# 2015 American Journal of Engineering Research (AJER)

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4 k is the Boltzmann constant (1.38*10-23 J/K), B is the photodiode bandwidth, and T(K) is the absolute temperature. So the overall signal to noise ratio is - = (7) Where F n represents the noise figure, defined by- [15] F n = ( S / N ) ( S / N ) in out In the Avalanche Photodiode the signal current in the amplifier is increased and the overall SNR is increased as thermal noise remains the same. But the multiplication factor (M) increases the dark current noise and quantum noise which may be a limiting factor. The signal-to-noise ratio for APD receiver can be expressed as- [11] = (8) Where the factor x ranges between 0 and 1.0 and depending on photodiode material. It is apparent from Eq. (8) that the first term in the denominator increases with increasing M whereas the second term decreases. For low M the combined thermal and amplifier noise term dominates and the total noise power is virtually unaffected when the signal level is increased, giving an improved SNR. However, when M is large, the thermal and amplifier noise term becomes insignificant and the SNR decreases with increasing M at the rate of M x. Therefore, an optimum value of the multiplication factor M should be used. [11] IV. RESULT AND DISCUSSION From the mathematical model described above the system performance has been analyzed with various parameters. The SNR is determined for different input power, bandwidth, amplifier gain and hop length. Also the system performance has been demonstrated for different types of receivers and their gains. And finally the system performance has been plotted for different receiver gain and bandwidth for the selection of these parameters. Fig. 2 Amplifier SNR vs input Power for Hop length L=100km, N=10 varying Gain (G=5dB, 10dB, 15dB, 20 db) Fig. 2 demonstrate the variation of SNR with the input power to the optical amplifier with a hop length of 100km, no of amplifier 10 and various amplifier gain of 5dB, 10dB, 15 db and 20 db. The SNR increases with the increase of optical input power. The SNR is highest for the amplifier gain of 5dB. So the SNR increases with the decrease of amplifier gain. w w w. a j e r. o r g Page 4

5 Fig. 3 SNR vs input Power for Hop length L=100km G=10dB varying N=10, 20, 30, 40 In Fig. 3, the SNR has been demonstrated for different amplifier numbers. The SNR has been plotted for the number of amplifiers 10, 20, 30, 40. The output is maximum when the number of amplifiers 40. So it can be concluded that the SNR increases with the increase of number of amplifier. Fig. 4 Amplifier SNR vs Optical Input Power Varying Hop Length L In Fig. 4, the SNR has been plotted against optical input power with a hop length of 100 km, 200km and 300 km. The SNR is highest for the hop length of 100km. So the SNR increases with the decrease of hop length. Fig. 5 Path Penalty Factor ( F path ) vs amplifier gain Fig. 5 shows the path penalty factor for different amplifier gain. For a higher amplifier gain the path penalty factor increases. w w w. a j e r. o r g Page 5

6 BER American Journal of Engineering Research (AJER) Power Penalty Number of Amplifiers Fig. 6 Power Penalty vs No. of Amplifiers for a fixed SNR=200 In Fig. 6, the power penalty vs no of amplifiers have been demonstrated with a fixed SNR. The power penalty decreases with the increase of number of amplifier B= 2.5 GHz B= 5 GHz B= 7.5 GHz B= 10 GHz Optical Input Power (dbm) Fig. 7 BER vs Optical Input Power Varying Bandwidth for P-i-N Receiver In Fig. 7, Bit Error Rate (BER) vs Optical input power has been plotted for different bandwidth. From Eq. (7) and (8) it can be seen that both in a p-i-n photodiode and APD receiver, the noises increase with the increase of bandwidth. Hence the SNR decreases with the increase of bandwidth. When SNR decreases, BER increases. In Fig. 7, the BER is highest when the bandwidth is 10GHz. Fig.8 SNR vs APD Gain w w w. a j e r. o r g Page 6

7 Fig. 9 BER vs Input Power varying APD Gain for a fixed Bandwidth B=5GHz In Fig 8, the SNR has been plotted against APD gain (M). From M=0 to M=30, the SNR increases rapidly, but after M=30, the increase of the SNR is not significant. In Fig. 9, the BER is plotted vs optical input power for different APD gain. From equation (7) & (8), when the value of M=1, the SNR expression is similar to P-i-N receiver. From Fig. 9, it can be concluded that the BER decreases when the value of M increases. So APD receiver is shows better performance in respect of SNR. Fig. 10 BER versus APD gain (M) varying bandwidth In Fig. 10, BER has been plotted against APD gain varying bandwidth. The BER increases when the bandwidth is increased. So combining Fig. 8 and Fig. 10, it can be concluded that for better performance only the value of M should not be limited but also the bandwidth should be limited. Again a small bandwidth corresponds to a smaller receiver size thus minimizes the cost. Fig. 11 BER vs Input Power varying Bandwidth for APD Receiver with APD gain M=2 (solid line) and M=5 (dotted line) In Fig. 11, BER vs input power has been plotted with varying bandwidth and APD gain. The solid line shows the result for M=2 and the dotted line is for M=5. The Figure combines the overall result of analysis of the system. It shows the value of BER is higher for M=2 lower for M=5. Again relatively smaller bandwidth has a lower BER than that of a larger bandwidth. w w w. a j e r. o r g Page 7

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