Waveguides Seminary 5

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.

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

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?

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?

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.