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by Nannapaneni Narayana Rao Edward C. Jordan Professor of Electrical and Computer Engineering

Edward C. Jordan Memorial Offering of the First Course under the Indo-US Inter-University Collaborative Initiative in Higher Education and Research: Electromagnetics for Electrical and Computer Engineering. by Nannapaneni Narayana Rao

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by Nannapaneni Narayana Rao Edward C. Jordan Professor of Electrical and Computer Engineering

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  1. Edward C. Jordan Memorial Offering of the First Course under the Indo-US Inter-University Collaborative Initiative in Higher Education and Research: Electromagnetics for Electrical and Computer Engineering by Nannapaneni Narayana Rao Edward C. Jordan Professor of Electrical and Computer Engineering University of Illinois at Urbana-Champaign Urbana, Illinois, USA Amrita Viswa Vidya Peetham, Coimbatore July 10 – August 11, 2006

  2. 3.6 • Polarization of Sinusoidally • Time-Varying Fields

  3. Polarization is the characteristic which describes how the position of the tip of the vector varies with time. • Linear Polarization: • Tip of the vector • describes a line. • Circular Polarization: • Tip of the vector • describes a circle.

  4. Elliptical Polarization: • Tip of the vector • describes an ellipse. • (i) Linear Polarization • Linearly polarized in the x direction. Direction remains along the x axis Magnitude varies sinusoidally with time

  5. Direction remains along the y axis Magnitude varies sinusoidally with time Linearly polarized in the y direction. If two (or more) component linearly polarized vectors are inphase, (or in phaseopposition), then their sum vector is also linearly polarized. Ex:

  6. (ii)Circular Polarization • If two component linearly polarized vectors are • (a) equal to amplitude • (b) differ in direction by 90˚ • (c) differ in phase by 90˚, • then their sum vector is circularly polarized.

  7. Example:

  8. (iii)Elliptical Polarization • In the general case in which either of (i) or (ii) is not satisfied, then the sum of the two component linearly polarized vectors is an elliptically polarized vector. • Ex:

  9. Example:

  10. D3.17 • F1 and F2 are equal in amplitude (= F0) and differ in direction by 90˚. The phase difference (say f) depends on z in the manner –2pz – (–3pz) = pz. • (a) At (3, 4, 0), f = p(0) = 0. • (b) At (3, –2, 0.5), f = p(0.5) = 0.5 p.

  11. (c)At (–2, 1, 1), f = p(1) = p. • (d) At (–1, –3, 0.2) = f = p(0.2) = 0.2p.

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