MODULATOR BIAS OPTIMIZATION OF RADIO OVER ... - IEEE Xplore

25th Biennial Symposium on Communications

MODULATOR BIAS OPTIMIZATION OF RADIO OVER FIBER LINKS CONSIDERING NOISE FIGURE AND RF GAIN Mohamed Daoud, Udari Maheeka, Tahrima Alam and X. Fernando, Senior Member, IEEE ABSTRACT Abstract- Optimum bias level for Mach-Zehnder modulator is important for the performance of radio over fiber links. This paper proposes a method to optimize the bias point of the external modulator of a radio over fiber system considering both RF gain and noise figure. In suboctave systems, there is a trade-off between these parameters. RF gain first nonlinearly increases and then decreases with the bias voltage while, the noise figure has an inverse relationship with the bias voltage. Therefore, a figure of merit is proposed in this paper that takes into account gain, noise figure and spurious-free dynamic range. Simulation results show that an optimal bias point can be obtained by using this figure of merit. Index Terms- Optical fiber communications, radio over fiber, Mach-Zehnder modulator, microwave photonics, noise figure I. INTRODUCTION Wireless communication sector is experiencing phenomenal growth and today’s wireless systems are under pressure to offer higher data rates to enable rich content delivery to ever increasing number of wireless subscribers. Radio-over-fiber (ROF) links offer high data rates to address the demand. ROF is a technology where light signal is modulated at radio frequencies, then transmitted over fiber. ROF links are used not only in wireless communications field but also in cable television (CATV) and satellite base stations. Since external modulators used in ROF links suffer from nonlinear distortion, appropriate bias control is important. Previously, Marco et al. has done carrier to noise ratio optimization by modulator bias control [1]. In [2] again, Marco et al. studied the gain optimization by modulator bias control but did not consider the effect on noise figure or spurious free dynamic range (SFDR). In [3] Jason and Adil proposed a method to minimize the noise figure in sub octave links that increases the SFDR but they didn’t mention the effect on the gain. In [4] Jason and Adil proposed a linearity figure of merit that considers noise figure, output intercept power (OIP3) and power consumption but they didn’t include the link gain in their expression. In [5] Urick et al. provided a complete

978-1-4244-5711-3/10/$26.00 ©2010 IEEE

Fig. 1. Schematic for the RoF system

analysis of an analog fiber optic link employing MZM and EDFA, expression for RF gain, RF noise figure and SFDR were derived. In this paper we present a technique to optimize the bias point of the external modulator of a RoF system considering both the RF gain and the noise figure that improved the SFDR. The link consists of a Distributed feedback laser (DFB), Mach-Zehnder modulator (MZM), Erbium doped fiber amplifier (EDFA) and a detector. In section II, we describe the set up of the system, along with driving expressions for maximum RF gain, minimum NF and SFDR. In section III, the figure of merit concept is introduced and in section IV, we conclude the results and give a brief suggestion for future work. II. THEORY Fig. 1 shows the ROF system. Only the down link is considered for simplicity. The MZM converts the RF signal from electrical to optical domains, the DFB laser source provides CW light wave. EDFA provides adequate amplification and the detector converts the signal from optical to electrical domain. II.A. RF Gain The total RF gain

for the link in Fig. 1 is given by ,

(1)

is the output power at the detector, and is the , input power at the modulator. Following the gain analysis

234


in [2] and full link analysis in [5], follows.

can be calculated as

Ф

(2)

Here, Ф

(3)

and K is a constant that depends on the detector and MZM losses responsivity , fiber losses (ά (ά ). The gain of the EDFA is, (4)

, ,

Fig. 2. RF link gain vs. Фbias/π of the MZM

is the EDFA small signal gain, is the where, empirical constant and is the maximum power , after which the amplifier will saturate.

From equations (1) to (5)

can be given by, Ф

,

1

cos Ф

.

(5)

Here, corresponds to the output power from the , is the power of the DFB laser source and MZM, is the zero order Bessel function of the first kind. The RF signal is given by sin

(6)

Where, is the angular frequency of the applied voltage and can be given by 2

(7)

, is the load resistance and is the modulator efficiency. Unless otherwise noted, the following values are used for all simulations and calculations: EDFA Small signal gain Power from the DFB laser source P Modulator switching voltage V Maximum saturated output power from the EDFA P , Modulator efficiency η Load resistance R Fiber losses άf MZM losses ά Empirical constant α Input power at the modulator P

-8dB at 5 GHz signal 50 Ω 0dB -4.5dB ≈1 0dBm

Table 1. Values used for the simulation

(8)

,

The dependence of on is very clear from the , we can easily get the above equation; thus, using point at which the gain is maximized. For simplicity we use a simple tone with frequency 5GHz as the RF signal to be transmitted over the fiber, from equation (6) and (7) we got the value of the RF signal. ⁄ for In Fig. 2. The gain is plotted against Ф the values of between [0, 2], maximum gain is found to be 12.8 at Ф ⁄ 0.086, as a conclusion MZM should be biased at this bias point for maximum gain. However, note that this bias point gives a large noise figure as next section explains. II.B. Noise Figure The noise figure

37dB -2dBm 3.35V 17dBm

. Ф

for the link in Fig.1 is given by (9)

Where is the gain from equation (8), is Boltzmann’s constant, is the total noise in the system and is the temperature given in Kelvin. Following the same analysis as in [3] and [5] (10) Where , , are the power spectral densities for; thermal, shot, laser and EDFA noise respectively. Thermal and shot noise values are given by

235


Fig. 3. NF noise figure vs. Фbias/π for the MZM

1 ά

Fig. 4. SFDR plotted against Фbias⁄π

(11)

ά

Ф

ά

Ф

the range of output power of the system. It is simple to show that for the case of the link shown in Fig. 1 3

(12)

(13) (14)

For a standard MZM [3], 3 is calculated as in (14), where changing the laser power or the bias angle does not affect 3. For a given MZM half wave voltage , the modulator bias voltage where the minimum occurs is the same bias voltage where the maximum SFDR occurs [3]. ⁄ , In Fig. 4 SFRD in . is plotted against Ф maximum SFDR occurs at the bias voltage when, the has a different curve. is minimum [3], but In the next section we present a method to get the optimum from a set of modulator bias points that and SFDR while decreasing . increases

II.C. Spurious Free Dynamic Range (SFDR) SFDR is defined by [6], the range of input power levels from which the output signal just exceeds the output noise floor, and for which any distortion components remain buried below the noise floor. In practice, the signal power has a slope of 1 and the third order intermodulation distortion power (IMD3) has a slope of 3, The minimum discernable signal power (MDS) occurs where the signal power crosses the noise floor and the third order intercept point (IP3) occurs at the level where IMD3 and the signal have equal power, SFDR is the difference between MDS and the point at which IMD3 crosses the noise floor [7]. In RoF systems the SFDR is of great importance as it indicates the range of input power the system can detect and handle without distortion, also

.

3

,

Where is the electron charge. The laser noise also known as the relative intensity noise (RIN) is chosen to be ⁄ . -150 can’t generally be written in a closed form expression [5], therefore we use a fixed measured ⁄ quantity of -146 as shown in [5]. Room temperature is considered, 290 . ⁄ is shown in Fig. 3 The calculated in dB vs. Ф for the values of between [0, 2]. It’s clear that the minimum occurs at high bias value; near quadrature. ⁄ 0.48. Minimum is found to be 10.4 at Ф Therefore, clearly there is a tradeoff between maximizing and minimizing . A value in between that with acceptable should be found. gives high

174

III. FIGURE OF MERIT It’s very clear that the optimum modulator bias point is somewhere between quadrature and minimum bias point. After calculating the maximum from (8), and minimum from (9) we propose the figure of merit to be (15) The expression for was chosen considering the following facts. Simply put, we want high and low (that will also yield high SFDR). Therefore, expression for is simply chosen to be the ratio between these two.

236


IV. CONCLUSION

Fig. 5. The proposed figure of Merit vs. Фbias⁄π

By choosing the appropriate value that maximizes the , we can see a balanced link performance; increase in and decrease in . ⁄ , the The is plotted in Fig.5 against Ф maximum is found to be between quadrature and minimum bias point. In our example the maximum Ф = -31.6 occurs at = 0.31 which corresponds to = -18.9 dB, = 12.7dB the following link values:

In this paper, we derived an expression for maximum gain, minimum noise figure, SFDR and introduced the concept for an ROF link. We also gave a numerical example which is verified by simulation results. Different Ф operating points were studied for the RoF link; near quadrature, at minimum bias point and at maximum . It is found that at maximum , the best link performance in terms of gain, noise figure and SFDR is achieved. By best link performance we mean high gain, high SFDR and acceptable noise figure; maximizing the increases the , decreases the and since the SFDR is automatically optimized with optimizing the , thus the SFDR increases. Further work should be done to verify the concept when using multiple RF carriers and with randomly modulated stochastic RF signals like the ones that belong to Wi-Fi 802.11 a/g/n, Wi-Max, WCDMA and GSM wireless systems. REFERENCES [1] M.M. Sisto, S. LaRochelle, and L.A. Rusch, “Carrierto-Noise Ratio Optimization by Modulator Bias Control in Radio-Over-Fiber Links,” IEEE photonics technology letters, vol. 18, no. 17, pp. 1840-1842, Sept. 1, 2006. [2] M.M. Sisto, S. LaRochelle, and L.A. Rusch, “Gain Optimization by Modulator-Bias Control in RadioOver-Fiber Links,” Journal of light wave technology, vol. 24, no. 12, pp. 4974-4982, Dec. 2006. [3] J. Devenport, and A. Karim, “Optimization of an Externally Modulated RF Photonic Link,” Fiber and integrated optics, 27:7-14, Jan. 1, 2008. [4] A. Karim, and J. Devenport, “Optimization of Linearity Figure of Merit for Microwave Photonics Links,” IEEE photonics technology letters, vol. 21, no. 13, pp. 950-952, July 1, 2009. [5] V.J. Urick, M.E. Godinez, P.S. Devgan, J.D. McKinney, and F. Bucholtz, “Analysis of an Analog Fiber-Optic Link Employing a Low-Biased MachZehnder Modulator Followed by an Erbium-Doped Fiber Amplifier,” Journal of light wave technology, vol. 27, no. 12, pp. 2013-2019, June 15, 2009. [6] L. Besser, and R. Gilmore, Practical RF Circuit Design for modern Wireless Systems- volume I: passive circuits and systems, edition 1, Artech House Publishers, Massachusetts, 2003. [7] D. Wake, M. Webster, G. Wimpenny, K. Beacham, and L. Crawford, “Radio over Fiber for mobile communications,” Microwave photonics, pp. 157-160, Jan. 2004.

and SFDR= 107.6 . . Using the concept introduced in this paper; high gain is achieved along with acceptable noise figure and high SFDR. In our calculations the value is negative because of the optimization technique used to maximize the function. Our expression gives high , low and high SFDR using a simple, non-complicated closed form expression, it’s different from the figure of merit introduced in [4], where they used the OIP3 and the noise figure in their expression but not the link gain. Ф

⁄

SFDR

Max. Merit

0.31

-18.9

12.7

107.6

Max. Gain Min. Noise Figure

0.086

-12.8

30.9

95

0.48

-23.3

10.4

109.1

Table 2. Comparing the merit concept to the max. gain and min. noise figure calculations

From the summary of simulation results shown in Table.2, It’s clear that our concept gives a balanced link performance with regards to gain, noise figure and SFDR.

237