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

Chapter 44: Transmission lines

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

Example 1, page no. 873

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Determine (a) the wavelength on the line, and (b) the speed of transmission of a signal.\n", "from __future__ import division\n", "import math\n", "import cmath\n", "#initializing the variables:\n", "f = 1910;# in Hz\n", "b = 0.05;# in rad/km\n", "\n", "#calculation:\n", "w = 2*math.pi*f\n", " #wavelength \n", "Y = 2*math.pi/b\n", " #speed of transmission\n", "u = f*Y\n", "\n", "\n", "#Results\n", "print \"\\n\\n Result \\n\\n\"\n", "print \"\\n wavelength Y is \",round(Y,1),\" km\"\n", "print \"\\n speed of transmission \",round(u,1),\"km/sec\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", "\n", " Result \n", "\n", "\n", "\n", " wavelength Y is 125.7 km\n", "\n", " speed of transmission 240017.7 km/sec" ] } ], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 2, page no. 873

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Determine, for a frequency of operation of 1 kHz, \n", "#(a) the phase delay, \n", "#(b) the wavelength on the line, and \n", "#(c) the velocity of propagation (in metres per second) of the signal.\n", "from __future__ import division\n", "import math\n", "import cmath\n", "#initializing the variables:\n", "L = 0.004;# in Henry/loop\n", "C = 0.004E-6;# in F/loop\n", "f = 1000;# in Hz\n", "\n", " #calculation:\n", "w = 2*math.pi*f\n", " #phase delay\n", "b = w*(L*C)**0.5\n", " #wavelength \n", "Y = 2*math.pi/b\n", " #speed of transmission\n", "u = f*Y\n", "\n", "\n", "#Results\n", "print \"\\n\\n Result \\n\\n\"\n", "print \"\\n phase delay is \",round(b,3),\" rad/km\"\n", "print \"\\n wavelength Y is \",Y,\" km\"\n", "print \"\\n speed of transmission \",u,\"km/sec\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", "\n", " Result \n", "\n", "\n", "\n", " phase delay is 0.025 rad/km\n", "\n", " wavelength Y is 250.0 km\n", "\n", " speed of transmission 250000.0 km/sec" ] } ], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 3, page no. 874

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#determine the voltage at a point 10 km down the line,\n", "from __future__ import division\n", "import math\n", "import cmath\n", "#initializing the variables:\n", "a = 0.25;# in Np/km\n", "b = 0.20;# in rad/km\n", "Vs = 5;# in Volts\n", "n = 10;# in km\n", "f = 2000;# in Hz\n", "\n", " #calculation:\n", "w = 2*math.pi*f\n", " #the voltage 10 km down the line\n", "r = a + 1j*b\n", "VR = Vs*cmath.e**(-1*n*r)\n", "\n", "\n", "#Results\n", "print \"\\n Result \\n\\n\"\n", "print \"voltage 10 km down the line is \",round(abs(VR),2),\"/_\",round(cmath.phase(complex(VR.real,VR.imag))*180/math.pi,2),\"deg V\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", " Result \n", "\n", "\n", "voltage 10 km down the line is 0.41 /_ -114.59 deg V\n" ] } ], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 4, page no. 875

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Determine the magnitude and phase of the current at the receiving end,\n", "from __future__ import division\n", "import math\n", "import cmath\n", "#initializing the variables:\n", "a = 0.5;# in Np/km\n", "b = 0.25;# in rad/km\n", "rvs = 2;# in Volts\n", "thetavs = 0;# in degrees\n", "rzo = 800;# in ohm\n", "thetazo = -25;# in degrees\n", "n = 5;# in km\n", "\n", "#calculation:\n", " #voltage\n", "Vs = rvs*math.cos(thetavs*math.pi/180) + 1j*rvs*math.sin(thetavs*math.pi/180)\n", " #characteristic impedance\n", "Zo = rzo*math.cos(thetazo*math.pi/180) + 1j*rzo*math.sin(thetazo*math.pi/180)\n", " # receiving end voltage\n", "r = a + 1j*b\n", "VR = Vs*cmath.e**(-1*n*r)\n", " #Receiving end current,\n", "IR = VR/Zo\n", "\n", "\n", "#Results\n", "print \"\\n\\n Result \\n\\n\"\n", "print \"Receiving end current, IR is \",round(abs(IR)*1E3,3),\"/_\",round(cmath.phase(complex(IR.real,IR.imag))*180/math.pi,2),\"deg mA\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", "\n", " Result \n", "\n", "\n", "Receiving end current, IR is 0.205 /_ -46.62 deg mA\n" ] } ], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 5, page no. 875

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Determine the output voltage if the length of the line is doubled.\n", "from __future__ import division\n", "import math\n", "import cmath\n", "#initializing the variables:\n", "Vs = 8;# in Volts\n", "VR = 2;# in Volts\n", "x = 2; \n", "\n", "#calculation:\n", " # receiving end voltage VR = Vs*e**(-nr)\n", " #e**-nr = p\n", "p = VR/Vs\n", " #If the line is doubled in length, then\n", "VR = Vs*(p)**2\n", "\n", "\n", "#Results\n", "print \"\\n\\n Result \\n\\n\"\n", "print \"\\n Receiving end voltage If the line is doubled in length, VR is \",abs(VR),\" V\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", "\n", " Result \n", "\n", "\n", "\n", " Receiving end voltage If the line is doubled in length, VR is 0.5 V" ] } ], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 6, page no. 876

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Determine the characteristic impedance of the line at this frequency.\n", "from __future__ import division\n", "import math\n", "import cmath\n", "#initializing the variables:\n", "rzoc = 800;# in ohm\n", "thetazoc = -50;# in degrees\n", "rzsc = 413;# in ohm\n", "thetazsc = -20;# in degrees\n", "f = 1500;# in Hz\n", "\n", " #calculation:\n", " #open circuit impedance\n", "Zoc = rzoc*math.cos(thetazoc*math.pi/180) + 1j*rzoc*math.sin(thetazoc*math.pi/180)\n", " #short circuit impedance\n", "Zsc = rzsc*math.cos(thetazsc*math.pi/180) + 1j*rzsc*math.sin(thetazsc*math.pi/180)\n", " #characteristic impedance Zo\n", "Zo = (Zoc*Zsc)**0.5\n", "\n", "\n", "#Results\n", "print \"\\n\\n Result \\n\\n\"\n", "print \"characteristic impedance Zo is\",round(abs(Zo)),\"/_\",round(cmath.phase(complex(Zo.real,Zo.imag))*180/math.pi,2),\"deg ohm\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", "\n", " Result \n", "\n", "\n", "characteristic impedance Zo is 575.0 /_ -35.0 deg ohm\n" ] } ], "prompt_number": 3 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 7, page no. 877

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Determine the characteristic impedance of the line when the frequency is 2 kHz.\n", "from __future__ import division\n", "import math\n", "import cmath\n", "#initializing the variables:\n", "R = 15;# in ohm/loop km\n", "L = 0.0034;# in H/loop km\n", "C = 10E-9;# in F/km\n", "G = 3E-6;# in S/km\n", "f = 2000;# in Hz\n", "\n", " #calculation:\n", "w = 2*math.pi*f\n", " #characteristic impedance Zo\n", "Zo = ((R + 1j*w*L)/(G + 1j*w*C))**0.5\n", "\n", "\n", "#Results\n", "print \"\\n\\n Result \\n\\n\"\n", "print \"characteristic impedance Zo is \",round(abs(Zo),0),\"/_\",round(cmath.phase(complex(Zo.real,Zo.imag))*180/math.pi,2),\"deg ohm\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", "\n", " Result \n", "\n", "\n", "characteristic impedance Zo is 600.0 /_ -8.99 deg ohm\n" ] } ], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 8, page no. 879

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Determine, at an operating frequency of 400 kHz, (a) the characteristic impedance,\n", "#(b) the propagation coefficient, (c) the wavelength on the line, and \n", "#(d) the velocity of propagation, in metres per second, of a signal.\n", "from __future__ import division\n", "import math\n", "import cmath\n", "#initializing the variables:\n", "L = 0.0005;# in H/loop km\n", "C = 0.12E-6;# in F/km\n", "f = 400000;# in Hz\n", "\n", "#calculation:\n", "w = 2*math.pi*f\n", " #characteristic impedance Zo\n", "Zo = (L/C)**0.5\n", " #the propagation coefficient\n", "r = 1j*w*(L*C)**0.5\n", " #the attenuation coefficient \n", "a = r.real\n", " #the phaseshift coefficient\n", "b = r.imag\n", " #wavelength\n", "Y = 2*math.pi/b\n", " #velocity of propagation \n", "u = f*Y\n", "\n", "\n", "#Results\n", "print \"\\n\\n Result \\n\\n\"\n", "print \"\\n characteristic impedance Zo is \",abs(Zo),\"ohm\"\n", "print \"\\n propagation coefficient is \",a,\" +(\",round(b,2),\")i\"\n", "print \"\\n wavelength Y is \",round(Y*1E3,0),\"m\"\n", "print \"\\n speed of transmission \",round(u,2),\"km/sec\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", "\n", " Result \n", "\n", "\n", "\n", " characteristic impedance Zo is 64.5497224368 ohm\n", "\n", " propagation coefficient is 0.0 +( 19.47 )i\n", "\n", " wavelength Y is 323.0 m\n", "\n", " speed of transmission 129099.44 km/sec" ] } ], "prompt_number": 8 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 9, page no. 880

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Determine for the line (a) the characteristic impedance,\n", "#(b) the propagation coefficient, (c) the attenuation coefficient and\n", "#(d) the phase-shift coefficient\n", "from __future__ import division\n", "import math\n", "import cmath\n", "#initializing the variables:\n", "R = 25;# in ohm/loop km\n", "L = 0.005;# in H/loop km\n", "C = 0.04E-6;# in F/km\n", "G = 80E-6;# in S/km\n", "f = 1000;# in Hz\n", "\n", " #calculation:\n", "w = 2*math.pi*f\n", " #characteristic impedance Zo\n", "Zo = ((R + 1j*w*L)/(G + 1j*w*C))**0.5\n", " #the propagation coefficient\n", "r = ((R + 1j*w*L)*(G + 1j*w*C))**0.5\n", " #the attenuation coefficient \n", "a = r.real\n", " #the phaseshift coefficient\n", "b = r.imag\n", "\n", "\n", "#Results\n", "print \"\\n\\n Result \\n\\n\"\n", "print \"characteristic impedance Zo is\",round(abs(Zo),2),\"/_\",round(cmath.phase(complex(Zo.real,Zo.imag))*180/math.pi,2),\"deg ohm\"\n", "print \"\\n propagation coefficient is \",round(abs(r),4),\"/_\",round(cmath.phase(complex(a,b))*180/math.pi,2),\"deg\"\n", "print \"\\n attenuation coefficient is \",round(a,4),\" Np/km\"\n", "print \"\\n the phase-shift coefficient \",round(b,4),\" rad/km\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", "\n", " Result \n", "\n", "\n", "characteristic impedance Zo is 390.16 /_ -10.43 deg ohm\n", "\n", " propagation coefficient is 0.1029 /_ 61.92 deg\n", "\n", " attenuation coefficient is 0.0484 Np/km\n", "\n", " the phase-shift coefficient 0.0908 rad/km\n" ] } ], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 10, page no. 881

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#determine (a) the characteristic impedance, \n", "#(b) the propagation coefficient, \n", "#(c) the attenuation and phase-shift coefficients, \n", "#(d) the sending-end current, \n", "#(e) the receiving-end current, \n", "#(f) the wavelength on the line, and \n", "#(g) the speed of transmission of signal.\n", "from __future__ import division\n", "import math\n", "import cmath\n", "#initializing the variables:\n", "R = 8;# in ohm/loop km\n", "L = 0.003;# in H/loop km\n", "C = 7500E-12;# in F/km\n", "G = 0.25E-6;# in S/km\n", "f = 1000;# in Hz\n", "n = 300;# in km\n", "Zg = 400 + 1j*0;# in ohm\n", "Vg = 10;# in Volts\n", "\n", " #calculation:\n", "w = 2*math.pi*f\n", " #characteristic impedance Zo\n", "Zo = ((R + 1j*w*L)/(G + 1j*w*C))**0.5\n", " #the propagation coefficient\n", "r = ((R + 1j*w*L)*(G + 1j*w*C))**0.5\n", " #the attenuation coefficient \n", "a = r.real\n", " #the phaseshift coefficient\n", "b = r.imag\n", " #the sending-end current,\n", "Is = Vg/(Zg + Zo)\n", " #the receiving-end current,\n", "IR = Is*cmath.e**(-1*n*r)\n", " #wavelength\n", "Y = 2*math.pi/b\n", " #velocity of propagation \n", "u = f*Y\n", "\n", "\n", "#Results\n", "print \"\\n\\n Result \\n\\n\"\n", "print \"characteristic impedance Zo is\",round(abs(Zo),1),\"/_\",round(cmath.phase(complex(Zo.real,Zo.imag))*180/math.pi,2),\"deg ohm\"\n", "print \"propagation coefficient is \",round(abs(r),5),\"/_\",round(cmath.phase(complex(r.real,r.imag))*180/math.pi,2),\"deg\"\n", "print \"attenuation coefficient is \",round(a,5),\" Np/km and the phaseshift coefficient \",round(b,5),\" rad/km\"\n", "print \"sending-end current Is is \",round(abs(Is)*1E3,3),\"/_\",round(cmath.phase(complex(Is.real,Is.imag))*180/math.pi,2),\"deg mA\"\n", "print \"receiving-end current IR is\",round(abs(IR)*1E3,3),\"/_\",round(cmath.phase(complex(IR.real,IR.imag))*180/math.pi,2),\"deg mA\"\n", "print \"wavelength Y is \",round(Y,1),\" km\"\n", "print \"speed of transmission \",round(u,1),\"km/sec\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", "\n", " Result \n", "\n", "\n", "characteristic impedance Zo is 659.2 /_ -11.35 deg ohm\n", "propagation coefficient is 0.03106 /_ 78.35 deg\n", "attenuation coefficient is 0.00627 Np/km and the phaseshift coefficient 0.03042 rad/km\n", "sending-end current Is is 9.485 /_ 7.07 deg mA\n", "receiving-end current IR is 1.445 /_ -155.88 deg mA\n", "wavelength Y is 206.5 km\n", "speed of transmission 206521.1 km/sec\n" ] } ], "prompt_number": 6 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 11, page no. 884

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Determine by how much the inductance should be increased to satisfy the condition for minimum distortion.\n", "from __future__ import division\n", "import math\n", "import cmath\n", "#initializing the variables:\n", "R = 10;# in ohm/loop km\n", "L = 0.0015;# in H/loop km\n", "C = 0.06E-6;# in F/km\n", "G = 1.2E-6;# in S/km\n", "\n", " #calculation:\n", " #the condition for minimum distortion is given by LG = CR, from which,\n", "Lm = C*R/G\n", "dL = Lm - L\n", "\n", "\n", "#Results\n", "print \"\\n\\n Result \\n\\n\"\n", "print \"\\n inductance should be increased by \",round(dL*1E3,1),\"mH/loop km for minimum distortion\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", "\n", " Result \n", "\n", "\n", "\n", " inductance should be increased by 498.5 mH/loop km for minimum distortion" ] } ], "prompt_number": 11 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 12, page no. 884

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Determine, for minimum distortion at a frequency of 1.5 kHz \n", "#(a) the value of inductance per loop kilometre required, \n", "#(b) the propagation coefficient, \n", "#(c) the velocity of propagation of signal, and \n", "#(d) the wavelength on the line\n", "from __future__ import division\n", "import math\n", "import cmath\n", "#initializing the variables:\n", "R = 80;# in ohm/loop km\n", "C = 5E-9;# in F/km\n", "G = 2E-6;# in S/km\n", "f = 1500;# in Hz\n", "\n", " #calculation:\n", "w = 2*math.pi*f\n", " #the condition for minimum distortion is given by LG = CR, from which, inductance\n", "L = C*R/G\n", " #attenuation coefficient,\n", "a = (R*G)**0.5\n", " #phase shift coefficient,\n", "b = w*(L*C)**0.5\n", " #propagation coefficient,\n", "r = a + 1j*b\n", " #velocity of propagation,\n", "u = 1/(L*C)**0.5\n", " #wavelength\n", "Y = u/f\n", "\n", "\n", "#Results\n", "print \"\\n\\n Result \\n\\n\"\n", "print \"\\n inductance is \",round(L,2),\" H\"\n", "print \"\\n propagation coefficient is \",round(a,2),\" +(\",round(b,2),\")i\"\n", "print \"\\n speed of transmission \",round(u,2),\"km/sec\"\n", "print \"\\n wavelength Y is \",round(Y,2),\" km\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", "\n", " Result \n", "\n", "\n", "\n", " inductance is 0.2 H\n", "\n", " propagation coefficient is 0.01 +( 0.3 )i\n", "\n", " speed of transmission 31622.78 km/sec\n", "\n", " wavelength Y is 21.08 km\n" ] } ], "prompt_number": 7 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 13, page no. 888

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#calculate the value of (a) the reflection coefficient for the line, (b) the incident current, \n", "#(c) the incident voltage, (d) the reflected current, and (e) the reflected voltage \n", "from __future__ import division\n", "import math\n", "import cmath\n", "#initializing the variables:\n", "Zo = 75;# in ohm\n", "ZR = 250;# in ohm\n", "VR = 10;# in Volts\n", "\n", "#calculation:\n", " #reflection coefficient\n", "p = (Zo - ZR)/(Zo + ZR)\n", " #Current flowing in the terminating load\n", "IR = VR/ZR\n", " #incident current, Ii\n", "Ii = IR/(1 + p)\n", " #incident voltage, Vi \n", "Vi = Ii*Zo\n", " #reflected current, Ir\n", "Ir = IR - Ii\n", " #reflected voltage, Vr\n", "Vr = -1*Ir*Zo\n", "\n", "\n", "#Results\n", "print \"\\n\\n Result \\n\\n\"\n", "print \"\\n reflection coefficient is \",round(p,3),\"\"\n", "print \"\\n incident current, Ii is \",round(Ii,4),\" A\"\n", "print \"\\n incident voltage, Vi is \",round(Vi,2),\" V\"\n", "print \"\\n reflected current, Ir is \",round(Ir,4),\" A\"\n", "print \"\\n reflected voltage, Vr is \",round(Vr,2),\" V\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", "\n", " Result \n", "\n", "\n", "\n", " reflection coefficient is -0.538 \n", "\n", " incident current, Ii is 0.0867 A\n", "\n", " incident voltage, Vi is 6.5 V\n", "\n", " reflected current, Ir is -0.0467 A\n", "\n", " reflected voltage, Vr is 3.5 V" ] } ], "prompt_number": 13 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 14, page no. 889

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Determine the magnitude of the reflection coefficient in each case.\n", "from __future__ import division\n", "import math\n", "import cmath\n", "#initializing the variables:\n", "Zo = 500 - 1j*40;# in ohm\n", "ZR1 = 500 + 1j*40;# in ohm\n", "ZR2 = 600 + 1j*0;# in ohm\n", "\n", " #calculation:\n", " #reflection coefficient\n", "p1 = (Zo - ZR1)/(Zo + ZR1)\n", "p2 = (Zo - ZR2)/(Zo + ZR2)\n", "p1mag = abs(p1)\n", "p2mag = abs(p2)\n", "\n", "\n", "#Results\n", "print \"\\n\\n Result \\n\\n\"\n", "print \"\\n reflection coefficient (a)\",p1mag,\" and (b)\", round(p2mag,2),\"\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", "\n", " Result \n", "\n", "\n", "\n", " reflection coefficient (a) 0.08 and (b) 0.1 " ] } ], "prompt_number": 14 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 15, page no. 890

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Determine (a) the magnitude of the ratio of the reflected to the incident voltage wave, and \n", "#(b) the incident voltage\n", "from __future__ import division\n", "import math\n", "import cmath\n", "#initializing the variables:\n", "rzo = 500;# in ohm\n", "thetazo = 0;# in degrees\n", "ZR = 320 + 1j*240;# in ohm\n", "rvr = 20;# in volts\n", "thetavr = 35;# in degrees\n", "\n", " #calculation:\n", " #voltage\n", "VR = rvr*math.cos(thetavr*math.pi/180) + 1j*rvr*math.sin(thetavr*math.pi/180)\n", " #characteristic impedance\n", "Zo = rzo*math.cos(thetazo*math.pi/180) + 1j*rzo*math.sin(thetazo*math.pi/180)\n", " #the ratio of the reflected to the incident voltage \n", " #vr = VR/Vi\n", "vr = (ZR - Zo)/(Zo + ZR)\n", "vrmag = abs(vr)\n", " #incident voltage, Vi\n", "Vi = VR/vr\n", "\n", "\n", "#Results\n", "print \"\\n\\n Result \\n\\n\"\n", "print \"\\n the magnitude of the ratio Vr : Vi is \",round(vrmag,3),\"\"\n", "print \"\\n incident voltage, Vi is \",round(abs(Vi),1),\"/_\",round(cmath.phase(complex(Vi.real,Vi.imag))*180/math.pi,2),\"deg V\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", "\n", " Result \n", "\n", "\n", "\n", " the magnitude of the ratio Vr : Vi is 0.351 \n", "\n", " incident voltage, Vi is 57.0 /_ -75.56 deg V\n" ] } ], "prompt_number": 8 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 16, page no. 895

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#determine (a) the reflection coefficient and (b) the standing-wave ratio.\n", "from __future__ import division\n", "import math\n", "import cmath\n", "#initializing the variables:\n", "rzo = 600;# in ohm\n", "thetazo = 0;# in degrees\n", "ZR = 400 + 250j;# in ohm\n", "\n", " #calculation:\n", " #characteristic impedance\n", "Zo = rzo*math.cos(thetazo*math.pi/180) + 1j*rzo*math.sin(thetazo*math.pi/180)\n", " #reflection coefficient\n", "p = (Zo - ZR)/(Zo + ZR)\n", "pmag = abs(p)\n", " #standing-wave ratio,\n", "s = (1 + pmag)/(1 - pmag)\n", "\n", "\n", "#Results\n", "print \"\\n\\n Result \\n\\n\"\n", "print \"\\n reflection coefficient, is \",round(abs(p),4),\"/_\",round(cmath.phase(complex(p.real,p.imag))*180/math.pi,2),\"deg\"\n", "print \"\\n standing-wave ratio, s is \",round(s,3),\"\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", "\n", " Result \n", "\n", "\n", "\n", " reflection coefficient, is 0.3106 /_ -65.38 deg\n", "\n", " standing-wave ratio, s is 1.901 " ] } ], "prompt_number": 16 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 17, page no. 896

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Calculate (a) the standing-wave ratio, \n", "#(b) the load impedance, and\n", "#(c) the incident current flowing if the reflected current is 10 mA.\n", "from __future__ import division\n", "import math\n", "import cmath\n", "#initializing the variables:\n", "rp = 0.2; \n", "thetap = -120;# in degrees\n", "Zo = 80;# in ohm\n", "Ir = 0.01;# in Amperes\n", "\n", "#calculation:\n", " #reflection coefficient\n", "p = rp*math.cos(thetap*math.pi/180) + 1j*rp*math.sin(thetap*math.pi/180)\n", " #standing-wave ratio,\n", "s = (1 + rp)/(1 - rp)\n", " #load impedance ZR \n", "ZR = Zo*(1 - p)/(1 + p)\n", " #incident current\n", "Ii = Ir*(s + 1)/(s - 1)\n", "\n", "\n", "#Results\n", "print \"\\n\\n Result \\n\\n\"\n", "print \"\\n standing-wave ratio, s is \",s,\"\"\n", "print \"\\n load impedance ZR is \",round(ZR.real,2),\" +(\",round(ZR.imag,1),\")i ohm\"\n", "print \"\\n incident current is \",Ii,\" A\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", "\n", " Result \n", "\n", "\n", "\n", " standing-wave ratio, s is 1.5 \n", "\n", " load impedance ZR is 91.43 +( 33.0 )i ohm\n", "\n", " incident current is 0.05 A\n" ] } ], "prompt_number": 9 }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Example 18, page no. 897

" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#determine the value of the reflected power.\n", "from __future__ import division\n", "import math\n", "import cmath\n", "#initializing the variables:\n", "s = 1.6;\n", "Pi = 0.2;# in Watts\n", "\n", "#calculation:\n", " #reflected power, Pr\n", "Pr = Pi*((s - 1)/(s + 1))**2\n", "\n", "\n", "#Results\n", "print \"\\n\\n Result \\n\\n\"\n", "print \"\\n reflected power, Pr is \",round(Pr*1E3,2),\" mW\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", "\n", " Result \n", "\n", "\n", "\n", " reflected power, Pr is 10.65 mW" ] } ], "prompt_number": 18 } ], "metadata": {} } ] }