path: root/Analog_Integrated_Circuits_by_J._B._Gupta/Chaper07.ipynb

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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter-7 Active Filters"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.1 - Page  204"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from numpy import pi\n",
      "from __future__ import division\n",
      "# Given data\n",
      "f_H= 2*10**3 #cut-off frequency in Hz\n",
      "C= 0.01*10**-6 # in F\n",
      "passband_gain= 2.5 \n",
      "R= 1/(2*pi*f_H*C) # in \u03a9\n",
      "R= 8.2 # in k\u03a9 (standard value)\n",
      "# 1+Rf/R1= passband_gain or Rf should be equal to 1.5*R1 since Rf||R1= R\n",
      "R1= passband_gain/1.5*R # in k\u03a9\n",
      "print \"The value of R1 = %0.2f k\u03a9 (Standard value 15 k\u03a9)\" %R1 \n",
      "Rf= int(1.5*R1) # in k\u03a9\n",
      "print \"The value of Rf = %0.f k\u03a9\" % Rf"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The value of R1 = 13.67 k\u03a9 (Standard value 15 k\u03a9)\n",
        "The value of Rf = 20 k\u03a9\n"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.2 - Page  207"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Given data\n",
      "f_H= 2*10**3 #cut-off frequency in Hz\n",
      "C= 0.033*10**-6 # in F\n",
      "R= 1/(2*pi*f_H*C) # in \u03a9\n",
      "# 2*R= Rf*R1/(Rf+R1)= 0.586*R1**2/(1.586*R1) since Rf= 0.586*R1\n",
      "R1= 2*R*1.586/0.586 # in \u03a9\n",
      "R1= round(R1*10**-3) # in k\u03a9\n",
      "print \"The value of R1 = %0.f k\u03a9 (Standard value 15 kohm)\" %R1\n",
      "R1= 15 # in k\u03a9\n",
      "Rf= R1*0.586 # in k\u03a9\n",
      "#Rf= floor(1.5*R1) # in k\u03a9\n",
      "print \"The value of Rf = %0.2f k\u03a9\" %Rf\n",
      "print \"(The value of Rf may be taken as a pot of 10 k\u03a9)\" "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The value of R1 = 13 k\u03a9 (Standard value 15 kohm)\n",
        "The value of Rf = 8.79 k\u03a9\n",
        "(The value of Rf may be taken as a pot of 10 k\u03a9)\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.3 - Page  207"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Given data\n",
      "f_H= 1*10**3 #cut-off frequency in Hz\n",
      "C= 0.0047*10**-6 # in F\n",
      "R= 1/(2*pi*f_H*C) # in \u03a9\n",
      "R= (R*10**-3) # in k\u03a9\n",
      "R1= 30 # in k\u03a9 (assume)\n",
      "Rf= 0.586*R1 # in k\u03a9\n",
      "C= C*10**6 # in \u00b5F\n",
      "print \"The value of R'= R = %0.2f k\u03a9 (standard value 33 k\u03a9)\" %R\n",
      "print \"The value of C'= C = %0.4f \u00b5F \" %C\n",
      "print \"The value of R1= %0.2f k\u03a9 \" %R1 \n",
      "print \"The value of Rf= %0.2f k\u03a9 (standard value 20 k\u03a9 pot)\" %Rf "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The value of R'= R = 33.86 k\u03a9 (standard value 33 k\u03a9)\n",
        "The value of C'= C = 0.0047 \u00b5F \n",
        "The value of R1= 30.00 k\u03a9 \n",
        "The value of Rf= 17.58 k\u03a9 (standard value 20 k\u03a9 pot)\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.4 - Page  212"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "# Given data\n",
      "fc= 1*10**3 # in Hz\n",
      "alpha= 1.414 \n",
      "C= 0.1*10**-6 # in F (assume)\n",
      "C_desh= C*alpha**2/4 # in F\n",
      "C_desh= C_desh*10**6 # in \u00b5F\n",
      "print \"The value of C' = %0.2f \u00b5F\" %C_desh\n",
      "C_desh= C_desh*10**-6 # in F\n",
      "R_desh= 1/(2*pi*fc*math.sqrt(C*C_desh)) # in \u03a9\n",
      "R_desh= R_desh*10**-3 # in k\u03a9\n",
      "print \"The value of R' = %0.2f k\u03a9 (standard value 2.2 k\u03a9)\"%R_desh"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The value of C' = 0.05 \u00b5F\n",
        "The value of R' = 2.25 k\u03a9 (standard value 2.2 k\u03a9)\n"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.5 - Page  213"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Given data\n",
      "alpha= 1.414 # passband\n",
      "C= 0.01*10**-6 # in F (assume)\n",
      "fc= 1*10**3 # in Hz\n",
      "dc_gain= 6 \n",
      "R= 1/(2*pi*C*fc) # in \u03a9\n",
      "R= R*10**-3 # in k\u03a9\n",
      "print \"The value of R = %0.1f k\u03a9 (standard value 15 k\u03a9)\" %R\n",
      "R= 15 # in k\u03a9\n",
      "Af= 3-alpha # and Af= 1+Rf/R1 or\n",
      "# Rf= (Af-1)*R1    (i)\n",
      "# 2*R= Rf || R1, hence from (i)\n",
      "R1= 2*R*Af/(Af-1) # in k\u03a9\n",
      "print \"The value of R1 = %0.1f k\u03a9 (standard value 82 k\u03a9)\" %R1\n",
      "R1= 82 # in k\u03a9\n",
      "Rf= (Af-1)*R1 # in k\u03a9\n",
      "print \"The value of Rf = %0.f k\u03a9 (standard value 47 k\u03a9)\" %Rf\n",
      "Aamp= dc_gain/Af \n",
      "print \"The value of Aamp = %0.2f\" %Aamp"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The value of R = 15.9 k\u03a9 (standard value 15 k\u03a9)\n",
        "The value of R1 = 81.2 k\u03a9 (standard value 82 k\u03a9)\n",
        "The value of Rf = 48 k\u03a9 (standard value 47 k\u03a9)\n",
        "The value of Aamp = 3.78\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.7 - Page  221"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Given data\n",
      "R= 2.1*10**3 # in k\u03a9\n",
      "C= 0.05*10**-6 # in F\n",
      "R1= 20*10**3 # in \u03a9\n",
      "Rf= 60*10**3 # in \u03a9\n",
      "# Low cut-off frequency,\n",
      "f_L= 1/(2*pi*R*C) # in Hz\n",
      "f_L= f_L*10**-3 # in kHz\n",
      "print \"The cut-off frequency = %0.3f kHz\" %f_L"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The cut-off frequency = 1.516 kHz\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.8 - Page  225"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "from __future__ import division\n",
      "# Given data\n",
      "R1= 2*10**3 # in \u03a9\n",
      "R2= 2/3*10**3 # in \u03a9\n",
      "R3= 200*10**3 # in \u03a9\n",
      "C= 0.1*10**-6 # in F\n",
      "Af= R3/(2*R1) # gain\n",
      "print \"The value of Af = %0.f\" %Af\n",
      "# R1= Q/(2*pi*f_C*C*Af)           (i)\n",
      "# R2= Q/(2*pi*f_C*C*(2*Q**2-Af))  (ii)\n",
      "# R3= Q/(pi*f_C*C)                (iii)\n",
      "Q= math.sqrt((R3/(2*R2)+Af)/2) # from (ii) and (iii)\n",
      "print \"The value of Q = %0.f\" %Q\n",
      "f_C= Q/(R3*pi*C) # in Hz  (from (iii))\n",
      "print \"The value of f_C = %0.f Hz\" %f_C\n",
      "omega_0= 2*pi*f_C # in radians/second\n",
      "print \"The value of omega_0 = %0.f radians/seconds\" %omega_0"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The value of Af = 50\n",
        "The value of Q = 10\n",
        "The value of f_C = 159 Hz\n",
        "The value of omega_0 = 1000 radians/seconds\n"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.10 - Page  227"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Given data\n",
      "f_L= 2*10**3 # in Hz\n",
      "f_H= 2.5*10**3 # in Hz\n",
      "Af= -5 \n",
      "f_C= math.sqrt(f_L*f_H) # centre frequency in Hz\n",
      "del_f= f_H-f_L #bandwidth in Hz\n",
      "Q= f_C/del_f # selectivity\n",
      "# Assume C1= C2= C= 0.01\u00b5F\n",
      "C= 0.01*10**-6 # in F\n",
      "R3= 1/(pi*del_f*C) # in \u03a9\n",
      "R3= R3*10**-3 # in k\u03a9\n",
      "print \"The value of R3 = %0.2f k\u03a9 (standard value 64 k\u03a9)\" %R3\n",
      "R3= 64 # in k\u03a9\n",
      "R3= R3*10**3 # in \u03a9\n",
      "R1= -R3/(2*Af) #in \u03a9\n",
      "R2= R1/(4*pi**2*f_C**2*R1*R3*C**2-.1)\n",
      "R1= R1*10**-3 # in k\u03a9\n",
      "C=C*10**6 # in \u00b5F\n",
      "print \"The value of R1 = %0.1f k\u03a9 \" %R1\n",
      "print \"The value of R2 = %0.f k\u03a9 (standard value 800\u03a9)\" %R2\n",
      "print \"The value of C = %0.2f \u00b5F \" %C"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The value of R3 = 63.66 k\u03a9 (standard value 64 k\u03a9)\n",
        "The value of R1 = 6.4 k\u03a9 \n",
        "The value of R2 = 801 k\u03a9 (standard value 800\u03a9)\n",
        "The value of C = 0.01 \u00b5F \n"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.11 - Page 228  "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Given data\n",
      "f_C= 1*10**3 #centre frequency in Hz\n",
      "f_C_desh= 2*10**3 #new centre frequency in Hz\n",
      "Q= 5 # selectivity\n",
      "Af= -8 \n",
      "C= 0.01*10**-6 # in F (assume)\n",
      "R3= Q/(pi*f_C*C) #in \u03a9\n",
      "R3= R3*10**-3 # in k\u03a9\n",
      "print \"The value of R3 = %0.1f k\u03a9 (160 k\u03a9 (approx))\" %R3\n",
      "R1= round(-R3/(2*Af)) # in k\u03a9\n",
      "print \"The value of R1 = %0.f k\u03a9\" %R1\n",
      "R2= R1*10**3/(4*pi**2*f_C**2*R1*10**3*R3*10**3*C**2-1) # in \u03a9\n",
      "R2= R2*10**-3 # in k\u03a9\n",
      "print \"The value of R2 = %0.2f k\u03a9 (2 k\u03a9 (approx))\" %R2\n",
      "R2= 2 # in k\u03a9 (approx)\n",
      "R2_desh= R2*(f_C/f_C_desh)**2 # in k\u03a9\n",
      "R2_desh= R2_desh*10**3 # in \u03a9\n",
      "print \"The value of R2' = %0.f \u03a9\" %R2_desh"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The value of R3 = 159.2 k\u03a9 (160 k\u03a9 (approx))\n",
        "The value of R1 = 10 k\u03a9\n",
        "The value of R2 = 1.89 k\u03a9 (2 k\u03a9 (approx))\n",
        "The value of R2' = 500 \u03a9\n"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.12 - Page  229"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Given data\n",
      "R= 10*10**3 # in \u03a9\n",
      "C1= 0.1*10**-6 # in F \n",
      "C2= 0.0025*10**-6 # in F \n",
      "f_H= 1/(2*pi*R*C2) #higher cut-off frequency in Hz\n",
      "f_H= f_H*10**-3 # in kHz\n",
      "f_L= 1/(2*pi*R*C1) #lower cut-off frequency in Hz\n",
      "BW= f_H-f_L*10**-3 # bandwidth in kHz\n",
      "print \"The higher cut-off frequency = %0.3f kHz\" %f_H\n",
      "print \"The lower cut-off frequency = %0.2f Hz\" %f_L\n",
      "print \"The bandwidth = %0.1f kHz\" %BW"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The higher cut-off frequency = 6.366 kHz\n",
        "The lower cut-off frequency = 159.15 Hz\n",
        "The bandwidth = 6.2 kHz\n"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.13 - Page  230"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Given data\n",
      "f_L= 200 # in Hz\n",
      "f_H= 1*10**3 # in Hz\n",
      "alpha=4 # passband gain\n",
      "C_desh= 0.01*10**-6 # in F (assume)\n",
      "R_desh= 1/(2*pi*f_H*C_desh) # in \u03a9\n",
      "R_desh= R_desh*10**-3 # in k\u03a9\n",
      "print \"The value of R' = %0.1f k\u03a9 (Standard value 20 k\u03a9)\" %R_desh\n",
      "R_desh= 20 # in k\u03a9 (standard value)\n",
      "# First Order High-Pass Filter\n",
      "C= 0.05*10**-6 # in F (assume)\n",
      "R= 1/(2*pi*f_L*C) # in \u03a9\n",
      "R= R*10**-3 # in k\u03a9\n",
      "R1= 10 # in k\u03a9\n",
      "Rf= R1 # in k\u03a9\n",
      "C_desh= C_desh*10**6 # in \u00b5F\n",
      "C= C*10**6 # in \u00b5F\n",
      "print \"The value of R = %0.1f k\u03a9 (Standard value 20 k\u03a9)\" %R\n",
      "R= 20 # in k\u03a9 (standard value)\n",
      "print \"The value of R1 and Rf = %0.f k\u03a9\" %R1\n",
      "print \"The value of C' = %0.2f \u00b5F\" %C_desh\n",
      "print \"The value of C = %0.2f \u00b5F\" %C"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The value of R' = 15.9 k\u03a9 (Standard value 20 k\u03a9)\n",
        "The value of R = 15.9 k\u03a9 (Standard value 20 k\u03a9)\n",
        "The value of R1 and Rf = 10 k\u03a9\n",
        "The value of C' = 0.01 \u00b5F\n",
        "The value of C = 0.05 \u00b5F\n"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.14 - Page 231"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Given data\n",
      "f_H= 200 # in Hz\n",
      "f_L= 2*10**3 # in Hz\n",
      "C= 0.05*10**-6 # in F\n",
      "# For low-pass filter,\n",
      "R_desh= 1/(2*pi*f_H*C) # in \u03a9\n",
      "R_desh= R_desh*10**-3 # in k\u03a9\n",
      "print \"The value of R' = %0.1f k\u03a9 (standard value 20 k\u03a9)\" %R_desh\n",
      "# For high-pass filter,\n",
      "R= 1/(2*pi*f_L*C) # in \u03a9\n",
      "R= R*10**-3 # in k\u03a9\n",
      "print \"The value of R = %0.2f k\u03a9 (standard value 2 k\u03a9)\" %R"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The value of R' = 15.9 k\u03a9 (standard value 20 k\u03a9)\n",
        "The value of R = 1.59 k\u03a9 (standard value 2 k\u03a9)\n"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.15 - Page 232"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from numpy import pi\n",
      "# Given data\n",
      "C= 0.068*10**-6 # in F\n",
      "f_N= 50 # in Hz\n",
      "R= 1/(2*pi*f_N*C) # in \u03a9\n",
      "R= R*10**-3 # in k\u03a9\n",
      "print \"The value of R = %0.1f k\u03a9 (standard value 50 k\u03a9)\" %R"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The value of R = 46.8 k\u03a9 (standard value 50 k\u03a9)\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.16 - Page  233"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "# Given data\n",
      "R= 15*10**3 # in \u03a9\n",
      "C= 0.01*10**-6 # in F\n",
      "f= 2*10**3 # in Hz\n",
      "PhaseShift= -2*(math.atan(2*pi*f*R*C))*180/pi # in \u00b0\n",
      "print \"The phase shift = %0.f\u00b0\" %PhaseShift\n",
      "print \"i.e. %0.f\u00b0 (lagging)\" %abs(PhaseShift)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The phase shift = -124\u00b0\n",
        "i.e. 124\u00b0 (lagging)\n"
       ]
      }
     ],
     "prompt_number": 45
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.18 - Page 240"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Given data\n",
      "R_A= 2.2*10**3 # in \u03a9\n",
      "R_B= 1.2*10**3 # in \u03a9\n",
      "Rf= 4.7*10**3 # in \u03a9\n",
      "C= 0.01*10**-6 # in F\n",
      "k_lp= 1.238 \n",
      "k_hp= 1/k_lp \n",
      "# Part (i)\n",
      "alpha= 3*R_B/(R_A+R_B) \n",
      "print \"Part (i) : The value of alpha = %0.3f\" %alpha \n",
      "print \"Given filter is 1db peak Chebyshev\" \n",
      "\n",
      "# Part (ii)\n",
      "f_0= 1/(2*pi*Rf*C) #critical frequency in Hz\n",
      "f_0= f_0*10**-3 # in kHz\n",
      "f_low_pass= f_0*k_lp # in kHz\n",
      "print \"\\nPart (ii) : The low-pass frequency = %0.3f kHz\" %f_low_pass\n",
      "f_high_pass= f_0*k_hp # in kHz\n",
      "print \"The high-pass frequency = %0.3f kHz\" %f_high_pass\n",
      "\n",
      "# Part (iii)\n",
      "fc= f_0 # bandpass centre frequency in kHz\n",
      "print \"Part (iii) : The bandpass centre frequency = %0.3f kHz\" %fc\n",
      "\n",
      "# Part (iv)\n",
      "# Formula used : delta_f= fc/Q= fc/(1/alpha)\n",
      "delta_f= fc/(1/alpha) # in kHz\n",
      "print \"Part (iv) : The bandpass width = %0.3f kHz\" %delta_f\n",
      "\n",
      "# Part (v)\n",
      "A0= 1/alpha # bandpass gain at centre frequency\n",
      "print \"Part (v) : The bandpass gain at centre frequency = %0.4f\" %A0"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Part (i) : The value of alpha = 1.059\n",
        "Given filter is 1db peak Chebyshev\n",
        "\n",
        "Part (ii) : The low-pass frequency = 4.192 kHz\n",
        "The high-pass frequency = 2.735 kHz\n",
        "Part (iii) : The bandpass centre frequency = 3.386 kHz\n",
        "Part (iv) : The bandpass width = 3.585 kHz\n",
        "Part (v) : The bandpass gain at centre frequency = 0.9444\n"
       ]
      }
     ],
     "prompt_number": 47
    }
   ],
   "metadata": {}
  }
 ]
}