path: root/Linear_Integrated_Circuits/Chapter_4.ipynb

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  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<h1>Chapter 4: Applications of Operational Amplifiers<h1>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<h3>Example No. 4.1, Page No: 185<h3>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%pylab inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "WARNING: pylab import has clobbered these variables: ['prod', 'plotting', 'Circle', 'power', 'diag', 'fmax', 'sinh', 'trunc', 'binomial', 'plot', 'eye', 'f', 'det', 'tan', 'product', 'roots', 'sin', 'zeros', 'cosh', 'conjugate', 'take', 'solve', 'trace', 'beta', 'pylab', 'ones', 'transpose', 'vectorize', 'cos', 'interactive', 'diff', 'invert', 'tanh', 'Polygon', 'reshape', 'sqrt', 'floor', 'source', 'add', 'multinomial', 'test', 'poly', 'mod', 'sign', 'gamma', 'log', 'var', 'seterr', 'flatten', 'nan', 'pi', 'exp']\n",
        "`%pylab --no-import-all` prevents importing * from pylab and numpy\n"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "#Variable Declaration:\n",
      "import math\n",
      "R1=20.0*10**3             #Resistance in ohm\n",
      "R=39.0*10**3              #Resistance in ohm\n",
      "f=2000.0                  #Frequencuy in hertz\n",
      "Rf=R1                     #Value of Rf is equal to R1 in ohm\n",
      "C=10**-9                  #Capacitance in farad\n",
      "\n",
      "#Calculations:\n",
      "fo=1/(2*math.pi*R*C)      #Calculating output frequency\n",
      "\n",
      "theta=-2*math.atan(f/fo)  #Calculating phase angle\n",
      "theta=theta*180/math.pi   #Calculating phase angle\n",
      "\n",
      "td=theta/(f*360)          #Calculating time delay\n",
      "td=-td*10**6              #Calculating time delay\n",
      "\n",
      "#Results:\n",
      "print('Phase angle=%.1f degree'%theta)\n",
      "print('\\nTime delay td= %.1f us'%td)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Phase angle=-52.2 degree\n",
        "\n",
        "Time delay td= 72.5 us\n"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<h3>Example No. 4.2, Page No: 187<h3>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "#Variable Declaration:\n",
      "Vee=12.0            #Volatge Vee in volt\n",
      "Vcc=5.0             #Voltage Vcc in volt\n",
      "RL=1000.0           #Resistance RL in ohm\n",
      "\n",
      "#Calculations:\n",
      "Vdiff=Vee-Vcc       #Calculating voltage difference\n",
      "IL=Vdiff/RL         #Calculating current\n",
      "IL=IL*1000.0        #Calculating current\n",
      "\n",
      "#Results:\n",
      "print('Current through RL is IL= %d mA'%IL)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Current through RL is IL= 7 mA\n"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<h3>Example No. 4.3, Page NO: 187<h3>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "#Variable Declaration:\n",
      "V=5.0               #Voltage in volt\n",
      "R=1000.0            #Resistance in ohm\n",
      "\n",
      "#Calculations:\n",
      "I=V/R               #Calculating current\n",
      "I=I*1000.0          #Calculating current\n",
      "\n",
      "#Results:\n",
      "print('Current= %d mA'%I)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Current= 5 mA\n"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<h3>Example No.4.4, Page NO: 187<h3>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "#Variable Declaration:\n",
      "Vcc=15.0                #Voltage in volt\n",
      "Re2=1000.0              #Resistance in ohm\n",
      "Vc1=5.0                 #Voltage in volt\n",
      "Ve2=5.0                 #Voltage in volt\n",
      "\n",
      "#Calculations:\n",
      "I=(Vcc-Ve2)/Re2         #Calculating current\n",
      "I=I*1000.0              #Calculating current\n",
      "\n",
      "#Results:\n",
      "print('Current= %d mA'%I)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Current= 10 mA\n"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<h3>Example No. 4.5, Page No: 189<h3>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "#Variable Declaration:\n",
      "R1=22.0*10**3              #Resistance in ohm\n",
      "Rf=1000.0                  #Feedback Resistance in ohm\n",
      "RL=10.0*10**3              #Load Resistance in ohm           \n",
      "Ii=10.0*10**-6             #Current in ampere\n",
      "\n",
      "#Calculations:\n",
      "Ai=1+R1/Rf                 #Calculating gain \n",
      "Io=Ai*Ii                   #Calculating output current\n",
      "Io=Io*10**6                #Calculating output current\n",
      "print('Current Io= %f uA'%Io)\n",
      "\n",
      "Io=Io/10**6                #Calculating output current \n",
      "Vmax=Io*RL + Ii*R1         #Calculating maximum voltage\n",
      "\n",
      "#Results:\n",
      "print('\\nVmax= %.2f V'%Vmax)\n",
      "print('\\nHence output clipping doesnot occur')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Current Io= 230.000000 uA\n",
        "\n",
        "Vmax= 2.52 V\n",
        "\n",
        "Hence output clipping doesnot occur\n"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<h3>Example No. 4.6, Page No: 192<h3>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "#Variable Declaration:\n",
      "Rf=10.0*10**3      #Feedback resistance in ohm\n",
      "RL=2000.0          #Load resistance in ohm\n",
      "Vi=0.5             #Input voltage in volt\n",
      "\n",
      "#Calculations:\n",
      "IL=Vi/Rf           #Calculating current\n",
      "IL=IL*10**6        #Calculating current\n",
      "print('Current IL= %d uA'%IL)\n",
      "\n",
      "IL=IL/10**6        #Calculating current\n",
      "Vmax=IL*RL + IL*Rf #Calculating maximum voltage\n",
      "\n",
      "#Results:\n",
      "print('\\nVmax= %.2f V'%Vmax)\n",
      "print('\\nHence output clipping doesnot occur')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Current IL= 50 uA\n",
        "\n",
        "Vmax= 0.60 V\n",
        "\n",
        "Hence output clipping doesnot occur\n"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<h3>Example No. 4.7, Page No: 194<h3>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "#Variable Declaration:\n",
      "V1=2.0                  #Voltage in volt\n",
      "V2=3.0                  #Voltage in volt\n",
      "V3=4.0                  #Voltage in volt\n",
      "Rf=1000.0               #Feedback resistance in ohm\n",
      "R1=Rf                   #Resistance value of the R1 is equal to Rf in ohm\n",
      "R2=Rf                   #Resistance value of the R2 is equal to Rf in ohm  \n",
      "R3=Rf                   #Resistance value of the R3 is equal to Rf in ohm\n",
      "R=Rf                    #Resistance value of the R is equal to Rf in ohm \n",
      "\n",
      "#Calculations:\n",
      "Vo=-(Rf/R1)*(V1+V2+V3)  #Calculating output voltage\n",
      "\n",
      "#Results:\n",
      "print('Vo= %d V'%Vo)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Vo= -9 V\n"
       ]
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<h3>Example No: 4.9, Page NO: 207<h3>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "#Variable Declaration:\n",
      "import math\n",
      "R1=10.0*10**3            #Resistance in ohm\n",
      "Rf=100.0*10**3           #Resistance in ohm\n",
      "Cf=10.0*10**-9           #Capacitance in farad\n",
      "\n",
      "#Calculations:\n",
      "fa=1/(2*math.pi*Rf*Cf)   #Calculating lower frequency limit\n",
      "\n",
      "#PART (a)\n",
      "Vo1=10**4/(2*3.14*2500)     \n",
      "#PART (b)\n",
      "Vo2 = -10**4*0.2*10**-3 \n",
      "#PART (c)\n",
      "Vo3 = -10**4*0.6*10**-3\n",
      "#Results:\n",
      "print('fa= %d Hz'%fa)\n",
      "print('output voltage for sine wave input is %.3f volt'%Vo1)\n",
      "print('output voltage for square wave input is %d volt'%Vo2)\n",
      "print('output voltage for step input is %d volt'%Vo3)\n",
      "\n",
      "##############(1)#############\n",
      "t = arange(0.001, 1, 0.005)\n",
      "k = arange(0.0001, 0.2, 0.0005)\n",
      "subplot(221)\n",
      "plot(t, sin(16*t))\n",
      "plot(t,0.637*cos(16*t))\n",
      "plot(t,(0*t)/t,'-')\n",
      "plot(k,(-0.637*k)/k,'--')\n",
      "ylim( (-1,1) )\n",
      "text(-0.11,-0.637,'-0.637')\n",
      "text(0.2,0.2,'Green = Vo')\n",
      "text(0.07,0.5,'Blue = Vi')\n",
      "ylabel('Vin')\n",
      "xlabel('time in ms')\n",
      "title('Input & output waveforms of integrator')\n",
      "\n",
      "##############(2)#################\n",
      "n = arange(0.0001,0.2, 0.0005)\n",
      "n1= arange(0.2, 2*0.2, 0.0005)\n",
      "n2= arange(2*0.2, 3*0.2, 0.0005)\n",
      "n3= arange(3*0.2,4*0.2, 0.0005)\n",
      "n4= arange(4*0.2,5*0.2, 0.0005)\n",
      "n5= arange(0.0001,5*0.2, 0.0005)\n",
      "\n",
      "a=arange(-1,1,0.0005)\n",
      "\n",
      "x5=(0.2*a)/a\n",
      "x10=(2*0.2*a)/a\n",
      "x15=(3*0.2*a)/a\n",
      "x25=(4*0.2*a)/a\n",
      "\n",
      "subplot(223)\n",
      "\n",
      "plot(n5,(0*n5)/n5,'-')\n",
      "plot(n,1*n/n,'b')\n",
      "plot(n1,-1*n1/n1,'b')\n",
      "plot(n2,1*n2/n2,'b')\n",
      "plot(n3,-1*n3/n3,'b')\n",
      "plot(n4,1*n4/n4,'b')\n",
      "\n",
      "plot(x5,a,'b')\n",
      "plot(x10,a,'b')\n",
      "plot(x15,a,'b')\n",
      "plot(x25,a,'b')\n",
      "\n",
      "plot(n,(-10*n+1),'r')\n",
      "plot(n1,(10*n-1),'r')\n",
      "plot(n+0.4,(-10*n+1),'r')\n",
      "plot(n3,(10*n-1),'r')\n",
      "\n",
      "ylim( (-1.1,1.1) )\n",
      "text(0.3,-0.4,'Red = Vo')\n",
      "text(0.05,0.5,'Blue = Vi')\n",
      "ylabel('Vin')\n",
      "xlabel('time in ms')\n",
      "\n",
      "###############(3)##################\n",
      "t = arange(0.0001, 1, 0.0005)\n",
      "t2 = arange(0.0001, 0.6, 0.0005)\n",
      "a=arange(-6,0.0001,0.0005)\n",
      "x=(0.6*a)/a\n",
      "subplot(222)\n",
      "plot(t,1*t/t,'r')\n",
      "plot(t,0*t/t,'--')\n",
      "plot(t2,-6*t2/t2,'--')\n",
      "plot(x,a,'--')\n",
      "plot(t,(-10*t),'b')\n",
      "text(0.4,-4,'Vo')\n",
      "text(0.3,1.1,'Vi')\n",
      "xlabel('time in ms')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "fa= 159 Hz\n",
        "output voltage for sine wave input is 0.637 volt\n",
        "output voltage for square wave input is -2 volt\n",
        "output voltage for step input is -6 volt\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 33,
       "text": [
        "<matplotlib.text.Text at 0xce594e0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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7LcYP53+Ar42vQjqU2vLHj/mlauHDqsurMLvr7HJxGlURHQ3YGxvDs30Afo76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\n",
       "text": [
        "<matplotlib.figure.Figure at 0xcb7c6a0>"
       ]
      }
     ],
     "prompt_number": 33
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<h3>Example No: 4.10, Page No: 210<h3>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "#Variable Declaration:\n",
      "import math\n",
      "fa=1.0*10**3              #Upper cut off frequency in hertz\n",
      "C1=1.0*10**-6             #Capacitance in farad\n",
      "\n",
      "#Calculations:\n",
      "Rf=1/(2*math.pi*fa*C1)    #Calculating value of resistance\n",
      "Rf=Rf/100.0               #Calculating value of resistance \n",
      "\n",
      "#Results:\n",
      "print('Rf= %.2f kohm'%Rf)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Rf= 1.59 kohm\n"
       ]
      }
     ],
     "prompt_number": 34
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<h3>Example No. 4.11, Page No: 213<h3>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "#Variable Declaration:\n",
      "import math\n",
      "import pylab\n",
      "import numpy\n",
      "fa=200.0                  #frequency in hertz\n",
      "fmax=fa                   #frequency fmax is equal to fa\n",
      "C1=0.1*10**-6             #Capacitance in farad\n",
      "\n",
      "#Calculations:\n",
      "             \n",
      "Rf=1/(2*math.pi*fa*C1)    #Calcukating resistance value \n",
      "Rf=Rf/1000.0              #Calculating resistance value\n",
      "\n",
      "fb=10.0*fa                #Calculating frequency\n",
      "R1=1/(2*math.pi*fb*C1)    #Calculating resistance \n",
      "R1=R1/1000.0              #Calculating resistance\n",
      "\n",
      "Cf=R1*C1/Rf               #Calculating capacitance \n",
      "Cf=Cf*10**6               #Calculating capacitance\n",
      "\n",
      "subplot(211)\n",
      "plot(t,1*sin(2*pi*t))\n",
      "\n",
      "ylim( (-1,1) )\n",
      "ylabel('Vin')\n",
      "title('Input Waveform')\n",
      "\n",
      "\n",
      "#Results:\n",
      "print('Rf= %.3f kohm'%Rf)\n",
      "print('\\nR1= %.3f kohm'%R1)\n",
      "print('\\nCf= %.2f uF'%Cf)\n",
      "\n",
      "############PLOT###################\n",
      "\n",
      "##########(1)###############\n",
      "t = arange(0.001, 5*pi, 0.005)\n",
      "subplot(221)\n",
      "plot(t, sin(pi*t/4))\n",
      "plot(t,(0*t)/t,'-')\n",
      "ylim( (-1,1) )\n",
      "ylabel('Vin')\n",
      "title('Input Waveform')\n",
      "\n",
      "###########(2)#######\n",
      "subplot(223)\n",
      "plot(t, cos((pi*t/4-135)))\n",
      "plot(t,(0*t)/t,'-')\n",
      "ylim( (-1,1) )\n",
      "ylabel('Vout')\n",
      "xlabel('(a)')\n",
      "title('Output Waveform')\n",
      "\n",
      "##########(3)#########\n",
      "k = arange(0.0001, pi, 0.0005)\n",
      "k1= arange(pi, 2*pi, 0.0005)\n",
      "k2= arange(2*pi, 3*pi, 0.0005)\n",
      "k3= arange(3*pi,4*pi, 0.0005)\n",
      "k4= arange(4*pi,5*pi, 0.0005)\n",
      "m=arange(-1,1,0.0005)\n",
      "x5=(pi*m)/m\n",
      "x10=(2*pi*m)/m\n",
      "x15=(3*pi*m)/m\n",
      "x25=(4*pi*m)/m\n",
      "subplot(222)\n",
      "plot(t,(0*t)/t,'-')\n",
      "plot(k,1*k/k,'b')\n",
      "plot(k1,-1*k1/k1,'b')\n",
      "plot(k2,1*k2/k2,'b')\n",
      "plot(k3,-1*k3/k3,'b')\n",
      "plot(k4,1*k4/k4,'b')\n",
      "plot(x5,m,'b')\n",
      "plot(x10,m,'b')\n",
      "plot(x15,m,'b')\n",
      "plot(x25,m,'b')\n",
      "ylim( (-1.1,1.1) )\n",
      "ylabel('Vin')\n",
      "title('Input Waveform')\n",
      "\n",
      "############(4)############\n",
      "subplot(224)\n",
      "m1=arange(0.001,13,0.0005)\n",
      "m2=arange(-13,0.001,0.0005)\n",
      "y1=(0.01*pi*m2)/m2\n",
      "y5=(pi*m1)/m1\n",
      "y10=(2*pi*m2)/m2\n",
      "y15=(3*pi*m1)/m1\n",
      "y25=(4*pi*m2)/m2\n",
      "plot(t,(0*t)/t,'-')\n",
      "plot(y5,m1,'b')\n",
      "plot(y10,m2,'b')\n",
      "plot(y1,m2,'b')\n",
      "plot(y15,m1,'b')\n",
      "plot(y25,m2,'b')\n",
      "plot(y5+0.1,m1,'b')\n",
      "plot(y10+0.1,m2,'b')\n",
      "plot(y1+0.1,m2,'b')\n",
      "plot(y15+0.1,m1,'b')\n",
      "plot(y25+0.1,m2,'b')\n",
      "text(-2.5,13,'Vsat')\n",
      "text(-2.5,-13,'-Vsat')\n",
      "ylim(-13,13)\n",
      "ylabel('Vout')\n",
      "xlabel('(b)')\n",
      "title('Output Waveform')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Rf= 7.958 kohm\n",
        "\n",
        "R1= 0.796 kohm\n",
        "\n",
        "Cf= 0.01 uF\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 35,
       "text": [
        "<matplotlib.text.Text at 0xd0e5c18>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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aU+rGDaBzZ37KOHIEGDaMH9lCY2kJdOwIZGTQ4Tw+iI+vWV+adNvbtGmD48eP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\nTLIKPpISrGkAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0xcb7cc18>"
       ]
      }
     ],
     "prompt_number": 35
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<h3>Example No.4.13, Page No: 226<h3>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import sympy\n",
      "from sympy import *\n",
      "sympy.init_printing()\n",
      "\n",
      "s = Symbol(\"s\")\n",
      "H = 4/(s**2+3.3*s+0.9)\n",
      "print(\"The given transfer function is:\")\n",
      "display(H.simplify())\n",
      "print(\"\\n\\n\\nThe above transfer function can be represented after factoring as given by:\")\n",
      "display(factor(H))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The given transfer function is:\n"
       ]
      },
      {
       "latex": [
        "$$\\frac{4}{s^{2} + 3.3 s + 0.9}$$"
       ],
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "       4        \n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        " 2              \n",
        "s  + 3.3\u22c5s + 0.9"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "\n",
        "\n",
        "The above transfer function can be represented after factoring as given by:\n"
       ]
      },
      {
       "latex": [
        "$$\\frac{40.0}{\\left(1.0 s + 3.0\\right) \\left(10.0 s + 3.0\\right)}$$"
       ],
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "            40.0            \n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "(1.0\u22c5s + 3.0)\u22c5(10.0\u22c5s + 3.0)"
       ]
      }
     ],
     "prompt_number": 42
    }
   ],
   "metadata": {}
  }
 ]
}