EE 164 Problem Set 5 Solution

EE 164 Problem Set 5 Solution - EE 164 Problem 1: a)...

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EE 164 Problem Set 5 Spring 2005 Problem 1: For a GRIN fiber, let 1 1.5 n = , 0.01 ∆ = , 2 α = , and 50 am µ = . a) Plot ( ) nr within the core to scale. () ( ) () ( ) 2 1 1 2 / 1.5 1 2 /50 0.01 a nr n ra r =− = b) Repeat on the same graph, changing to 10. () ( ) ( ) 10 1.5 1 2 0.01 r c) Repeat on the same graph with 0.001 ∆ = and 2 = () ( )( ) 2 1.5 1 2 0.001 r / ( ) a ( ) b ( ) c 0 1.5 1.5 1.5 0.1 1.4998 1.5 1.4999 0.2 1.4994 1.5 1.4999 0.3 1.4986 1.5 1.4999 0.4 1.4976 1.5 1.4998 0.5 1.4962 1.5 1.4996 0.6 1.4946 1.4999 1.4995 0.7 1.4926 1.4996 1.4993 0.8 1.4904 1.4984 1.4990 0.9 1.4878 1.4948 1.4988 1.0 1.4849 1.4849 1.4985 00 . 2 0.4 0.6 0.8 1.0 1.485 1.490 1.495 1.500 ( ) a ( ) b ( ) c / ( ) n r Problem 2: For a single-mode and a multimode GRIN fiber, 1 1.48 n = , and 2 1.46 n = , wavelength = 0.82 m , linewidth = 20 nm. 12 1.48, 1.46, 0.82 , 20 , 0.0135 nn m n m λ µλ == = = = M = material dispersion (from figure in text) g M = waveguide dispersion (assumed negligible). a) Compute the 3-dB bandwidth-length product. Neglect waveguide dispersion. ( )( ) / 110 20 2200 g DIS L M M ps nm xkm nm ps km τλ ∆= + = = ( ) 11 01 sin 2 sin 1.5 2 0.01 12.247 n θ −− =∆ = = 22 / 2.2456 TOTAL DIS MOD LL L n s k m ττ τ ⎡⎤ ∆+ = ⎣⎦
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() 3 11 0.227 22 2 . 2 db DIS f L GHz km Ln s k m τ == = (single mode) 3 0.2227 2 2 2.2456 db TOT f L GHz km L = (multimode) b) Repeat if linewidth = 1 nm.
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This note was uploaded on 03/23/2011 for the course EEE 174 taught by Professor Kasab during the Spring '11 term at ASU.

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EE 164 Problem Set 5 Solution - EE 164 Problem 1: a)...

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