hw7_sol - Optical Communication Components and Subsystems...

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Unformatted text preview: Optical Communication Components and Subsystems ECE 565 Spring 2005 Homework 7 Solutions Problem 4.9. Differentiate the SNR expression given by Equation (4.4.19) in the text, with respect to M, and set the derivative to zero to obtain the implicit equation that characterizes the optimal M: k M 3 + (1-k)M – 4k B TF n /qR L (RP in + I d ) = 0, which is independent of the bandwidth. The approximation in Equation (4.4.23) in the text is given by M ≈ (4k B TF n /kqR L (RP in + I d )) 1/3 . 10-4 10-3 10-2 10-1 10 20 40 60 80 100 120 140 k M opt Exact Approximation The approximation is good down to k=0.01 . %Matlab Code for problem 4.9 in HW#7 close all clear all Fn=2; RL=1000; Pin=1e-6; R=1; Id=2e-9; kB=1.3807e-23; q=1.6e-19; T=300; k=0.0 Mo=zeros(1,10000); Ma=zeros(1,10000); for i=1:10000 K(i)=k; C=[k 0 1-k -4*kB*T*Fn/(RL*q*(R*Pin+Id))]; X=roots(C); if length(X)==3 Y=find([isreal(X(1)), isreal(X(2)), isreal(X(3))]); else Y=1; end Mo(i)=X(Y); Ma(i)=(4*kB*T*Fn/(k*q*RL*(R*Pin+Id)))^(1/3);...
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This note was uploaded on 03/06/2012 for the course ENGINEERIN 605 taught by Professor Rahmir during the Spring '11 term at University of Wisconsin.

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hw7_sol - Optical Communication Components and Subsystems...

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