{
"metadata": {
"name": "",
"signature": "sha256:a49a8ec12fc3b73c3ede4bd700b2981c396abe3970143184cc460eca3744fac1"
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"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"CHAPTER04:ANGLE MODULATION"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example E03 : Pg 4.9"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Page Number: 4.9\n",
"# Example 4.3\n",
"# Given\n",
"fc=1.*10.**6.; # Hz\n",
"kf=5.;\n",
"mt=1.*10.**5.; # Hz\n",
"\n",
"# (a) mi(t) with fm\n",
"mi=(fc+(kf*mt));\n",
"print\"Max, Inst. Frequency with FM\",mi,\"Hz\"\n",
"import math \n",
"kp=3.;\n",
"# (b) mi2(t) with pm\n",
"mi2=fc+(mt*(kp/(2*math.pi)));\n",
"\n",
"print\"Max, Inst. Frequency with PM\",mi2,\"Hz\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Max, Inst. Frequency with FM 1500000.0 Hz\n",
"Max, Inst. Frequency with PM 1047746.48293 Hz\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example E09 : Pg 4.13"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Page Number: 4.13\n",
"# Example 4.9\n",
"# Given\n",
"delf=20.*10.**3.; # hz\n",
"fm=10.*10.**3.; # Hz\n",
"\n",
"B=delf/fm;\n",
"print\"Beta: \",B"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Beta: 2.0\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example E13 : Pg 4.16"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Page Number: 4.16\n",
"# Example 4.13\n",
"# Given\n",
"# x(t)=10cos((2*pi*10**8*t)+(200cos(2*pi*10**3*t)))\n",
"# on differentiating\n",
"# wi=2*pi*(1D+8)-4*pi*sin(2*pi*(1D+3)*t)\n",
"# Therefore\n",
"import math \n",
"delw=4.*math.pi*(1.*10.**5.);\n",
"wm=2.*math.pi*(1.*10.**3.);\n",
"B=delw/wm;\n",
"wb=2.*(B+1.)*wm;\n",
"fb=wb/2.*math.pi;\n",
"print\"Wb\",wb,\"rad/s\"\n",
"print\"Fb\",fb,\"Hz\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Wb 2525840.49349 rad/s\n",
"Fb 3967580.96924 Hz\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example E14 : Pg 4.17"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Page Number: 4.17\n",
"# Example 4.14\n",
"# Given\n",
"delf=100.*10.**3; # Hz\n",
"fc=20.*10.**6.; # Hz\n",
"\n",
"# As B=delf/fm;\n",
"# (a) fm1=1*10.**3hz\n",
"print'Part a'\n",
"fm1=1.*10.**3.; # Hz\n",
"B1=delf/fm1;\n",
"print'Modulation Index',B1\n",
"fb1=2.*delf;\n",
"print'Bandwidth',fb1,'Hz'\n",
"# (b) fm2=100*10.**3hz\n",
"print'\\nPart b'\n",
"fm2=100.*10.**3.; # Hz\n",
"B2=delf/fm2;\n",
"print'Modulation Index',B2\n",
"fb2=2.*(B2+1.)*fm2;\n",
"print'Bandwidth',fb2,'Hz'\n",
"# (c) fm3=500*10.**3hz\n",
"print'\\nPart c'\n",
"fm3=500.*10.**3.; # Hz\n",
"B3=delf/fm3;\n",
"print'Modulation Index',B3\n",
"fb3=2.*fm3;\n",
"print'Bandwidth',fb3,'Hz'"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Part a\n",
"Modulation Index 100.0\n",
"Bandwidth 200000.0 Hz\n",
"\n",
"Part b\n",
"Modulation Index 1.0\n",
"Bandwidth 400000.0 Hz\n",
"\n",
"Part c\n",
"Modulation Index 0.2\n",
"Bandwidth 1000000.0 Hz\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example E15 : Pg 4.17"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Page Number: 4.17\n",
"# Example 4.15\n",
"# Given\n",
"# x(t)=10cos(wct+3sinwmt)\n",
"# Comparing with standard equation\n",
"B=3.;\n",
"fm=1.*10.**3.; # hz\n",
"fb=2.*(B+1.)*fm;\n",
"\n",
"# (a)fm is doubled\n",
"fma=2.*fm;\n",
"fba=2.*(B+1.)*fma;\n",
"print\"fb with 2fm: \",fba\n",
"\n",
"# (b)fm is one halved\n",
"fmb=fm/2.;\n",
"fbb=2.*(B+1.)*fmb;\n",
"print\"fb with 0.5fm: \",fbb"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"fb with 2fm: 16000.0\n",
"fb with 0.5fm: 4000.0\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example E16 : Pg 4.18"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Page Number: 4.18\n",
"# Example 4.16\n",
"# Given\n",
"# x(t)=10cos(wct+3sinwmt)\n",
"# Comparing with standard equation of fm\n",
"B=3.;\n",
"fm=1.*10.**3.; # hz\n",
"fb=2.*(B+1.)*fm;\n",
"\n",
"# B is inversaly proportional to fm\n",
"\n",
"# (a)fm is doubled\n",
"Ba=B/2.;\n",
"fma=2.*fm;\n",
"fba=2.*(Ba+1.)*fma;\n",
"print\"fb with 2fm: \",fba\n",
"\n",
"\n",
"\n",
"# (b)fm is one halved\n",
"Bb=2.*B;\n",
"fmb=fm/2.;\n",
"fbb=2.*(Bb+1.)*fmb;\n",
"print\"fb with 0.5fm: \",fbb"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"fb with 2fm: 10000.0\n",
"fb with 0.5fm: 7000.0\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example E17 : Pg 4.18"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Page Number: 4.18\n",
"# Example 4.17\n",
"\n",
"# Given\n",
"fm=2.*10.**3.; # Hz\n",
"delf=5.*10.**3.; # Hz\n",
"\n",
"# (a) Bandwidth of modulated signal\n",
"B=delf/fm;\n",
"\n",
"fb=2.*(B+1.)*fm;\n",
"print'Bandwidth',fb,'Hz'\n",
"\n",
"# (b)Max. frequency deviation and Bandwidth of new signal\n",
"# Given\n",
"fm1=fm-(1.*10.**3.);\n",
"delf1=3.*delf;\n",
"\n",
"B1=delf1/fm1;\n",
"\n",
"fd=B1*fm1;\n",
"print'Maximum frequency deviation',fd,'Hz'\n",
"\n",
"fb1=2.*(B1+1.)*fm1;\n",
"print'Bandwidth',fb1,'Hz'"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Bandwidth 14000.0 Hz\n",
"Maximum frequency deviation 15000.0 Hz\n",
"Bandwidth 32000.0 Hz\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example E18 : Pg 4.19"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Page Number: 4.19\n",
"# Example 4.18\n",
"# Given\n",
"delf=75.*10.**3.; # Hz\n",
"fM=15.*10.**3.; # Hz\n",
"\n",
"D=delf/fM;\n",
"# Given formula fb=2(*10.**2)*fM\n",
"fb1=2.*10.**2.*fM;\n",
"print'BW uing formula',fb1,'Hz'\n",
"\n",
"# Carsons Rule\n",
"fb2=2.*10.**1.*fM;\n",
"print'BW uing Carsons Rule',fb2,'Hz'\n",
"\n",
"# High quality Fm radios require minimum 200kHz\n",
"# Therefore, carsons rule underestimates bandwidth"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"BW uing formula 3000000.0 Hz\n",
"BW uing Carsons Rule 300000.0 Hz\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example E19 : Pg 4.19"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Page Number: 4.19\n",
"# Example 4.19\n",
"# Given\n",
"fm1=50.; # Hz\n",
"fm2=15.*10.**3.; # Hz\n",
"\n",
"delf=75.*10.**3.; # Hz\n",
"\n",
"# As B=delf/fm\n",
"Bmin=delf/fm2;\n",
"Bmax=delf/fm1;\n",
"\n",
"# Let B1=0.5\n",
"B1=0.5;\n",
"n=(Bmax/B1);\n",
"print'Multiplication factor',n\n",
"\n",
"delf1=(delf/n);\n",
"print'Max allowed frequency deviation',delf1,'Hz'"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Multiplication factor 3000.0\n",
"Max allowed frequency deviation 25.0 Hz\n"
]
}
],
"prompt_number": 10
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example E20 : Pg 4.20"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Page Number: 4.20\n",
"# Example 4.20\n",
"# Given\n",
"f1=2.*10.**5.; # Hz\n",
"fLO=10.8*10.**6.; # Hz\n",
"delf1=25.; # Hz\n",
"n1=64.;\n",
"n2=48.;\n",
"\n",
"delf=(delf1*n1*n2);\n",
"print'Maximum frequency deviation',delf,'Hz'\n",
"\n",
"f2=n1*f1;\n",
"\n",
"f3a=f2+fLO;\n",
"f3b=f2-fLO;\n",
"\n",
"# For f3a\n",
"fca=n2*f3a;\n",
"print'Carrier frequency 1',fca,'Hz'\n",
"\n",
"# For f3b\n",
"fcb=n2*f3b;\n",
"print'Carrier frequency 2',fcb,'Hz'"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Maximum frequency deviation 76800.0 Hz\n",
"Carrier frequency 1 1132800000.0 Hz\n",
"Carrier frequency 2 96000000.0 Hz\n"
]
}
],
"prompt_number": 11
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example E21 : Pg 4.20"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Page Number: 4.20\n",
"# Example 4.21\n",
"# Given\n",
"delf=20.*10.**3.; # Hz\n",
"fc=200.*10.**3.; # Hz\n",
"of=96.*10.**6.; # hz\n",
"# delf=n1*n2 and as only doublers are used, n1*n2 has to be power of 2\n",
"# By trail and error, we find\n",
"n1=64.;\n",
"n2=32.;\n",
"# Output of first Multiplier\n",
"o1=n1*fc;\n",
"print'Output of first multiplier: ',o1,'Hz'\n",
"i2=of/n2;\n",
"flo=o1-i2;\n",
"print'fLO',flo,'Hz'"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Output of first multiplier: 12800000.0 Hz\n",
"fLO 9800000.0 Hz\n"
]
}
],
"prompt_number": 12
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example E22 : Pg 4.20"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Page Number: 4.20\n",
"# Example 4.22\n",
"# Given\n",
"B=0.2; \n",
"f1=200.*10.**3.; # Hz\n",
"fml=50.; # Hz\n",
"fmh=15.*10.**3.; # Hz\n",
"delf=75.*10.**3.; # hz\n",
"fc=108.*10.**6.; # Hz\n",
"\n",
"delf1=B*fml;\n",
"n1n2=delf/delf1;\n",
"\n",
"# Let n2=150\n",
"n2=150.;\n",
"flo=((delf*f1)-fc)/n2;\n",
"print'fLO',flo,'Hz'\n",
"\n",
"n1=n1n2/n2;\n",
"print\"n1 with n2=150:\",n1"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"fLO 99280000.0 Hz\n",
"n1 with n2=150: 50.0\n"
]
}
],
"prompt_number": 13
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example E23 : Pg 4.21"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Page Number: 4.21\n",
"# Example 4.23\n",
"# Given,\n",
"\n",
"delfd1=50.; # Hz\n",
"f1=120.; # Hz\n",
"\n",
"delfd2=20000.; # Hz\n",
"f2=240.; # Hz\n",
"# (a)PM\n",
"delf1=(f2/f1)*delfd1;\n",
"n1=delfd2/delf1;\n",
"print'Frequency multiplication factor in PM',n1\n",
"\n",
"# (b)FM\n",
"n2=delfd2/delfd1;\n",
"print'Frequency multiplication factor in FM',n2"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Frequency multiplication factor in PM 200.0\n",
"Frequency multiplication factor in FM 400.0\n"
]
}
],
"prompt_number": 14
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example E29 : Pg 4.25"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Page Number: 4.25\n",
"# Example 4.29\n",
"# Given,\n",
"f1=108.; # MHz\n",
"f2=157.; # MHz\n",
"\n",
"# (a) Image frequency overlaps RF band\n",
"fIF=12.; # MHz\n",
"\n",
"fL01=f1-fIF;\n",
"print'fL01',fL01,'MHz'\n",
"fim1=fL01-fIF;\n",
"print'fim1',fim1,'MHz'\n",
"\n",
"fL02=f2-fIF;\n",
"print'fL02',fL02,'MHz'\n",
"fim2=fL02-fIF;\n",
"print'fim2',fim2,'MHz'\n",
"\n",
"# Clearly image and RF band overlap"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"fL01 96.0 MHz\n",
"fim1 84.0 MHz\n",
"fL02 145.0 MHz\n",
"fim2 133.0 MHz\n"
]
}
],
"prompt_number": 15
}
],
"metadata": {}
}
]
}