Lect 3.4 - Department of Electrical and Computer...

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Department of Electrical and Computer Engineering ECSE 352 Electromagnetic Waves and Optics 3.4 Wave propagation in arbitrary directions References: Section 12.4 Andrew Kirk 3.4-1 Additional comments from previous class • Multilayers d – Calculate wave impedance se this to find – Use this to find effective reflection coefficient E 1 + η 2 η 3 η 1 E 1 - ECSE 352 3.4-2 Examples again 1. Dielectric coating 2. Radome η 2 η 1 = η 0 η 3 = 9 η 0 d η 2 η 1 = η 0 η 3 = η 0 | Γ eff | | Γ eff | 0.6 0.8 1 η 2 = 2 η 0 1 l l 3 l €€ l 0.2 0.4 η 2 = 3 η 0 η 2 = 4 η 0 ECSE 352 3.4-3 €€€ 8 4 €€€€€ 8 2 l 8 l 4 3 l 8 l 2 Impedance matching (1) η η Dielectric 2 Dielectric 1 Dielectric 3 η Γ eff Γ 23 1 2 3 E 2 + E 2 - E 3 + Z (z=0) E i + E r - Another way of thinking about preventing reflection: z =0 =d 2 Reflection arises due to a discontinuity in the impedance So, for zero reflectance, we require that Z 2 (0)= η 1 3 xp xp ECSE 352 3.4-4 ( ) ( ) ( ) () ( ) 1 2 23 2 2 23 2 2 2 exp exp exp exp 0 η β = Γ Γ + = = d j d j d j d j z Z
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Impedance matching (2) This is called IMPEDANCE MATCHING When impedances are matched there will be no reflection From definition of Z 2 (0): η 2 3 cos β 2 d + j 2 sin 2 d () = 1 2 cos 2 d + j 3 sin 2 d ( ) quating each of the real cos d = cos d (1) Equating each of the real and imaginary parts: eal: 3 2 1 2 2 2 sin 2 d = 1 3 sin 2 d (2) Real: Imaginary: ECSE 352 3.4-5 Results in same conditions as before for half wave and quarter wave coatings.
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This note was uploaded on 02/14/2011 for the course ECSE 352 taught by Professor Mi during the Fall '10 term at McGill.

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Lect 3.4 - Department of Electrical and Computer...

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