The frequency response of an LED is determined by the carrier dynamics (and therefore is limited by the carrier lifetime *T*_{n}) and the parasitic capacitance of the LED (described by the RC constant *T*_{RC}[2].

If a small, constant forward bias is applied, the influence of the parasitic capacitance of the LED can be neglected. The LED 3-dB modulation optical bandwidth is defined as the modulation frequency at the LED power transfer function is reduced by 3 dB [1]. The LED 3-dB modulation optical bandwidth could be expressed as:

ƒ_{3dB} = √3 / 2π / (*T _{n} + T*

_{RCn}).

We would like to demonstrate the modulation response properties of the LED. The project is depicted in Figure 1.

**Figure 1: Project layout**

The default values of the carrier lifetime *T*n and the RC constant *T*_{RC}, are 1 ns and

1 ns, respectively. Therefore, the ƒ_{3dB} is approximately 140 MHz.

Discussion of the numerical parameters: for example, bit rate is 300 Mb/s and sequence length 128 bits, therefore, the time window is about 430 ns. Samples per bit are 256, therefore, the sample rate is 76 GHz. The default resolution therefore is about 2 MHz.

Let us first keep the carrier lifetime *T*_{n} and the RC constant *T*_{RC}, which means ƒ_{3dB}

is about 140 MHz, and analyze the closure of the eye diagram as a measure for the

performance of the system. The results for 100Mb/s and 300Mb/s transmission are

shown in Figure 2.

**Figure 2: System performance with increased bit rate**

Clearly the performance of the digital system is considerably worsened by increasing the bit rate above the LED 3-dB modulation optical bandwidth.

The influence of the modulation response of the LED can be studied also by keeping

the bit rate, for example 300 Mb/s, and reducing the carrier lifetime *T*_{n} and the RC

constant *T*_{RC}, therefore increasing ƒ_{3dB} . Let us assume *T*_{n }= *T*_{RC} = 0.5ns,

therefore ƒ_{3dB} will be about 280MHz.

A large improvement in the system performance at 300 Mb/s compared to the latest figure should be seen. This is illustrated in Figure 3.

**Figure 3: Improved system performance at 300Mb/s**

**References**

[1]G.P. Agrawal, Fiber-Optic Communication Systems, Joinery & Sons, Inc, second edition, 1997.

[2]G. Keiser, Optical Fiber Communications, McGraw-Hill Higher Education, third edition, 2000.