{
"cells": [
 {
		   "cell_type": "markdown",
	   "metadata": {},
	   "source": [
       "# Chapter 4: Angle Modulation"
	   ]
	},
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 4.10_A: Angle_Modulation.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc;\n",
"clear;\n",
"\n",
"//f(t)=5cos(Wc*t+3sin(2000*t)+5sin(2000*pi*t))\n",
"\n",
"fm=2000*%pi/(2*%pi); //bandwidth is the highest frequency component\n",
"\n",
"//a)\n",
"\n",
"Freq_dev=(6000+10000*%pi)/(2*%pi);\n",
"\n",
"//b)\n",
"\n",
"B=Freq_dev/fm;\n",
"\n",
"//c)\n",
"Phase_dev=8;//Highest value of[3sin(2000t)+5sin(2000*pi*t)]\n",
"\n",
"//d)\n",
"Bw= 2*(fm+Freq_dev);\n",
"\n",
"disp(Freq_dev,' a) Frequency Deviation(in Hz)=');\n",
"disp(B,' b) Devaition Ratio=');\n",
"disp(Phase_dev,' c) Phase Deviation( in rad)=');\n",
"disp(Bw,' d) Bandwidth( in Hz)=')"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 4.1_A: Frequency_Deviation.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"\n",
"clc;\n",
"clear;\n",
"Freq_dev=6; //Frequency Deviation in kHz\n",
"Vm=3; //Modulating Voltage in V\n",
"\n",
"Dev=Freq_dev*10^(3)/Vm;\n",
"\n",
"// for Vm=6V\n",
"\n",
"Vm=6;\n",
"Freq_dev_new=Dev*Vm;\n",
"\n",
"disp(Freq_dev_new,'the new deviation( in Hz)');"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 4.1: phase_and_frequency_deviation.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc;\n",
"clear;\n",
"\n",
"t=0:0.01:1;                                               \n",
"Freq=2*%pi*10^(5)+3*2*%pi*100*cos(2*%pi*100*(t));//Phase=2*%pi*10^(5)*t+3*sin(2*%pi*100*t);\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",
"\n",
"//change in answer due to calculation error in book\n",
"disp(Freq,'Instantaneous Frequency(in Hz) at (t=0.4ms)N =');\n",
"\n",
"\n",
"Max_pha_Dev=3; //max(3sin(2*%pi*100t))\n",
"\n",
"disp(Max_pha_Dev,' Maximum Phase Deviation(in rad) =');\n",
" \n",
"Max_fre_Dev=6*%pi*100;//max(6*pi*100*cos(2*pi*100t))\n",
"\n",
"\n",
"\n",
"disp(Max_fre_Dev/(2*%pi),'MAximum Frequency Deiation(in Hz)');"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 4.2_A: Power_in_FM_system.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc;\n",
"clear;\n",
"Wc=8*10^(8);// Angular Frequency of Carrier Signal\n",
"fc=Wc/(2*%pi);\n",
"\n",
"Wm=1300;//Angular Frequency of Message Signal\n",
"fm=Wm/(2*%pi);\n",
"\n",
"B=3;//Modulation Index\n",
"R=12;\n",
"Vc_rms=15/sqrt(2);\n",
"\n",
"Max_dev=B*fm; \n",
"Power=Vc_rms^(2)/R;\n",
"\n",
"disp(Power,'Power Dissipated (in W) is');"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 4.2: Peak_Frequency_Deviation.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc;\n",
"clear;\n",
"a=3;//amplitude in volts\n",
"Dev_sen=4;// deviation sensitivity in KHz/volts\n",
"fm=1.5;// frequency modulating signal in KHz\n",
"\n",
"f=Dev_sen*10^(3)*3;//peak frequency deviation\n",
"B=f/(fm*10^3);\n",
"\n",
"disp(f,'Peak Frequency Deviation( in Hz) ');\n",
"disp(B,'modulation index ');"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 4.3_A: BAndwidth_of_FM.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc;\n",
"clear;\n",
"fm=3; //Modulating Frequency in kHZ\n",
"Max_Dev=18; //MAximum Deviation in kHz\n",
" \n",
" B=Max_Dev/fm; //modulation index\n",
" \n",
" J=12;//from Bessel Table, for B=6\n",
" Bw=fm*J*2*10^(3);\n",
" \n",
" disp(Bw,'The Bandwidth (in Hz) is') ;"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 4.3: Peak_Phase_Deviatio.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc;\n",
"clear;\n",
"Dev_sen=3.5;// Deviation Sensitivity in rad/volt\n",
"a=2.5;// amplitude in volts\n",
"\n",
"B=a*Dev_sen; //Peak Phase Deviation\n",
"\n",
"disp(B,'Peak Phase Deviation( in rad)');"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 4.4_A: Peak_Deviation_in_FM.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc;\n",
"clear;\n",
"Wm=18850;//Angular Frequency of message signal\n",
"fm=Wm/(2*%pi);\n",
"a=3;// amplitude of message signal\n",
"\n",
"Dev_sen=6;//Deviation Sensitivity in kHz/V\n",
"Max_Freq_Dev=a*Dev_sen*10^(3);\n",
"\n",
"B=Max_Freq_Dev/(fm);\n",
"\n",
"disp(Max_Freq_Dev,'Maximum Frequency Deviation(in Hz)');\n",
"disp(B,'Modulation Index');"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 4.4: Frequency_Modulation.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc;\n",
"clear;\n",
"a=3; //amplitude in Volts\n",
"Dev=4;// Deviation in kHz\n",
"fm=1;// modulating frequency in kHz\n",
"\n",
"Dev_sen=Dev*10^(3)/a; //Deviation Sensitivity\n",
"B=Dev/fm; // Modulation Index\n",
"\n",
"disp(Dev_sen,'Deviation Sensitivity(in kHz/V)');\n",
"disp(B,'Modulation Index');\n",
"\n",
"//a)\n",
"a=5;\n",
"Dev_sen_1=a*Dev_sen;\n",
"B=Dev_sen_1/(fm*10^(3));\n",
"\n",
"disp(Dev_sen_1,'Deviation Sensitivity for 5V (in Hz)');\n",
"disp(B,'Modulation index');\n",
"\n",
"\n",
"//b)\n",
"a=10;\n",
"fm=400;\n",
"Dev_sen_2=a*Dev_sen;\n",
"B=Dev_sen_2/fm;\n",
"\n",
"\n",
"disp(Dev_sen_2,'Deviation Sensitivity for 10V (in Hz)');\n",
"disp(B,'Modulation index');"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 4.5_A: side_frequencies_and_Aplitudes.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc;\n",
"clear;\n",
"disp('for B=2, The number of significant frequencies are 6');\n",
"disp('They are J1,J2,J3,J4,J5 and J6');\n",
"disp('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",
"disp(J6, J5,J4,J3,J2,J1,J0,'they are (in V)');"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 4.5: CArson_Bandwidth.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc;\n",
"clear;\n",
"fm=3; //Modulating Frequency in kHZ\n",
"Max_dev=15;// Maximum Deviatin in kHZ\n",
"\n",
"B=Max_dev/fm;\n",
"\n",
"J=8; // Bessel table,the highest J coefficient\n",
"BW=J*fm*10^(3);//Bandwidth in kHz\n",
"\n",
"BW1=2*(fm+Max_dev)*10^(3);//  According to carson rule, BAndwidth\n",
"\n",
"disp(BW,'Bandwidth required (in Hz)');\n",
"disp(BW1,'According to Carsons rule, Bandwidth(in Hz)');"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 4.6_A: Carson_Bandwidth.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc;\n",
"clear;\n",
"Max_Freq_Dev=12; //Maximum Frequency Deviation in kHZ\n",
"fm=6; //Modulating frquency in kHz\n",
"\n",
"B=Max_Freq_Dev/fm;// Modulation index\n",
"\n",
"J=6;//From Bessel Table, for B=2\n",
"\n",
"Bw=2*J*6*10^(3);\n",
"BW_carson=2*(fm + Max_Freq_Dev)*10^(3);\n",
"\n",
"disp(Bw,' Minimum Bandwidth (in Hz) is');\n",
"disp(BW_carson,' Approximate Minimum Bandwidth according to carson rule( in Hz) is');"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 4.6: Average_Power_of_signal.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc;\n",
"clear;\n",
"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",
"\n",
"disp(' For B=5 from the Bessel table,The Bessel Function is taken upto J9');\n",
"disp(Pt,' Hence the average power of the modulated signal (in W) is');\n",
"disp('Hence, the average power of the modulated signal is equal to ');\n",
"disp('unmodulated carrier power');"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 4.7_A: Unmodulated_Carrier_Power.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc;\n",
"clear;\n",
"a=8;// amplitude in V\n",
"r=30; //resistance in ohms\n",
"\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",
"\n",
"// change in answer due to approximations in the book\n",
"\n",
"disp(Pc_unmodulated,'Unmodulated Power Carrier(in W)=');\n",
"disp(Pt,'Total Power  in modulated wave(in W)=');\n",
"disp('Power in the modulated wave is equal to');\n",
"disp('power  in the unmodulated wave');\n",
"disp('Small error due to rounded off values in Bessel functions');"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 4.7: Phase_Modulatio.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc;\n",
"clear;\n",
"syms t pi;\n",
"\n",
"Pha_dev=3; //Phase_Deviation constant in rad/V\n",
"\n",
"// Phase Modulation Function \n",
"\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",
"\n",
"disp( Pha_function,'the Phase Modulation Function = ');\n",
"\n",
"disp(Mod_wave ,'The Modulated Wave Function = ');"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 4.8_A: Balanced_Modulator.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc;\n",
"clear;\n",
"\n",
"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",
"\n",
"disp('The outputs of the balanced modulator for these parameters');\n",
"disp('are same as the inputs');\n",
"disp('They remain unaltered');\n",
"\n",
"//at the output of the multiplier\n",
"\n",
"m=12;// multiplication factor\n",
"\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",
"\n",
"disp('At the output of the Multiplier,');\n",
"disp(fc_final,'Fc(in kHz)=',fm_final,'Fm(in kHz)=',B_final,'B=');\n",
"disp(final_Freq_Dev,' Frequency Deviation(in kHz)=');"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 4.9_A: Frequency_Deviation.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc;\n",
"clear;\n",
"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",
"\n",
"//a)\n",
"fc=ft/25;\n",
"\n",
"//b)\n",
"Freq_Dev=Freq_Dev_ft/25;\n",
"\n",
"//c)\n",
"B=Freq_Dev/fm;\n",
"\n",
"//d)\n",
"Bt=B*m;\n",
"\n",
"disp(fc,'a) MAster Oscillator Centre Frequency(in MHz) =');\n",
"disp(Freq_Dev, 'b) Frequency Deviation at the output of modulator(in KHz)=');\n",
"disp(B,'c)Devaition ratio at the output of modulator');\n",
"disp(Bt,'d)deviation ratio at power amplifier');"
   ]
   }
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