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+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 14 : Transmission lines"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 1 : pg 461"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The inductance of 1m length is 225.0 nH/m\n"
+ ]
+ }
+ ],
+ "source": [
+ " \n",
+ "#page no 461\n",
+ "#prob no. 14.1\n",
+ "#calculate the inductance\n",
+ "#A coaxial cable with capacitance=90pF/m & characteristic impedance=50 ohm\n",
+ "#given\n",
+ "C=90.*10**-12;Zo=50.;\n",
+ "#Determination of inductance of 1m length\n",
+ "#calculations\n",
+ "L=(Zo**2)*C;\n",
+ "#results\n",
+ "print 'The inductance of 1m length is',L*10**9,'nH/m'"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 2 : pg 462"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "a)The characteristic impedance of conductor is 227.399 ohm\n",
+ "b)The characteristic impedance of coaxial cable is 54.784 ohm\n"
+ ]
+ }
+ ],
+ "source": [
+ " \n",
+ "#page no 462\n",
+ "#prob no. 14.2\n",
+ "#calculate the imepdance \n",
+ "from math import log10,sqrt\n",
+ "#a)Determination of impedance of open wire with diameter 3mm & r=10mm\n",
+ "#given\n",
+ "D=3./2.;r=10.;#All values are in mm\n",
+ "#calculations and results\n",
+ "Zo1=276*log10(r/D); \n",
+ "print 'a)The characteristic impedance of conductor is',round(Zo1,3),'ohm'\n",
+ "#b)Determination of impedance of coaxial with er=2.3,inner diameter=2mm & outer diameter=8mm\n",
+ "er=2.3;D=8.;d=2;#All diameter values in mm\n",
+ "Zo2=(138/sqrt(er))*log10(D/d);\n",
+ "print 'b)The characteristic impedance of coaxial cable is',round(Zo2,3),'ohm'"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 3 : pg 463"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The value of velocity factor is 0.69\n",
+ "The value of propagation velo. is 207019667.803 m/s\n"
+ ]
+ }
+ ],
+ "source": [
+ " \n",
+ "#page no 463\n",
+ "#prob no. 14.3\n",
+ "#calculate the velocity factor and propagation velocity\n",
+ "#Cable with teflon dielectric er=2.1\n",
+ "from math import sqrt\n",
+ "#given\n",
+ "er=2.1;c=3.*10**8;#Velocity of light\n",
+ "#calculations and results\n",
+ "#Determination of velocity factor\n",
+ "Vf=1/sqrt(er);\n",
+ "print 'The value of velocity factor is',round(Vf,3)\n",
+ "#Determination of propagation velocity\n",
+ "Vp=Vf*c;\n",
+ "print 'The value of propagation velo. is',Vp,'m/s'"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 4 : pg 468"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The total voltage at the load is 0.333 V\n",
+ "The voltage across the line 0.333 V\n"
+ ]
+ }
+ ],
+ "source": [
+ " \n",
+ "#page no 468\n",
+ "#prob no. 14.4\n",
+ "#calculate the voltage\n",
+ "#Refer fig. 14.13(a)\n",
+ "vs=1;#source voltage\n",
+ "Rs=50.;#source resistance\n",
+ "Zo=50.;#line impedance\n",
+ "RL=25.;#load resistance\n",
+ "l=10.;#length of line\n",
+ "vf=0.7;#velocity factor\n",
+ "Vi=0.5;\n",
+ "c=3.*10**8;#velo of light\n",
+ "#calculations\n",
+ "#Vs will divide between Rs and Zo of the line.Since two resistors are equal,the voltage will divide equally.\n",
+ "#Therefore at t=0,the voltage at the source end of the line will rise from zero to 0.5V. \n",
+ "#The voltage at the load will remain zero untill the surge reaches it.The time for this is\n",
+ "T=l/(vf*c);\n",
+ "# After T sec, the voltage at the load will rise.The reflection coefficient is given as\n",
+ "refl_coeff=(RL-Zo)/(RL+Zo)\n",
+ "#Now reflection voltage is \n",
+ "Vr=refl_coeff * Vi;\n",
+ "#The total voltage at the load is\n",
+ "Vt=Vr+Vi;\n",
+ "# The reflected voltage will propogate back along the line,reaching \n",
+ "#the source at time 2T.After this the voltage will be 0.3335V all along the line\n",
+ "#The voltage across the line, and the load will be\n",
+ "VL=vs*(RL/(RL+Zo));\n",
+ "#results\n",
+ "print 'The total voltage at the load is',round(Vt,3),'V'\n",
+ "print 'The voltage across the line',round(VL,3),'V'"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 5 : pg 472"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The length reqd for phase shift is 0.12375 m\n"
+ ]
+ }
+ ],
+ "source": [
+ " \n",
+ "#page no 472\n",
+ "#prob no. 14.5\n",
+ "#calculate the length reqd\n",
+ "#Standard coaxial cable RG-8/U with 45 degree phase shift at 200MHz\n",
+ "#given\n",
+ "p=45.;f=200.*10**6;c=3.*10**8;#Speed of light in m/s\n",
+ "vf=0.66;#velo. factor for this line\n",
+ "#calculations\n",
+ "vp=vf*c;#Determination of propagation velo.\n",
+ "wav=vp/f;#Determination of wavelength of signal\n",
+ "#Determination of reqd length for 45 degree phase shift\n",
+ "L=wav*(p/360.);\n",
+ "#results\n",
+ "print 'The length reqd for phase shift is',L,'m'"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 6 : pg 476"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The value of SWR is 2.0\n"
+ ]
+ }
+ ],
+ "source": [
+ " \n",
+ "#page no 476\n",
+ "#prob no. 14.6\n",
+ "#calculate the value of SWR\n",
+ "#A 50ohm line terminated in 25ohm resistance\n",
+ "Zo=50.;Zl=25.;\n",
+ "#calculations\n",
+ "#Determination of SWR\n",
+ "SWR=Zo/Zl;#In this case Zo>Zl\n",
+ "#results\n",
+ "print 'The value of SWR is',SWR"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 7 : pg 477"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The amount of power reflected is 12.5 mW\n",
+ "The power dissipated in load is 37.5 mW\n"
+ ]
+ }
+ ],
+ "source": [
+ " \n",
+ "#page no 477\n",
+ "#prob no. 14.7\n",
+ "#calculate the power\n",
+ "#A generator sends 50mW at 50ohm line & reflection coeff I=0.5\n",
+ "#given\n",
+ "Pi=50.;I=0.5;\n",
+ "#calculations\n",
+ "#Determination of amount of power reflected\n",
+ "Pr=(I**2)*Pi;\n",
+ "#Determination of remainder power that reaches load\n",
+ "Pl=Pi-Pr;\n",
+ "#results\n",
+ "print 'The amount of power reflected is',Pr,'mW'\n",
+ "print 'The power dissipated in load is',Pl,'mW'"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 8 : pg 478"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The power absorbed by load is 44.444 W\n"
+ ]
+ }
+ ],
+ "source": [
+ " \n",
+ "#page no 478\n",
+ "#prob no. 14.8\n",
+ "#A transmitter supplies 50W with SWR 2:1\n",
+ "#calculate the power\n",
+ "#given \n",
+ "Pi=50.;SWR=2.;\n",
+ "#calculations\n",
+ "#Determination of power absorbed by load\n",
+ "Pl=(4*SWR*Pi)/(1+SWR)**2;\n",
+ "#results\n",
+ "print 'The power absorbed by load is',round(Pl,3),'W'"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 9 : pg 480"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The impedance looking toward the load (40-30j) ohm\n"
+ ]
+ }
+ ],
+ "source": [
+ " \n",
+ "# page no 545\n",
+ "# prob no 14.9\n",
+ "#calculate the impedance\n",
+ "from math import pi,tan\n",
+ "#given\n",
+ "Zo=50.;# line impedence in ohm\n",
+ "ZL=100.;# load impedance in ohm\n",
+ "vf=0.8;#velocity factor\n",
+ "l=1.;#length of line\n",
+ "f=30.*10**6;# freq of operation\n",
+ "c=3.*10**8;#velo of light\n",
+ "#calculations\n",
+ "# we have to find the length of line in degree\n",
+ "wl=vf*c/f#wavelength\n",
+ "# Then the length of line in degree is\n",
+ "ang=l/wl*360\n",
+ "# calculation of impedance\n",
+ "Z=Zo*(ZL+(1j*Zo*tan(ang*pi/180)))/(Zo+(1j*ZL*tan(ang*pi/180.)));\n",
+ "print 'The impedance looking toward the load',Z,'ohm'"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 10 : pg 481"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The length should be 0.1425 m\n"
+ ]
+ }
+ ],
+ "source": [
+ " \n",
+ "#page no 481\n",
+ "#prob no. 14.10\n",
+ "#calculate the length required\n",
+ "#A series tuned ckt tuned at 1GHz\n",
+ "#given\n",
+ "vf=0.95;c=3.*10**8;f=10**9;\n",
+ "#calculations\n",
+ "vp=vf*c;#determination of propagation velo.\n",
+ "wav=vp/f;#Determination of wavelength \n",
+ "#Determination of length\n",
+ "L=wav/2;#Since half wavelength section wiil be series resonant\n",
+ "#results\n",
+ "print 'The length should be',L,'m'"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 11 : pg 481"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The transmitter power must be 151.356 W\n"
+ ]
+ }
+ ],
+ "source": [
+ " \n",
+ "#page no 481\n",
+ "#prob no. 14.10\n",
+ "#calculate the transmitter power\n",
+ "#A Tx deliver 100W to antenna through 45m coaxial cable with loss=4dB/100m\n",
+ "#given\n",
+ "loss=4./100;L=45.;Pout=100.;\n",
+ "#calculations\n",
+ "loss_dB=L*loss;#Determination of loss in dB\n",
+ "Pin_Pout=10**(loss_dB/10);\n",
+ "#Determination of Tx power\n",
+ "Pin=Pout*Pin_Pout;\n",
+ "#results\n",
+ "print 'The transmitter power must be',round(Pin,3),'W'"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 13 : pg 490"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Input impedance is (19.36+5.44j) ohm\n"
+ ]
+ }
+ ],
+ "source": [
+ " \n",
+ "#page no 490\n",
+ "#prob no. 14.13\n",
+ "#calculate the input impedance\n",
+ "Zo=50.;#line impedance in ohm\n",
+ "f=100.*10**6;#operating freq\n",
+ "vf=0.7;#velocity factor\n",
+ "L=6.;#length in m\n",
+ "c=3.*10**8;#velo of light\n",
+ "ZL=50+1j*50;#load impedance in ohm\n",
+ "#calculations\n",
+ "# we have to calculate length in degree,so for this first find wl\n",
+ "wl=vf*c/f;#wavength in m\n",
+ "ang=360*L/wl;\n",
+ "# now from the graph input impedance is 19.36+%i5.44;\n",
+ "Zi=19.36+1j*5.44;\n",
+ "#results\n",
+ "print 'Input impedance is',Zi,'ohm'"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 14 : pg 492"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The required turn ratio is (0.752156137344+0j)\n"
+ ]
+ }
+ ],
+ "source": [
+ " \n",
+ "#page no 492\n",
+ "#prob no. 14.14\n",
+ "from cmath import sqrt\n",
+ "#given\n",
+ "Zo=50.;#line impedance in ohm\n",
+ "ZL=75.+1j*25;\n",
+ "# the requirment of this is simply to match the 50ohm line to the impedsnce at this point on the line,which is 88.38 ohm,resistive.\n",
+ "Z2=88.38;#in ohm\n",
+ "#calculations\n",
+ "#The required turn ratio is\n",
+ "N1_N2=sqrt(Zo/Z2);\n",
+ "#results\n",
+ "print 'The required turn ratio is',N1_N2"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 15 : pg 494"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Zo = 66.476\n"
+ ]
+ }
+ ],
+ "source": [
+ " \n",
+ "#page no 494\n",
+ "#prob no. 14.15\n",
+ "#calculate the impedance\n",
+ "# refer prob no 14.14\n",
+ "from math import sqrt\n",
+ "#given\n",
+ "Zo=50.;#line impedance in ohm\n",
+ "Z2=88.38;#in ohm\n",
+ "#calculations\n",
+ "Zo_=sqrt(Zo*Z2);\n",
+ "#results\n",
+ "print 'Zo = ',round(Zo_,3)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 16 : pg 494"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Capacitance is 2.12206590789e-11 F\n"
+ ]
+ }
+ ],
+ "source": [
+ " \n",
+ "#page no 494\n",
+ "#prob no. 14.16\n",
+ "#calculate the capacitance\n",
+ "from math import pi\n",
+ "#given\n",
+ "Zo=50.;#line impedance in ohm\n",
+ "f=100.*10**6;#operating freq in Hz\n",
+ "ZL1=50+1j*75;# load impedance with Xc=75\n",
+ "Xc=75;\n",
+ "#calculations\n",
+ "# Capacitance in farads is given as\n",
+ "C=1/(2*pi*f*Xc);\n",
+ "#results\n",
+ "print 'Capacitance is',C,'F'"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 17 : pg 497"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 17,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The value of stude is 0.014 S\n"
+ ]
+ }
+ ],
+ "source": [
+ " \n",
+ "#page no 497\n",
+ "#prob no. 14.17\n",
+ "#calculate the value of stude\n",
+ "#given\n",
+ "Zo=72.;#line impedance in ohm\n",
+ "ZL=120.-1j*100;#load impedance\n",
+ "#calculations\n",
+ "#The stub must be inserted at a point on the line where the real part of the load admittance is correct. This value is\n",
+ "s=1/Zo;\n",
+ "#results\n",
+ "print 'The value of stude is',round(s,3),'S'"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 18 : pg 501"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 18,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The distance is 168.0 m\n"
+ ]
+ }
+ ],
+ "source": [
+ " \n",
+ "#page no 501\n",
+ "#prob no. 14.18\n",
+ "#calculate the distance\n",
+ "#given\n",
+ "#A TDR display shows dscontinuity at 1.4us & vf=0.8\n",
+ "t=1.4*10**-6;vf=0.8;c=3.*10**8;#Speed of light\n",
+ "#Determination of distance of fault\n",
+ "#calculations\n",
+ "d=(vf*c*t)/2;#One-half time is used to calculate\n",
+ "#results\n",
+ "print 'The distance is',d,'m'"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 19 : pg 503"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 19,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The wavelength is 46.0 cm\n",
+ "The freq is 619.565 MHz\n"
+ ]
+ }
+ ],
+ "source": [
+ " \n",
+ "#page no 503\n",
+ "#prob no. 14.19\n",
+ "#calculate the wavelength and freq\n",
+ "#given\n",
+ "#2 adjacent minima on slotted are 23cm apart with velo factor=95%\n",
+ "L=23*10**-2;vf=0.95;c=3*10**8;#Velo. of light in m/s\n",
+ "#calculations and results\n",
+ "#Determination of wavelength\n",
+ "wav=2*L;#Minima are seperated by one-half wavelength\n",
+ "print 'The wavelength is',wav*100,'cm'\n",
+ "#Determination of freq.\n",
+ "f=(vf*c)/wav;#vp=vf*c\n",
+ "print 'The freq is' ,round(f/10**6,3),'MHz'"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 20 : pg 504"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 20,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The value of SWR is 2.15\n"
+ ]
+ }
+ ],
+ "source": [
+ " \n",
+ "#page no 504\n",
+ "#prob no. 14.20\n",
+ "#calculate the value of SWR\n",
+ "from math import sqrt\n",
+ "#given\n",
+ "#Frwd power in Tx line is 150W,Reverse power=20W\n",
+ "Pi=150.;Pr=20.;#All power in watt\n",
+ "#calculations\n",
+ "#Determination of SWR\n",
+ "SWR=(1+sqrt(Pr/Pi))/(1-sqrt(Pr/Pi));\n",
+ "#results\n",
+ "print 'The value of SWR is',round(SWR,3)"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 2",
+ "language": "python",
+ "name": "python2"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 2
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
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generated by cgit (git 2.34.1) at 2025-06-17 06:46:21 +0000