{ "metadata": { "name": "", "signature": "sha256:bcad4cfb691dedbc6343f0aa16a777a3c81354536e69fb16f52f5b492443bac9" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Chapter 13 : Performance of Modulation systems with noise" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 13.1 Page No : 442" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\n", "# Variables\n", "Gb = 1.;\n", "print 'a) SSB: Gb = %i '%(Gb);\n", "print ' GbdB = %i dB'%(10*math.log10(Gb));\n", "print 'b) DSB: Gb = %i '%(Gb);\n", "print ' GbdB = %i dB'%(10*math.log10(Gb));\n", "m = 0.5;\n", "Gb = m**2/(2+m**2);\n", "print 'c) AMm = .5): Gb = %.3f '%(Gb);\n", "print ' GbdB = %.3f dB'%(10*math.log10(Gb));\n", "m = 1.;\n", "Gb = m**2/(2+m**2);\n", "print 'd) AMm = 1): Gb = %.3f '%(Gb);\n", "print ' GbdB = %.3f dB'%(10*math.log10(Gb));\n", "delta_phi = 5.;\n", "Gb = delta_phi**2/2;\n", "print 'e) FMdelta phi = 5)): Gb = %.1f '%(Gb);\n", "print ' GbdB = %.3f dB'%(10*math.log10(Gb));\n", "D = 5.;\n", "Gb = 3.*D**2/2;\n", "print 'f) FMD = 5): Gb = %.1f '%(Gb);\n", "print ' GbdB = %.3f dB'%(10*math.log10(Gb));\n", "Wf1 = 7.07;\n", "Gb = 3./2*D**2*math.pi/6*Wf1;\n", "print 'g) FMD = 5, W/f1 = 7.07): Gb = %.1f '%(Gb);\n", "print ' GbdB = %.2f dB'%(10*math.log10(Gb));\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "a) SSB: Gb = 1 \n", " GbdB = 0 dB\n", "b) DSB: Gb = 1 \n", " GbdB = 0 dB\n", "c) AMm = .5): Gb = 0.111 \n", " GbdB = -9.542 dB\n", "d) AMm = 1): Gb = 0.333 \n", " GbdB = -4.771 dB\n", "e) FMdelta phi = 5)): Gb = 12.5 \n", " GbdB = 10.969 dB\n", "f) FMD = 5): Gb = 37.5 \n", " GbdB = 15.740 dB\n", "g) FMD = 5, W/f1 = 7.07): Gb = 138.8 \n", " GbdB = 21.42 dB\n" ] } ], "prompt_number": 3 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 13.2 Page No : 443" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\n", "# Calculations and Results\n", "GR = 1.;\n", "print 'a) SSB: GR = %i '%(GR);\n", "print ' GRdB = %i dB'%(10*math.log10(GR));\n", "GR = 2.;\n", "print 'b) DSB: GR = %i '%(GR);\n", "print ' GRdB = %.2f dB'%(10*math.log10(GR));\n", "m = 0.5;\n", "GR = 2*m**2/(2+m**2);\n", "print 'c) AMm = .5): GR = %.4f '%(GR);\n", "print ' GRdB = %.3f dB'%(10*math.log10(GR));\n", "m = 1.;\n", "GR = 2*m**2/(2+m**2);\n", "print 'd) AMm = 1): GR = %.3f '%(GR);\n", "print ' GRdB = %.2f dB'%(10*math.log10(GR));\n", "delta_phi = 5.;\n", "GR = (1+delta_phi)*delta_phi**2;\n", "print 'e) FMdelta phi = 5)): GR = %.1f '%(GR);\n", "print ' GRdB = %.3f dB'%(10*math.log10(GR));\n", "D = 5.;\n", "GR = 3*D**2*(1+D);\n", "print 'f) FMD = 5): GR = %.1f '%(GR);\n", "print ' GRdB = %.3f dB'%(10*math.log10(GR));\n", "Wf1 = 7.07;\n", "GR = 3*(1+D)*D**2*math.pi/6*Wf1;\n", "print 'g) FMD = 5, W/f1 = 7.07): GR = %.1f '%(GR);\n", "print ' GRdB = %.2f dB'%(10*math.log10(GR));\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "a) SSB: GR = 1 \n", " GRdB = 0 dB\n", "b) DSB: GR = 2 \n", " GRdB = 3.01 dB\n", "c) AMm = .5): GR = 0.2222 \n", " GRdB = -6.532 dB\n", "d) AMm = 1): GR = 0.667 \n", " GRdB = -1.76 dB\n", "e) FMdelta phi = 5)): GR = 150.0 \n", " GRdB = 21.761 dB\n", "f) FMD = 5): GR = 450.0 \n", " GRdB = 26.532 dB\n", "g) FMD = 5, W/f1 = 7.07): GR = 1665.8 \n", " GRdB = 32.22 dB\n" ] } ], "prompt_number": 6 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 13.3 Page No : 447" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\n", "# Variables\n", "k = 1.38*10**-23; #Boltzmann's const\n", "#Temperatures in K\n", "Ti = 150.;\n", "Te = 325.;\n", "\n", "# Calculations and Results\n", "Tsys = Ti+Te;\n", "print ' Tsys = %i K '%(Tsys);\n", "D = 5;\n", "W = 15; #kHz\n", "B = 2*(1+D)*W;\n", "print ' B = %i kHz'%(B);\n", "Nsys = k*Tsys*B*10**3; #W\n", "print ' Nsys = %.3f fW'%(Nsys*10**15);\n", "PR = 50*10**-12; #W\n", "SNsys = PR/Nsys; \n", "print ' S/N)sys = %i '%(SNsys);\n", "GR = 3*(1+D)*D**2\n", "print ' GR = %.0f '%(GR);\n", "SNoutput = GR*SNsys;\n", "print ' S/N)output = %.0f '%(SNoutput);\n", "print ' S/N)out,dB = %.2f dB'%(10*math.log10(SNoutput));\n", "print ' S/N)sys, dB = %.2f dB'%(10*math.log10(SNsys));\n", "GRdb = 10*math.log10(GR);\n", "print ' GR, dB = %.2f dB '%(GRdb);\n", "print ' S/N)output ,dB = %.2f dB'%(10*math.log10(SNoutput));\n", "\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ " Tsys = 475 K \n", " B = 180 kHz\n", " Nsys = 1.180 fW\n", " S/N)sys = 42376 \n", " GR = 450 \n", " S/N)output = 19069413 \n", " S/N)out,dB = 72.80 dB\n", " S/N)sys, dB = 46.27 dB\n", " GR, dB = 26.53 dB \n", " S/N)output ,dB = 72.80 dB\n" ] } ], "prompt_number": 7 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 13.4 Page No : 450" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Variables\n", "N = 16; #bit\n", "\n", "# Calculations\n", "SNoutdB = 1.76+6.02*N;\n", "\n", "# Results\n", "print ' (S/N)output, dB = %.2f dB '%(SNoutdB);\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ " (S/N)output, dB = 98.08 dB \n" ] } ], "prompt_number": 8 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 13.5 Page No : 450" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Variables\n", "SNoutdB = 53;\n", "\n", "# Calculations and Results\n", "N = (SNoutdB-1.76)/6.02;\n", "print ' N = %.2f bits '%(N);\n", "N = 9; #roundup\n", "print ' N = %i bits '%(N);\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ " N = 8.51 bits \n", " N = 9 bits \n" ] } ], "prompt_number": 9 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 13.6 Page No : 453" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\n", "# Variables\n", "N = 6.; #bits per word\n", "\n", "# Calculations and Results\n", "M = 2**N;\n", "print ' M = %i '%(M);\n", "Pr = 200.*10**-15; #W\n", "R = 2.*10**6; #bits/s\n", "Eb = Pr/R;\n", "print ' Bit energy ,Eb = %.0f*10**-21 '%(Eb*10**21);\n", "k = 1.38*10**-23; #Boltzmann cons\n", "Ti = 300.; #K\n", "Te = 425.; #K\n", "Tsys = Ti+Te;\n", "nsys = k*Tsys; \n", "print ' Noise power spectral density ,nsys = %.0f*10**-20 W/Hz '%(nsys*10**20);\n", "rho = Eb/nsys;\n", "print ' Bit energy , rho = %.0f '%(rho);\n", "rhodB = 10*math.log10(rho);\n", "print ' Bit energy in db, rho,dB = %.0f dB '%(rhodB);\n", "#part a\n", "Pe = 4*10**-6;\n", "SNout = 1.5*M**2/(1+4*M**2*Pe);\n", "print ' a) S/N)output = %.0f or %0.2f dB) '%(SNout,10*math.log10(SNout));\n", "#part b\n", "Pe = 2.3*10**-5;\n", "SNout = 1.5*M**2/(1+4*M**2*Pe);\n", "print ' b) S/N)output = %.0f or %0.2f dB) '%(SNout,10*math.log10(SNout));\n", "#part c\n", "Pe = 8*10**-4;\n", "SNout = 1.5*M**2/(1+4*M**2*Pe);\n", "print ' c) S/N)output = %.1f or %0.2f dB) '%(SNout,10*math.log10(SNout));\n", "#part d\n", "Pe = 3.5*10**-3;\n", "SNout = 1.5*M**2/(1+4*M**2*Pe);\n", "print ' d) S/N)output = %.1f or %0.2f dB) '%(SNout,10*math.log10(SNout));\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ " M = 64 \n", " Bit energy ,Eb = 100*10**-21 \n", " Noise power spectral density ,nsys = 1*10**-20 W/Hz \n", " Bit energy , rho = 10 \n", " Bit energy in db, rho,dB = 10 dB \n", " a) S/N)output = 5766 or 37.61 dB) \n", " b) S/N)output = 4462 or 36.50 dB) \n", " c) S/N)output = 435.5 or 26.39 dB) \n", " d) S/N)output = 105.3 or 20.22 dB) \n" ] } ], "prompt_number": 11 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 13.7 Page No : 455" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\n", "# Variables\n", "#data from ex 13.6\n", "M = 2.**6;\n", "Pr = 200.*10**-15; #W\n", "R = 8.*10**6; #bits/s (changed)\n", "Eb = Pr/R;\n", "\n", "# Calculations and Results\n", "k = 1.38*10**-23; #Boltzmann cons\n", "Ti = 300; #K\n", "Te = 425; #K\n", "Tsys = Ti+Te;\n", "nsys = k*Tsys; \n", "#print ' Noise power spectral density %(nsys = %.0f*10**-20 W/Hz '%(nsys*10**20);\n", "rho = Eb/nsys;\n", "print ' Bit energy , rho = %.1f '%(rho);\n", "rhodB = 10*math.log10(rho);\n", "print ' Bit energy in db, rho,dB = %.2f dB '%(rhodB);\n", "\n", "Pe = 1.3*10**-2;\n", "SNout = 1.5*M**2/(1+4*M**2*Pe);\n", "print ' S/N)output = %.2f or %0.2f dB) '%(SNout,10*math.log10(SNout));\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ " Bit energy , rho = 2.5 \n", " Bit energy in db, rho,dB = 3.98 dB \n", " S/N)output = 28.71 or 14.58 dB) \n" ] } ], "prompt_number": 13 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 13.8 Page No : 455" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\n", "# Variables\n", "Pe = 10.**-5;\n", "R = 1*10**6; #bits/s\n", "k = 1.38*10**-23; #Boltzmann cons\n", "Ti = 475.; #K\n", "Te = 250.; #K\n", "Tsys = Ti+Te;\n", "nsys = k*Tsys; #W/Hz \n", "\n", "# Calculations\n", "def E(rhodb): #function for Eb\n", " rho = 10**(rhodb/10);\n", " return nsys*rho;\n", "\n", "def P(E): #function for Pr\n", " return R*Eb;\n", "\n", "def lay(rhodb,pt):\n", " Eb = E(rhodb);\n", " print P(E);\n", " print '%c)Bit energy , Eb = %.2f*10**-21 J '%(pt,Eb*10**21);\n", " print ' Required reciver carrier power , Pr = %.2f fW '%(Pr*10**15);\n", "\n", "#Part a\n", "rhodb = 9.6;\n", "lay(rhodb,'a');\n", "\n", "#Part b\n", "rhodb = 10.3;\n", "lay(rhodb,'b');\n", "\n", "#Part c\n", "rhodb = 12.6;\n", "lay(rhodb,'c');\n", "\n", "#Part d\n", "rhodb = 13.4;\n", "lay(rhodb,'d');\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "2.5e-14\n", "a)Bit energy , Eb = 91.25*10**-21 J \n", " Required reciver carrier power , Pr = 200.00 fW \n", "2.5e-14\n", "b)Bit energy , Eb = 107.21*10**-21 J \n", " Required reciver carrier power , Pr = 200.00 fW \n", "2.5e-14\n", "c)Bit energy , Eb = 182.06*10**-21 J \n", " Required reciver carrier power , Pr = 200.00 fW \n", "2.5e-14\n", "d)Bit energy , Eb = 218.89*10**-21 J \n", " Required reciver carrier power , Pr = 200.00 fW \n" ] } ], "prompt_number": 14 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 13.9 Page No : 456" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\n", "#Data form ex13.8\n", "\n", "# Variables\n", "Pe = 10**-5;\n", "R = 2*10**6; #bits/s (changed)\n", "k = 1.38*10**-23; #Boltzmann cons\n", "Ti = 475; #K\n", "Te = 250; #K\n", "Tsys = Ti+Te;\n", "nsys = k*Tsys; #W/Hz \n", "\n", "# Calculations\n", "def E(rhodb): #function for Eb\n", " rho = 10**(rhodb/10);\n", " return nsys*rho;\n", "\n", "def P(E): #function for Pr\n", " return R*Eb;\n", "\n", "\n", "rhodb = 9.6;\n", "Eb = E(rhodb);\n", "Pr = P(E);\n", "\n", "# Results\n", "print 'Bit energy , Eb = %.2f*10**-21 J '%(Eb*10**21);\n", "print ' Required reciver carrier power , Pr = %.2f fW '%(Pr*10**15);\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Bit energy , Eb = 91.25*10**-21 J \n", " Required reciver carrier power , Pr = 182.49 fW \n" ] } ], "prompt_number": 15 } ], "metadata": {} } ] }