# Comparison between DWDM Transmission Systems over SMF and NZDSF with 25 40Gb/s signals and 50GHz Channel Spacing

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2 modulator arms as well as the frequency limitations of the modulator. Fig. 2 - Representation of a modulator Fig. 2 presents a scheme of the modulator. This device was presented in [1] and is composed by an input Y junction connecting two arms with independent drive electrodes and an output Y junction. The input optical signal is splited in the input junction. The signal is affected in amplitude and phase as it propagates through the modulator arms, according to the applied voltage. The on or off states are obtained by constructive or destructive sum of the signals coming from both arms to the output junction. To obtain the characteristics of the modulator it was essential to evaluate the amplitude and phase characteristics of each arm. The electric field at the output of a modulator arm is given by [1]: () v = exp{ [ 1 2 α() v + j β()] v L} (1) where α and β are the power attenuation and phase constants. L is the interaction length of the arm, v the applied voltage and the input electric field. The non-linear characteristic of this device lies in the dependence of α and β on the applied voltage. This characteristic was determined in [1] experimentally. A set of these experimental points, shown in Fig. 3, was used to perform interpolation attenuation [db] phase [rad] Voltage applied to arm [V] Fig. 3 - Attenuation and phase characteristics of one arm of the modulator With the dependence of α and β on the applied voltage it is possible to obtain the electric field at the output [1]: [ ( v, v ) = i SRin SRout exp{ [ 1 2 α( v ) + β( v )] L} + exp{ [ 1 2 α( v ) + j β ( v ) + φ ] L} ] j (2) v and v are the voltages applied to arms 1 and 2 respectively. i is related to the input electric field by [1]: i = ( 1+ SR ) ( 1+ SR ) in out (3) SR in and SR out are the input and output power splitting ratios respectively, φ is the phase difference resulting from the different lengths of the modulator arms. φ is radians for the conventional modulator and π radians for the π-shift modulator. The frequency limitations of the modulator are modelled by a 4 th order Butterworth filter with a 3dB bandwidth of 5GHz, since the experimental results described in [2] show an amplitude response similar to that one of that filter. In order to define the modulator model some assumptions are considered. The splitting ratios (SR in and SR out ) were considered identical, SR in =SR out =SR, in order to maximise the output power [1]. Additionally, in ref. [1] it is stated that the use of a π-shift (φ =π) modulator leads to better performance with SMF due to an exclusively negative chirp parameter. This can impose a significant time compression of transmitted pulses and therefore lead to system performance improvement. Fig. 4 shows an equivalent block diagram of the transmitter for each one of the DWDM channels. Data sequence v(t) lectrical Generator Voltage Converter v a (t) v (t) v (t) Butterworth Filter Modulator Optical Signal Fig. 4 - Block diagram of the optical transmitter. Slope and frequency limitations of the electrical generator are taken into account and lead to trapezoidal pulses with slope rate of 15% of the bit-time. The resulting signal is passed through the Butterworth filter (which describes the frequency limitations of the modulator) and follows to a voltage converter. This device produces the correct voltages of arms 1 and 2 of the modulator given, respectively, by: v v () t = VB 1 + vb 1 v() t () t = V + v v() t V and V are the bias voltages and v b1 and v b2 are the peakto-peak voltages of the modulators arms. From expression (2) the normalized optical power characteristic of the modulator can be obtained. Fig. 5 shows such a characteristic for a splitting ratio of peak-to-peak voltage applied to arm b peak-to-peak voltage applied to arm 2 Fig. 5 modulator output optical intensity as a function of the applied voltages to arm 1 and 2 (4)

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