This preview shows pages 1–4. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: 23 Signal transmission, circular polarization Since in perfect dielectrics the propagation velocity v p = v and the intrinsic impedance η are frequency independent (i.e., propagation is nondispersive), d’Alembert plane wave solutions of the form E = ˆ xf ( t z v ) and H = ˆ y f ( t z v ) η are valid in such media. t t42 2 4 6642 2 4 642 2 4 6642 2 4 6 m ( t ) m ( t ) cos( ωt ) • Consider a waveform f ( t ) = m ( t ) cos( ωt ) , where – ω is some specific frequency having a corresponding period T = 2 π ω , – 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 – ω 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( ωt βz )ˆ x and H = m ( t z v ) η cos( ωt βz )ˆ y where β = ω √ μ as usual 1 . • With reference to the expressions above, we could say that the AM wave field has an xpolarized carrier . • By contrast, Field 2 E = m ( t z v ) cos( ωt βz )ˆ y represents an AM wave field with a ypolarized carrier , and so does Field 3 E = m ( t z v ) sin( ωt βz )ˆ y but with a carrier that has been timedelayed 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( ωt βz )ˆ x + sin( ωt βz )ˆ y ] 1 In dispersive media where β is a nonlinear function of ω , narrowband AM can propagate as m ( t z v g ) cos( ωt βz )ˆ x where v g ≡ ∂ω ∂β 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 d’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....
View
Full
Document
This note was uploaded on 07/19/2010 for the course ECE ECE329 taught by Professor Kudeki during the Summer '10 term at University of Illinois at Urbana–Champaign.
 Summer '10
 KUDEKI
 Frequency, Impedance

Click to edit the document details