Exmple Questions for the Examination for 4041 OPTICAL COMMUNICATION ENGINEERING

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1 Exmple Questios for the Examiatio for 441 OPTICAL COMMUNICATION ENGINEERING Official Readig Time: 1 mis Writig Time: 1 mis Total Duratio: 13 mis NOTE: The 8 Exam will have of 6 (!) Questios ad thus will have a total duratio of 19 mi! Istructios: This is a closed book examiatio. Attempt ALL FOUR questios. All questios carry equal marks; part marks are give i brackets where appropriate. Begi each aswer o a ew page. Examiatio materials must ot be removed from the examiatio room. ANSWERS TO QUESTIONS SHOULD BE EXPRESSED CLEARLY AND WRITTEN LEGIBLY. THESE ASPECTS OF PRESENTATION WILL BE TAKEN INTO ACCOUNT IN ASSESSMENT. Materials: Oe Pik Book The use of calculators is permitted, this equipmet to be supplied by the cadidate. No pre-recorded material or calculator istructio book is permitted, ad calculators with remote commuicatio liks will be barred from the examiatio room. Formulae sheets (3 pages) are attached at the ed of the paper. DO NOT COMMENCE WRITING UNTIL INSTRUCTED TO DO SO. Questio 1 begis o page

2 Example Questios for Optical Comm.(cotd.) 1. Cosider a heterodye receiver for a digital optical fibre commuicatios system. (a) Briefly explai how a heterodye receiver detects phase, give that photodetectors ca oly detect amplitude or optical power. (b) What type of modulatio scheme ca a heterodye system permit that is ot otherwise achievable with direct detectio usig a stadard receiver? (c) State the key advatage of phase detectio over amplitude detectio. (d) Heterodye receivers offer icreased sesitivity. Briefly state why. (e) Usig a heterodye receiver, compute the local-oscillator (LO) power required to make the SNR 1 db less that the quatum limit. You may assume the IF badwidth is 5 MHz ad the received optic power is costat at 5 W whe a biary 1 is received. The dark curret of the photodetector is I D = A, ad its resposivity is ρ =.5 A/W. Assume the temperature is 7ºC ad a load resistace of 1 Ω. (11 marks) (f) If this were ot a heterodye system, the the receiver s badwidth could be as small as 5 MHz. For this case determie the sigal power required to achieve a SNR equal to that i part (e). You are remided to clearly highlight your aswers with a double uderlie, otherwise marks may be deducted. 19 Page of 6 Pages

3 Example Questios for Optical Comm.(cotd.). (a) A compact disc (CD) has several levels of error detectio ad correctio. Provide a very brief descriptio of the followig, ad explai their purpose: (i) (ii) (iii) Eight to Fourtee Modulatio (EFM) Reed-Solomo Code Iterleavig (b) A DVD is a storage techology which provides sufficiet data capacity ad data rate to store high quality stadard-defiitio video. Give that a covetioal audio compact disc (CD) ca store up to 73 miutes of audio, derive the approximate umber of hours of stadard defiitio TV (SDTV) video that a DVD ca store usig all its available layers. (5 marks) (c) Assume that oe day we will have 1 billio homes o plaet earth, each home havig oe phoe o average. If these phoes were to trasmit simultaeously over oe 4 MHz lie, usig frequecy divisio multiplexig (FDM), what is the badwidth required? Could a sigle optical beam, with a spectral wavelegth λ = 1 µm, carry this multiplexed sigal? (3 marks) (d) Still usig the same case of 1 billio phoes ad same spectral frequecy, ow assume digital modulatio, with time divisio multiplexig (TDM) ad a data rate of 64 kbps for each voice message. Demostrate whether the sigle optical beam ca carry this frequecy or ot. (e) A fibre telephoe cable cotais 144 fibres, at the T3 stadard, implyig each fibre is capable of carryig 67 voice messages. A coductig telephoe cable cotais 9 copper twisted pairs, ad each pair ca carry 4 messages. Compare the capacities of the fibre ad coductig cables. How may of the coductig cables are required to equal the capacity of the fibre cable? Repeat the calculatio if each fibre operates at the DS-4 stadard (Note: DS-4 allows upto 43 voice messages per fibre). You are remided to clearly highlight your aswers with a double uderlie, otherwise marks may be deducted. 19 Page 3 of 6 Pages

4 , Example Questios for Optical Comm.(cotd.) 3. (a) Prove Johso s thermal oise formula have all their usual meaigs, by takig the followig steps: e = 4kTR f, where the symbols (i) (ii) (iii) Cosider a resistor i parallel with a capacitor. Draw the equivalet circuit assumig the oisy resistor ca be modelled by a sigle source i series with a lumped ideal resistor. Label the source oise across the capacitor Label the source oise curret through the loop averages. i e v. Label the mea square. Label the mea square. The agle brackets represet temporal Apply Kirchhoff s voltage law (KVL) aroud the loop, ad write dow the equatio i terms of time limited variables e (, t τ ), v( t, τ ) ad i ( t, τ ) assumig that we sample these radom sigals for a fiite time widow of duratio τ. Here we assume the widow is sufficietly log ad that statioarity holds. Briefly explai what statioarity meas. Assumig this equatio is free of delta fuctios, ow write dow the same equatio i terms of widow-limited Fourier trasformed variables, V( ωτ, ) ad I( ωτ, ). (iv) By substitutig i the relatio I( ωτ, ) = jωcv( ωτ, ) ad the applyig Placherel s theorem (i.e. the eergy theorem), prove that, (v) + (, ) 1 E ωτ e = lim dω τ π. τ (6 marks) Explai why we caot take the limit iside the itegral without first takig esemble averages. Now, by assumig the system is ergodic, i.e. lim e = e, where the overbar idicates esemble averagig, show τ that, τ + 1 e = S( ω) dω π where S( ω) is the oe-sided power spectral desity (PSD). (3 marks) (vi) Explai why for thermal oise, we ca simply rewrite this expressio as 1 e = S ω, where S is a costat PSD. π 19 Page 4 of 6 Pages

5 Example Questios for Optical Comm.(cotd.) (vii) By idetical argumets to part (v), we ca write dow a similar expressio for the mea square oise voltage across the capacitor as v + 1 V = lim dω π. τ τ E Now, substitute this ito V =, ad the show that 1 + ( ωrc) 1 π v = S. π RC 1 1 (viii) From the equipartitio theorem you may assume that C v = kt. Use this relatio to ow fially arrive at the thermal oise formula. (b) A laser diode has a RIN of -135 db/hz. A receiver badwidth of 1 GHz ad a received average power of µw. (i) Compute the laser oise power at the receiver. (ii) Compute the average laser oise curret if the detector has a resposivity of.3 A/W. You are remided to clearly highlight your aswers with a double uderlie, otherwise marks may be deducted. 19 Page 5 of 6 Pages

6 ad,, Example Questios for Optical Comm.(cotd.) 4. Cosider a sigle mode fibre operatig at 155 m. The specificatio is to trasmit 4 Mbps NRZ data over the 1 km fibre lik with a bit error rate (BER) of 1-9 or better. (a) Give that τ = 1/ RNRZ ad allowig for the system rise time to be 7% of τ, compute the system rise time t S. (b) Give a material dispersio of M = - ps/m/km ad a waveguide dispersio of M g = 4.5 ps/m/km, compute the fibre rise time, t F. The spectral liewidth is give as.15 m. (c) If the rise time of the light source is t LS = 1 s fid a upper limit o the photodetector rise time t PD. (d) Assume a basic BJT amplifier circuit at the receiver. If the photodetector has a trasit time limited rise time of t TR =.5 s a juctio capacitace of C d = 1 calculate a upper limit o the load resistor. (e) Give that the fibre loss is.5 db/km, the couplig efficiecy to the fibre is 3 db, there are two coectors with 1 db loss each, there are 5 splices with.1 db loss each ad that the source power is 5 dbm, fid the power at the receiver. (f) Calculate the optical power eeded to achieve the specified BER assumig a quatum limited system. Commet o the result. You may assume dark curret is s egligible ad therefore the expressio for probability of a error Pe = e holds. The quatum efficiecy of the detector is η =.7. (g) Now calculate the optical power eeded to achieve the specified BER assumig a thermal limited system. Commet o the result. You may assume a detector resposivity of ρ = 1 A/W ad a oise figure of F =. Room temperature coditios hold, thus let T = 3 K. (6 marks) You are remided to clearly highlight your aswers with a double uderlie, otherwise marks may be deducted. 19 Page 6 of 6 Pages