{ "metadata": { "name": "", "signature": "sha256:3caeb5ca80f9060d923ecab5e68747215440e54b9d8723f23ecf08701ce3af01" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Chapter10, Broadband & Frequency Independent Antenna" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example No. 10.5.1, page : 10-16" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from __future__ import division\n", "from math import sqrt, atan, pi\n", "N=5 #no. of turns\n", "f=400 #MHz(Frequency)\n", "c=3*10**8 #m/s(Speed of light)\n", "lamda=c/(f*10**6) #m(Wavelength)\n", "print \"Part (i):\" \n", "S=lamda/50 #m(Spacing between turns)\n", "S_BY_lamda=1/50 #(Spacing/wavelength)\n", "C_BY_lamda=sqrt(2*S_BY_lamda) #(Circumference/wavelength)\n", "print \"\\tCircumference is\",C_BY_lamda,\"*lamda\" \n", "C=sqrt(2*lamda*S) #m(Circumference)\n", "print \"\\tCircumference = %0.2f meter \"%C \n", "print \"Part (ii):\" \n", "Lo_BY_lamda=sqrt(S_BY_lamda**2+C_BY_lamda**2) #(Length/wavelength)\n", "print \"\\tLength of single turn is\",round(Lo_BY_lamda,6),\"*lamda\" \n", "Lo=sqrt(S**2+C**2) #m(Length of single turn)\n", "print \"\\tLength of single turn = %0.5f meter \"%Lo \n", "print \"Part (iii):\" \n", "Ln_BY_lamda=N*Lo_BY_lamda #(Overall length/wavelength)\n", "print \"\\tOverall Length is\",round(Ln_BY_lamda,7),\"*lamda\" \n", "Ln=N*Lo #m(Overall length)\n", "print \"\\tOverall Length = %0.5f meter \"%Ln \n", "print \"Part (iv):\" \n", "alfa=atan(S/C)*180/pi #degree(Pitch angle)\n", "print \"\\tPitch angle, \u03b1 = %0.2f degree\"%alfa" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Part (i):\n", "\tCircumference is 0.2 *lamda\n", "\tCircumference = 0.15 meter \n", "Part (ii):\n", "\tLength of single turn is 0.200998 *lamda\n", "\tLength of single turn = 0.15075 meter \n", "Part (iii):\n", "\tOverall Length is 1.0049876 *lamda\n", "\tOverall Length = 0.75374 meter \n", "Part (iv):\n", "\tPitch angle, \u03b1 = 5.71 degree\n" ] } ], "prompt_number": 10 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example No. 10.5.2, page : 10-16" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from math import tan, pi, sqrt, log10\n", "from __future__ import division\n", "N=5 #no. of turns\n", "f=300 #MHz(Frequency)\n", "c=3*10**8 #m/s(speed of light)\n", "print \"Part (i):\" \n", "lamda=c/(f*10**6) #m(Wavelength)\n", "C_BY_lamda=1 #(Circumference/wavelength)\n", "print \"\\tNear optimum circumference is\",C_BY_lamda,\"*lamda\" \n", "C=lamda #m(Circumference)\n", "print \"\\tNear optimum circumference = %0.f meter\" %C\n", "print \"Part (ii):\" \n", "alfa=14 #degree#(Pitch angle)#for near optimum\n", "S_BY_lamda=C_BY_lamda*tan(alfa*pi/180) \n", "print \"\\tSpacing is\",round(S_BY_lamda,4),\"*lamda\" \n", "S=C*tan(alfa*pi/180) #m(Spacing)\n", "print \"\\tSpacing = %0.4f meter \"%S \n", "print \"Part (iii):\" \n", "Rin=140*C/lamda #\u03a9(Input impedence)\n", "print \"\\tInput impedence = %0.2f \u03a9 \"%Rin \n", "print \"Part (iv):\" \n", "HPBW=52/(C/lamda*sqrt(N*S/lamda)) #degree(HPBW)\n", "print \"\\tHPBW = %0.2f degree \"%HPBW \n", "print \"Part (v):\" \n", "FNBW=115/(C/lamda*sqrt(N*S/lamda)) #degree(FNBW)\n", "print \"\\tFNBW = %0.2f degree \" %FNBW \n", "print \"Part (vi):\" \n", "Do=15*(C/lamda)**2*N*(S/lamda) #unitless##Directivity\n", "print \"\\tDirectivity(unitless) : %0.4f\"%Do \n", "Do_dB=10*log10(Do) #dB(Directivity)\n", "print \"\\tDirectivity = %0.3f dB \"%Do_dB \n", "print \"Part (vii):\" \n", "AR=(2*N+1)/2/N #axial ratio\n", "print \"\\tAxial ratio : \",AR \n", "print \"Part (viii):\" \n", "Rin=140*(C/lamda) #\u03a9(Input impedence)\n", "#50 \u03a9 line\n", "Zo=50 #\u03a9(Output impedence)\n", "Tau=(Rin-Zo)/(Rin+Zo) #Scaling factor\n", "VSWR=(1+Tau)/(1-Tau) #(VSWR)\n", "print \"\\tVSWR for 50\u03a9 line : \",VSWR \n", "#75 \u03a9 line\n", "Zo=75 #\u03a9(Output impedence)\n", "Tau=(Rin-Zo)/(Rin+Zo) #Scaling factor\n", "VSWR=(1+Tau)/(1-Tau) #(VSWR)\n", "print \"\\tVSWR for 75\u03a9 line : %0.3f\"%VSWR " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Part (i):\n", "\tNear optimum circumference is 1 *lamda\n", "\tNear optimum circumference = 1 meter\n", "Part (ii):\n", "\tSpacing is 0.2493 *lamda\n", "\tSpacing = 0.2493 meter \n", "Part (iii):\n", "\tInput impedence = 140.00 \u03a9 \n", "Part (iv):\n", "\tHPBW = 46.57 degree \n", "Part (v):\n", "\tFNBW = 103.00 degree \n", "Part (vi):\n", "\tDirectivity(unitless) : 18.6996\n", "\tDirectivity = 12.718 dB \n", "Part (vii):\n", "\tAxial ratio : 1.1\n", "Part (viii):\n", "\tVSWR for 50\u03a9 line : 2.8\n", "\tVSWR for 75\u03a9 line : 1.867\n" ] } ], "prompt_number": 15 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example No. 10.5.3, page : 10-18" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from math import tan, pi, sqrt, log10\n", "HPBW=39 #degree(HPBW)\n", "alfa=12.5 #degree(Pitch angle)\n", "f=475 #MHz(Frequency)\n", "c=3*10**8 #m/s(Speed of light)\n", "lamda=c/(f*10**6) #m(Wavelength)\n", "C=lamda #m(Circumference)\n", "print \"Part (i):\" \n", "#it is in axial mode as 3/4*lamda<C<4/3*lamda\n", "S=C*tan(alfa*pi/180) #meter(Spacing)\n", "N=52**2/HPBW**2/(S/lamda)/(C/lamda)**2 #turns\n", "print \"\\tNumber of turns : \",round(N) \n", "print \"Part (ii):\" \n", "N=round(N) #turns\n", "Do=15*(C/lamda)**2*N*(S/lamda) #unitless(Directivity)\n", "Do_dB=10*log10(Do) #dB(Directivity)\n", "print \"\\tDirectivity = %0.2f decibels\"%Do_dB \n", "print \"Part (iii):\" \n", "AR=(2*N+1)/2/N #axial ratio\n", "print \"\\tAxial ratio : \",AR \n", "print \"Part (iv):\" \n", "#3/4*lamda<C<4/3*lamda\n", "lamda1=C/(3/4) #meter(Wavelength)\n", "lamda2=C/(4/3) #meter(Wavelength)\n", "f1=c/lamda1 #Hz(Frequency)\n", "f2=c/lamda2 #Hz(Frequency)\n", "print \"\\tFrequency range is\",(f1/10**6),\"MHz to\",round(f2/10**6,2),\"MHz.\"\n", "print \"Part (v):\" \n", "#At design frequency\n", "Rin=140*C/lamda #\u03a9(Input impedence)\n", "print \"\\tAt design frequency, Input impedence = %0.2f \u03a9 \"%Rin \n", "#3/4*lamda<C<4/3*lamda\n", "#At high frequency end\n", "Rin=140*C/lamda2 #\u03a9(Input impedence)\n", "print \"\\tAt high frequency end, Input impedence = %0.2f \u03a9 \"%Rin \n", "#At low frequency end\n", "Rin=140*C/lamda1 #\u03a9(Input impedence)\n", "print \"\\tAt low frequency end, Input impedence = %0.2f \u03a9 \"%Rin " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Part (i):\n", "\tNumber of turns : 8.0\n", "Part (ii):\n", "\tDirectivity = 14.25 decibels\n", "Part (iii):\n", "\tAxial ratio : 1.0625\n", "Part (iv):\n", "\tFrequency range is 356.25 MHz to 633.33 MHz.\n", "Part (v):\n", "\tAt design frequency, Input impedence = 140.00 \u03a9 \n", "\tAt high frequency end, Input impedence = 186.67 \u03a9 \n", "\tAt low frequency end, Input impedence = 105.00 \u03a9 \n" ] } ], "prompt_number": 18 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example No. 10.5.4, page : 10-20" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from math import tan, pi, sqrt, log10\n", "Do_dB=14 #dB(Directivity\n", "f=2.4 #GHz(Frequency)\n", "c=3*10**8 #m/s(Speed of light)\n", "lamda=c/(f*10**6) #m(Wavelength)\n", "Do=10**(Do_dB/10) #unitless(Directivity)\n", "C=lamda #m##for optimum result(Circumference)\n", "alfa=14 #degree ##for optimum result(Pitch angle)\n", "S=C*tan(alfa*pi/180) #m(Spacing)\n", "N=Do/15/(C/lamda)**2/(S/lamda) #turns\n", "N=round(N) #turns\n", "Rin=140*C/lamda #\u03a9(Input impedence)\n", "print \"Input impedence = %0.2f \u03a9 \"%Rin \n", "HPBW=52/(C/lamda*sqrt(N*S/lamda)) #degree\n", "print \"HPBW = %0.2f degree \"%HPBW \n", "FNBW=115/(C/lamda*sqrt(N*S/lamda)) #degree\n", "print \"FNBW = %0.f degree \"%FNBW \n", "AR=(2*N+1)/2/N #(Axial ratio)\n", "print \"Axial ratio : \" ,round(AR,1)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Input impedence = 140.00 \u03a9 \n", "HPBW = 39.36 degree \n", "FNBW = 87 degree \n", "Axial ratio : 1.1\n" ] } ], "prompt_number": 21 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example No. 10.8.1, page : 10-36" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from math import tan, pi, sqrt, log10, exp\n", "f=10 #MHz(Frequency)\n", "c=3*10**8 #m/s(Speed of light)\n", "lamda=c/(f*10**6) #m(Wavelength)\n", "d0=10**-3*lamda #m(spacing)\n", "Lo=1*lamda #m(Length)\n", "fi=pi; fi0=0 #radian\n", "r0=d0/2 #m\n", "print \"Part (i):\" \n", "#R=r0*exp(a*fi-a*fi0) #m\n", "#a=sqrt(1/Lo**2/(R-r0)**2-1) #per adian\n", "a=1.166 #rad**-1(by above equation)\n", "print \"\\tRate of spiral = %0.3f rad^-1 \"%a \n", "R_BY_lamda=r0/lamda*exp(a*2*pi) #m(Radius/wavelength)\n", "print \"\\tRadius of terminal point is\",round(R_BY_lamda,5),\"*lamda\" \n", "print \"Part (ii):\" \n", "R=r0*exp(a*2*pi) #m(Radius)\n", "print \"\\tRadius at terminal point = %0.2f meter \" %R " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Part (i):\n", "\tRate of spiral = 1.166 rad^-1 \n", "\tRadius of terminal point is 0.75979 *lamda\n", "Part (ii):\n", "\tRadius at terminal point = 22.79 meter \n" ] } ], "prompt_number": 27 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example No. 10.8.2, page : 10-37" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from fractions import Fraction\n", "from math import tan, pi, sqrt, log, atan\n", "fU=900 #MHz(Upper frequency)\n", "fL=450 #MHz(Lower frequency)\n", "c=3*10**8 #m/s(Speed of light)\n", "lamdaU=c/(fU*10**6) #m(Upper wavelength)\n", "lamdaL=c/(fL*10**6) #m(Lower wavelength)\n", "Exp_ratio=4 #expansion ratio\n", "a=log(Exp_ratio)/(2*pi) #rad**-1##rate of spiral\n", "Beta=atan(1/a*pi/180) #degree\n", "r0=lamdaU/4 #meter##minimum radius\n", "print \"Minimum radius = %0.1f cm\"%(r0*100) \n", "R=lamdaL/4 #meter##minimum radius\n", "print \"Maximum radius = %0.1f cm \"%(R*100) \n", "fi_m=log(R/r0)/a #radian\n", "fi_m=fi_m*180/pi #degree\n", "print \"\u03a6m = %0.2f degree \"%(fi_m) \n", "N=1/2 #for \u03a6m=180 #degree\n", "print \"Number of turns, N is\",Fraction(N)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Minimum radius = 8.3 cm\n", "Maximum radius = 16.7 cm \n", "\u03a6m = 180.00 degree \n", "Number of turns, N is 1/2\n" ] } ], "prompt_number": 34 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example No. 10.10.1, page :10-49" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from math import tan, pi, sqrt, log, atan\n", "Gain=8.5 #dB(Gain)\n", "tau=0.822;sigma=0.149 #for given gain\n", "alfa=2*atan((1-tau*180/pi)/4/sigma) #degree\n", "fL=54 #MHz(Lower frequency)\n", "fU=216 #MHz(Upper frequency)\n", "c=3*10**8 #m/s(Speed of light)\n", "lamdaU=c/(fU*10**6) #m(Upper wavelength)\n", "lamdaL=c/(fL*10**6) #m(Lower wavelength)\n", "l1=lamdaU/2 #m(Length of element1)\n", "lN=lamdaL/2 #m(Length of longest element)\n", "l2=l1/tau; l3=l2/tau; l4=l3/tau; l5=l4/tau; l6=l5/tau; l7=l6/tau; l8=l7/tau; l9=l8/tau #m(Length of elements)\n", "#Spacing between elements in meter\n", "d1=2*sigma*l1 \n", "d2=2*sigma*l2 \n", "d3=2*sigma*l3 \n", "d4=2*sigma*l4 \n", "d5=2*sigma*l5 \n", "d6=2*sigma*l6 \n", "d7=2*sigma*l7 \n", "d8=2*sigma*l8 \n", "d9=2*sigma*l9 \n", "d=d1+d2+d3+d4+d5+d6+d7+d8+d9 #meter(total spacing)\n", "print \"Length of longest element = %0.2f m\"%lN \n", "print \"Length of element1 = %0.3f m\"%l1\n", "print \"Length of element1 = %0.3f m\"%l2\n", "print \"Length of element1 = %0.3f m\"%l3\n", "print \"Length of element1 = %0.3f m\"%l4\n", "print \"Length of element1 = %0.3f m\"%l5\n", "print \"Length of element1 = %0.3f m\"%l6\n", "print \"Length of element1 = %0.3f m\"%l7\n", "print \"Length of element1 = %0.3f m\"%l8\n", "print \"Length of element1 = %0.3f m\\n\"%l9\n", "print \"Spacing of element1 = %0.3f m\" %d1\n", "print \"Spacing of element1 = %0.3f m\" %d2\n", "print \"Spacing of element1 = %0.3f m\" %d3\n", "print \"Spacing of element1 = %0.3f m\" %d4\n", "print \"Spacing of element1 = %0.3f m\" %d5\n", "print \"Spacing of element1 = %0.3f m\" %d6\n", "print \"Spacing of element1 = %0.3f m\" %d7\n", "print \"Spacing of element1 = %0.3f m\" %d8\n", "print \"Spacing of element1 = %0.3f m\" %d9\n", "print \"Total Spacing length = %0.3f m \"%d \n", "#Answer is not accurate in the book." ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Length of longest element = 2.78 m\n", "Length of element1 = 0.694 m\n", "Length of element1 = 0.845 m\n", "Length of element1 = 1.028 m\n", "Length of element1 = 1.250 m\n", "Length of element1 = 1.521 m\n", "Length of element1 = 1.850 m\n", "Length of element1 = 2.251 m\n", "Length of element1 = 2.739 m\n", "Length of element1 = 3.332 m\n", "\n", "Spacing of element1 = 0.207 m\n", "Spacing of element1 = 0.252 m\n", "Spacing of element1 = 0.306 m\n", "Spacing of element1 = 0.373 m\n", "Spacing of element1 = 0.453 m\n", "Spacing of element1 = 0.551 m\n", "Spacing of element1 = 0.671 m\n", "Spacing of element1 = 0.816 m\n", "Spacing of element1 = 0.993 m\n", "Total Spacing length = 4.622 m \n" ] } ], "prompt_number": 40 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example No. 10.10.2, page : 10-52" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from math import tan, pi\n", "from numpy import array\n", "tau=0.895 #scale factor\n", "sigma=0.166 #(spacing factor)\n", "fU=30 #MHz(Upper frequency)\n", "fL=10 #MHz(Lower frequency)\n", "c=3*10**8 #m/s(Speed of light)\n", "lamdaU=c/(fU*10**6) #m(Upper wavelength)\n", "lamdaL=c/(fL*10**6) #m(Lower wavelength)\n", "l1=lamdaU/2 #m(Length of shortest element)\n", "print \"Length of shortest element, l1 = %0.2f meter \"%l1 \n", "#Length of element in meter\n", "l2=l1/tau; l3=l2/tau; l4=l3/tau; l4=l3/tau; l5=l4/tau; l6=l5/tau; l7=l6/tau; l8=l7/tau; l9=l8/tau;\n", "l10=l9/tau; l11=l10/tau #\n", "print \"\"\"Other elements length l2, l3, l4, l5, l6, l7, l8, l9, l10, l11 are :\n", "%0.2f, %0.2f, %0.2f, %0.2f, %0.2f, %0.2f, %0.2f, %0.2f, %0.2f, %0.2f meter respectively.\"\"\"%(l2,l3,l4,l5,l6,l7,l8,l9,l10,l11)\n", "alfa=17.97 #degree(angle)\n", "R1=(l1/2)/tan(alfa/2*pi/180) #m(Spacing between elements)\n", "R2=R1/tau; R3=R2/tau; R4=R3/tau; R4=R3/tau; R5=R4/tau; R6=R5/tau; R7=R6/tau; R8=R7/tau; R9=R8/tau; R10=R9/tau; R11=R10/tau #m\n", "print \"Spacing between elements R1, R2, R3, R4, R5, R6, R7, R8,R9, R10, R11 are : \"\n", "print \"%0.2f, %0.2f, %0.2f, %0.2f, %0.2f, %0.2f, %0.2f, %0.2f, %0.2f, %0.2f, %0.2f meter respectively.\"%(R1,R2,R3,R4,R5,R6,R7,R8,R9,R10,R11)\n", "#Answer is not accurate in the book." ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Length of shortest element, l1 = 5.00 meter \n", "Other elements length l2, l3, l4, l5, l6, l7, l8, l9, l10, l11 are :\n", "5.59, 6.24, 6.97, 7.79, 8.71, 9.73, 10.87, 12.14, 13.57, 15.16 meter respectively.\n", "Spacing between elements R1, R2, R3, R4, R5, R6, R7, R8,R9, R10, R11 are : \n", "15.81, 17.67, 19.74, 22.05, 24.64, 27.53, 30.76, 34.37, 38.40, 42.91, 47.94 meter respectively.\n" ] } ], "prompt_number": 53 } ], "metadata": {} } ] }