path: root/Analog_and_digital_communication_by_S_Sharma/Chapter2.ipynb

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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 2 - Amplitude Modulation"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1 - pg 51"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#calcualate the carrier frequency\n",
      "#given\n",
      "import math\n",
      "L = 50*10**-6#in henry\n",
      "C = 1*10**-9#in farads\n",
      "#calculation\n",
      "F_c = 1/(2.*math.pi*math.sqrt(L*C))/1000.;\n",
      "#results\n",
      "print '%s %d %s' %(\"Carrier frequency F_c =\",math.ceil(F_c),\" kHz\")\n",
      "print(\"Now , it is given that the highest modulation frequency is 8KHz \");\n",
      "print(\"Therefore, the frequency range occupied by the sidebands will range from 8KHz \\nabove to 8KHz below the carrier frequency, extending fom 712KHz to 720KHz.\");\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Carrier frequency F_c = 712  kHz\n",
        "Now , it is given that the highest modulation frequency is 8KHz \n",
        "Therefore, the frequency range occupied by the sidebands will range from 8KHz \n",
        "above to 8KHz below the carrier frequency, extending fom 712KHz to 720KHz.\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 2 - pg 51"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#calculate the modulation index, upper and lower sideband frequency, bandwidth of modulation signal\n",
      "\n",
      "\n",
      "#given\n",
      "#v_m = 10*sin(2*%pi*10^3*t)\n",
      "#by comparing with v_m = V_m*sin(2*%pi*f_c*t) we get\n",
      "V_m = 10.#in volts\n",
      "f_m = 1*10**3#in hertz\n",
      "V_c = 20.#in volts\n",
      "f_c = 1*10**4#in hertz\n",
      "\n",
      "#calculations\n",
      "m_a = V_m/V_c;#modulation index formula\n",
      "m_a1 = m_a*100;#percentage modulation index\n",
      "f_usb = f_c + f_m;#Upper sideband\n",
      "f_lsb = f_c - f_m;#lower sideband\n",
      "A = (m_a*V_c)/2#amplitude of upper as well as lower sideband\n",
      "B = 2*f_m;#bandwidth of the modulation signal\n",
      "\n",
      "#results\n",
      "print '%s %.2f' %(\"i.a.Modulation index= \",m_a);\n",
      "print '%s %d %s' %(\"   b.Percentage modulation index=\",m_a1,\" percent\");\n",
      "print '%s %.f %s' %(\"ii.a.Upper sidebandfrequency=\",f_usb,\"Hz\");\n",
      "print '%s %.f %s' %(\"    b.Lower sideband frequency=\",f_lsb,\"Hz \"); \n",
      "print '%s %.f %s' %(\"iii.Amplitude of Upper sideband and Lower sideband =\",A,\"V\");\n",
      "print '%s %.f %s' %(\"\\iv.Bandwidth of the modulation signal=\",B,\"Hz\");\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "i.a.Modulation index=  0.50\n",
        "   b.Percentage modulation index= 50  percent\n",
        "ii.a.Upper sidebandfrequency= 11000 Hz\n",
        "    b.Lower sideband frequency= 9000 Hz \n",
        "iii.Amplitude of Upper sideband and Lower sideband = 5 V\n",
        "\\iv.Bandwidth of the modulation signal= 2000 Hz\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3 - pg 54"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#calculate the total power in the amplitude modulated wave\n",
      "\n",
      "\n",
      "#given\n",
      "m_a = .75;#modulation index\n",
      "P_c = 400.;#carrier power in watts\n",
      "\n",
      "#calculation\n",
      "P_t = P_c*(1+(m_a**2/2));#total power \n",
      "\n",
      "#results\n",
      "print \"Total power in  the amplitude modulated wave (in W) = \",P_t;\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Total power in  the amplitude modulated wave (in W) =  512.5\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 4 - pg 54"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#calculate the carrier power\n",
      "#given\n",
      "P_t = 10*10**3;#total power in watts\n",
      "m_a = .6;#modulation index\n",
      "#calculation\n",
      "P_c = (P_t/(1+(m_a**2/2)));# carrier power\n",
      "#results\n",
      "print \"Carrier power (in kW) = \",round(P_c/1000.,2)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Carrier power (in kW) =  8.47\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 5 - pg 55"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#calculate the modulation index and antenna current\n",
      "\n",
      "import math\n",
      "#given\n",
      "I_t = 8.93;#total modulated current in ampers\n",
      "I_c= 8;#carrier or unmodulated current in ampers\n",
      "#calculation\n",
      "m_a = math.sqrt(2*((I_t/I_c)**2 -1));#formula for modulation index\n",
      "M_a=m_a*100;#percentage modulation\n",
      "#for \n",
      "m_a1 = .8;#given modulation index\n",
      "\n",
      "#calculation\n",
      "I_t1 = I_c*math.sqrt(1+(m_a1**2/2));#new antenna current \n",
      "\n",
      "#results\n",
      "print \"i.a. Modulation index = \",round(m_a,3)\n",
      "print \"b.Percentage modulation index (percent) = \",round(M_a,1)\n",
      "print \"ii. Antenna current (in A) = \",round(I_t1,2)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "i.a. Modulation index =  0.701\n",
        "b.Percentage modulation index (percent) =  70.1\n",
        "ii. Antenna current (in A) =  9.19\n"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 6 - pg 56"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#calculate the carrier signal current, modulation indexes\n",
      "import math\n",
      "#given\n",
      "I_t1 = 10#antenna current in amps\n",
      "m1 = .3#modulation index\n",
      "I_t2 = 11#increased antenna current\n",
      "\n",
      "#calculation\n",
      "I_c = (I_t1/(1+(m1**2/2))**.5);#formula for carrier signal current\n",
      "m_t = math.sqrt(2*((I_t2/I_c)**2 -1));#formula for modulation index\n",
      "m2 = math.sqrt(m_t**2 - m1**2);\n",
      "m3 = m2*100;#percentage modulation index\n",
      "\n",
      "#results\n",
      "print \"i.Carrier signal current (in A) = \",round(I_c,2)\n",
      "print \"ii.Modulation index of signal = \",round(m_t,2)\n",
      "print \"iii.a.Modulation index of second signal = \",round(m2,2)\n",
      "print \"b.Percentage modulation index of second signal (percent) = \",round(m3,0)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "i.Carrier signal current (in A) =  9.78\n",
        "ii.Modulation index of signal =  0.73\n",
        "iii.a.Modulation index of second signal =  0.66\n",
        "b.Percentage modulation index of second signal (percent) =  66.0\n"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7 - pg 56"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#calculate the modulating. maximum, minimum voltage\n",
      "\n",
      "#given v_c = 10*sinwt\n",
      "\n",
      "m = .5#modulation index\n",
      "#by comparing with v_c = V_c*sinwt\n",
      "V_c = 10#carrier voltage in volts\n",
      "\n",
      "#calculation\n",
      "V_m = m*V_c;#amplitude of modulating index\n",
      "V_max = V_c + V_m;#maximum voltage\n",
      "V_min = V_c - V_m;#minimum voltage\n",
      "\n",
      "#results\n",
      "print \" i.Modulating  voltage =\",round(V_m,2),\"V\" \n",
      "print \" ii. Maximum voltage =\",round(V_max,2),\"V\"\n",
      "print \" iii.Minimum voltage =\",round(V_min,2),\"V\" \n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " i.Modulating  voltage = 5.0 V\n",
        " ii. Maximum voltage = 15.0 V\n",
        " iii.Minimum voltage = 5.0 V\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 9 - pg 57"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#calculate the percentag4e modulation index\n",
      "\n",
      "#given\n",
      "V_max = 4.#maximum voltage in volts\n",
      "V_min = 1.#minimum voltage in volts\n",
      "\n",
      "#calculation\n",
      "m = (V_max - V_min)/(V_max + V_min) ;#formula for modulation index\n",
      "m1 = m*100.#percentage modultion index\n",
      "\n",
      "#result\n",
      "print \"Percentage modulation index =\",round(m1,2),\"percent\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "EXAMPLE 2.9(PAGENO 57)\n",
        "Percentage modulation index = 60.0 percent\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 10 - pg 57"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#calculate the carrier current and total modulation index\n",
      "import math\n",
      "#given\n",
      "m1 = .4#modulation index\n",
      "I_t1 = 11.#initial antenna current in ampers\n",
      "I_t2 = 12.#final antenna current in ampers\n",
      "\n",
      "#calculations\n",
      "I_c = (I_t1/(1+(m1**2/2))**.5);# formula for carrier current in ampers\n",
      "m_t = math.sqrt(2*((I_t2/I_c)**2 -1));#total modulation index\n",
      "m2 = math.sqrt(m_t**2 - m1**2);#modulation index to the second wave\n",
      "m3 = m2*100;#percentage modulation index to the second wave\n",
      "\n",
      "#results\n",
      "print \" Carrier current =\",round(I_c,2),\"A\"\n",
      "print\"Total modulation index =\",round(m_t,4)\n",
      "print \"Percentage modulation index of second wave=\",round(m3,2),\" percent\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " Carrier current = 10.58 A\n",
        "Total modulation index = 0.7554\n",
        "Percentage modulation index of second wave= 64.08  percent\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 11 - pg 58"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#calculate the modulation index and new transmitted power\n",
      "import math\n",
      "from math import sqrt\n",
      "#given\n",
      "P_c = 10.*10**3#carrier power in watts\n",
      "P_t = 12.*10**3#total power in watts\n",
      "m_2 = .5#modulation index of second wave\n",
      "\n",
      "#calculations\n",
      "m_1 = sqrt(2*((P_t/P_c)-1));#modulation index of first wave\n",
      "m_t = sqrt(m_1**2 +m_2**2);#total modulation index\n",
      "P_t1 = P_c*(1+(m_t**2/2))/1000.#total new transmitted power\n",
      "\n",
      "#results\n",
      "print \"Modulation index of first wave =\", round(m_1,4)\n",
      "print \"Total modulation index = \",round(m_t,1)\n",
      "print \"total new transmitted power =\",round(P_t1,1),\"kW\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Modulation index of first wave = 0.6325\n",
        "Total modulation index =  0.8\n",
        "total new transmitted power = 13.3 kW\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 12 - pg 60"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#calculate the modulation index and total radiated power\n",
      "import math\n",
      "from math import sqrt\n",
      "#given\n",
      "P_t = 10.125*10**3#modulated or total power in watts\n",
      "P_c = 9*10**3#unmodulated of carrier power\n",
      "m_2 = .4#modulation index of second wave\n",
      "\n",
      "#calculations\n",
      "m_1 = sqrt(2*((P_t/P_c) - 1))#modulation index of first wave\n",
      "m_a = m_1*100#percentage modulation index of first wave\n",
      "m_t = sqrt(m_1**2 + m_2**2)#total modulation index\n",
      "P_t1 = P_c*(1+(m_t**2/2))#total radiated power\n",
      "\n",
      "#results\n",
      "print \"i.a.Modulation index of first wave = \",round(m_1,4)\n",
      "print \" b.Percentage modulation index of first wave =\",round(m_a,2),\" percent\"\n",
      "print \"ii.Total radiated power =\",round(P_t1,2)/1000.,\"kW\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "i.a.Modulation index of first wave =  0.5\n",
        " b.Percentage modulation index of first wave = 50.0  percent\n",
        "ii.Total radiated power = 10.845 kW\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 13 - pg 90"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#calculate the percentage power saving for both signals\n",
      "#given\n",
      "m1 = 1.#modulation index of first signal\n",
      "m2 = .5#modulation index of second signal\n",
      "#let\n",
      "P_c = 1.#carrier power in watts \n",
      "\n",
      "#calculations\n",
      "P_1= P_c*(1+(m1**2/2b))#total power of first signal\n",
      "P_2 = P_c*(1+(m2**2/2))#total power of second signal\n",
      "P_a = (P_c*100)/(P_1)#percentage power saving for first signal\n",
      "P_b = (P_c*100)/(P_2)#percentage power saving for second signal\n",
      "\n",
      "#results\n",
      "print \"i.Percentage power saving for first signal=\",round(P_a,2),\" percent\"\n",
      "print \"ii.Percentage power saving for second signal=\",round(P_b,2),\"percent\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "i.Percentage power saving for first signal= 66.67  percent\n",
        "ii.Percentage power saving for second signal= 88.89 percent\n"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 15 - pg 98"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#calculate the percentage power saving for both signals\n",
      "#given\n",
      "m1 = 1.#modulation index of first signal\n",
      "m2 = .5#modulation index of second signal\n",
      "#let\n",
      "P_c = 1.#carrier power in watts \n",
      "\n",
      "#calculations\n",
      "P_cssb1 = P_c*(1+(m1**2/4))#power in carrier plus power in one sideband for first signal\n",
      "P_cssb2 = P_c*(1+(m2**2/4))#power in carrier plus power in one sideband for second signal\n",
      "P_1= P_c*(1+(m1**2/2))#total power of first signal\n",
      "P_2 = P_c*(1+(m2**2/2))#total power of second signal\n",
      "P_a = (P_cssb1*100)/(P_1)#percentage power saving for first signal\n",
      "P_b = (P_cssb2*100)/(P_2)#percentage power saving for second signal\n",
      "\n",
      "#results\n",
      "print \"i.Percentage power saving for first signal=\",round(P_a,2),\" percent\"\n",
      "print \"ii.Percentage power saving for second signal=\",round(P_b,2),\"percent\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "i.Percentage power saving for first signal= 83.33  percent\n",
        "ii.Percentage power saving for second signal= 94.44 percent\n"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 16 - pg 109"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#calculate the power content of the carrier in upper and lower sidebands\n",
      "#given\n",
      "P_ssb  = 10*10**3#power in ssb transmission  in watts\n",
      "P_t = P_ssb# total power in watts\n",
      "m_a = .8#modulation index\n",
      "\n",
      "#calculations\n",
      "P_c = (P_t/(1+(m_a**2/4)+(m_a**2/4)))#carrier power in watts\n",
      "P_SB = P_t - P_c#power in sidebands\n",
      "P_usb =  P_SB/2.#power in upper sideband\n",
      "P_lsb =P_usb#power in upper sideband\n",
      "\n",
      "#results\n",
      "print \"i.Power content of the carrier =\",round(P_c,2),\"W\"\n",
      "print \"ii.a.Power content in upper sideband  =\",round(P_usb),\"W\"\n",
      "print \"   b.Power content in lower sideband =\",round(P_lsb),\"W\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "i.Power content of the carrier = 7575.76 W\n",
        "ii.a.Power content in upper sideband  = 1212.0 W\n",
        "   b.Power content in lower sideband = 1212.0 W\n"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 17 - pg 109"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#calculate the modulation index\n",
      "#given from the figure\n",
      "P_maxpp = 2*80.#maximum peak to peak power in watts\n",
      "P_minpp = 2*20.#minimum peak to peak power in watts\n",
      "\n",
      "#calcualtions\n",
      "m_a = (P_maxpp - P_minpp)/(P_maxpp + P_minpp)#modultaion index\n",
      "M = m_a*100#percentage modulation index\n",
      "\n",
      "#results\n",
      "print \"i.Modulation index = \",m_a\n",
      "print \"ii.Percentage modulation index =\",round(M,2),\" percent\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "i.Modulation index =  0.6\n",
        "ii.Percentage modulation index = 60.0  percent\n"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 18 - pg 110"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#calculate the modulation index\n",
      "#given from the figure\n",
      "P_maxpp = 2*50.#maximum peak to peak power in watts\n",
      "P_minpp = 2*15.#minimum peak to peak power in watts\n",
      "\n",
      "#calculations\n",
      "m_a = (P_maxpp - P_minpp)/(P_maxpp + P_minpp)#modultaion index\n",
      "M = m_a*100#percentage modulation index\n",
      "\n",
      "#results\n",
      "print \"i.Modulation index = \",round(m_a,3)\n",
      "print \"ii.Percentage modulation index =\",round(M,1),\"percent\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "i.Modulation index =  0.538\n",
        "ii.Percentage modulation index = 53.8 percent\n"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 21 - pg 111"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#calculate the carrier power,transmission efficiency and carrier amplitude\n",
      "#given\n",
      "import cmath\n",
      "import math\n",
      "p_t = 50*10**3#total power\n",
      "m_a = .707#modulation index\n",
      "z = 50+0*1j;#load\n",
      "\n",
      "#calculations\n",
      "\n",
      "#first case\n",
      "p_x = .5*(m_a)**2;\n",
      "p_c = p_t/(1+p_x)#carrier power\n",
      "\n",
      "#second case\n",
      "n = ((p_c*p_x)/(p_c+(p_c*p_x)))*100;#transmission efficiency\n",
      "\n",
      "#third case\n",
      "a_c = cmath.sqrt(2*z*p_c);#peak carrier amplitude \n",
      "#results\n",
      "print \"i. Carrier Power = \",round(p_c/1000.,0),\" kW\"\n",
      "print \"ii. Percentage Transmission efficiency =\",round(n,2),\"percent\"\n",
      "print \"iii. Carrier amplitude  =\",round(abs(a_c),0),\" V\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "i. Carrier Power =  40.0  kW\n",
        "ii. Percentage Transmission efficiency = 20.0 percent\n",
        "iii. Carrier amplitude  = 2000.0  V\n"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 22 - pg 112"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#calculate the efficiency for ma=0.5 and for ma=1\n",
      "#given\n",
      "ma1=0.5\n",
      "ma2=1.\n",
      "\n",
      "#calculations\n",
      "eta1=ma1**2 /(ma1**2 +2) *100.\n",
      "eta2= ma2**2 /(ma2**2 +2) *100.\n",
      "\n",
      "#results\n",
      "print \"In case 1, efficiency = \",round(eta1,1),\"percent\"\n",
      "print \"In case 2, efficiency = \",round(eta2,1),\"percent\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "In case 1, efficiency =  11.1 percent\n",
        "In case 2, efficiency =  33.3 percent\n"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 29 - pg 118"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#calculate the modulation depth\n",
      "#given\n",
      "k = 2*10**-3#constants in amperes/square volts\n",
      "k_1 = 0.2*10**-3#constant in amperes/square volts\n",
      "print \"we know that V_i(t) = cos(w_c*t) + .5*cos(w_m*t)\"\n",
      "print \"given i_0 = 10 + k*V_i + k_1*V_i**2 \"\n",
      "print \"therefore i_0 = 10 + 2*10**-3*[cos(w_c*t) + .5*cos(w_m*t)] + 2*10**-3*[cos(w_c*t) + .5*cos(w_m*t)]\"\n",
      "print \"i_0 = 2*10**-3*cos(w_c*t) + ((.2*10**-3)/.5)*.5*cos(w_c*t)*cos(w_m*t)\"\n",
      "#Now the modulation depth will be\n",
      "m = (.2*10**-3)/.5;\n",
      "\n",
      "#result\n",
      "print \"Modulation depth = \",m\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "we know that V_i(t) = cos(w_c*t) + .5*cos(w_m*t)\n",
        "given i_0 = 10 + k*V_i + k_1*V_i**2 \n",
        "therefore i_0 = 10 + 2*10**-3*[cos(w_c*t) + .5*cos(w_m*t)] + 2*10**-3*[cos(w_c*t) + .5*cos(w_m*t)]\n",
        "i_0 = 2*10**-3*cos(w_c*t) + ((.2*10**-3)/.5)*.5*cos(w_c*t)*cos(w_m*t)\n",
        "Modulation depth =  0.0004\n"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 31 - pg 119"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#calculate the power saving in both cases\n",
      "#given\n",
      "#percentage modulation for first case\n",
      "Pm_1 = 100.\n",
      "#percentage modulation for second case\n",
      "Pm_2 = 50.\n",
      "m_1 = 1.#modulation index for first case\n",
      "m_2 = .5#modulation index for second case\n",
      "P_c = 1.#let carrier power be one\n",
      "\n",
      "#calcualations\n",
      "\n",
      "#first case\n",
      "P_t1 = P_c*(1+(m_1**2/2.))#total power\n",
      "P_sb1 = P_c*(m_1**2/4.)#power in one side band\n",
      "P_s1 = ((P_t1-P_sb1)/P_t1)*100.#power saving\n",
      "\n",
      "#second case\n",
      "P_t2 = P_c*(1+(m_2**2/2))#total power\n",
      "P_sb2 = P_c*(m_2**2/4)#power in one side band\n",
      "P_s2 = ((P_t2-P_sb2)/P_t2)*100.#power saving\n",
      "\n",
      "#results\n",
      "print \"i. Power saving with percentage modulation 100 =\",round(P_s1,1),\" percent \"\n",
      "print \"ii. Power saving with percentage modulation 50 =\",round(P_s2,1),\" percent\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "i. Power saving with percentage modulation 100 = 83.3  percent \n",
        "ii. Power saving with percentage modulation 50 = 94.4  percent\n"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 32 - pg 119"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#calculate the minimum value of fc\n",
      "import math\n",
      "#given\n",
      "#the product signal is given by\n",
      "#v(t) = s(t) * cos(2*%pi*t +phi) = x(t) *cos(2*%pi*f_c*t)*cos(2*%pi*f_c*t +phi)\n",
      "#v(t) = x(t) *(cos(4*%pi*f_c*t +phi) +cos(phi))/2 = (x(t)/2)*cos(4*%pi*f_c*t +phi)+(x(t)/2)*cos(phi)\n",
      "#the low pass filter will reject the first term. The maximum allowable value of phase angle(phi) can be found as under:\n",
      "print \"cos(phi_max) = ((x(t)/2)*cos(phi))/max((x(t)/2)*cos(phi))\"\n",
      "phi_max = math.acos(.95)*180/math.pi;\n",
      "print \"phi_max = \",round(phi_max,2)\n",
      "print \"In order to recover x(t) from v(t) using filter method, it is essential that the lowest frequency contained in the first term of v(t) must be greater than the highest frequency contained in the second term,i.e,\"\n",
      "print \"2f_c -10KHz > 10KHz\"\n",
      "print \"f_c >10KHz\"\n",
      "print \"Hence, the minimum value of f_c will be\"\n",
      "print \"f_c = 10KHz\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "cos(phi_max) = ((x(t)/2)*cos(phi))/max((x(t)/2)*cos(phi))\n",
        "phi_max =  18.19\n",
        "In order to recover x(t) from v(t) using filter method, it is essential that the lowest frequency contained in the first term of v(t) must be greater than the highest frequency contained in the second term,i.e,\n",
        "2f_c -10KHz > 10KHz\n",
        "f_c >10KHz\n",
        "Hence, the minimum value of f_c will be\n",
        "f_c = 10KHz\n"
       ]
      }
     ],
     "prompt_number": 28
    }
   ],
   "metadata": {}
  }
 ]
}