B.  Bandwidth and Rise Time Budgets

The transmission data rate of a digital fiber optic communication system is limited by the rise time of the various components, such as amplifiers and LEDs, and the dispersion of the fiber. The cumulative effect of all the components should not limit the bandwidth of the system. The rise time t_r and bandwidth BW are related by

This equation is used to determine the required system rise time. The appropriate components are then selected to meet the system rise time requirements. The relationship between total system rise time and component rise time is given by Equation 8-23

(8-23)

where t_s is the total system rise time and t_r1, t_r2, ... are the rise times associated with the various components.

To simplify matters, divide the system into five groups:

1. Transmitting circuits (t_tc)

2. LED or laser (t_L)

3. Fiber dispersion (t_f)

4. Photodiode (t_ph)

5. Receiver circuits (t_rc)

The system rise time can then be expressed as

(8-24)

The system bandwidth can then be calculated using Equation 8-25 from the total rise time t_s as given in Equation 8-24.

Electrical and Optical Bandwidth

• Electrical bandwidth (BW_el) is defined as the frequency at which the ratio current out/current in (I_out/I_in) drops to 0.707. (Analog systems are usually specified in terms of electrical bandwidth.)
  
  
• Optical bandwidth (BW_opt) is the frequency at which the ratio power out/power in (P_out/P_in ) drops to 0.5.

Because P_in and P_out are directly proportional to I_in and I_out (not I ²_in and I ²_out), the half-power point is equivalent to the half-current point. This results in a BW_opt that is larger than the BW_el as given in Equation 8-26.

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Example 9

A 10-km fiber with a BW ´ length product of 1000 MHz ´ km (optical bandwidth) is used in a communication system. The rise times of the other components are t_tc = 10 ns, t_L = 2 ns, t_ph = 3 ns, and t_rc = 12 ns. Calculate the electrical BW for the system.

Solution:

Because we are looking for the electrical BW, first calculate the electrical BW of the 2-km fiber from the optical BW and then calculate the rise time t_r = t_f.

BW_opt = (1000 MHz ´ km)/10 km = 100 MHz

BW_el = 0.707 ´ 100 MHz = 70.7 MHz

The fiber rise time is

t_r = t_f = 0.35/(70.7 MHz) = 4.95 ns

The system rise time is

t_s = (10² + 2² + 4.95² + 3² + 12²)^1/2 = 16.8 ns

System BW_el is

BW_el = 0.35/(16.8 × 10^–9) = 20.8 Mhz

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