path: root/Electronic_Devices_/Chapter10.ipynb

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 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<h1>Chapter 10: Amplifier Frequency Response<h1>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<h3>Example 10.1, Page Number: 311<h3>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "import math\n",
      "#Pout/P in=250;\n",
      "A_p=250.0\n",
      "A_p_dB=10*math.log10(A_p)\n",
      "print('Power gain(dB) when power gain is 250 = %d'% math.ceil(A_p_dB));\n",
      "A_p=100.0\n",
      "A_p_dB=10*math.log10(A_p)\n",
      "print('Power gain(dB) when power gain is 100 = %d'%A_p_dB)\n",
      "A_p=10.0\n",
      "A_p_dB=20*math.log10(A_p)\n",
      "print('Voltage gain(dB) when Voltage gain is 10 = %d'%A_p_dB)\n",
      "A_p=0.50\n",
      "A_p_dB=10*math.log10(A_p)\n",
      "print('Power gain(dB) when voltage gain is 0.50 = %d'%A_p_dB)\n",
      "A_p=0.707\n",
      "A_p_dB=20*math.log10(A_p)\n",
      "print('Power gain(dB) when power gain is 0.707 = %d'%A_p_dB)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Power gain(dB) when power gain is 250 = 24\n",
        "Power gain(dB) when power gain is 100 = 20\n",
        "Voltage gain(dB) when Voltage gain is 10 = 20\n",
        "Power gain(dB) when voltage gain is 0.50 = -3\n",
        "Power gain(dB) when power gain is 0.707 = -3"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<h3>Example 10.2, Page Number: 313<h3>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "\n",
      "\n",
      "v_out=0.707*10;\n",
      "print('output voltage in volts at -3dB gain  = %.2f'%v_out)\n",
      "#at -6dB voltage gain from table is 0.5\n",
      "v_out=0.5*10;\n",
      "print('output voltage in volts at -6dB gain = %d'%v_out)\n",
      "#at -12dB voltage gain from table is 0.25\n",
      "v_out=0.25*10;\n",
      "print('output voltage in volts at -12dB gain = %.1f'%v_out)\n",
      "#at -24dB voltage gain from table is 0.0625\n",
      "v_out=0.0625*10;\n",
      "print('output voltage in volts at -24dB gain = %.3f'%v_out)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "output voltage in volts at -3dB gain  = 7.07\n",
        "output voltage in volts at -6dB gain = 5\n",
        "output voltage in volts at -12dB gain = 2.5\n",
        "output voltage in volts at -24dB gain = 0.625"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<h3>Example 10.3, Page Number: 316<h3>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "import math\n",
      "R_in=1.0*10**3;\n",
      "C1=1.0*10**-6;\n",
      "A_v_mid=100.0;    #mid range voltage gain\n",
      "f_c=1/(2*math.pi*R_in*C1);\n",
      "#at f_c, capacitive reactance is equal to resistance(X_C1=R_in)\n",
      "attenuation=0.707;\n",
      "#A_v is gain at lower critical frequency\n",
      "A_v=0.707*A_v_mid;\n",
      "print('lower critical frequency = %f Hz'%f_c)\n",
      "print('attenuation at lower critical frequency =%.3f'%attenuation)\n",
      "print('gain at lower critical frequency = %.1f'%A_v)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "lower critical frequency = 159.154943 Hz\n",
        "attenuation at lower critical frequency =0.707\n",
        "gain at lower critical frequency = 70.7"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<h3>Example 10.4, Page Number: 317<h3>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "A_v_mid=100.0;\n",
      "#At 1Hz frequency,voltage gain is 3 dB less than at midrange. At -3dB, the voltage is reduced by a factor of 0.707\n",
      "A_v=0.707*A_v_mid;\n",
      "print('actual voltage gain at 1Hz frequency = %.1f'%A_v)\n",
      "#At 100Hz frequency,voltage gain is 20 dB less than at critical frequency (f_c ). At -20dB, the voltage is reduced by a factor of 0.1\n",
      "A_v=0.1*A_v_mid;\n",
      "print('actual voltage gain at 100Hz frequency = %d'%A_v)\n",
      "#At 10Hz frequency,voltage gain is 40 dB less than at critical frequency (f_c). At -40dB, the voltage is reduced by a factor of 0.01\n",
      "A_v=0.01*A_v_mid;\n",
      "print('actual voltage gain at 10Hz frequency = %d'%A_v)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "actual voltage gain at 1Hz frequency = 70.7\n",
        "actual voltage gain at 100Hz frequency = 10\n",
        "actual voltage gain at 10Hz frequency = 1"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<h3>Example 10.5, Page Number: 319<h3>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "import math\n",
      "R_C=10.0*10**3;\n",
      "C3=0.1*10**-6;\n",
      "R_L=10*10**3;\n",
      "A_v_mid=50;\n",
      "f_c=1/(2*math.pi*(R_L+R_C)*C3);\n",
      "print('lower critical frequency = %f Hz'%f_c)\n",
      "#at midrange capacitive reactance is zero\n",
      "X_C3=0;\n",
      "attenuation=R_L/(R_L+R_C);    \n",
      "print('attenuation at midrange frequency = %.1f'%attenuation)\n",
      "#at critical frequency, capacitive reactance equals total resistance\n",
      "X_C3=R_L+R_C;\n",
      "attenuation=R_L/(math.sqrt((R_C+R_L)**2+X_C3**2));\n",
      "print('attenuation at critical frequency = %f'%attenuation)\n",
      "A_v=0.707*A_v_mid;\n",
      "print('gain at critical frequency = %.2f'%A_v)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "lower critical frequency = 79.577472 Hz\n",
        "attenuation at midrange frequency = 0.5\n",
        "attenuation at critical frequency = 0.353553\n",
        "gain at critical frequency = 35.35"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<h3>Example 10.6, Page Number: 321<h3>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "import math\n",
      "B_ac=100.0;\n",
      "r_e=12.0;\n",
      "R1=62.0*10**3;\n",
      "R2=22.0*10**3;\n",
      "R_S=1.0*10**3;\n",
      "R_E=1.0*10**3;\n",
      "C2=100.0*10**-6;\n",
      "#Base circuit impedance= parallel combination of R1, R2, R_S\n",
      "R_th=(R1*R2*R_S)/(R1*R2+R2*R_S+R_S*R1);\n",
      "#Resistance looking at emitter\n",
      "R_in_emitter=r_e+(R_th/B_ac);\n",
      "#resistance of equivalent bypass RC is parallel combination of R_E,R_in_emitter\n",
      "R=(R_in_emitter*R_E)/(R_E+R_in_emitter);\n",
      "f_c=1/(2*math.pi*R*C2);\n",
      "print('critical frequency of bypass RC circuit = %f Hz'%f_c)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "critical frequency of bypass RC circuit = 75.893960 Hz"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<h3>Example 10.7, Page Number:323<h3>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "import math\n",
      "V_GS=-10.0;\n",
      "I_GSS=25.0*10**-9;\n",
      "R_G=10.0*10**6;\n",
      "C1=0.001*10**-6;\n",
      "R_in_gate=abs((V_GS/I_GSS));\n",
      "R_in=(R_in_gate*R_G)/(R_G+R_in_gate);\n",
      "f_c=1/(2*math.pi*R_in*C1);\n",
      "print('critical frequency = %f Hz'%f_c)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "critical frequency = 16.313382 Hz"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<h3>Example 10.8, Page Number: 324<h3>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "import math\n",
      "V_GS=-12.0;\n",
      "I_GSS=100.0*10**-9;\n",
      "R_G=10.0*10**6;\n",
      "R_D=10.0*10**3;\n",
      "C1=0.001*10**-6;\n",
      "C2=0.001*10**-6;\n",
      "R_in_gate=abs((V_GS/I_GSS));\n",
      "R_in=(R_in_gate*R_G)/(R_G+R_in_gate);\n",
      "R_L=R_in;    #according to question\n",
      "f_c_input=1/(2*math.pi*R_in*C1);\n",
      "print('critical frequency of input RC circuit = %f Hz'%f_c_input)\n",
      "f_c_output=1/(2*math.pi*(R_D+R_L)*C2)\n",
      "print('critical frequency of output RC circuit = %f Hz'%f_c_output)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "critical frequency of input RC circuit = 17.241786 Hz\n",
        "critical frequency of output RC circuit = 17.223127 Hz"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<h3>Example 10.9, Page Number: 327<h3>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "import math\n",
      "B_ac=100.0;\n",
      "r_e=16.0;\n",
      "R1=62.0*10**3;\n",
      "R2=22.0*10**3;\n",
      "R_S=600.0;\n",
      "R_E=1.0*10**3;\n",
      "R_C=2.2*10**3;\n",
      "R_L=10.0*10**3;\n",
      "C1=0.1*10**-6;\n",
      "C2=10.0*10**-6;\n",
      "C3=0.1*10**-6;\n",
      "#input RC circuit\n",
      "R_in=(B_ac*r_e*R1*R2)/(B_ac*r_e*R1+B_ac*r_e*R2+R1*R2);\n",
      "f_c_input=1/(2*math.pi*(R_S+R_in)*C1);\n",
      "print('input frequency = %f Hz'%f_c_input)\n",
      "#For bypass circuit; Base circuit impedance= parallel combination of R1, R2, R_S\n",
      "R_th=(R1*R2*R_S)/(R1*R2+R2*R_S+R_S*R1);\n",
      "#Resistance looking at emitter\n",
      "R_in_emitter=r_e+(R_th/B_ac);\n",
      "#resistance of equivalent bypass RC is parallel combination of R_E,R_in_emitter\n",
      "R=(R_in_emitter*R_E)/(R_E+R_in_emitter);\n",
      "f_c_bypass=1/(2*math.pi*R*C2);\n",
      "print('critical frequency of bypass RC circuit = %f Hz'%f_c_bypass)\n",
      "f_c_output=1/(2*math.pi*(R_C+R_L)*C3)\n",
      "print('output frequency circuit = %f Hz'%f_c_output)\n",
      "R_c=R_C*R_L/(R_C+R_L);\n",
      "A_v_mid=R_c/r_e;\n",
      "attenuation=R_in/(R_in+R_S);\n",
      "A_v=attenuation*A_v_mid;    #overall voltage gain\n",
      "A_v_mid_dB=20*math.log10(A_v);    \n",
      "print('overall voltage gain in dB = %f'%A_v_mid_dB)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "input frequency = 773.916632 Hz\n",
        "critical frequency of bypass RC circuit = 746.446517 Hz\n",
        "output frequency circuit = 130.454871 Hz\n",
        "overall voltage gain in dB = 38.042470"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<h3>Example 10.10, Page Number: 330<h3>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "import math\n",
      "B_ac=125.0;\n",
      "C_be=20.0*10**-12;\n",
      "C_bc=2.4*10**-12;\n",
      "R1=22.0*10**3;\n",
      "R2=4.7*10**3;\n",
      "R_E=470.0;\n",
      "R_S=600.0;\n",
      "R_L=2.2*10**3;\n",
      "V_CC=10.0;\n",
      "V_B=(R2/(R1+R2))*V_CC;\n",
      "V_E=V_B-0.7;\n",
      "I_E=V_E/R_E;\n",
      "r_e=25.0*10**-3/I_E;\n",
      "#total resistance of input circuit is parallel combination of R1,R2,R_s,B_ac*r_e\n",
      "R_in_tot=B_ac*r_e*R1*R2*R_S/(B_ac*r_e*R1*R2+B_ac*r_e*R1*R_S+B_ac*r_e*R2*R_S+R1*R2*R_S);\n",
      "R_c= 1100.0#R_C*R_L/(R_C+R_L)\n",
      "A_v_mid=R_c/r_e;\n",
      "C_in_Miller=C_bc*(A_v_mid+1)\n",
      "C_in_tot=C_in_Miller+C_be;\n",
      "C_in_tot=C_in_tot*10**10\n",
      "f_c=1/(2*math.pi*R_in_tot*C_in_tot);\n",
      "print('total resistance of circuit = %f Ohm'%R_in_tot)\n",
      "print('total capacitance = %f * 10^-10 F'%C_in_tot)\n",
      "print('critical frequency = %f Hz'%f_c)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "total resistance of circuit = 377.815676 Ohm\n",
        "total capacitance = 2.606290 * 10^-10 F\n",
        "critical frequency = 0.000162 Hz"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<h3>Example 10.11, Page Number: 333<h3>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "import math\n",
      "C_bc=2.4*10**-12;    #from previous question\n",
      "A_v=99.0;    #from previous question\n",
      "R_C=2.2*10**3;\n",
      "R_L=2.2*10**3;\n",
      "R_c=R_C*R_L/(R_C+R_L);\n",
      "C_out_Miller=C_bc*(A_v+1)/A_v;\n",
      "f_c=1/(2*math.pi*R_c*C_bc);    #C_bc is almost equal to C_in_Miller\n",
      "C_out_Miller=C_out_Miller*10**12\n",
      "print('equivalent resistance = %d Ohm'%R_c)\n",
      "print('equivalent capacitance =%f *10^-12 F'%C_out_Miller)\n",
      "print('critical frequency =%f Hz'%f_c)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "equivalent resistance = 1100 Ohm\n",
        "equivalent capacitance =2.424242 *10^-12 F\n",
        "critical frequency =60285963.292385 Hz"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<h3>Example 10.12, Page Number: 334<h3>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "C_iss=6.0*10**-12;\n",
      "C_rss=2.0*10**-12;\n",
      "C_gd=C_rss;\n",
      "C_gs=C_iss-C_rss;\n",
      "C_gd=C_gd*10**12\n",
      "C_gs=C_gs*10**12\n",
      "print('gate to drain capacitance = %.1f * 10^-12 F'%C_gd)\n",
      "print('gate to source capacitance = %.1f * 10^-12 F'%C_gs)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "gate to drain capacitance = 2.0 * 10^-12 F\n",
        "gate to source capacitance = 4.0 * 10^-12 F"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<h3>Example 10.13, Page Number:335 <h3>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "import math\n",
      "C_iss=8.0*10**-12;\n",
      "C_rss=3.0*10**-12;\n",
      "g_m=6500.0*10**-6;    #in Siemens\n",
      "R_D=1.0*10**3;\n",
      "R_L=10.0*10**6;\n",
      "R_s=50.0;\n",
      "C_gd=C_rss;\n",
      "C_gs=C_iss-C_rss;\n",
      "R_d=R_D*R_L/(R_D+R_L);\n",
      "A_v=g_m*R_d;\n",
      "C_in_Miller=C_gd*(A_v+1);\n",
      "C_in_tot=C_in_Miller+C_gs;\n",
      "f_c=1/(2*math.pi*C_in_tot*R_s);\n",
      "print('critical frequency of input RC circuit =%.3f *10^8 Hz'%(f_c*10**-8))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "critical frequency of input RC circuit =1.158 *10^8 Hz"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<h3>Example 10.14, Page Number: 336<h3>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "import math\n",
      "C_gd=3.0*10**-12;    #from previous question\n",
      "A_v=6.5;             #from previous question\n",
      "R_d=1.0*10**3;       #from previous question\n",
      "C_out_Miller=C_gd*(A_v+1)/A_v;\n",
      "f_c=1/(2*math.pi*R_d*C_out_Miller);\n",
      "print('critical frequency of the output circuit = %d Hz'%f_c)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "critical frequency of the output circuit = 45978094 Hz"
       ]
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<h3>Example 10.15, Page Number: 339<h3>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "f_cu=2000.0;\n",
      "f_cl=200.0;\n",
      "BW=f_cu-f_cl;\n",
      "print('bandwidth = %d Hz'%BW)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "bandwidth = 1800 Hz"
       ]
      }
     ],
     "prompt_number": 33
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<h3>Example 10.16, Page Number: 340<h3>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "f_T=175.0*10**6;    #in hertz\n",
      "A_v_mid=50.0;\n",
      "BW=f_T/A_v_mid;\n",
      "print('bandwidth = %d Hz'%BW)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "bandwidth = 3500000 Hz"
       ]
      }
     ],
     "prompt_number": 34
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<h3>Example 10.17, Page Number: 341<h3>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "f_cl=1.0*10**3;    #lower critical frequency of 2nd stage in hertz\n",
      "f_cu=100.0*10**3;  #upper critical frequency of 1st stage in hertz\n",
      "BW=f_cu-f_cl;\n",
      "print('bandwidth = %d Hz'%BW)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "bandwidth = 99000 Hz"
       ]
      }
     ],
     "prompt_number": 35
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<h3>Example 10.18, Page Number: 341<h3>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "import math\n",
      "n=2.0;    #n is the number of stages of amplifier\n",
      "f_cl=500.0;\n",
      "f_cu=80.0*10**3;\n",
      "f_cl_new=f_cl/(math.sqrt(2**(1/n)-1));\n",
      "f_cu_new=f_cu*(math.sqrt(2**(1/n)-1));\n",
      "BW=f_cu_new-f_cl_new;\n",
      "print('bandwidth = %f Hz'%BW)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "bandwidth = 50710.653245 Hz"
       ]
      }
     ],
     "prompt_number": 36
    }
   ],
   "metadata": {}
  }
 ]
}