Radio over Fiber for Wireless Communications: From Fundamentals to Advanced Topics (Wiley - IEEE) by Fernando Xavier N

Author:Fernando, Xavier N
Language: eng
Format: epub, azw3
ISBN: 9781118797037
Publisher: Wiley
Published: 2014-06-15T16:00:00+00:00

7.4.1 Maximizing RF Gain

The RF link gain seen in the electrical domain is the ratio between the input RF power to the MZI and the output RF power from the photodetector. This is given by

7.6

where is the output power at the photodetector and is the input power at the modulator. Following the gain analysis in [2006] and full link analysis in [2009], can be written as follows:

7.7

where is the bias angle corresponding to the bias voltage . is the voltage that will give a phase shift to the modulated signal. The voltages and have already been defined in Chapter 2. Here, is a scaling constant that depends on factors like detector responsivity (), fiber losses (), and MZI internal losses ().

Now, the EDFA gain is not a linear function of the input power. Erbium-doped fiber amplifiers have this well-known gain saturation property which tends to limit the gain for high input power.1

Hence, the EDFA gain can be written as

7.8

where is the EDFA small signal gain, is an empirical constant, is the output from the MZI, and is the maximum power that the EDFA can work with safely. Note that when is much smaller than ,.

The output power of the MZI is actually given by a Bessel function series. For practical reasons only the first term can be considered. This approximated expression is

7.9

Here, is the power from the DFB laser source and is the zero-order Bessel function of the first kind.

The sinusoidal RF modulating voltage can be written as , where is the angular frequency of the RF signal (applied voltage) and is the peak value of the same. Hence, the power is given by

7.10

and

7.11

Here, is the load resistance seen by the RF source and is the modulator efficiency.

By back substitution of these expressions, we can write an expression for as follows:

7.12

Therefore, the RF gain of the externally modulated ROF link depends on the bias voltage of the MZI in a nonlinear manner. This is clear from the above equation.

Therefore, by varying the bias voltage and computing the RF gain, the point of maximum gain can be found. The values shown in Table 7.1 are used to numerically evaluate these expressions and get a quick understanding of the link behavior.

Table 7.1 Values used for numerical evaluations

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