Reflection and transmission	Mar. 5, 2007

+ Problem statement: Power transmitted across a boundary of two lossless media (called dielectrics)? (medium 1: [equation] , [equation] and medium 2: [equation] , [equation] ) (Sect. 7.6)

+ Normal incident (in z direction) plane wave onto dielectrics with mismatching impedances, i.e. [equation]
Medium 1: [equation] , [equation] , incident wave ([equation] ) and reflected wave ([equation] )
Medium 2: [equation] , [equation] , transmitted wave ([equation] )
Find magnetic field & match [equation] and [equation] at the boundary

+ Reflection coef [equation] [equation]
Transmission coef [equation] [equation]
Example 2.11: Reflection at the boundary

+ Power transmissivity = [equation]
Power reflectivity = [equation] ; [equation] .

+ Voltage standing wave ratio: reflected and incident waves superposed and formed a standing wave
[equation] , [equation] for reflected wave and [equation] for incident wave.
They can cancel or enhance each other at certain time and location, i.e. constructive and destructive interference.

+ Use of Decibel: [equation]
[equation] [equation]
[equation] input power and [equation] output power.
Power [equation] [equation] [equation] .
Attenuation coef. [equation] .
Example 2.12: Plane wave normal incident to an interface and VSWR
Example 2.13: Plane wave with two components at a conductive boundary

+ Reflection of wave in electric circuits
Any lossless wire (transmission line) can be model with capacitors (C) and inductors (L)
Voltage and current in the wire vary as wave: [equation] Applicable to Ethernet, TV cable and power line.

+ Parameters of a cable: inductance per unit length L, capacitance per unit length C and impedance [equation] .

+ Phase velocity [equation] and impedance [equation] .

+ Reflectivity [equation] . Eliminate reflection by termination and match impedance.
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HW #12 (no late homework) 	Due 3/13/07

1. Problem 7.14 and also find d) average Poynting vector of the reflected wave and e) average Poynting vector of the transmitted wave (page 332) (notice that you should do b) before performing a) and [equation] in b) means VSWR in dB).
Extra-Credit:
A plane wave in free space ([equation] ) is incident normally on a large block of material with [equation] , [equation] , [equation] which occupies [equation] . If the incident electric field is [equation] V/m. Find (a) [equation] (notice what is k), (b) the voltage standing wave ratio, (c) the reflected magnetic field, (d) the average Poynting vector of the transmitted wave.

Discussion in uwm.course.ee361

Last Modified: March 04, 2007
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