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Waveguides Seminary 5

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Problem 5.1 Attenuation and crosstalk of a wire pair A carrier frequency connection is transmitted on twisted pairs with the following parameters: R =54.3 Ω/km, G =54.3 μS/km, L =0.7 mH/km, C =38.5 nF/km a) What are the characteristic impedance ( Z 0 ), attenuation (α) and phase coefficient (β) of the cable? b) What can be the maximum section length between the amplifiers if the near end crosstalk (NEXT) attenuation is 91dB and a 65dB crosstalk protection is prescribed at least.

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Gaussian Filters (power) (voltage) -3σ t -2σ t -σ t 0 σtσt 2σ t 3σ t 0.5h 0 h0h0 2σ t w Cascading Gaussian systems: 0 σfσf 3σ f 0 0.5H 0 H0H0

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Problem 5.2 Planning of monomode transmission line A monomode optical line operating on nm wavelength is made up of components with the following parameters: chromatic dispersion ( Dc ):5 ps/(nmkm) fiber attenuation (α):1.2 dB/km manufacturing length of the cables ( l 0 ):1500 m attenuation of splicings ( a s ):0.2 dB attenuation of connectors (2 pcs) ( a c ):2 dB spectral width of the transmitter laser (Δλ):10 nm launched optical power at the transmitter ( P T ): 10 mW transmitter’s bandwidth ( B T ):1 GHz noise limited sensitivity of the receiver ( P R ):100 pW receiver’s bandwidth ( B R ):800 MHz a) What is the spectral bandwidth of the transmitter laser in Hz? b) What is the maximum repeater span if we want transmit a signal with 100 MHz bandwidth?

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Problem 5.3 Compensation of chromatic dispersion A monomode optical transmission system is operating at 1550 nm. The chromatic dispersion coefficient ( D c ) of the fiber at the operating wavelength is 15 ps/(nm·km), while the polarization modal dispersion ( D p ) is 0.1 ps/√km The length of the connection is 42 km. a) What is the total dispersion of the connection if the spectral width of the laser transmitter is 5 nm? b) How long chromatic dispersion compensation fiber should be applied at the end of the connection if the compensating fiber’s dispersion coefficient is –90 ps/(nm·km)? c) What is the remanent dispersion if the polarization modal dispersion of the compensating fiber is identical with the transmission one?

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Problem 5.4 Joint effect of modal and chromatic dispersion We want to build a fiber optics connection with multimode fiber. The specific modal dispersion bandwidth ( b m ) of the fiber is 500 MHz·√km, while the chromatic dispersion ( D c ) is 10 ps/(nm·km). The spectral width (Δλ) of the transmitter’s LED is 25 nm. a) What is the optical bandwidth of a 5 km long connection? b) On the basis of the result for the 5 km span, estimate the bandwidth of a 10 km connection.

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