmps'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example No. 27_12 Page No.  891"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Source Current = 0.075 Amps\n",
      "i.e 75 mAmps\n",
      "The Load Current = 0.03 Amps\n",
      "i.e 30 mAmps\n",
      "The Zener Current = 0.045 Amps\n",
      "i.e 45 mAmps\n",
      "The Power Dissipation of Zener = 0.3375 Watts\n",
      "i.e 337.5 mWatts\n"
     ]
    }
   ],
   "source": [
    "# If R L increases to 250 Ohms, calculate the following: Is, Il, Iz, and Pz.\n",
    "\n",
    "# Given data\n",
    "\n",
    "Vin = 25#       # Input voltage=25 Volts\n",
    "Vz = 7.5#        # Zener voltage=7.5 Volts\n",
    "Rl = 250#    # Load Resistance=250 Ohms\n",
    "Is = 75*10**-3#  # Source current=75 mAmps\n",
    "\n",
    "print 'The Source Current = %0.3f Amps'%Is\n",
    "print 'i.e 75 mAmps'\n",
    "\n",
    "Il = Vz/Rl#\n",
    "print 'The Load Current = %0.2f Amps'%Il\n",
    "print 'i.e 30 mAmps'\n",
    "\n",
    "Iz = Is-Il#\n",
    "print 'The Zener Current = %0.3f Amps'%Iz\n",
    "print 'i.e 45 mAmps'\n",
    "\n",
    "Pz = Vz*Iz#\n",
    "print 'The Power Dissipation of Zener = %0.4f Watts'%Pz\n",
    "print 'i.e 337.5 mWatts'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example No. 27_13 Page No.  892"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Source Current = 0.06 Amps.\n",
      "i.e 60 mAmps\n",
      "The Load Current for 200 ohms Load = 0.05 Amps.\n",
      "i.e 50 mAmps\n",
      "The Zener Current for 200 ohms Load = 0.01 Amps.\n",
      "i.e 10 mAmps\n",
      "The Load Current for 500 ohms Load = 0.02 Amps.\n",
      "i.e 20 mAmps\n",
      "The Zener Current for 500 ohms load = 0.04 Amps.\n",
      "i.e 40 mAmps\n"
     ]
    }
   ],
   "source": [
    "# Calculate Is, Il and Iz for (a)Rl=200 ohms# (b)Rl=500 ohms.\n",
    "\n",
    "# Given data\n",
    "\n",
    "Vin = 16.#       # Vin=16 Volts given\n",
    "Vz = 10.#        # Vz=10 Volts given\n",
    "Rs = 100.#       # Source Resistance = 100 ohms given\n",
    "Rla = 200.#      # Load Resistance A = 200 ohms given\n",
    "Rlb = 500.#      #Load Resistance B = 500 ohms given\n",
    "\n",
    "# For Rl 200 ohms\n",
    "\n",
    "Is = (Vin-Vz)/Rs#\n",
    "print 'The Source Current = %0.2f Amps.'%Is\n",
    "print 'i.e 60 mAmps'\n",
    "\n",
    "Ila = Vz/Rla#\n",
    "print 'The Load Current for 200 ohms Load = %0.2f Amps.'%Ila\n",
    "print 'i.e 50 mAmps'\n",
    "\n",
    "Iza = Is-Ila\n",
    "print 'The Zener Current for 200 ohms Load = %0.2f Amps.'%Iza\n",
    "print 'i.e 10 mAmps'\n",
    "\n",
    "# For Rl 500 ohms\n",
    "\n",
    "Ilb = Vz/Rlb#\n",
    "print 'The Load Current for 500 ohms Load = %0.2f Amps.'%Ilb\n",
    "print 'i.e 20 mAmps'\n",
    "\n",
    "Izb = Is-Ilb\n",
    "print 'The Zener Current for 500 ohms load = %0.2f Amps.'%Izb\n",
    "print 'i.e 40 mAmps'"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}