{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter 4 Angle Modulation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exa 4.1.A page.no: 286"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12000 the new deviation( in Hz)\n"
     ]
    }
   ],
   "source": [
    "Freq_dev=6; #Frequency Deviation in kHz\n",
    "Vm=3; #Modulating Voltage in V\n",
    "Dev=Freq_dev*10**3/Vm; \n",
    "# for Vm=6V\n",
    "Vm=6;\n",
    "Freq_dev_new=Dev*Vm;\n",
    "print Freq_dev_new,\"the new deviation( in Hz)\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exa 4.1 page.no: 287"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Instantaneous Frequency(in Hz) at (t=0.4 ms)N =  100290.574948\n",
      "Maximum Phase Deviation (in rad) =  3\n",
      "MAximum Frequency Deiation (in Hz)=  300.0\n"
     ]
    }
   ],
   "source": [
    "from math import pi,cos\n",
    "\n",
    "t1=0.4;# time in ms\n",
    "Ang_Freq =2*pi*10**5 +3*2*pi*100*cos(2*pi*100*(t1*10**(-3)));\n",
    "Freq=Ang_Freq/(2*pi);\n",
    "#change in answer due to calculation error in book\n",
    "print \"Instantaneous Frequency(in Hz) at (t=0.4 ms)N = \",Freq\n",
    "Max_pha_Dev=3; #max(3sin(2∗pi∗100t))\n",
    "print \"Maximum Phase Deviation (in rad) = \",Max_pha_Dev\n",
    "Max_fre_Dev=6*pi*100;  #max(6∗pi∗100∗cos(2∗pi∗100t))\n",
    "print \"MAximum Frequency Deiation (in Hz)= \",Max_fre_Dev/(2*pi)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exa 4.2.A page.no: 287"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Power Dissipated (in W) is  9.375\n"
     ]
    }
   ],
   "source": [
    "from math import pi,sqrt\n",
    "\n",
    "Wc=8*10**(8);# Angular Frequency of Carrier Signal\n",
    "fc=Wc/(2*pi);\n",
    "Wm=1300;#Angular Frequency of Message Signal\n",
    "fm=Wm/(2*pi);\n",
    "B=3;#Modulation Index\n",
    "R=12;\n",
    "Vc_rms=15/sqrt(2);\n",
    "Max_dev=B*fm;\n",
    "Power=Vc_rms**(2)/R;\n",
    "print \"Power Dissipated (in W) is \",Power"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exa 4.2 page.no: 287"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Peak Frequency Deviation(in Hz) is  12000\n",
      "modulation index  8.0\n"
     ]
    }
   ],
   "source": [
    "a=3;#amplitude in volts\n",
    "Dev_sen=4;# deviation sensitivity in KHz/volts\n",
    "fm=1.5;# frequency modulating signal in KHz\n",
    "f=Dev_sen*10**(3)*3;#peak frequency deviation\n",
    "B=f/(fm*10**3);\n",
    "print \"Peak Frequency Deviation(in Hz) is \",f\n",
    "print \"modulation index \",B"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exa 4.3.A page.no: 289"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Bandwidth (in Hz) is  72000\n"
     ]
    }
   ],
   "source": [
    "fm=3; #Modulating Frequency in kHZ\n",
    "Max_Dev=18; #MAximum Deviation in kHz\n",
    "B=Max_Dev/fm; # modulation index 7\n",
    "J=12;#from Bessel Table , for B=6\n",
    "Bw=fm*J*2*10**(3);\n",
    "print \"The Bandwidth (in Hz) is \",Bw"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exa 4.3 page.no: 289"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Peak Phase Deviation( in rad)  8.75\n"
     ]
    }
   ],
   "source": [
    "Dev_sen=3.5 # Deviation Sensitivity in rad/volt\n",
    "a=2.5; #amplitude in volts\n",
    "B=a*Dev_sen; # Peak Phase Deviation\n",
    "print \"Peak Phase Deviation( in rad) \",B"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exa 4.4.A page.no: 290"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Maximum Frequency Deviation (in Hz) is  18000\n",
      "Modulation Index is  5.99985864877\n"
     ]
    }
   ],
   "source": [
    "from math import pi\n",
    "\n",
    "Wm=18850;#Angular Frequency of message signal\n",
    "fm=Wm/(2*pi);\n",
    "a=3;# amplitude of message signal\n",
    "Dev_sen=6;#Deviation Sensitivity in kHz/V\n",
    "Max_Freq_Dev=a*Dev_sen*10**(3);\n",
    "B=Max_Freq_Dev/(fm);\n",
    "print \"Maximum Frequency Deviation (in Hz) is \",Max_Freq_Dev\n",
    "print \"Modulation Index is \",B"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exa 4.4 page.no: 291"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Deviation Sensitivity(in kHz/V)  1333\n",
      "Modulation Index is  4\n",
      "Deviation Sensitivity for 5V (in Hz)  6665\n",
      "Modulation index 6\n",
      "Deviation Sensitivity for 10V (in Hz)  13330\n",
      "Modulation index is  33\n"
     ]
    }
   ],
   "source": [
    "a=3; #amplitude in Volts\n",
    "Dev=4;# Deviation in kHz\n",
    "fm=1;# modulating frequency in kHz\n",
    "Dev_sen=Dev*10**(3)/a; #Deviation Sensitivity\n",
    "B=Dev/fm; # Modulation Index\n",
    "print \"Deviation Sensitivity(in kHz/V) \",Dev_sen\n",
    "print \"Modulation Index is \",B\n",
    "#a)\n",
    "a=5;\n",
    "Dev_sen_1=a*Dev_sen;\n",
    "B=Dev_sen_1/(fm*10**(3));\n",
    "print \"Deviation Sensitivity for 5V (in Hz) \",Dev_sen_1\n",
    "print \"Modulation index\",B\n",
    "#b)\n",
    "a=10;\n",
    "fm=400;\n",
    "Dev_sen_2=a*Dev_sen;\n",
    "B=Dev_sen_2/fm;\n",
    "print \"Deviation Sensitivity for 10V (in Hz) \",Dev_sen_2\n",
    "print \"Modulation index is \",B"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exa 4.5.A page.no: 291"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "for B=2, The number of significant frequencies are 6\n",
      "They are J1,J2,J3,J4,J5 and J6\n",
      "Their amplitudes with carriers are \n",
      "they are (in V) 1.792 4.616 2.824 1.032 0.272 0.056 0.008\n"
     ]
    }
   ],
   "source": [
    "print \"for B=2, The number of significant frequencies are 6\"\n",
    "print \"They are J1,J2,J3,J4,J5 and J6\"\n",
    "print \"Their amplitudes with carriers are \"\n",
    "J0= 0.224*8;\n",
    "J1= 0.577*8;\n",
    "J2= 0.353*8;\n",
    "J3= 0.129*8;\n",
    "J4= 0.034*8;\n",
    "J5= 0.007*8;\n",
    "J6= 0.001*8;\n",
    "print\"they are (in V)\",J0,J1,J2,J3,J4,J5,J6"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exa 4.5 page.no: 292"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Bandwidth required (in Hz)  24000\n",
      "According to Carsons rule , Bandwidth (in Hz)  36000\n"
     ]
    }
   ],
   "source": [
    "fm=3; #Modulating Frequency in kHZ\n",
    "Max_dev=15;# Maximum Deviatin in kHZ\n",
    "B=Max_dev/fm; \n",
    "J=8; # Bessel table , the highest J coefficient\n",
    "BW=J*fm*10**(3);#Bandwidth in kHz\n",
    "BW1=2*(fm+Max_dev)*10**(3);# According to carson rule , BAndwidth\n",
    "print \"Bandwidth required (in Hz) \",BW\n",
    "print \"According to Carsons rule , Bandwidth (in Hz) \",BW1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exa 4.6.A page.no: 292"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Minimum Bandwidth (in Hz) is  72000\n",
      "Approximate Minimum Bandwidth is  36000\n"
     ]
    }
   ],
   "source": [
    "Max_Freq_Dev=12; #Maximum Frequency Deviation in kHZ\n",
    "fm=6; #Modulating frquency in kHz\n",
    "B=Max_Freq_Dev/fm;# Modulation index 7\n",
    "J=6;#From Bessel Table , for B=2\n",
    "Bw=2*J*6*10**(3);\n",
    "BW_carson=2*(fm + Max_Freq_Dev)*10**(3);\n",
    "print \"Minimum Bandwidth (in Hz) is \",Bw\n",
    "print \"Approximate Minimum Bandwidth is \",BW_carson"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exa 4.6.A page.no: 283"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For B=5 from the Bessel table ,The Bessel Function is taken upto J9\n",
      "Hence the average power of the modulated signal (in W) is  9.936\n",
      "Hence, the average power of the modulated signal is equal to \n",
      "unmodulated carrier power\n"
     ]
    }
   ],
   "source": [
    "a=10; #Amplitude in V\n",
    "Pt=a*(0.18**2 +2*(0.33**2+0.05**2+0.36**2+0.39**2+0.26**2+0.13**2+0.05**2+0.02**2+0.01**2))\n",
    "print \"For B=5 from the Bessel table ,The Bessel Function is taken upto J9\"\n",
    "print \"Hence the average power of the modulated signal (in W) is \",Pt\n",
    "print \"Hence, the average power of the modulated signal is equal to \"\n",
    "print \"unmodulated carrier power\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exa 4.7.A page.no: 294"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Unmodulated Power Carrier ( in W) =  1\n",
      "Total Power in modulated wave(in W)=  1.06767573333\n",
      "Power in the modulated wave is equal to \n",
      "power in the unmodulated wave \n"
     ]
    }
   ],
   "source": [
    "a=8;# amplitude in V\n",
    "r=30; # resistance in ohms\n",
    "Pc_unmodulated=a**2/(2*r);\n",
    "Pt=1.792**2/(2*30)+2*(4.616)**2/(2*30)+2*(2.824**2)/(2*30) +2*(1.032) **2/(2*30) +2*(0.272) **2/(2*30) +2*(0.056)**2/(2*30)+2*(0.008)**2/(2*30);\n",
    "# change in answer due to approximations in the book\n",
    "print \"Unmodulated Power Carrier ( in W) = \",Pc_unmodulated\n",
    "print \"Total Power in modulated wave(in W)= \",Pt\n",
    "print \"Power in the modulated wave is equal to \"\n",
    "print \"power in the unmodulated wave \" \n",
    "#\"Small error due to rounded off values in Bessel functions\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exa 4.7 page.no: 295"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "the Phase Modulation Function =  12.0*sin(3000.0*pi*t)\n",
      "The Modulated Wave Function =  12.0*sin(3000.0*pi*t) + 8*cos(20000*pi*t)\n"
     ]
    }
   ],
   "source": [
    "from sympy import symbols,sin,cos\n",
    "\n",
    "t,pi=symbols('t,pi') \n",
    "Pha_dev=3.; #Phase Deviation constant in rad/V 6\n",
    "# Phase Modulation Function\n",
    "Pha_function=Pha_dev*4*sin(2.*pi*1.5*10**3*t);\n",
    "Mod_wave=8*cos(2*pi*10**4*t)+Pha_function\n",
    "print \"the Phase Modulation Function = \",Pha_function\n",
    "print \"The Modulated Wave Function = \",Mod_wave"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exa 4.8 page.no: 295"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The outputs of the balanced modulator for these parameters\n",
      "are same as the inputs \n",
      "They remain unaltered \n",
      "At the output of the Multiplier , \n",
      "Fc(in kHz)=  9600 , Fm(in kHz)=  10 , B=  6.0\n",
      "Frequency Deviation ( in kHz)=  60\n"
     ]
    }
   ],
   "source": [
    "initial_Freq_Dev=5; # frequency in kHz\n",
    "B_initial=0.5; #modulation index\n",
    "fm_initial=10;# message signal frequency in kHz\n",
    "fc_initial=800; # carrier frequency in kHz\n",
    "print \"The outputs of the balanced modulator for these parameters\"\n",
    "print \"are same as the inputs \"\n",
    "print \"They remain unaltered \"\n",
    "#at the output of the multiplier 14\n",
    "m=12;# multiplication factor\n",
    "final_Freq_Dev=initial_Freq_Dev*m;\n",
    "B_final=0.5*m;\n",
    "fm_final=10; #modulating signal remains unaltered\n",
    "fc_final=800*m;\n",
    "print \"At the output of the Multiplier , \"\n",
    "print \"Fc(in kHz)= \",fc_final,\", Fm(in kHz)= \",fm_final,\", B= \",B_final\n",
    "print \"Frequency Deviation ( in kHz)= \",final_Freq_Dev"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exa 4.9.A page.no: 296"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a) MAster Oscillator Centre Frequency(in MHz) =  4.008\n",
      "b) Frequency Deviation at the output of modulator(in KHz)=  2.4\n",
      "c)Devaition ratio at the output of modulator  0.24\n",
      "d)deviation ratio at power amplifier 6.0\n"
     ]
    }
   ],
   "source": [
    "ft=100.2; #final carrier frequency in MHz\n",
    "Freq_Dev_ft=60.;# Frequency Deviation in KHz at power amplifier\n",
    "fm=10.;#modulating frequency in KHz\n",
    "m=25.;#multiplication factor\n",
    "#a)\n",
    "fc=ft/25.;\n",
    "#b)\n",
    "Freq_Dev=Freq_Dev_ft/25;\n",
    "#c)\n",
    "B=Freq_Dev/fm;\n",
    "#d)\n",
    "Bt=B*m;\n",
    "print \"a) MAster Oscillator Centre Frequency(in MHz) = \",fc\n",
    "print \"b) Frequency Deviation at the output of modulator(in KHz)= \",Freq_Dev\n",
    "print \"c)Devaition ratio at the output of modulator \",B\n",
    "print \"d)deviation ratio at power amplifier\",Bt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exa 4.10.A page.no: 297"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a) Frequency Deviation(in Hz)=  5954.92965855\n",
      "b) Devaition Ratio=  5.95492965855\n",
      "c) Phase Deviation( in rad)=  8\n",
      "d) Bandwidth( in Hz)=  13909.8593171\n"
     ]
    }
   ],
   "source": [
    "from math import pi\n",
    "\n",
    "#f(t)=5cos(Wc∗t+3sin(2000∗t)+5sin(2000∗pi∗t)) 5\n",
    "fm=2000*pi/(2*pi); #bandwidth is the highest frequency component\n",
    "#a) \n",
    "Freq_dev=(6000+10000*pi)/(2*pi); 11\n",
    "#b)\n",
    "B=Freq_dev/fm; \n",
    "#c)\n",
    "Phase_dev=8;#Highest value of[3sin(2000t)+5sin(2000∗ pi∗t)]\n",
    "#d)\n",
    "Bw= 2*(fm+Freq_dev);\n",
    "print \"a) Frequency Deviation(in Hz)= \",Freq_dev\n",
    "print \"b) Devaition Ratio= \",B\n",
    "print \"c) Phase Deviation( in rad)= \",Phase_dev\n",
    "print \"d) Bandwidth( in Hz)= \",Bw"
   ]
  }
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