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Workshop09Tlines

# Workshop09Tlines - ECE 3030 Electromagnetic Fields and...

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ECE 3030: Electromagnetic Fields and Waves Fall 2009 WORKSHOP 9 INSTRUCTOR NOTES: Multi-Layer Dielectrics Reminder: Date: Thursday 10/29 1. There was no Demo 9 Tuesday, October 28 (because of Prelim 2) and no Homework 8. 2. Problem 14.4 A wave of frequency 3 GHz is normally incident of the dielectric slabs shown in Figure 1. Use a Smith Chart to calculate the fraction of incident power that passes through all of the dielectrics and the fraction that is reflected. k & 0 9 ε Air 0 25 ε 0 ε 2 cm 2cm 0 4 ε Figure 1: Dielectric slabs for Problem 14.4. Solution: From left to right we have η 1 = η 0 / 3, η 2 = η 0 / 2, and η 3 = η 0 / 5, with wavelengths of λ 1 = 3 . 3 cm, λ 2 = 5 cm, and λ 3 = 2 cm, and the two given lengths cor- respond to lengths in fractional wavelengths of 0.6, and 0.4. The normalized impedance of the third dielectric is η 0 3 = η 3 2 = 0 . 4. Plot and go clockwise 0.4 lambda to η in - 2 = 0 . 55 - j 0 . 57. Un-normalizing and re-normalizing gives (0 . 55 - j 0 . 57) η 2 η 3 = 0 . 825 - j 0 . 855 Plotting this impedance, and going clockwise 0.1 lambda (i.e., all the way around once plus a tenth more) gives a reflection coefficient magnitude of 0.43. So the fraction of

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Workshop09Tlines - ECE 3030 Electromagnetic Fields and...

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