**1. Introduction**

A classical method to characterize the spectral density of phase noise of microwave oscilla‐ tors is to compare the device under test (DUT) to another one, we call it the reference, with the same frequency if noise is expected to be better for the reference. In most of case it is possible to then characterize oscillators or synthesizers. But it is only possible if we can as‐ sign the same frequency to the DUT and the reference signal. However for some applica‐ tions, we see that the DUT delivers a frequency hard to predict during the fabrication. We here focus on characterizing a special class of oscillators, called optoelectronic oscillators (OEO) [1]. An OEO is generally an oscillator based on an optical delay line and delivering a microwave signal [2]. Purity of microwave signal is achieved thanks to a delay line inserted into the loop. For example, a 4 km delay corresponds to a 20 μs-long storage of the optical energy in the line. The continuous optical energy coming from a laser is converted to the mi‐ crowave signal. This kind of oscillators were investigated [3]. By the way, such OEO based on delay line are still sensitive to the temperature due to the use of optical fiber. Recently, progress were made to set compact OEO thanks to optical mini-resonators or spheres [4 - 7]. Replacing the optical delay line with an ultra-high Q whispering gallery-mode optical reso‐ nator allows for a more compact setup and an easier temperature stabilization. In order to introduce into the loop the fabricated resonator in MgF2 [8], CaF2 or fused silica, it has to be coupled to the optical light coming from a fiber. Best way to couple is certainly to use a cut optical fiber through a prism. But a good reproducible way in a laboratory is to use a ta‐ pered fibber glued on a holder. Then appears a problem for determining the phase noise of such compact OEO, because the frequency is rarely predictable. It is impossible to choose the frequency of the modulation (for instance exactly 10 GHz) and that's why it is necessary to develop new instruments and systems to determine phase noise for any delivered signal

© 2013 Salzenstein; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2013 Salzenstein; licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

in X-band (8.2-12.4 GHz) for instance. Here we come to our goal. The aim of this chapter is to provide a tool for a better knowledge of the phase noise characterization of OEO's using an optoelectronic phase noise system. We logically start by giving the main principle of how work such a system. We see that the main idea is to use delay lines to perform phase noise measurements. We also consderably increase the performances of such a system by cross correlation measurement, thanks to the two quasi-identical arms developed instrument. Then we present a realized system and the evaluation of its uncertainty based on interna‐ tional standard for determination of uncertainties when characterizing an OEO in X-band.

#### **2. Principle of the phase noise measurement system**

A quasi-perfect RF-microwave sinusoidal signal can be written as :

$$\mathbf{U}\cdot\boldsymbol{\nu}(t) = V\_0 \mathbf{I} + \alpha(t) \mathbf{J} \cos\{2\pi\nu\_0 t + \boldsymbol{\varphi}(t)\}\tag{1}$$

Reference is no more required for homodyne measurement with a delay line discriminator. At microwave frequencies, electrical delay is not suitable because of its high losses. Howev‐ er photonic delay line offers high delay and low attenuation equal to 0.2 dB/km at the wave‐ length λ=1.55 μm. Optoelectronic phase noise measurement system is schematically

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It consists on two equal and fully independent channels. The phase noise of the oscillator is determined by comparing phase of the transmitted signal to a delayed replica through opti‐ cal delay using a mixer. It converts the phase fluctuations into voltage fluctuations. An elec‐ tro-optic modulator allows modulation of the optical carrier at microwave frequency. The length of the short branch where microwave signal is propagating is negligible compared to the optical delay line. Mixers are used as phase detectors with both saturate inputs in order to reduce the amplitude noise contribution. The low pass filters are used to eliminate high frequency contribution of the mixer output signal. DC amplifiers are low flicker noise.

The oscillator frequency fluctuation is converted to phase frequency fluctuation through the delay line. If the mixer voltage gain coefficient is Kφ (volts/radian), then mixer output rms

Where │Hφ(jf)│² = 4.sin²(πfτ) is the transfer function of optical delay line, and f is the offset frequency from the microwave carrier. Equation (3) shows that the sensitivity of the bench depends directly on K²φ and │Hφ(jf)│. The first is related to the mixer and the second es‐ sentially depends on the delay τ. In practice, we need an FFT analyzer to measure the spec‐ tral density of noise amplitude V²out(f)/B, where B is the bandwidth used to calculate Vout(f)/B. The phase noise of the DUT is finally defined by Eq. (4) and taking into account the

*V* ²*out* ( *f* ) = *K*²*<sup>φ</sup>* │*Hφ*( *jf* )│²*Sφ*( *f* ) (3)

represented on Figure 1.

**Figure 1.** Phase noise bench.

voltage can be expressed as :

gain of DC amplifier GDC as :

where V0 is the amplitude, ν0 is the frequency, α(t) is the fractional amplitude fluctuation, and φ(t) is the phase fluctuation. Equation (1) defines α(t) and φ(t) in low noise conditions: | α(t)| <<1 and |φ(t)| <<1. Short-term instabilities of signal are usually characterized in terms of the single sideband noise spectral density PSD S(f). Phase noise £(f) is typically expressed in units of dBc/Hz, representing the noise power relative to the carrier contained in a 1 Hz bandwidth centered at a certain offsets from the carrier. So, S is typically expressed in units of decibels below the carrier per hertz (dBc/Hz) and is defined as the ratio between the oneside-band noise power in 1 Hz bandwidth and the carrier power:

$$
\varepsilon(f) = \mathbb{W} \cdot \operatorname{Sq}(f) \tag{2}
$$

This definition given in equation (2) includes the effect of both amplitude and phase fluctua‐ tions. Phase noise is the frequency domain representation of rapid, short-term, random fluc‐ tuations in the phase of a waveform, caused by time domain instabilities. However we must know the amplitude and phase noise separately because they act differently in the circuit. For example, the effect of amplitude noise can be reduced by amplitude limiting mechanism and mainly suppressed by using a saturated amplifier. Phase noise of microwave oscillators can usually be characterized by heterodyne measurement. Whereas, for such a system, we need a reference oscillator operating exactly at the frequency of the DUT with lower phase noise. Phase noise can be measured using a spectrum analyzer if the phase noise of the de‐ vice under test (DUT) is large with respect to the spectrum analyzer's local oscillator. Care should be taken that observed values are due to the measured signal and not the Shape Fac‐ tor of the spectrum analyzer's filters. Spectrum analyzer based measurement can show the phase-noise power over many decades of frequency. The slope with offset frequency in vari‐ ous offset frequency regions can provide clues as to the source of the noise, e.g. low frequen‐ cy flicker noise decreasing at 30 dB per decade.

Reference is no more required for homodyne measurement with a delay line discriminator. At microwave frequencies, electrical delay is not suitable because of its high losses. Howev‐ er photonic delay line offers high delay and low attenuation equal to 0.2 dB/km at the wave‐ length λ=1.55 μm. Optoelectronic phase noise measurement system is schematically represented on Figure 1.

**Figure 1.** Phase noise bench.

in X-band (8.2-12.4 GHz) for instance. Here we come to our goal. The aim of this chapter is to provide a tool for a better knowledge of the phase noise characterization of OEO's using an optoelectronic phase noise system. We logically start by giving the main principle of how work such a system. We see that the main idea is to use delay lines to perform phase noise measurements. We also consderably increase the performances of such a system by cross correlation measurement, thanks to the two quasi-identical arms developed instrument. Then we present a realized system and the evaluation of its uncertainty based on interna‐ tional standard for determination of uncertainties when characterizing an OEO in X-band.

where V0 is the amplitude, ν0 is the frequency, α(t) is the fractional amplitude fluctuation, and φ(t) is the phase fluctuation. Equation (1) defines α(t) and φ(t) in low noise conditions: | α(t)| <<1 and |φ(t)| <<1. Short-term instabilities of signal are usually characterized in terms of the single sideband noise spectral density PSD S(f). Phase noise £(f) is typically expressed in units of dBc/Hz, representing the noise power relative to the carrier contained in a 1 Hz bandwidth centered at a certain offsets from the carrier. So, S is typically expressed in units of decibels below the carrier per hertz (dBc/Hz) and is defined as the ratio between the one-

This definition given in equation (2) includes the effect of both amplitude and phase fluctua‐ tions. Phase noise is the frequency domain representation of rapid, short-term, random fluc‐ tuations in the phase of a waveform, caused by time domain instabilities. However we must know the amplitude and phase noise separately because they act differently in the circuit. For example, the effect of amplitude noise can be reduced by amplitude limiting mechanism and mainly suppressed by using a saturated amplifier. Phase noise of microwave oscillators can usually be characterized by heterodyne measurement. Whereas, for such a system, we need a reference oscillator operating exactly at the frequency of the DUT with lower phase noise. Phase noise can be measured using a spectrum analyzer if the phase noise of the de‐ vice under test (DUT) is large with respect to the spectrum analyzer's local oscillator. Care should be taken that observed values are due to the measured signal and not the Shape Fac‐ tor of the spectrum analyzer's filters. Spectrum analyzer based measurement can show the phase-noise power over many decades of frequency. The slope with offset frequency in vari‐ ous offset frequency regions can provide clues as to the source of the noise, e.g. low frequen‐

*υ*(*t*)=*V*<sup>0</sup> 1 + *α*(*t*) *cos*(2*πν*0*t* + *φ*(*t*)) (1)

£( *f* ) = ½⋅ *Sφ*( *f* ) (2)

**2. Principle of the phase noise measurement system**

338 Optoelectronics - Advanced Materials and Devices

A quasi-perfect RF-microwave sinusoidal signal can be written as :

side-band noise power in 1 Hz bandwidth and the carrier power:

cy flicker noise decreasing at 30 dB per decade.

It consists on two equal and fully independent channels. The phase noise of the oscillator is determined by comparing phase of the transmitted signal to a delayed replica through opti‐ cal delay using a mixer. It converts the phase fluctuations into voltage fluctuations. An elec‐ tro-optic modulator allows modulation of the optical carrier at microwave frequency. The length of the short branch where microwave signal is propagating is negligible compared to the optical delay line. Mixers are used as phase detectors with both saturate inputs in order to reduce the amplitude noise contribution. The low pass filters are used to eliminate high frequency contribution of the mixer output signal. DC amplifiers are low flicker noise.

The oscillator frequency fluctuation is converted to phase frequency fluctuation through the delay line. If the mixer voltage gain coefficient is Kφ (volts/radian), then mixer output rms voltage can be expressed as :

$$V^2\_{\
uat} \begin{Bmatrix} f \end{Bmatrix} = K^2\_{\varphi} \begin{Bmatrix} H\_{\varphi} \begin{Bmatrix} \dot{f} \end{Bmatrix} \end{Bmatrix} \begin{Bmatrix} \dot{f} \end{Bmatrix} \begin{Bmatrix} f \end{Bmatrix} \tag{3}$$

Where │Hφ(jf)│² = 4.sin²(πfτ) is the transfer function of optical delay line, and f is the offset frequency from the microwave carrier. Equation (3) shows that the sensitivity of the bench depends directly on K²φ and │Hφ(jf)│. The first is related to the mixer and the second es‐ sentially depends on the delay τ. In practice, we need an FFT analyzer to measure the spec‐ tral density of noise amplitude V²out(f)/B, where B is the bandwidth used to calculate Vout(f)/B. The phase noise of the DUT is finally defined by Eq. (4) and taking into account the gain of DC amplifier GDC as :

$$\mathbb{E}\{f\} = \left[V^2\mathbb{I}\_{\text{out}}\{f\}\right] \cdot \left|\cdot\right| \cdot \left[\mathbb{Z}K^2\mathbb{I}\_{\text{\textquotedblleft}\emptyset}\cdot \left|\,H\_{\text{\textquotedblleft}\{\mathcal{J}\}}\right|\right|\,^2G^2\_{\text{DC}}\cdot\mathbb{B}\right] \tag{4}$$

**Figure 3.** Picture of the double channels *Hewlett-Packard* HP3561A FFT analyzer.

[11] with the phase noise we measure using our system.

The measured phase noise includes the DUT noise and the instrument background. The cross correlation method allows to decrease the cross spectrum terms of uncommon phase noise as √(1/m), where m is the average number. Thereby uncorrelated noise is removed and sensitivity of measure is improved. To validate the measure of our phase noise bench, we need to compare data sheet of the commercial frequency synthesizer Anritsu/Wiltron 69000B

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**Figure 4.** Phase noise (dBc/Hz) of the synthesizer measured at 10 GHz with Kφ=425 mV/rad and GDC= 40dB versus

**4. Validation of the performances**

Fourier Frequency between 10 Hz and 100 kHz.

Such instruments has been recently introduced [3,9,10]. In section 3, we present concretely a realized optoelectronic phase noise measurement system.
