Question 6 of 6: 1550 nm, 250 Mb/s, 75 km Single-Mode Link Design

Question 6: 1550 nm, 250 Mb/s, 75 km Single-Mode Link Design (equal value)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given.

Find. (a) Total link loss, system margin, and detector photocurrent. (b) Maximum allowable system risetime, a receiver bandwidth choice, and confirmation the risetime budget is met. (c) Whether NRZ format would also work. (d) Maximum direct-modulation bit rate and its practical limitations.

Approach. (a) Sum every loss term in dB from transmitter to receiver and compare the arriving power to the stated sensitivity. (b) Combine transmitter, fiber (chromatic-dispersion-limited), and receiver risetimes in quadrature against the RZ risetime budget ($0.35\,T_b$) to find the receiver bandwidth needed. (d) Use the laser's relaxation oscillation frequency, set by the photon and carrier lifetimes and the drive-current margin above threshold, as the direct-modulation ceiling.

Part (a) — power budget and margin

1. Transmitted power in dBm. $$P_{out}(\text{dBm})=10\log_{10}\frac{5\ \text{mW}}{1\ \text{mW}}=6.99\ \text{dBm}.$$
2. Total loss budget. $$\text{Loss}=\underbrace{1.0}_{\text{in-coupling}}+\underbrace{0.5}_{\text{out-coupling}} +\underbrace{(0.25)(75)}_{\text{fiber}=18.75}+\underbrace{(0.2)(75)}_{\text{splice}=15.0} +\underbrace{2.5}_{\text{excess}}=37.75\ \text{dB}.$$
3. Received power and margin. $$P_r=6.99-37.75=-30.76\ \text{dBm},\qquad \text{Margin}=P_r-P_{sens}=-30.76-(-36)=\boxed{5.24\ \text{dB}}.$$ A positive margin confirms the link closes with room to spare for component aging.
4. Detector photocurrent. $$P_r=10^{-30.76/10}\ \text{mW}=8.39\times10^{-4}\ \text{mW}=8.39\times10^{-7}\ \text{W},$$ $$I_p=RP_r=(0.6)(8.39\times10^{-7})=\boxed{0.504\ \mu\text{A}}.$$

Part (b) — system risetime budget

1. RZ risetime budget. With $T_b=1/B=4$ ns and the RZ criterion $t_{sys}\le0.35\,T_b$, $$t_{sys}=0.35\times4\ \text{ns}=1.40\ \text{ns}.$$
2. Fiber (chromatic dispersion) risetime. $$t_{fiber}=D\,\Delta\lambda\,L=(2.5\ \text{ps/nm/km})(5\ \text{nm})(75\ \text{km})=937.5\ \text{ps}=0.938\ \text{ns}.$$
3. Allowable receiver risetime. Combining transmitter, fiber and receiver risetimes in quadrature and solving for the receiver's share: $$t_{rx}=\sqrt{t_{sys}^2-t_{tx}^2-t_{fiber}^2}=\sqrt{1.40^2-0.5^2-0.938^2}=0.912\ \text{ns}.$$
4. Receiver bandwidth choice. Using the standard risetime-bandwidth product $t_r\approx0.35/B_{rx}$ (a Bessel-Thomson-like matched-filter response, the same relation used in Q4(d)), $$B_{rx}\ge\frac{0.35}{t_{rx}}=\frac{0.35}{0.912\times10^{-9}}=\boxed{384\ \text{MHz}}.$$ Choosing $B_{rx}\approx400$ MHz (comfortably above the 250 Mb/s data rate and above this 384 MHz floor) gives a small additional margin.
5. Check. At $B_{rx}=400$ MHz, $t_{rx}=0.35/(4\times10^8)=0.875$ ns, so $$t_{total}=\sqrt{0.5^2+0.938^2+0.875^2}=1.38\ \text{ns}\ \lt\ t_{sys}=1.40\ \text{ns}\ \checkmark$$ — the risetime requirement is met with a small margin.

Part (c) — would NRZ work?

Yes, and more comfortably. NRZ's risetime budget is the looser $t_{sys}=0.7\,T_b=2.8$ ns (an NRZ pulse occupies the full bit slot, so more accumulated spreading is tolerable before adjacent bits interfere), versus the $\sqrt{t_{tx}^2+t_{fiber}^2}=1.06$ ns already consumed by the transmitter and fiber alone. Since $2.8\ \text{ns}\gg1.06\ \text{ns}$, an NRZ system would close its risetime budget with far more margin than the RZ design above (which used the tighter $0.35\,T_b$ criterion) — the power budget in part (a) is unaffected by the line code, so the same 5.24 dB margin applies. NRZ is, if anything, the easier format for this link dispersion-wise.

Part (d) — maximum direct-modulation rate

1. Relaxation oscillation frequency. A directly modulated laser diode cannot respond faithfully to modulation much faster than its relaxation oscillation frequency, set by the photon and (spontaneous) carrier lifetimes and the bias point above threshold: $$\omega_r=\sqrt{\frac{1}{\tau_p\tau_n}\left(\frac{I_{op}}{I_{th}}-1\right)} =\sqrt{\frac{1}{(5\times10^{-12})(1\times10^{-9})}\left(\frac{10}{2}-1\right)}=2.83\times10^{10}\ \text{rad/s},$$ $$f_r=\frac{\omega_r}{2\pi}=\boxed{4.50\ \text{GHz}}.$$
2. Maximum direct-modulation bit rate is set by this relaxation frequency — on the order of $f_r\approx4.5$ GHz, far above the 250 Mb/s (or even a few Gb/s) needed here, confirming direct modulation is not the limiting factor for this particular link (dispersion and loss are).

Practical problems with pushing direct modulation toward $f_r$: relaxation- oscillation ringing/overshoot on the leading edge of each pulse as carrier and photon densities exchange energy before settling; frequency chirp (the modulated carrier density perturbs the refractive index, sweeping the instantaneous wavelength across each pulse), which interacts with fiber chromatic dispersion to add extra pulse spreading beyond the static-linewidth estimate used in part (b); and relative intensity noise (RIN) peaking sharply near $f_r$, degrading receiver SNR for any modulation frequency close to the resonance. These are the standard reasons high-speed links either bias the laser well below its relaxation-oscillation ceiling or use external modulation instead of direct current modulation.