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Unformatted text preview: 24 Signal transmission, circular polarization Since in perfect dielectrics the propagation velocity v p = v and the intrinsic impedance Î· are frequency independent (i.e., propagation is nondispersive), dâ€™Alembert plane wave solutions of the form E = Ë† xf ( t z v ) and H = Ë† y f ( t z v ) Î· are valid in such media. t t42 2 4 6642 2 4 642 2 4 6642 2 4 6 m ( t ) m ( t ) cos( Ï‰t ) â€¢ Consider a waveform f ( t ) = m ( t ) cos( Ï‰t ) , where â€“ Ï‰ is some specific frequency having a corresponding period T = 2 Ï€ Ï‰ , â€“ m ( t ) is some arbitrary signal (e.g., a voice signal, a message) changing slowly compared to period T . In that case, â€“ f ( t ) specified above can be called narrowband AM , and â€“ Ï‰ the carrier frequency of modulating cosine of the message signal m ( t ) . 1 The corresponding xpolarized wave fields propagating in z direction can then be represented as Field 1 E = m ( t z v ) cos( Ï‰t Î²z )Ë† x and H = m ( t z v ) Î· cos( Ï‰t Î²z )Ë† y where Î² = Ï‰ âˆš Î¼ as usual 1 . â€¢ With reference to the expressions above, we could say that the AM wave field has an xpolarized carrier . â€¢ By contrast, Field 2 E = m ( t z v ) cos( Ï‰t Î²z )Ë† y represents an AM wave field with a ypolarized carrier , and so does Field 3 E = m ( t z v ) sin( Ï‰t Î²z )Ë† y but with a carrier that has been timedelayed by a quarter period. â€¢ Suppose Fields 1 and 3 above were transmitted simultaneously and therefore superpose. In that case we will have a wave field with Circular polarized carrier E = m ( t z v )[cos( Ï‰t Î²z )Ë† x + sin( Ï‰t Î²z )Ë† y ] 1 In dispersive media where Î² is a nonlinear function of Ï‰ , narrowband AM can propagate as m ( t z v g ) cos( Ï‰t Î²z )Ë† x where v g â‰¡ âˆ‚Ï‰ âˆ‚Î² is known as group velocity â€” covered in detail in ECE 450. 2 which has a circular polarized carrier . Since this is just a superpo sition of two dâ€™Alembert waves, the accompanying H is easily found to be x y z t = 0 t > CIRCULAR POLARIZATION: Field vector rotates instead of oscillating. The rotation frequency is also the wave frequency....
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This note was uploaded on 06/20/2011 for the course ECE 329 taught by Professor Kim during the Spring '08 term at University of Illinois, Urbana Champaign.
 Spring '08
 Kim
 Frequency, Impedance

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