FIELD AND WAVES I
FIELD AND WAVES I ECSE 2100
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This 4 page Class Notes was uploaded by Immanuel Brakus PhD on Monday October 19, 2015. The Class Notes belongs to ECSE 2100 at Rensselaer Polytechnic Institute taught by James Lu in Fall. Since its upload, it has received 21 views. For similar materials see /class/224774/ecse-2100-rensselaer-polytechnic-institute in ELECTRICAL AND COMPUTER ENGINEERING at Rensselaer Polytechnic Institute.
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Date Created: 10/19/15
Fields and Waves Fall 2009 Homework 1 Due 9 September 2009 at 600 pm 1 Waves and Phasor Notation Be sure that you read the following questions carefully Also when you convert an expression from phasor to time domain form or vice versa convert it back carefully following the rules to check your answer J77 a Write the following voltage phasor expression in time domain form 100e 4 Note that this is just a voltage not a voltage wave Assume f 30MH2 b Write the following time domain current wave expression in phasor at formizt a s1n a2t j a c Is the expression in part b a standing or traveling wave Ifit is a traveling wave what direction does it travel and what is its velocity 2 Plane Wave Representations The numbers given in this problem are realistic but not necessarily real That is your answers should come out in a reasonable range but the numbers are not based on a real commercially available transmission line The current on a transmission line is given byiz t cos77r106t 003712 a Is this a standing wave or a traveling wave If it is a traveling wave what direction does it travel and what is its velocity b What is the period of this wave T What is the wavelength xi c Plot this expression as a function of space at t 0 tT3 t2T3 using Maple or Matlab or some similar program d Write this current expression in phasor form e Assume that the transmission line has a capacitance per unit length of43p Find the characteristic impedance of the line Z0 and then the voltage on the line in phasor form 3 PSpice Simulated Experiments PSpice can show us a lot about how the voltages look at the input and output ends of transmission lines The simulation can in effect replace an experiment by giving us essentially the same results a To get some practice using PSpice set up the following simulation using the parameters of your transmission line from problem 2 That is the source line and load impedances should all be equal to the characteristic impedance of the line you determined in problem 2 The source voltage and frequency should be selected to obtain the current given in problem 2 on the line Set the offset voltage to zero Use the lossless line model and assume the length of the line is 40meters Be careful to use the zero ground since it is the only one that works with PSpice 1 K A Connor Rensselaer Polytechnic Institute September 2009 Fields and Waves Fall 2009 Homework 1 0 Run the simulation shown below and display your results The numbers given are aproximate You ma want to chane them some to et a better dis 1 s General AnalPSlS nclude Files Libraries Stimulus Uptions Data Collection Probe Window Flun to time Sus seconds TSTUF Start saving data after 3us seconds Analysis type quot Transient upliurrs Maximum step size lns seconds l Skip the initial transient bias point calculation SKIPBP EllDad Bias POW Output File Options UK I Cancel rlJGl u Help b Explain why your result makes sense Be sure to thoroughly label your plot 2 K A Connor Rensselaer Polytechnic Institute September 2009 Fields and Waves Fall 2009 Homework 1 4 Lumped Transmission Lines A transmission line can be replaced by a series of lumped circuit elements under certain conditions In this exercise you will compare the response of such a lumped model line with the coil of coax Obtain a coil of coax a 50 Ohm terminator and one of the lumped component transmission lines from a TA Note we will be analyzing the lumped configuration using PSpice in lecture Thus your measurements should be guided by what we obtain there Provide the number of your coax coil and lumped model below Coax 39 LumpedModel s a First we will repeat an experiment from the first studio session at a different frequency Put the 50 Ohm terminator across the output of the coaxial cable and simultaneously measure input and output signals on the oscilloscope Set the input voltage at lep with a frequency of 3MHZ Measure the time delay between the signals What else is different about the input and output voltages b Replace the coaxial cable with the lumped version and repeat the experiment c You should have observed that the lumped line behaves in a qualitatively similar manner to the spool of coax Thus it must represent a similar length of line We want to determine the actual length of line Each L C combination represents some equivalent length of line Since there are 20 such combinations we only need to figure out what length each combo represents and multiply it by 20 To understand better how the lumped circuit is con gured look at the diagram below done with PSpice This diagram has a load impedance R2 of 93 Ohms which is not what we are using here Note that the inductance and capacitance for each section is indicated Given your knowledge of the actual capacitance and inductance per unit length for the RG5 8U coaxial cable approximately what length does each section represent 3 K A Connor Rensselaer Polytechnic Institute September 2009 Fields and Waves Fall 2009 Homework 1 d Remove the load resistor and replace it with a short circuit Measure the voltage at the 11111 node Adjust the frequency somewhere between MHz and 4MHz until the voltage at the 11111 node is a minimum It should be somewhere around 100mV Put the terminating resistor back on as a load Measure the voltage at each of the nodes for the case where the lumped line is terminated with 50 Ohms Remove the resistor and repeat for the short circuit Where are the minimas and maximas located One minimum should be at node 11 Plot your results for the measured voltages as a function of distance using the distance between nodes that you determined above Plot your results again but now in terms of wavelength rather than meters You can use the same plot if you wish and provide two sets of labels e Show that the maXimas and minimas are located where they should be in terms of wavelength f Run the corresponding case using the simulation at BesserNet mentioned in lecture Note that the lumped lines work slightly di Qrently if di erent capacitors are used Thus please note the color of the capacitors on the board you are using The correct answer to part d will depend on what capacitors are used on your board 4 K A Connor Rensselaer Polytechnic Institute September 2009