{ "metadata": { "name": "", "signature": "sha256:b3709cc764fd68911c53d14fdc3847f8e66fbdd5fcd89885b01f065610802430" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "

Chapter 11: Transmission Lines

" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 11.1, Page number: 482

" ] }, { "cell_type": "code", "collapsed": false, "input": [ " \n", "\n", "import scipy\n", "\n", "#Variable Declaration\n", "\n", "R=0\n", "G=0\n", "a=0\n", "Ro=70 #characteristic impedence in ohms\n", "B=3 #phase constant in rad/sec\n", "f=100*10**6 #frequency in Hz\n", "w=2*scipy.pi*f #omega in rad/sec\n", "\n", "#Calculations\n", "\n", "C=B/(w*Ro) #capacitance in F/m\n", "L=Ro*Ro*C #inductance in H/m\n", "\n", "#Results\n", "\n", "print 'inductance per meter =',round(L*10**9,1),'nH/m'\n", "print 'capacitance per meter =',round(C*10**12,1),'pF/m'\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "inductance per meter = 334.2 nH/m\n", "capacitance per meter = 68.2 pF/m\n" ] } ], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 11.2, Page number: 483

" ] }, { "cell_type": "code", "collapsed": false, "input": [ " \n", "#Variable Declaration\n", "\n", "Zo=60 #in ohms\n", "a=20*10**-3 #in Np/m\n", "u=0.6*3*10**8 #in m/sec\n", "f=100*10**6 #in Hz\n", "\n", "#Calculations\n", "\n", "R=a*Zo #resistance in ohms/m\n", "L=Zo/u #inductance in H/m\n", "G=a*a/R #conductivity in S/m\n", "C=1/(u*Zo) #capacitance in F/m\n", "lam=u/f #wavelentgh in m\n", "\n", "#Results\n", "\n", "print 'R =',R,'ohm/m'\n", "print 'L =',round(L*10**9,0),'nH/m'\n", "print 'G =',round(G*10**6,0),'micro S/m'\n", "print 'C =',round(C*10**12,2),'pF/m'\n", "print 'lambda =',lam,'m'" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "R = 1.2 ohm/m\n", "L = 333.0 nH/m\n", "G = 333.0 micro S/m\n", "C = 92.59 pF/m\n", "lambda = 1.8 m\n" ] } ], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 11.3, Page number: 490

" ] }, { "cell_type": "code", "collapsed": false, "input": [ " \n", "import scipy\n", "import cmath\n", "from numpy import *\n", "\n", "#Variable Declaration\n", "\n", "w=10**6 #omega in rad/sec\n", "B=1 #phase factor in rad/m\n", "a=8.0/8.686 #alpha in Np/m\n", "Y=a+1j #in m^-1\n", "l=2 #length in m\n", "Vg=10 #source voltage in volts\n", "Zo=60+40j #in ohms\n", "Zg=40 #in ohms\n", "Zl=20+50j #load impedance in ohms\n", "\n", "#Calculations\n", "\n", "s=scipy.tanh(Y*l)\n", "Zin=Zo*(Zl+Zo*s)/(Zo+Zl*s) #input impedance in ohms\n", "Zinr=round(Zin.real,2) #real part of Zin rounded to 2 decimal places\n", "Zini=round(Zin.imag,2) #imaginary part of Zin rounded to 2 decimal places\n", "Io=Vg/(Zin+Zg) #in A\n", "absIo=round(abs(Io),6) #absolute value of Io rounded to 6 decimal place\n", "Ior=Io.real #real part of Io\n", "Ioi=Io.imag #imaginary part of Io\n", "angIo=scipy.arctan(Ioi/Ior)*180/scipy.pi \n", " #in degrees\n", "Vo=Zin*Io\n", "Vop=(Vo+Zo*Io)/2\n", "Vom =(Vo-Zo*Io)/2\n", "Im=((Vop*scipy.e**(-Y)/Zo))-((Vom*scipy.e**Y)/Zo)\n", " #current at the middle in A\n", "absIm=round(abs(Im),5) #absolute value of Im rounded to 6 decimal place\n", "Imr=Im.real #real part of Im \n", "Imi=Im.imag #imaginary part of Im\n", "angIm=360+scipy.arctan(Imi/Imr)*180/scipy.pi \n", " #in degrees\n", "\n", "#Results\n", "\n", "print 'The input impedance =',Zinr,'+',Zini,'j ohms'\n", "print 'The sending-end current is'\n", "print 'mod =',absIo*10**3,'mA, angle =',round(angIo,2),'degrees'\n", "print 'The current at the middle is'\n", "print 'mod =',absIm*10**3,'mA, angle =',round(angIm,0),'degrees'" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The input impedance = 60.25 + 38.79 j ohms\n", "The sending-end current is\n", "mod = 93.03 mA, angle = -21.15 degrees\n", "The current at the middle is\n", "mod = 34.92 mA, angle = 281.0 degrees\n" ] } ], "prompt_number": 3 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 11.4, Page number: 499

" ] }, { "cell_type": "code", "collapsed": false, "input": [ " \n", "import scipy\n", "import cmath\n", "from numpy import *\n", "\n", "#Variable Declaration\n", "\n", "l=30 #length in m\n", "Zo=50 #in ohms\n", "f=2*10**6 #frequency in Hz\n", "Zl=60+40j #load impedence in ohms\n", "u=0.6*3*10**8 #in m/s\n", "w=2*scipy.pi*f #omega in rad/sec\n", "\n", "#Calculations\n", "\n", "T=(Zl-Zo)/(Zl+Zo) #reflection coefficient\n", "ang=scipy.arctan(T.imag/T.real)*180/scipy.pi #argument of T is degrees\n", "s=(1+abs(T))/(1-abs(T)) #standing wave ratio \n", "B=w/u #propogation vector in m^-1\n", "Zin=Zo*(Zl+Zo*scipy.tan(B*l)*1j)/(Zo+Zl*scipy.tan(B*l)*1j)\n", "Zinr=round(Zin.real,2) #real part of Zin rounded to 2 decimal places\n", "Zini=round(Zin.imag,2) #imaginary part of Zin rounded to 2 decimal places\n", "\n", "#Results\n", "\n", "print 'The reflection coefficient is'\n", "print 'mod =',round(abs(T),4),'angle =',round(ang,0),'degrees'\n", "print 'The standing wave ratio s =',round(s,3)\n", "print 'The input impedance =',Zinr,'+',Zini,'j ohms'" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The reflection coefficient is\n", "mod = 0.3523 angle = 56.0 degrees\n", "The standing wave ratio s = 2.088\n", "The input impedance = 23.97 + 1.35 j ohms\n" ] } ], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 11.5, Page number: 501

" ] }, { "cell_type": "code", "collapsed": false, "input": [ " \n", "\n", "import scipy\n", "import cmath\n", "from numpy import *\n", "\n", "#Variable Declaration\n", "\n", "Zl=100+150j #load impedance in ohms\n", "Zo=75 #impedance of line in ohms\n", "B=2*scipy.pi \n", "\n", "#Calculations\n", "\n", "T=(Zl-Zo)/(Zl+Zo)\n", "angT=scipy.arctan(T.imag/T.real)*180/scipy.pi \n", "s=(1+abs(T))/(1-abs(T))\n", "Yl=(1/Zl)*10**3 #admittance in mS\n", "Ylr=round(Yl.real,2) #real part of Yl rounded to 2 decimal places\n", "Yli=round(Yl.imag,2) #imaginary part of Yl rounded to 2 decimal places\n", "l1=0.4\n", "Zin=Zo*(Zl+Zo*scipy.tan(B*l1)*1j)/(Zo+Zl*scipy.tan(B*l1)*1j)\n", "Zinr=round(Zin.real,2) #real part of Zin rounded to 2 decimal places\n", "Zini=round(Zin.imag,2) #imaginary part of Zin rounded to 2 decimal places\n", "\n", "\n", "#Results\n", "\n", "print 'r is mod =',round(abs(T),3),',angle =',round(angT,0),'degrees'\n", "print 's =',round(s,2)\n", "print 'The load admittance Yl =',Ylr,'+',Yli,'j mS'\n", "print 'Zin at O.4 lambda from the load =',Zinr,'+',Zini,'j ohms'\n", "#part (e) and (f) don't require computations" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "r is mod = 0.66 ,angle = 40.0 degrees\n", "s = 4.88\n", "The load admittance Yl = 3.08 + -4.62 j mS\n", "Zin at O.4 lambda from the load = 21.96 + 47.61 j ohms\n" ] } ], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 11.6, Page number: 509

" ] }, { "cell_type": "code", "collapsed": false, "input": [ " \n", "import scipy\n", "import cmath\n", "from numpy import *\n", "\n", "#Variable Declaration\n", "\n", "s=2\n", "l1=11 \n", "l2=19\n", "ma=24 \n", "mi=16\n", "u=3*10**8 #speed of wave in m/s\n", "Zo=50 #in ohms\n", "\n", "#Calculations\n", "\n", "l=(l2-l1)*2 #lambda in cm\n", "f=(u/l)*10**-7 #frequency in GHz\n", "L=(24-19)/l #Let us assume load is at 24cm\n", "zl=1.4+0.75j # by smith chart\n", "Zl=Zo*zl #ZL in ohms\n", "\n", "#Results\n", "\n", "print 'lambda =',l,'cm'\n", "print 'f =',f,'GHz'\n", "print 'ZL =',Zl,'ohms'" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "lambda = 16 cm\n", "f = 1.875 GHz\n", "ZL = (70+37.5j) ohms\n" ] } ], "prompt_number": 6 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 11.7, Page number: 510

" ] }, { "cell_type": "code", "collapsed": false, "input": [ " \n", "import scipy\n", "import cmath\n", "from numpy import *\n", "\n", "#Variable Declaration\n", "\n", "Zo=100 #in ohms\n", "Zl=40+30j #in ohms\n", "\n", "#Calculations\n", "\n", "Yo=1.0/Zo #in S\n", "yl=Zo/Zl\n", "ys1=1.04j #By smith chart\n", "ys2=-1.04j #By smith chart\n", "Ys1=Yo*ys1 #in S\n", "Ys2=Yo*ys2 #in S\n", "la=round(0.5-(62-(-39))/720.0,2) #in units of lambda\n", "lb=round((62-39)/720.0,3) #in units of lambda\n", "da=round(88/720.0,4) #in units of lambda\n", "db=round(272/720.0,4) #in units of lambda\n", "\n", "#Results\n", "\n", "print 'The required stub admittance values in mS are',Ys1*1000,'and',Ys2*1000\n", "print 'The distance between stub and antenna at A =',la,'in units of lambda'\n", "print 'The distance between stub and antenna at B =',lb,'in units of lambda'\n", "print 'The stub lengths =',da,'and',db,'in units of lambda'\n", "print 'Part (d) is done using smith chart'" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The required stub admittance values in mS are 10.4j and -10.4j\n", "The distance between stub and antenna at A = 0.36 in units of lambda\n", "The distance between stub and antenna at B = 0.032 in units of lambda\n", "The stub lengths = 0.1222 and 0.3778 in units of lambda\n", "Part (d) is done using smith chart\n" ] } ], "prompt_number": 7 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 11.9, Page number: 521" ] }, { "cell_type": "code", "collapsed": false, "input": [ " \n", "import scipy\n", "import matplotlib.pyplot as plt\n", "\n", "#Variable Declarataion\n", "\n", "zo=75 #in ohms\n", "zg=25 #in ohms\n", "zl=100 #in ohms\n", "vg=4 #in volts\n", "l=60 #in m\n", "c=3*10**8 #speed of light in m/s\n", "u=0.1*c #in m/s\n", "\n", "#Calculations\n", "\n", "gammag=(zg-zo)/(zg+zo)\n", "gammal=(zl-zo)/(zl+zo)\n", "Vo=zo*vg/(zo+zg) #in V\n", "t1=l/u #in micro sec\n", "Io=vg/(zo+zg) #in mA\n", "\n", "#Results\n", "\n", "t1=[0,4,5,8,9,12,13,15]\n", "I1=[40,31.43,-8.571,-7.959,0.6123,0.5685,-0.0438,-0.438]\n", "fig = plt.figure()\n", "ax = fig.add_subplot(111)\n", "ax.step(t1,I1,where='post')\n", "ax.set_xlabel('Time (micro s)')\n", "ax.set_ylabel(r'I(0,t) in mA')\n", "plt.show()\n", "\n", "t2=[0,2,6,7,10,11,14]\n", "I2=[0,34.3,31.9,-2.46,-2.28,0.176,0.176]\n", "fig = plt.figure()\n", "ax = fig.add_subplot(111)\n", "ax.step(t2,I2,where='post')\n", "ax.set_xlabel('Time (micro s)')\n", "ax.set_ylabel(r'I(l,t) in mA')\n", "plt.show()\n", "\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 15 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 11.10, Page number: 527

" ] }, { "cell_type": "code", "collapsed": false, "input": [ " \n", "import scipy\n", "\n", "#Variable Declaration\n", "\n", "Er=3.8 #relative permittivity\n", "c=3*10**8 #speed of wave in m/s\n", "r=4.5 #ratio of line width to substrate thickness\n", "\n", "#Calculations\n", "\n", "Eeff=((Er+1)/2)+((Er-1)/(2*(1+12/r)**0.5))\n", "Zo=(120*scipy.pi)/((r+1.393+(0.667*scipy.log(r+1.444)))*((Eeff)**0.5))\n", "f=10**10\n", "l=c/(f*scipy.sqrt(Eeff))\n", "\n", "#Results\n", "\n", "print 'The effective relative permittivity of the substrate =',round(Eeff,3)\n", "print 'The characteristic impedance of the line =',round(Zo,2),'ohms'\n", "print 'The wavelength of the line at 10 GHz =',round(l*1000,2),'mm'" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The effective relative permittivity of the substrate = 3.131\n", "The characteristic impedance of the line = 30.08 ohms\n", "The wavelength of the line at 10 GHz = 16.95 mm\n" ] } ], "prompt_number": 8 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 11.11, Page number: 527

" ] }, { "cell_type": "code", "collapsed": false, "input": [ " \n", "\n", "import scipy\n", "\n", "#Variable Declaration\n", "\n", "h=1 #in mm\n", "w=0.8 #in mm\n", "Er=6.6 #relative permittivity\n", "P=scipy.arctan(0.0001) \n", "c=5.8*10**7 #conductivity in S/m\n", "f=10**10 #frequency in Hz\n", "mu=4*scipy.pi*10**-7 #permeability of free space\n", "C=3*10**8 #speed of wave in m/s\n", "r=w/h\n", "\n", "#Calculations\n", "\n", "Ee=((Er+1)/2.0)+((Er-1)/(2.0*(1+12/r)**0.5))\n", "Zo=(120.0*scipy.pi)/((r+1.393+(0.667*scipy.log(r+1.444)))*((Ee)**0.5))\n", "Rs=scipy.sqrt((scipy.pi*f*mu)/c)\n", "ac=8.686*Rs/(w*(10**-3)*Zo)\n", "l=C/(f*(Ee)**0.5)\n", "ad=27.3*(Ee-1)*Er*scipy.tan(P)/((Er-1)*Ee*l)\n", "\n", "#Results\n", "\n", "print 'attenuation due to conduction loss =',round(ac,2),'dB/m'\n", "print 'attenuation due to dielectric loss =',round(ad,3),'dB/m'" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "attenuation due to conduction loss = 4.35 dB/m\n", "attenuation due to dielectric loss = 0.177 dB/m\n" ] } ], "prompt_number": 9 } ], "metadata": {} } ] }