{
 "metadata": {
  "name": "",
  "signature": "sha256:db1129af4b6edac97bc68145183b0a38a23673506c4e39ac725040265d12dfa4"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 7 : Waveforms and Signals"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.1  Page No : 98"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline\n",
      "\n",
      "import math \n",
      "from numpy import cos,sin,arange\n",
      "from matplotlib.pyplot import plot,suptitle,xlabel,ylabel\n",
      "#Example 7.1\")\n",
      "\n",
      "t1 = arange(-5,8+0.5,0.5)\n",
      "v1 = cos (t1)\n",
      "\n",
      "\n",
      "# Calculation and Results\n",
      "plot(t1,v1)\n",
      "suptitle ('v1 vs t1')\n",
      "xlabel('t1')\n",
      "ylabel('v1 ');\n",
      "#From the graph\n",
      "print \"Time period1 =  %3.3fs Frequency 1 = %0.3fHz\"%(6.2832,0.159)\n",
      "\n",
      "t2 = arange(-4,10+0.5,0.5)\n",
      "v2 = sin (t2)\n",
      "\n",
      "plot(t2,v2)\n",
      "suptitle ('v2 vs t2')\n",
      "xlabel('t2')\n",
      "ylabel('v2 ');\n",
      "#From the graph\n",
      "print \"Time period 2 =  %3.3fs Frequency 2 = %0.3fHz\"%(6.2832,0.159)\n",
      "\n",
      "t3 = arange(-1,1.5+0.05,0.05)\n",
      "v3 = 2* cos (2*math.pi*t3)\n",
      "\n",
      "plot(t3,v3)\n",
      "suptitle ('v3 vs t3')\n",
      "xlabel('t3')\n",
      "ylabel('v3 ');\n",
      "#From the graph\n",
      "print \"Time period 3 =  %ds Frequency 3 = %dHz\"%(1,1)\n",
      "\n",
      "t4 = arange(-5,12+0.5,0.5)\n",
      "v4 = 2*cos (math.pi*t4/4-math.pi/4)\n",
      "plot(t4,v4)\n",
      "suptitle ('v4 vs t4')\n",
      "xlabel('t4')\n",
      "ylabel('v4 ');\n",
      "#From the graph\n",
      "print \"Time period 4 =  %ds Frequency 4 = %0.3fHz\"%(8,0.125)\n",
      "\n",
      "t5 = arange(-1,1+0.005,0.005)\n",
      "v5 = 5*cos (10*t5+math.pi/3)\n",
      "\n",
      "plot(t5,v5)\n",
      "suptitle ('v5 vs t5')\n",
      "xlabel('t5')\n",
      "ylabel('v5 ');\n",
      "\n",
      "#From the graph\n",
      "print \"Time period 5 =  %0.3fs Frequency 5 = %3.2fHz\"%(.62832,1.59)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Time period1 =  6.283s Frequency 1 = 0.159Hz\n",
        "Time period 2 =  6.283s Frequency 2 = 0.159Hz\n",
        "Time period 3 =  1s Frequency 3 = 1Hz\n",
        "Time period 4 =  8s Frequency 4 = 0.125Hz\n",
        "Time period 5 =  0.628s Frequency 5 = 1.59Hz\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAYIAAAEhCAYAAABycqfJAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x105d91d90>"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.2  Page No : 102"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline\n",
      "\n",
      "import math \n",
      "from numpy import cos,arange\n",
      "from matplotlib.pyplot import plot,suptitle,xlabel,ylabel\n",
      "\n",
      "#Example 7.2\")\n",
      "\n",
      "# Input\n",
      "#Let wt = q\n",
      "q = arange(-8,8+0.5,0.5)\n",
      "\n",
      "# Calculation\n",
      "v = 5*cos (q)\n",
      "\n",
      "# Results\n",
      "plot(q,v)\n",
      "suptitle ('v vs wt')\n",
      "xlabel('wt')\n",
      "ylabel('v ');"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAX8AAAEhCAYAAACXwKDgAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRERERERERERERERERESkZv8H2P2XItlbZAwAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x105dac210>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.3  Page No : 106"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline\n",
      "\n",
      "import math \n",
      "from numpy import cos,arange\n",
      "from matplotlib.pyplot import plot,suptitle,xlabel,ylabel\n",
      "\n",
      "#Example 7.3\")\n",
      "\n",
      "# Input\n",
      "t1 = arange(-10,10+0.05,0.05)\n",
      "\n",
      "# Calculation\n",
      "v = 5*cos (math.pi*t1/6+math.pi/6)\n",
      "\n",
      "# Results\n",
      "plot(t1,v)\n",
      "suptitle ('v vs math.pi*t/6')\n",
      "xlabel('math.pi*t/6')\n",
      "ylabel('v ');\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAYIAAAEhCAYAAABycqfJAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\niIiIiIiIiIiIiIhIuvwfVVxwOOdIS2MAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1056b2ed0>"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.5  Page No : 108"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "#Example 7.5\")\n",
      "\n",
      "# Given\n",
      "#v(t) = math.cos5t+3math.sin(3t+45)\")\n",
      "#Finding the periods of individual terms\n",
      "#Period of math.cos5t = 2*math.pi/5\")\n",
      "#Period of 3*math.sin(3t+45) = 2*math.pi/3\")\n",
      "#If T = 2*math.pi\n",
      "T = 2*math.pi;\n",
      "#Now T = 5*T1 = 3*T2\")\n",
      "#Now the relation for T is the smallest common integral multiple of T1 and T2\n",
      "print \"Period  =  %3.2fs\"%(T)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Period  =  6.28s\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.13  Page No : 111"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "from scipy.integrate import quad \n",
      "#Example 7.13\")\n",
      "\n",
      "# Given\n",
      "#capacitance is 1uF\")\n",
      "C = 1*10**-6;\n",
      "#a)\")\n",
      "#Let k = 1 which results in t = 5ms\n",
      "t = 5*10**-3;\n",
      "\n",
      "def f2(t): \n",
      "\t return .004\n",
      "\n",
      "vac =  quad(f2,0,0.003)[0]\n",
      "\n",
      "print \"vac = %dV\"%(vac);\n",
      "\n",
      "#In general\n",
      "#At t = 5k voltage follows as v = 8k ms\")\n",
      "\n",
      "#b)\")\n",
      "#As vdc = 1/C*integrate(Idc*dt)\n",
      "#On solving for Idc\n",
      "vdc = vac\n",
      "\n",
      "def f3(t): \n",
      "\t return 1./vac\n",
      "\n",
      "Idc = (1/( quad(f3,0,0.005)[0]/C))\n",
      "\n",
      "print \"Idc = %3.2fmA\"%(Idc);\n",
      "#Idc is equal to <i(t)> in the period of 5ms\")\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "vac = 0V\n",
        "Idc = 0.00mA\n"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.17  Page No : 112"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "#Example 7.17\")\n",
      "\n",
      "# Given\n",
      "#capacitance is 100nF\")\n",
      "#The voltage across capacitor increases linearly from 0 to 10V\")\n",
      "C = 100*10**-9;\n",
      "#From figure 7.10(a)\n",
      "#a)\")\n",
      "#At t = T voltage across capacitor  = 10V\n",
      "vc = 10;\n",
      "Q = C*vc;\n",
      "print \"Charge across capacitor is %fC\"%(Q)\n",
      "#b)\")\n",
      "#The waveform shown in fig 7.10(a) can be written as\n",
      "#0                 t<0\")\n",
      "#I0 = 10**-6/T        0<t<T\")\n",
      "#0                 t>T\")\n",
      "\n",
      "\n",
      "#For T = 1s;\n",
      "T = 1.;\n",
      "I0 = 10**-6/T;\n",
      "print \"I01s) = %fA\"%(I0);\n",
      "\n",
      "#For T = 1ms;\n",
      "T = 1.*10**-3;\n",
      "I0 = 10**-6/T;\n",
      "print \"I01ms) = %0.3fA\"%(I0);\n",
      "\n",
      "#For T = 1us;\n",
      "T = 1.*10**-6;\n",
      "I0 = 10**-6/T;\n",
      "print \"I01us) = %dA\"%(I0);\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Charge across capacitor is 0.000001C\n",
        "I01s) = 0.000001A\n",
        "I01ms) = 0.001A\n",
        "I01us) = 1A\n"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.22  Page No : 117"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline\n",
      "\n",
      "import math \n",
      "from numpy import cos,arange,exp\n",
      "from matplotlib.pyplot import plot,suptitle,xlabel,ylabel\n",
      "\n",
      "#Example 7.22\")\n",
      "\n",
      "#The general equation of exponential decay function is given by\n",
      "#v(t) = A*e(-t/T)+B\")\n",
      "#We need to solve A and B\n",
      "#At t = 0 we get v(0) = A+B    (1)\n",
      "#at t = inf we get B = 1       (2)\n",
      "#Solving (1) and (2)\n",
      "A = 4;\n",
      "B = 1;\n",
      "T = 3;\n",
      "t = arange(0,10+0.05,0.05)\n",
      "v = 4*exp(-t/T)+1;\n",
      "\n",
      "# Results\n",
      "plot(t,v)\n",
      "suptitle ('v vs t')\n",
      "xlabel('t')\n",
      "ylabel('v');\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAYQAAAEhCAYAAAB/bNeOAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x105d11b90>"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.23  Page No : 120"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline\n",
      "\n",
      "import math \n",
      "from numpy import cos,arange,exp\n",
      "from matplotlib.pyplot import plot,suptitle,xlabel,ylabel\n",
      "\n",
      "#Example 7.23\")\n",
      "\n",
      "#Sketch voltage 'v'\n",
      "t = arange(-.001,0.00005,0.00005)\n",
      "t1 = arange(0,0.001+0.00005,0.00005)\n",
      "T = 1.*10**-3;\n",
      "V0 = 10.;\n",
      "v = V0*exp(t/T)\n",
      "v1 = V0*exp(-t1/T)\n",
      "\n",
      "# Results\n",
      "plot(t,v)\n",
      "plot(t1,v1)\n",
      "suptitle ('v vs t')\n",
      "xlabel('t (ms)')\n",
      "ylabel('v ');\n",
      "\n",
      "#Sketch current 'i'\n",
      "t = arange(-.001,0.00005,0.00005)\n",
      "t1 = arange(0,0.001+0.00005,0.00005)\n",
      "T = 1.*10**-3;\n",
      "I0 = 10.*10**-3;\n",
      "i = I0*exp(t/T)\n",
      "i1 = -I0*exp(-t1/T)\n",
      "\n",
      "plot(t,i)\n",
      "plot(t1,i1)\n",
      "suptitle ('i vs wt')\n",
      "xlabel('t (ms)')\n",
      "ylabel('i (mA)');\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAY0AAAEhCAYAAACDefxEAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nIiIiIiIiIiIiIiIiIiIiIiIiIhLG/h85Fy3n/7j3egAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x105d916d0>"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.25  Page No : 124"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "#Example 7.25\")\n",
      "\n",
      "Xavg = (2+4+11+5+7+6+9+10+3+6+8+4+1+3+5+12)/16.;\n",
      "#Let X = X**2eff\n",
      "X = (2**2+4**2+11**2+5**2+7**2+6**2+9**2+10**2+3**2+6**2+8**2+4**2+1**2+3**2+5**2+12**2)/16.\n",
      "Xeff = math.sqrt(X);\n",
      "\n",
      "# Results\n",
      "print \"Xavg = %d Xeff = %3.2f\"%(Xavg,Xeff)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Xavg = 6 Xeff = 6.78\n"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.26  Page No : 126"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "# Given\n",
      "#Period  = 10s\")\n",
      "#Interval is 1ms\")\n",
      "#Voltage of binary signal is either 0.5 or -0.5\")\n",
      "T = 10;\n",
      "#During 10s period there are 10000 intervals of 1ms each\n",
      "#For calculating average equal number of intervals are considered at 0.5V and -0.5V\n",
      "vavg = (0.5*5000-0.5*5000)/10000.\n",
      "#The effective value of v(t) is\n",
      "#Let V = V**2eff\n",
      "V = (0.5**2*5000+(-0.5)**2*5000)/10000.\n",
      "\n",
      "# Calculation\n",
      "Veff = math.sqrt(V)\n",
      "\n",
      "# Results\n",
      "print \"vavg = %dV Veff = %3.2fV\"%(vavg,Veff)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "vavg = 0V Veff = 0.50V\n"
       ]
      }
     ],
     "prompt_number": 19
    }
   ],
   "metadata": {}
  }
 ]
}