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Prof. David R. Jackson

ECE 3317. Prof. David R. Jackson. Notes 17 Polarization of Plane Waves. Polarization. z. y. x. The polarization of a plane wave refers to the direction of the electric field vector in the time domain. We assume that the wave is traveling in the positive z direction.

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Prof. David R. Jackson

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  1. ECE 3317 Prof. David R. Jackson Notes 17 Polarization of Plane Waves

  2. Polarization z y x The polarization of a plane wave refers to the direction of the electric field vector in the time domain. We assume that the wave is traveling in the positive z direction.

  3. Polarization (cont.) y Ey x Ex Consider a plane wave with both x and y components Phasor domain: Assume:

  4. Polarization (cont.) y E(t) At z = 0: x Time Domain: Depending on b and b, three different cases arise.

  5. Linear Polarization x´ y y´ b x a b = 0 or  ( + for 0, - for  ) At z = 0: (shown forb =0)

  6. Circular Polarization b = a ANDb = p /2 At z = 0:

  7. Circular Polarization (cont.) y a f x

  8. Circular Polarization (cont.) y b =+p / 2 a LHCP f x b =-p / 2 RHCP IEEE convention

  9. Circular Polarization (cont.) RHCP z z RHCP (opposite rotation in space and time)

  10. Circular Polarization (cont.) Power Density: Assume lossless medium ( is real): This expression is actually valid for any plane wave that has both Ex and Ey.

  11. Circular Polarization (cont.) receive antenna z Circular polarization is often used in communications to avoid problems with signal loss due to polarization changes. • Misalignment of receive antenna • Reflections off of buildings • Propagation through the atmosphere The antenna will always receive a signal, no matter how it is rotated about the z axis. However, for the same incident power density, an optimum linearly-polarized wave will give the maximum output signal (3 dB higher than from an incident CP wave).

  12. Circular Polarization (cont.) y antenna 2 antenna 1 x Two ways in which circular polarization can be obtained: 1) Use two identical antenna rotated by 90o, and fed 90o out of phase. This antenna will radiate a RHCP signal in the positive z direction, and LHCP in the negative z direction.

  13. Circular Polarization (cont.) y antenna 2 antenna 1 x Z01 l1 signal Z01 l2 feed line power slitter Realization with a 90o delay line:

  14. Circular Polarization (cont.) 2) Use an antenna that inherently radiates circular polarization. Helical antenna for WLAN communication at 2.4 GHz http://en.wikipedia.org/wiki/Helical_antenna

  15. Circular Polarization (cont.) y antenna 2 antenna 1 x Z0 l1 output signal Z0 l2 RHCP power combiner An antenna that radiates circular polarization will also receive circular polarization of the same handedness (and be blind to the opposite handedness). It does not matter how the receive antenna is rotated about the z axis.

  16. Elliptic Polarization y f x Includes all other cases that are not linear or circular (b 0or and b  p /2) or (b = p /2andb a) The tip of the electric field vector stays on an ellipse.

  17. Elliptic Polarization (cont.) y RHEP f x LHEP Rotation property:

  18. Elliptic Polarization (cont.) Here we give a proof that the tip of the electric field vector must stay on an ellipse. so or Squaring both sides, we have

  19. Elliptic Polarization (cont.) Collecting terms, we have or This is in the form of a quadratic expression:

  20. Elliptic Polarization (cont.) (determines the type of curve) so Hence, this is an ellipse.

  21. Elliptic Polarization (cont.) y f x Here we give a proof of the rotation property.

  22. Elliptic Polarization (cont.) Take the derivative: so (proof complete)

  23. Rotation Rule Im Ey b Ex Re phasor domain Here we give a simple graphical method for determining the type of polarization (left-handed or right handed) EyleadsEx Rule: The electric field vector rotates from the leading axis to the lagging axis y x time domain

  24. Rotation Rule (cont.) Im Ey lagsEx Ex b Re Ey y x Rule: The electric field vector rotates from the leading axis to the lagging axis phasor domain time domain

  25. Rotation Rule (cont.) z Ez y Ex x Example What is this wave’s polarization?

  26. Rotation Rule (cont.) Im EzleadsEx Ez Re Ex Example (cont.) In time, the wave rotates from the z axis to the x axis.

  27. Rotation Rule (cont.) z Ez y Ex x Example (cont.) LHEP or LHCP Note: and (so this is not LHCP)

  28. Rotation Rule (cont.) z Ez y Ex x Example (cont.) LHEP

  29. Axial Ratio (AR) and Tilt Angle () y B C  x D A

  30. Axial Ratio (AR) and Tilt Angle () Formulas Axial Ratio and Handedness Tilt Angle Note: The tilt angle  is ambiguous to the addition of  90o.

  31. Note on Title Angle Note: The title angle is zero or 90o if: y x Tilt Angle:

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