VIII. Further Aspects of Edge Diffraction

1. 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

2. 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

3. 5  RSBISB 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

4. 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

5. 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

6.  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

7. r0 q0 q< 0 dipole dAr r dA r Diffracted Field Amplitude Must Conserve Power in a Ray Tube ©2003 by H.L. Bertoni

8. Path Gain for Diffracted Field ©2003 by H.L. Bertoni

9. UTD Diffraction for Perpendicular Incidence of Rays From a Point Source ©2003 by H.L. Bertoni

10. 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

11. z  r q0 r0 dAr dA  rcos dipole  Diffraction of Point Source Rays Incident Oblique to the Edge ©2003 by H.L. Bertoni

12. Field incident on the edge Diffracted cylindrical wave Diffraction of Point Source Rays Incident Oblique to the Edge - cont. ©2003 by H.L. Bertoni

13. Path Gain for Paths Oblique to the Edge ©2003 by H.L. Bertoni

14. UTD Diffraction for Oblique Incidence of Rays From a Point Source ©2003 by H.L. Bertoni

15. 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

16. 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

17. Diffraction on Oblique Paths - cont.Cordless telephones over a brick wall ©2003 by H.L. Bertoni

18.  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

19. 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

20. 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

21. 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

22. q0 r0 q1 r r1 r q cylindrical wave near edge Diffraction of Dipole Fields by Successive Perpendicular Edges ©2003 by H.L. Bertoni

23. 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