Electromagnetic fields and waves lecture notes

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Published Date:19-07-2017
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Fields and Waves IThese Slides Were Prepared by Prof. Kenneth A. Connor Using Original Materials Written Mostly by the Following:  Kenneth A. Connor – ECSE Department, Rensselaer Polytechnic Institute, Troy, NY  J. Darryl Michael – GE Global Research Center, Niskayuna, NY  Thomas P. Crowley – National Institute of Standards and Technology, Boulder, CO  Sheppard J. Salon – ECSE Department, Rensselaer Polytechnic Institute, Troy, NY  Lale Ergene – ITU Informatics Institute, Istanbul, Turkey  Jeffrey Braunstein – Chung-Ang University, Seoul, Korea Materials from other sources are referenced where they are used. Those listed as Ulaby are figures from Ulaby’s textbook. 18 July 2017 Fields and Waves I 2Examples of Antennas 18 July 2017 Fields and Waves I 3Antennas 18 July 2017 Fields and Waves I 4moteiv Tmote Sky Inverted F Antenna 18 July 2017 Fields and Waves I 5moteiv Tmote Sky 18 July 2017 Fields and Waves I 6moteiv Tmote Sky 18 July 2017 Fields and Waves I 7moteiv Tmote Sky 18 July 2017 Fields and Waves I 8moteiv Tmote Sky 18 July 2017 Fields and Waves I 918 July 2017 Fields and Waves I 10Transmission Lines & Antennas  Review Transmission Lines  Review Boundary Conditions  Review Voltage, Current, Electric and Magnetic Fields  Etc. 18 July 2017 Fields and Waves I 11TEM Waves on Transmission Lines Connecting Uniform Plane Waves with Voltages and Currents on Transmission Lines:  jz jz E (z) E eE e x  jz jz E e E e  H (z) y  18 July 2017 Fields and Waves I 12TEM Waves These fields can exist in the region between the conducting plates if the boundary conditions on the plates are reasonably satisfied. Since the electric field has only an x component, it is totally normal to the conducting boundaries. This can occur if there is a surface charge on the boundary,  jz jz E (z)E eE e s x The magnetic field is totally tangent to the conducting boundary, which can occur if there is a surface current density given by  jz jz E e E e  J H (z) s y  18 July 2017 Fields and Waves I 13TEM Waves Then, assuming that the lower plate is grounded, the voltage on the upper plate will be s  jz jz jz jz v z E (z)dx sE esE eV eV e  x  0 where we have integrated the electric field along the vertical (red) w path shown. s 18 July 2017 Fields and Waves I 14TEM Waves To connect the magnetic field with the current, we must integrate along a closed path that encloses one of the two conductors. The bottom path shown includes the horizontal (green) path inside the field region and the blue path outside of the field region. (We assume no fringing in this ideal case.) The magnetic field only contributes along the green path. Thus  jz jz w wE ewE e  i z H (z)dy  y  0   jz jz jz jz wsE ewsE e V eV e   s s w 18 July 2017 Fields and Waves I 15TEM Waves For a parallel plate waveguide (stripline), the inductance and capacitance per unit length and intrinsic impedance are w s c l s w s l s s w Z o w c w w s 18 July 2017 Fields and Waves I 16TEM Waves so the current expression is  jz jz V eV e  i(z) Z o We could have determined this current from the surface current density so we should check to be sure that the two results agree. The total current at any z should be given by  jz jz jz jz E e E e V eV e  i(z) J w w s  Z o as before. 18 July 2017 Fields and Waves I 17TEM Waves Finally, we can check to see if the charge per unit length (as determined from the boundary condition) gives us the usual capacitance per unit length. w  jz jz jz jz q wwE ewE e V eV e cv z   s s as expected. The same analysis can be done for coaxial cables and two-wire lines. The general results are the same. 18 July 2017 Fields and Waves I 18Standing Waves: Voltage Standing Wave with Short Circuit Load Constructive Interference Destructive Interference 18 July 2017 Fields and Waves I 19Standing Waves: Voltage Standing Wave with Open Circuit Load 18 July 2017 Fields and Waves I 20