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   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter-5 : General Applications Of Op-Amps"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 5.1 - Page 156"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from numpy import pi\n",
      "import math\n",
      "# Given data\n",
      "fo= 15 # in kHz\n",
      "fo= fo*10**3 # in Hz\n",
      "C=0.01 # in micro F\n",
      "C=C*10**-6 # in F\n",
      "L= 1/(4*pi**2*fo**2*C) # in H\n",
      "L=math.ceil(L*10**3) # in mH\n",
      "# Let L be of 12 mH and internal resistance 30 ohm\n",
      "R=30 # internal resistance in ohm\n",
      "XL= 2*pi*L*10**-3*fo \n",
      "Q= XL/R \n",
      "R_P= Q**2*R # in ohm\n",
      "# If\n",
      "R1=100 # in ohm\n",
      "# Formula L= R_f*R_P/(R1*(R_f+R_P)) \n",
      "R_f= R1*L*R_P/(R_P-R1*L) # in ohm\n",
      "R_f=R_f*10**3 # in kohm\n",
      "R_f= 1.2 # in k ohm (Standard value)\n",
      "print \"The values of component chosen are:-\" \n",
      "print \"Value of L   = %0.f mH\" %L\n",
      "print \"Value of C   = %0.2f micro F\" %(C*10**6)\n",
      "print \"Value of R_f = %0.1f k ohm\" %R_f\n",
      "print \"Value of R1  = %0.f ohm\" %R1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The values of component chosen are:-\n",
        "Value of L   = 12 mH\n",
        "Value of C   = 0.01 micro F\n",
        "Value of R_f = 1.2 k ohm\n",
        "Value of R1  = 100 ohm\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 5.2 - Page 159"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "# Given data\n",
      "Rf= 12 # in k ohm\n",
      "Rs1= 12 # in k ohm\n",
      "Rs2= 2 # in k ohm\n",
      "Rs3= 3 # in k ohm\n",
      "Vi1= 9 # in volt\n",
      "Vi2= -3 # in volt\n",
      "Vi3= -1 # in volt\n",
      "Vout= -Rf*(Vi1/Rs1+Vi2/Rs2+Vi3/Rs3) # in volt\n",
      "print \"Output voltage = %0.f volt\" %Vout"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Output voltage = 13 volt\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 5.3 - Page NO 159"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Given expression Vout= -2*V1+3*V2+4*V3\n",
      "# For an operational amplifier\n",
      "# Vout= -Rf*[V1/R1+V2/R2+V3/R3]\n",
      "# Compare the above expression with the given expression for the output\n",
      "r_1=2 # value of Rf/R1\n",
      "r_2=3 # value of Rf/R2\n",
      "r_3=4 # value of Rf/R3\n",
      "# Resistance R3 will be minimum value of 10 k ohm\n",
      "R3=10 # in k ohm\n",
      "Rf= r_3*R3 # in k ohm\n",
      "R2= Rf/r_2 # in k ohm\n",
      "R1= Rf/r_1 # in k ohm\n",
      "print \"Value of Rf = %0.f k ohm\" %Rf\n",
      "print \"Value of R2 = %0.2f k ohm\" %R2\n",
      "print \"Value of R1 = %0.f k ohm\" %R1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Value of Rf = 40 k ohm\n",
        "Value of R2 = 13.33 k ohm\n",
        "Value of R1 = 20 k ohm\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example : 5.4 - Page No 159\n",
      "    "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Given data\n",
      "V1= 2 # in volt\n",
      "V2= -1 # in volt\n",
      "# Let R1= (R||R)/(R+(R||R))= (R/2)/(R+R/2) = 1/3\n",
      "R1=1/3 \n",
      "Vs1= V1*R1 # in volt\n",
      "# Let R2= (1+Rf/R)= (1+2*R/R)= 3\n",
      "R2= 3 \n",
      "Vo_desh= Vs1*R2 # in volt\n",
      "Vs2= V2*R1 # in volt\n",
      "Vo_doubleDesh= Vs2*R2 # in volt\n",
      "V_out= Vo_desh+Vo_doubleDesh # in volt\n",
      "print \"Output voltage = %0.f volt\" %V_out"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Output voltage = 1 volt\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example : 5.5 - Page No 160\n",
      "    "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Given expression Vout= 10*(V2-V1)\n",
      "# For a differential amplifier circuit\n",
      "# Vout= Rf/R*(V2-V1)\n",
      "# Compare the above expression with the given expression for the output, we have\n",
      "RfbyR= 10 \n",
      "R=10 # minimum value of resistancce to be used in kohm\n",
      "Rf= RfbyR * R # in k ohm\n",
      "print \"Value of Rf = %0.f k ohm\" %Rf"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Value of Rf = 100 k ohm\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example : 5.7 - Page No 164\n",
      "    "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "# Given data\n",
      "R1= 50 # in kohm\n",
      "# Let us choose\n",
      "R3= 15 # in k ohm\n",
      "R4= R3 \n",
      "# Ad= 1+2*R2/R1             (i)\n",
      "# Ad= ((1+2*R2/R1)*(V2-V1))/(V2-V1)= 1+2*R2/R1\n",
      "# For minimum differential voltage gain\n",
      "Ad_min=5 \n",
      "Ad= Ad_min \n",
      "R1_max= R1 # since Ad will be minimum only when R1 will be maximum\n",
      "# Putting values of Ad and R1 in eq(i)\n",
      "R2= (Ad-1)*R1/2 # in k ohm\n",
      "# For maximum differential voltage gain\n",
      "Ad_max=200 \n",
      "Ad= Ad_min \n",
      "# Putting values of Ad and R2 in eq(i)\n",
      "R1= 2*R2/(Ad_max-1) # in k ohm\n",
      "R1=int(R1)\n",
      "# For maximum value of Ad, R1 will have minimum value , therefore\n",
      "R1_min= 1 # in kohm\n",
      "print \"Value of R1_min = %0.f k ohm\" %R1_min\n",
      "print \"Value of R1     = %0.f-50 k ohm potentiometer\" %R1\n",
      "print \"Value of R2     = %0.f k ohm\" %R2\n",
      "print \"Value of R3     = %0.f k ohm\" %R3\n",
      "print \"Value of R4     = %0.f k ohm\" %R4"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Value of R1_min = 1 k ohm\n",
        "Value of R1     = 1-50 k ohm potentiometer\n",
        "Value of R2     = 100 k ohm\n",
        "Value of R3     = 15 k ohm\n",
        "Value of R4     = 15 k ohm\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example : 5.10 - Page No 179\n",
      "    "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Given data\n",
      "Vin= 10 # in volt\n",
      "R=2.2 # in k ohm\n",
      "R=R*10**3 #in ohm\n",
      "Ad=10**5 # voltage gain\n",
      "T= 1 # in ms\n",
      "T=T*10**-3 # in second\n",
      "C=1 # in micro F\n",
      "C=C*10**-6 # in F\n",
      "I= Vin/R # in volt\n",
      "V= I*T/C # in V\n",
      "print \"The output voltage at the end of the pulse = %0.3f volt\" %V\n",
      "RC_desh= R*C*Ad \n",
      "print \"The closed-loop time constant = %0.f second \" %RC_desh"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The output voltage at the end of the pulse = 4.545 volt\n",
        "The closed-loop time constant = 220 second \n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example : 5.11 - Page No 180\n",
      "    "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Given data\n",
      "C=0.01 # in micro F\n",
      "C=C*10**-6 # in F\n",
      "omega= 10000 # in  rad/second\n",
      "# Vout/V1= (Rf/R1)/(1+s*C*Rf)\n",
      "# substituting s= j*omega we have\n",
      "# Vout/V1 = (Rf/R1)/sqrt((omega*C*Rf)**2+1)\n",
      "# At omega=0\n",
      "# Vout/V1= Rf/R1\n",
      "# Formula omega= 1/(C*Rf)\n",
      "Rf= 1/(C*omega) # in ohm\n",
      "Rf= Rf*10**-3 # in k ohm\n",
      "# 20*log10(Rf/R1) = 20\n",
      "R1= Rf/10 # in k ohm\n",
      "print \"Value of Rf = %0.f k ohm\" %Rf\n",
      "print \"Value of R1 = %0.f k ohm\" %R1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Value of Rf = 10 k ohm\n",
        "Value of R1 = 1 k ohm\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example : 5.12 Page No 180\n",
      "    "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline\n",
      "import matplotlib.pyplot as plt\n",
      "import numpy as np\n",
      "#Given Data : \n",
      "R=40*1000 #in ohm(assumed)\n",
      "C=0.2*10**-6 #IN FARAD\n",
      "Vout=3 #in Volt\n",
      "V1=Vout #in Volt\n",
      "V2=Vout #in Volt\n",
      "plt.plot([0,50],[3,-9.5]) \n",
      "plt.title('Output voltage')\n",
      "plt.xlabel('Time in milliseconds')\n",
      "plt.ylabel('Output voltage in volts')\n",
      "plt.axis([0, 60, -12, 5])\n",
      "plt.show()\n",
      "print \"Assuming Ideal op-amp, sketch for Vout is shown in figure.\" \n",
      "\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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J9PT0Bo/pEpNE49y+DXz4IbBnD7BsGTB3rrqim4jMkyxLhVtaWiIrK0t6fenSJVhaarwp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\nYpIgIiKNmCSIiEgjJgkiItLo/wEJUlJyDeG+CgAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f28015d6c10>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Assuming Ideal op-amp, sketch for Vout is shown in figure.\n"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example : 5.13 - Page No 185"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sympy import symbols, simplify, sin\n",
      "t = symbols('t')\n",
      "# Given data\n",
      "R= 50*10**3 # in ohm\n",
      "C= 2*10**-6 # in F\n",
      "CR= C*R #scale factor\n",
      "# Vout= -CR*dvc/dt= -CR*d/dt(10*sin(4000*pi*t))\n",
      "print \"Output voltage : 12.56*cos(4000*pi*t) mV\"\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Output voltage : 12.56*cos(4000*pi*t) mV\n"
       ]
      }
     ],
     "prompt_number": 35
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example : 5.14 - Page No 185\n",
      "    "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "%matplotlib inline\n",
      "from sympy import symbols, simplify, sin\n",
      "import matplotlib.pyplot as plt\n",
      "import numpy as np\n",
      "# Given data\n",
      "fa= 1 # in kHz\n",
      "fa=fa*10**3 # in Hz\n",
      "Vp=1.5 # in volt\n",
      "f= 200 # in Hz\n",
      "C=0.1 # in micro F\n",
      "C=C*10**-6 # in F\n",
      "R= 1/(2*np.pi*fa*C) # in ohm\n",
      "R=R*10**-3 # in k ohm\n",
      "R=np.floor(R*10)/10 # in k ohm\n",
      "fb= 20*fa # in Hz\n",
      "R_desh= 1/(2*np.pi*fb*C) # in ohm\n",
      "# Let\n",
      "R_desh= 82 # in ohm\n",
      "R_OM= R # in k ohm\n",
      "print \"Value of R_OM = %0.1f k ohm\" %R_OM\n",
      "CR= C*R \n",
      "# Vin= Vp*sin(omega*t)= 1.5*sin(400*t)\n",
      "# v_out= -CR*diff(v_in) = -0.2827 Cos(400*pi*t)# in micro volt\n",
      "print \"Output Voltage = -0.2827 Cos(400*pi*t)\" \n",
      "t = np.arange(0, .015, 1.0/44100)\n",
      "v_out=-0.2827*np.sin(400*np.pi*t+np.pi/2)# in micro volt\n",
      "plt.plot(t,v_out) \n",
      "plt.title('Output Voltage Waveform')\n",
      "plt.xlabel('Time in ms')\n",
      "plt.ylabel('Vout in Volts') \n",
      "print \"Output Voltage waveform is shown in figure.\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Value of R_OM = 1.5 k ohm\n",
        "Output Voltage = -0.2827 Cos(400*pi*t)\n",
        "Output Voltage waveform is shown in figure."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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QnZ0tSo7FKDV/YkDrD8Pdu8CFC7zBUiKtWgEFBdpeL6TU/ImBDh1o4oS5COsT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\ngQyFIAiCkIT/D1aoyBiLHf2sAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f27e66ccf90>"
       ]
      }
     ],
     "prompt_number": 36
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example : 5.15 - Page No 186\n",
      "    "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "%matplotlib inline\n",
      "from sympy import symbols, simplify, sin\n",
      "import matplotlib.pyplot as plt\n",
      "import numpy as np\n",
      "from math import sin\n",
      "t = symbols('t')\n",
      "# Given data\n",
      "Vp= 1 # in volts\n",
      "f= 1000 # in Hz\n",
      "R= 1.5*10**3 # in ohm\n",
      "C= 0.1*10**-6 # in F\n",
      "omega= 2*np.pi*f # in radian\n",
      "print \"Output Voltage = -0.942 Cos(400*pi*t)\" \n",
      "t = np.arange(0, .015, 1.0/44100)\n",
      "v_out=-0.942*np.sin(400*np.pi*t+np.pi/2)# in micro volt\n",
      "plt.plot(t,v_out) \n",
      "plt.title('Output Voltage Waveform')\n",
      "plt.xlabel('Time in ms')\n",
      "plt.ylabel('Vout in Volts') \n",
      "print \"Output Voltage waveform is shown in figure.\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Output Voltage = -0.942 Cos(400*pi*t)\n",
        "Output Voltage waveform is shown in figure."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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0l2WQodjAqVNAp06Ao7CNlOvGYNB32kvprV+AIhQ13KMuXfR9jyyFDMUGlDoZ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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f27e7a28290>"
       ]
      }
     ],
     "prompt_number": 39
    }
   ],
   "metadata": {}
  }
 ]
}