Math Problem Statement

34A_Fung Tik Man__Assignment2.docx

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Check the answer of Tasks 1 to 7

Solution

The answers for Tasks 1 through 7 in your uploaded file seem well-documented and detailed. Here's a brief review of each:

  1. Maximum Overall Length Calculation (Task 1):
    The maximum overall length calculation uses the system rise time and bit rate constraints, resulting in 79.19 km. This appears correct as the steps follow the formula provided.

  2. Number of Fiber Segments (Task 2):
    Correctly calculates the number of 2.5 km segments needed (32) by dividing the total length by segment length.

  3. Number of Splices (Task 3):
    Correctly identifies the number of splices as one less than the number of segments (31).

  4. Minimum Required Optical Power (Task 4):
    Loss calculations and power requirements align with the given parameters. The result of -25.85 dBm is consistent with the computation.

  5. Laser Diode Power in mW (Task 5):
    Converts the optical power from dBm to mW, resulting in approximately 0.0026 mW. This is accurate.

  6. Improvements for Higher Bit Rate (Task 6):
    Suggesting a faster laser diode rise time is valid. The explanation relates appropriately to reducing system rise time to support higher bit rates.

  7. Impact of Switching to Graded-Index Multi-Mode Fiber (Task 7):
    The analysis of increased dispersion, attenuation, and reduced bandwidth-distance product effectively highlights the trade-offs of using multi-mode fiber. It provides a clear rationale for the implications on system performance.

If you'd like a deeper verification of specific calculations or further explanation, let me know!

Suggested Related Questions

  1. What other alternatives could be considered to reduce system cost while maintaining performance?
  2. How does the rise time of a laser diode affect data integrity at higher bit rates?
  3. Could the use of error correction methods mitigate the limitations of multi-mode fibers?
  4. What would be the impact of changing the EDFA gain on the system design?
  5. How does fiber splice quality influence the overall system performance?

Tip:

Ensure all assumptions and constants used in calculations align with industry standards and system requirements.

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Math Problem Analysis

Mathematical Concepts

Optical communication system design
Fiber optic loss calculations
Bit rate and system rise time analysis
Power conversion and signal degradation

Formulas

System rise time: T_sys = √(T_laser² + T_photodetector²)
Maximum bit rate: B_max = 0.35 / T_sys
Total loss: Loss = Fiber loss + Splice loss + Connector loss
Power conversion: mW = 10^(dBm/10)

Theorems

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Suitable Grade Level

Undergraduate engineering level