path: root/Linear_Integrated_Circuits_by_J._B._Gupta/chapter05.ipynb

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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": 56
    },
    {
     "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": 57
    },
    {
     "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": 58
    },
    {
     "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": 59
    },
    {
     "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": 60
    },
    {
     "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": 61
    },
    {
     "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": 62
    },
    {
     "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": 63
    },
    {
     "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",
      "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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uICUlBSkpKbh8+TIKCwuxaNEiXcZIREaEVdumReNwU69evXDx4kVYWNTOI5WV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\nYpIgIiKNmCSIiEgjJgkiItLo/wEJUlJyDeG+CgAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f0c532cff90>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Assuming Ideal op-amp, sketch for Vout is shown in figure.\n"
       ]
      }
     ],
     "prompt_number": 64
    },
    {
     "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",
      "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.\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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QnZ0tSo7FKDV/YkDrD8Pdu8CFC7zBUiKtWgEFBdpeL6TU/ImBDh1o4oS5COsT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\nU4ayYwfQv79oFfaNgwPQowcfR5cDMhT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dugAAvV5v3LHO8Lq4uBiMMXTo0AF79+6t1Xnr\n1asHAKhTp45x6MzUMYbrGV4brg3w3fSSk5OxceNGdOnSBQcPHoSrq2uttBCElNCQF0FUgTlzVdq1\na4fc3FwkJSUBAIqKipCWlmbx+WpLRkYGunfvjtmzZ6NFixZWb3dLENZCEQqhecrnN6r6f/ljyr92\ndHTEr7/+iqlTp6KgoADFxcV47bXXEBQUZPIa5rxf3Y6I5b/31ltv4dSpU2CMYeDAgZJtJ0sQlkLT\nhgmCIAhJoCEvgiAIQhLIUAiCIAhJIEMhCIIgJIEMhSAIgpAEMhSCIAhCEshQCIIgCEkgQyEIgiAk\ngQyFIAiCkIT/D1aoyBiLHf2sAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f0c53674cd0>"
       ]
      }
     ],
     "prompt_number": 65
    }
   ],
   "metadata": {}
  }
 ]
}