329lect24 - 24 Signal transmission, circular polarization...

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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 are frequency independent (i.e., propagation is non-dispersive), dAlembert plane wave solutions of the form E = xf ( t- z v ) and H = y f ( t- z v ) are valid in such media. t t-4-2 2 4 6-6-4-2 2 4 6-4-2 2 4 6-6-4-2 2 4 6 m ( t ) m ( t ) cos( t ) Consider a waveform f ( t ) = m ( t ) cos( t ) , where is some specific frequency having a corresponding period T = 2 , m ( t ) is some arbitrary signal (e.g., a voice signal, a message) changing slowly compared to period T . In that case, f ( t ) specified above can be called narrowband AM , and the carrier frequency of modulating cosine of the message signal m ( t ) . 1 The corresponding x-polarized wave fields propagating in z direction can then be represented as Field 1 E = m ( t- z v ) cos( t- z ) x and H = m ( t- z v ) cos( t- z ) y where = as usual 1 . With reference to the expressions above, we could say that the AM wave field has an x-polarized carrier . By contrast, Field 2 E = m ( t- z v ) cos( t- z ) y represents an AM wave field with a y-polarized carrier , and so does Field 3 E = m ( t- z v ) sin( t- z ) y but with a carrier that has been time-delayed by a quarter period. 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( t- z ) x + sin( t- z ) y ] 1 In dispersive media where is a non-linear function of , narrowband AM can propagate as m ( t- z v g ) cos( t- z ) x where v g is known as group velocity covered in detail in ECE 450. 2 which has a circular polarized carrier . Since this is just a superpo- sition of two dAlembert 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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329lect24 - 24 Signal transmission, circular polarization...

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