EEE340Lecture 391 For nonmagnetic media, 1 = 2 = : Total reflection When 1 > 2 (light travels from water to air) t > i If t = /2, the refracted will glaze along the interface. The critical angle (of the incident) (8.185) (8.187)
EEE340Lecture 392 What happens when i > c ? t must be a complex! Note: sin t is still real and the phase matching condition is still held, i.e. The propagation interface is different for i c. (8.189)
EEE340Lecture 393 The propagation factor Where Note this attenuation is not from lossy material! Even in lossless case, this alpha exists.
EEE340Lecture 394 Example 8.14: A dielectric slab is used to guide light or EM waves. Determine the minimum r so that the light cannot escape once it is trapped. Solution: And Since (8.193)
EEE340Lecture 395 From Snell’s law (8.186) From (8.193) and (8.194), Ie: Make (8.194)
EEE340Lecture : Parallel polarization The incident fields Reflected fields The transmitted fields (8.214 ) (8.213) (8.216) (8.215) (8.218) (8.217)
EEE340Lecture 397 Boundary conditions at z=0 lead to (8.222) (8.221) (8.223)
EEE340Lecture 398 Chapter 9: Transmission Lines 9-1: Introduction Power lines at 60 Hz Two-wire (twin-wire) Parallel plate Coaxial Strip and/or microstrip lines Transmission line study was originated in power lines Transmission line equations were derived from distributed circuit concepts. These equation can be derived from uniform plane wave of Chapter 8. Transmission line theory is the foundation of packaging and interconnect for high-speed digital circuits and systems
EEE340Lecture : General Transmission Line Equations Telegraphers equations They are derived from circuits, and are easy to remember, since they are generalized Faraday equations. (9.31) (9.33)
EEE340Lecture 3910 In the frequency domain Note that For parallel-plate transmission lines (9.35) (9.13) (9.15) (9.23) (9.29)
EEE340Lecture : Wave characteristics on infinite transmission lines. From the two telegrapher’s equations of (9.35), we have Where The impedance (9.36) (9.41) (9.37)