**6. Conclusion**

**5.3. Estimation of the global uncertainty of this system**

346 Optoelectronics - Advanced Materials and Devices

sigma interval of confidence is calculated as follows:

noise at 1 sigma.

**Table 1.** Budget of uncertainties.

Its leads to a global uncertainty of U = 2xuc = 1.58 dB at 2 sigma.

According to the Guide to the expression of uncertainty in measurement, uncertainty at 1

We deduce from equation (6) that uncertainty at 1 sigma, noted uc, is better than 0.79 dB.

Table 1 summarizes how is deduced the global uncertainty for the spectral density of phase

**Uncertainty Designation Value (in dB)** A1 Repeatability 0.68 A2 Reproductibility 0 A3 Uncertainty term due to the number of sample 0.1 A (ΣAi²)1/2 0.69 BR Not applicable 0 BL1 Gain of the DC amplifier 0.04 BL2 Influence of the temperature 0.1 BL3 Influence of the resolution of the instrument 0.1 BL4 Influence of the power of the DUT 0 BL5 Uncertainty on the determination of K<sup>Φ</sup> 0.08 BL6 Contribution of automatic/manual range 0.02 BL7 Influence of the variation of the input power 0.02 BL ΣBLi 0.38 uC Global uncertainty at 1 sigma: (A²+BR²+BL²)1/2 0.79

For convenience and to have an operational uncertainty in case of degradation or drift of any elementary term of uncertainty, it is wise to degrade the global uncertainty. That's why we choose to keep U = 2 dB at 2 sigma for a common use of the optoelectronic system for phase noise determination. According to this evaluation of the uncertainty at 1 sigma, it leads to 1.58 at two sigma. It concretely means that it is possible to determine the phase noise of a single oscillator in X-band with a global uncertainty set to be better than ±2 dB.

*uc* = √(*A*² + *BR* ² + *BL* ²) (6)

The author wish that the phase noise optoelectronic system presented in this chapter is use‐ ful for those who want to understand how the phase noise can be experimentally deter‐ mined. We detailed performances and consideration about estimation of the uncertainty to show the main advantage of such developed instrument for metrology or telecommunica‐ tion applications and characterizations of compact OEO's operating in X-band. With high performance better than -170 dBc/Hz at 10 kHz from the 10 GHz carrier, it is interesting to underline that it is possible to determine the phase noise of a single oscillator in X-band with a global uncertainty set to be better than ±2 dB. This system is to be extended at lower and higher microwave operating frequencies.
