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VIII. Further Aspects of Edge Diffraction. Other Diffraction Coefficients Oblique Incidence Spherical Wave Diffraction by an Edge Path Gain Diffraction by Two Edges Numerical Examples. r. Reflected plane wave. RSB. q. ISB. f. f . Incident plane wave.
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VIII. Further Aspects of Edge Diffraction • Other Diffraction Coefficients • Oblique Incidence • Spherical Wave Diffraction by an Edge • Path Gain • Diffraction by Two Edges • Numerical Examples ©2003 by H.L. Bertoni
r Reflected plane wave RSB q ISB f f Incident plane wave Other Diffraction Coefficients • Felsen’s Rigorous Solution for Absorbing Screen ( G = 0 ) • Conducting Screen ©2003 by H.L. Bertoni
5 RSBISB Edge 4 D4 2p k D ´ 3 D3 2 RSB ISB 90o wedge 1 D2 D1 0 -90 0 90 180 270 angle, q Comparison of Diffraction Coefficients D1: Kirchhoff -Huygens D3: Conductor for TE polarization D2: Felsen D4: 90 conducting wedge for TM polarization ©2003 by H.L. Bertoni
y p/2- p/2- z x Diffraction for Oblique Incidence Diffracted rays lie on a cone whose angle is the same as that between incident ray and edge. All waves have wave number k sin along edge k cos in (x,y) plane Replace k for normal incidence by k cos ©2003 by H.L. Bertoni
q < 0 r0 q0 dAr dipole r dA r Field incident on the edge Diffracted cylindrical wave Diffraction of an Incident Spherical Wave(for paths that are nearly perpendicular to the edge) In the horizontal plane, rays spread as if they came from a point r0 behind the edge. ©2003 by H.L. Bertoni
r W() W(r) • r • r L() • L(r) Dipole r0 Dipole r0 Top and Side Views of the Diffracted Rays Top View Side View ©2003 by H.L. Bertoni
r0 q0 q< 0 dipole dAr r dA r Diffracted Field Amplitude Must Conserve Power in a Ray Tube ©2003 by H.L. Bertoni
Path Gain for Diffracted Field ©2003 by H.L. Bertoni
UTD Diffraction for Perpendicular Incidence of Rays From a Point Source ©2003 by H.L. Bertoni
q =-30° 12 m 2 m 20 m 17.3 m f = 900 MHz, l =1/3 m, k =6 m-1 Example of Path Gain for Diffracted Field ©2003 by H.L. Bertoni
z r q0 r0 dAr dA rcos dipole Diffraction of Point Source Rays Incident Oblique to the Edge ©2003 by H.L. Bertoni
Field incident on the edge Diffracted cylindrical wave Diffraction of Point Source Rays Incident Oblique to the Edge - cont. ©2003 by H.L. Bertoni
Path Gain for Paths Oblique to the Edge ©2003 by H.L. Bertoni
UTD Diffraction for Oblique Incidence of Rays From a Point Source ©2003 by H.L. Bertoni
y x -7 ’ zw ’ r ro = 90o - Tx Located at (-7,-1.5,0) = 90o - 15 Example of Diffraction on Oblique PathsCordless telephones over a brick wall-perspective view Rx Located at (4,-1,15) z ©2003 by H.L. Bertoni
y -7 4 x Tx ’ Rx (-7,-1.5) (4,-1) Example of Diffraction on Oblique PathsCordless telephones over a brick wall-end view ©2003 by H.L. Bertoni
Diffraction on Oblique Paths - cont.Cordless telephones over a brick wall ©2003 by H.L. Bertoni
r W()W(r) Dipole r0r1 • r • r • ) • L(r) r0 r1 Diffraction by Successive, Parallel Edges--Top and Side Views-- Top View Side View ©2003 by H.L. Bertoni
cylindrical wave near edge Diffraction of Vertical Dipole Fields bySuccessive, Parallel Edges q q1 r1 Assume the second edge is not near the shadow boundary of the fist edge. r q0 r0 ©2003 by H.L. Bertoni
q1 =-30° 20 m f = 900 MHz l =1/3 m k =6 m-1 q =-30° 20 m 2 m 2 m 17.3 m 60 m 17.3 m Path Gain for Diffraction at Parallel Edges ©2003 by H.L. Bertoni
q =tan-1(10/5) =-1.107 rad 12 m 11.2 m 2 m 2 m 20 m 5 m 5 m Walk About Transmission Over a Building f = 450 MHz l =2/3 m k =3 m-1 ©2003 by H.L. Bertoni
q0 r0 q1 r r1 r q cylindrical wave near edge Diffraction of Dipole Fields by Successive Perpendicular Edges ©2003 by H.L. Bertoni
f = 900 MHz l =1/3 m k =6 m-1 60 m -30° 20 m 12 m 30° 20 m 12 m 2 m Path Gain for Perpendicular Edges ©2003 by H.L. Bertoni