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ENE 428 Microwave Engineering

ENE 428 Microwave Engineering. Lecture 3 Polarization, Reflection and Transmission at normal incidence. RS. Uniform plane wave (UPW) power transmission. from. W/m 2. Polarization. UPW is characterized by its propagation direction and frequency.

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ENE 428 Microwave Engineering

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  1. ENE 428Microwave Engineering Lecture 3 Polarization, Reflection and Transmission at normal incidence RS RS

  2. Uniform plane wave (UPW) power transmission from W/m2 RS

  3. Polarization • UPW is characterized by its propagation direction and frequency. • Its attenuation and phase are determined by medium’s parameters. • Polarization determines the orientation of the electric field in a fixed spatial plane orthogonal to the direction of the propagation. RS

  4. Linear polarization • Consider in free space, • At plane z = 0, a tip of field traces straight line segment called “linearly polarized wave” RS

  5. Linear polarization • A pair of linearly polarized wave also produces linear polarization At z = 0 plane At t = 0, both linearly polarized waves have their maximum values. RS

  6. More generalized linear polarization • More generalized of two linearly polarized waves, • Linear polarization occurs when two linearly polarized waves are in phase out of phase RS

  7. Elliptically polarized wave • Superposition of two linearly polarized waves that • If x = 0 and y = 45, we have RS

  8. Circularly polarized wave • occurs when Exoand Eyo are equal and • Right hand circularly polarized (RHCP) wave • Left hand circularly polarized (LHCP) wave RS

  9. Circularly polarized wave • Phasor forms: • for RHCP, • for LHCP, from Note: There are also RHEP and LHEP RS

  10. Ex1 Given,determine the polarization of this wave RS

  11. Ex2 The electric field of a uniform plane wave in free space is given by , determine • f • The magnetic field intensity RS

  12. c) d) Describe the polarization of the wave RS

  13. Reflection and transmission of UPW at normal incidence RS

  14. Incident wave • Normal incidence – the propagation direction is normal to the boundary Assume the medium is lossless, let the incident electric field to be or in a phasor form since then we can show that RS

  15. Transmitted wave • Transmitted wave Assume the medium is lossless, let the transmitted electric field to be then we can show that RS

  16. Reflected wave (1) • From boundary conditions, At z = 0, we have and  1 = 2are media the same? RS

  17. Reflected wave (2) • There must be a reflected wave and This wave travels in –z direction. RS

  18. Reflection and transmission coefficients (1) • Boundary conditions (reflected wave is included) from therefore at z = 0 (1) RS

  19. Reflection and transmission coefficients (2) • Boundary conditions (reflected wave is included) from therefore at z = 0 (2) RS

  20. Reflection and transmission coefficients (3) • Solve Eqs. (1) and (2) to get Reflection coefficient Transmission coefficient RS

  21. Types of boundaries: perfect dielectric and perfect conductor (1) From  . Since 2 = 0 then  = -1 and Ex10+= -Ex10-  RS

  22. Types of boundaries: perfect dielectric and perfect conductor (2) This can be shown in an instantaneous form as Standing wave RS

  23. Standing waves (1) When t = m, Ex1 is 0 at all positions. and when z = m, Ex1 is 0 at all time. Null positions occur at RS

  24. Standing waves (2) Since and , the magnetic field is or . Hy1 is maximum when Ex1 = 0 Poynting vector RS

  25. Power transmission for 2 perfect dielectrics (1) Then 1and 2are both real positive quantities and 1 = 2= 0  Average incident power densities RS

  26. Ex3 Let medium 1 have 1 = 100  and medium 2 have 2 = 300 , given Ex10+ = 100 V/m. Calculate average incident, reflected, and transmitted power densities RS

  27. Wave reflection from multiple interfaces (1) • Wave reflection from materials that are finite in extent such as interfaces between air, glass, and coating • At steady state, there will be 5 total waves RS

  28. Wave reflection from multiple interfaces (2) Assume lossless media, we have then we can show that RS

  29. Wave reflection from multiple interfaces (2) Assume lossless media, we have then we can show that RS

  30. Wave impedance w (1) Use Euler’s identity, we can show that RS

  31. Wave impedance w (2) Since from B.C. at z = -l we may write RS

  32. Input impedance in solve to get RS

  33. Refractive index Under lossless conditions, RS

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