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-{
- "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"
-   ]
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "Python 2",
-   "language": "python",
-   "name": "python2"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 2
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