# Estimating loss-limited transmission distance

• wu_weidong
In summary, the conversation discusses a high-speed optical data communication system that is composed of a transmitter, an unamplified transmission fiber link, and a receiver. The system operates at 10-Gb/s and uses a 1550-nm laser diode and a Mach-Zehnder modulator. After transmission over single-mode fiber, the signal is detected by a PIN receiver with a responsivity of 0.8 A/W and a load resistance of 50 W. The target bit-error rate is 10^-9 and the noise temperature is 300 K. The calculations involve determining the maximum fiber length based on the signal strength and noise power.
wu_weidong

## Homework Statement

A high-speed optical data communication system is composed of a transmitter, an unamplified transmission fiber link, and a receiver. The optical transmitter generates a 10-Gb/s non-return-to-zero (NRZ) signal using a 1550-nm laser diode (linewidth=2 MHz) followed by a chirp-free Mach-Zehnder modulator. The signal has a very high extinction ratio and the fiber launch power is 0 dBm. After transmission over single-mode fiber (loss: 0.2 dB/km, chromatic dispersion: 17 ps/nm/km), the signal is detected by a PIN receiver. The responsivity of the PIN detector is 0.8 A/W and the receiver has a load resistance of 50 W. The bandwidth of the receiver is 8 GHz. Assume that the noise temperature is 300 K, and the target bit-error rate (BER) is 10^-9.

## The Attempt at a Solution

First of all, even though I'm given the dispersion of 17 ps/nm/km, the "loss-limited" term refers only to the attenuation fiber loss, is this correct?

I've done the following, and I hope to know if I'm correct.

For BER of 10-9, Q-factor = 6.0.

For high extinction ratio, SNR ≈ 4Q2 = 144.

Power at transmitter, Ptrans = 0dBm = 1mW

SNR = (R2RL Prec2) / (4kBTΔf)
144 = (0.82×50×Prec2) / (4×1.38×10-23×300×8×109)
Prec = 2.44×10-5W

α = 0.2 = -(10/L)log (Prec / Ptrans)
L = 80.6 km ← loss-limited transmission distance

I think it is OK, still thinking. Is Q the peak to average noise voltage?

Q is the Quality factor, as described here.

wu_weidong said:

## Homework Statement

A high-speed optical data communication system is composed of a transmitter, an unamplified transmission fiber link, and a receiver. The optical transmitter generates a 10-Gb/s non-return-to-zero (NRZ) signal using a 1550-nm laser diode (linewidth=2 MHz) followed by a chirp-free Mach-Zehnder modulator. The signal has a very high extinction ratio and the fiber launch power is 0 dBm. After transmission over single-mode fiber (loss: 0.2 dB/km, chromatic dispersion: 17 ps/nm/km), the signal is detected by a PIN receiver. The responsivity of the PIN detector is 0.8 A/W and the receiver has a load resistance of 50 W. The bandwidth of the receiver is 8 GHz. Assume that the noise temperature is 300 K, and the target bit-error rate (BER) is 10^-9.

## The Attempt at a Solution

First of all, even though I'm given the dispersion of 17 ps/nm/km, the "loss-limited" term refers only to the attenuation fiber loss, is this correct?
Yes but the fiber length is not given so I would ignore this and the dispersion rate also.
Second, what is the problem statement?
I would just compute the noise over the receiver bandwidth assuming it all comes from the 50 ohm load resistor, & compare to the signal strength at the photodiode.
Seems like a flaky problem set; additionally, the receiver noise would probably be dominated by the amplifier and tghe laser, not the 50 ohm, but ...
Don't know about "Q" & forgot how to relate noise to BER. Sorry.

rude man said:
Yes but the fiber length is not given so I would ignore this and the dispersion rate also.
Second, what is the problem statement?
I would just compute the noise over the receiver bandwidth assuming it all comes from the 50 ohm load resistor, & compare to the signal strength at the photodiode.
Seems like a flaky problem set; additionally, the receiver noise would probably be dominated by the amplifier and tghe laser, not the 50 ohm, but ...
Don't know about "Q" & forgot how to relate noise to BER. Sorry.
Agree. Taking it a bit further using dB for simplicity:-
Boltzmann's Constant can be expressed as -228.6 dBW/K/Hz/
Noise power in 50 ohms at 300K = kTB
Pn = -228.6 + 10 log 300 + 10 log 8x10^9
Pn = -72.3dBW
Required signal power, Pr, in 50 ohm load = Pn + 20 log Q [Q seems to be the signal to RMS noise voltage for 10^-9 BER]
For BER 10^-9, Q = 6 [see web link quoted]
Signal to noise ratio for BER 10^-9 = 20 log 6 = 15.6dB
Pr = -72.3 + 15.6 = -56.7 dBW
Pr = 10^-5.67 W
Resistor Current
I ^2 x 50 = 10^-5.67
I = 2 x 10 ^-4 Amp
Optical Power required at diode 0.8A/W
Po = 2 x 10^-4 / 0.8 (W)
Po = 2.5 x 10^-4 (W)
Po = - 6 dBm
TX power
Pt = 0 dBm
Max path loss = 6 dB
Fibre attenuation = 0.2dB/km
Max fibre length = 6/0.2 = 30km
Sounds plausible??

tech99 said:
Agree. Taking it a bit further using dB for simplicity:-
Boltzmann's Constant can be expressed as -228.6 dBW/K/Hz/
Noise power in 50 ohms at 300K = kTB
Pn = -228.6 + 10 log 300 + 10 log 8x10^9
Pn = -72.3dBW
Required signal power, Pr, in 50 ohm load = Pn + 20 log Q [Q seems to be the signal to RMS noise voltage for 10^-9 BER]
For BER 10^-9, Q = 6 [see web link quoted]
Signal to noise ratio for BER 10^-9 = 20 log 6 = 15.6dB
Pr = -72.3 + 15.6 = -56.7 dBW
Pr = 10^-5.67 W
Resistor Current
I ^2 x 50 = 10^-5.67
I = 2 x 10 ^-4 Amp
Optical Power required at diode 0.8A/W
Po = 2 x 10^-4 / 0.8 (W)
Po = 2.5 x 10^-4 (W)
Po = - 6 dBm
TX power
Pt = 0 dBm
Max path loss = 6 dB
Fibre attenuation = 0.2dB/km
Max fibre length = 6/0.2 = 30km
Sounds plausible??
You're way ahead of me I'm afraid. My fiber background is with optical fiber sensors which do not involve digital data so I don't know how to relate BER to noise. Also, since the problem statement seems to ask for the permissible length of fiber I'm afraid dispersion and loss are material in coming up with the answer. Sorry, this is a pretty specific problem for us here at pf ...

rude man said:
You're way ahead of me I'm afraid. My fiber background is with optical fiber sensors which do not involve digital data so I don't know how to relate BER to noise. Also, since the problem statement seems to ask for the permissible length of fiber I'm afraid dispersion and loss are material in coming up with the answer. Sorry, this is a pretty specific problem for us here at pf ...
I notice you have a factor of 4 with the S/N calculation. I am guessing you are correct here as my definition of Q might not include a half amplitude term. I have taken Q = signal/RMS noise. I have 15dB S/N and you have 144 = 21.5 dB. Allowing for this, I think we agree, and your calculation is ten times shorter!

## 1. How is loss-limited transmission distance calculated?

Loss-limited transmission distance is calculated by taking into account the attenuation or loss of signal strength over a transmission medium, such as a fiber optic cable. This calculation involves measuring the signal strength at the source and the receiver, as well as taking into account any additional losses from connectors or splices in the transmission path.

## 2. What factors affect the loss-limited transmission distance?

There are several factors that can affect the loss-limited transmission distance, including the type of transmission medium being used (e.g. fiber optic cable, copper wire), the wavelength of the signal being transmitted, and the quality of the components used in the transmission path.

## 3. How does loss-limited transmission distance impact network performance?

The loss-limited transmission distance directly affects the reach or distance that a network can cover. If the loss-limited distance is too short, the network may not be able to reach all desired destinations, resulting in potential network outages or unreliable connections. Therefore, it is important to carefully consider and accurately estimate the loss-limited distance in order to ensure optimal network performance.

## 4. Can loss-limited transmission distance be improved?

Yes, there are several ways to improve the loss-limited transmission distance. One way is to use higher quality components and cables with lower signal loss. Another method is to use signal amplifiers or repeaters along the transmission path to boost the signal strength. Additionally, using different wavelengths or multiplexing techniques can also help increase the loss-limited distance.

## 5. How do different transmission mediums affect the loss-limited distance?

The type of transmission medium used can greatly impact the loss-limited distance. For example, fiber optic cables have much lower signal loss compared to copper wires, allowing for longer transmission distances. Additionally, different types of fiber optic cables, such as single mode and multimode, have different loss characteristics and can affect the loss-limited distance. It is important to carefully consider the transmission medium and its properties when estimating the loss-limited transmission distance.

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