arXiv subjects

Enrico Rubiola

Publications and source records attributed to Enrico Rubiola.

46 records · Page 3Linked to original sources

arXiv2007

Advanced bridge instrument for the measurement of the phase noise and of the short-term frequency stability of ultra-stable quartz resonators

High-stability quartz oscillators are needed in a number of space applications. A short-term stability of parts in 10^{-14} [Allan deviation σy(τ) ] is sometimes required, for integration time τof approximately 1-10 s. The Centre National d'Etudes Spatiales (CNES) and the FEMTO-ST Institute (formerly LPMO and LCEP), have been collaborating for many years in this domain, aiming at measuring and at understanding the oscillator noise. The highest stability has been observed on 5 MHz and 10 MHz bulk acoustic-wave resonators. Yet this stability is still not sufficient, or the the manufacturing method is not reproducible. Recently, the analysis of a few premium-stability oscillators has demonstrated that the oscillator frequency instability is due to the fluctuation of the resonator natural frequency, rather than to the noise of the sustaining amplifier via the Leeson effect. It is therefore natural to give attention to the measurement of the resonator fluctuations.

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arXiv2006

The effect of AM noise on correlation phase noise measurements

We analyze the phase-noise measurement methods in which correlation and averaging is used to reject the background noise of the instrument. All the known methods make use of a mixer, used either as a saturated phase detector or as a linear synchronous detector. Unfortunately, AM noise is taken in through the power-to-dc-offset conversion mechanism that results from the mixer asymmetry. The measurement of some mixers indicates that the unwanted amplitude-to-voltage gain is of the order of 5-50 mV, which is 12-35 dB lower than the phase-to-voltage gain of the mixer. In addition, the trick of setting the mixer at a sweet point -- off the quadrature condition -- where the sensitivity to AM nulls, works only with microwave mixers. The HF-VHF mixers have not this sweet point. Moreover, we prove that if the AM noise comes from the oscillator under test, it can not be rejected by correlation. At least not with the schemes currently used. An example shows that at some critical frequencies the unwanted effect of AM noise is of the same order -- if not greater -- than the phase noise. Thus, experimental mistakes are around the corner.

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arXiv2006

Tutorial on the double balanced mixer

Smart use of mixers is a relevant issue in radio engineering and in instrumentation design, and of paramount importance in phase noise metrology. However simple the mixer seems, every time I try to explain to a colleague what it does, something goes wrong. One difficulty is that actual mixers operate in a wide range of power (150 dB or more) and frequency (up to 3 decades). Another difficulty is that the mixer works as a multiplier in the time-domain, which is necessary to convert frequencies. A further difficulty is the interaction with external circuits, the input sources and the load. Yet far the biggest difficulty is that designing with mixers requires a deep comprehension of the whole circuit at system level and at a component level. As the electronic-component approach is well explained in a number of references, this tutorial emphasizes the system approach, aiming to provide wisdom and insight on mixes.

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arXiv2006

On the 1/f Frequency Noise in Ultra-Stable Quartz Oscillators

The frequency flicker of an oscillator, which appears as a 1/f^3 line in the phase noise spectral density, and as a floor on the Allan variance plot, originates from two basic phenomena, namely: (1) the 1/f phase noise turned into 1/f frequency noise via the Leeson effect, and (2) the 1/f fluctuation of the resonator natural frequency. The discussion on which is the dominant effect, thus on how to improve the stability of the oscillator, has been going on for years without giving a clear answer. This article tackles the question by analyzing the phase noise spectrum of several commercial oscillators and laboratory prototypes, and demonstrates that the fluctuation of the resonator natural frequency is the dominant effect. The investigation method starts from reverse engineering the oscillator phase noise in order to show that if the Leeson effect was dominant, the resonator merit factor Q would be too low as compared to the available technology.

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arXiv2005

The Measurement of AM noise of Oscillators

The close-in AM noise is often neglected, under the assumption that it is a minor problem as compared to phase noise. With the progress of technology and of experimental science, this assumption is no longer true. Yet, information in the literature is scarce or absent. This report describes the measurement of the AM noise of rf/microwave sources in terms of Salpha(f), i.e., the power spectrum density of the fractional amplitude fluctuation alpha. The proposed schemes make use of commercial power detectors based on Schottky and tunnel diodes, in single-channel and correlation configuration. There follow the analysis of the front-end amplifier at the detector output, the analysis of the methods for the measurement of the power-detector noise, and a digression about the calibration procedures. The measurement methods are extended to the relative intensity noise (RIN) of optical beams, and to the AM noise of the rf/microwave modulation in photonic systems. Some rf/microwave synthesizers and oscillators have been measured, using correlation and moderate averaging. As an example, the flicker noise of a low-noise quartz oscillator (Wenzel 501-04623E) is Salpha = 1.15E-13/f, which is equivalent to an Allan deviation of sigma_alpha = 4E-7. The measurement systems described exhibit the world-record lowest background noise.

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arXiv2005

Flicker noise in high-speed p-i-n photodiodes

The microwave signal at the output of a photodiode that detects a modulated optical beam contains the phase noise phi(t) and the amplitude noise alpha(t) of the detector. Beside the white noise, which is well understood, the spectral densities S_phi(f) and S_alpha(f) show flicker noise, proportional to 1/f. We report on the measurement of the phase and amplitude noise of high-speed p-i-n photodiodes. The main result is that the flicker coefficient of the samples is approximately 1E-12 rad^2/Hz (-120dB) for phase noise, and approximately 1E-12 Hz^-1 (-120dB) for amplitude noise. These values could be observed only after solving a number of experimental problems and in a protected environment. By contrast, in ordinary conditions insufficient EMI isolation, and also insufficient mechanical isolation, are responsible for additional noise to be taken in. This suggests that if package and EMC are revisited, applications can take the full benefit from the surprisingly low noise of the p-i-n photodiodes.

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arXiv2005

Advanced bridge (interferometric) phase and amplitude noise measurements

The measurement of the close-to-the-carrier noise of rf and microwave devices is a relevant issue in time and frequency metrology and in some fields of electronics, physics and optics. While phase noise is the main concern, amplitude noise is often of interest. The highest sensitivity is achieved with the bridge (interferometric) method, which consists of the amplification and synchronous detection of the noise sidebands after suppressing the carrier by vector subtraction of an equal signal. A substantial progress in understanding the flicker noise mechanism of the interferometer results in new schemes that improve by 20--30 dB the sensitivity at low Fourier frequencies. The article provides the complete theory and detailed design criteria, and reports on the implementation of a prototype. In real-time measurements, a background noise of -175 -180 dBrad^2/Hz has been obtained at f=1 Hz off the 100 MHz carrier. Exploiting correlation and averaging in similar conditions, the sensitivity exceeds -185 dBrad^2/Hz at f=1 Hz. A residual noise of -203 dBrad^2/Hz at f=250 Hz off the carrier has been obtained, while the ultimate noise floor is still limited by the averaging capability of the correlator. This is equivalent to a S/N ratio of 2E20 with a frequency spacing of 2.5E-6. Applications include the measurement of the properties of materials and the observation of weak flicker-type physical phenomena, out of reach for other instruments. We measured the flicker noise of a by-step attenuator (-171 dB[rad^2]/Hz at f=1 Hz) and of the ferrite noise of a reactive power divider (-173.7 dB[rad^2]/Hz at f=1 Hz) without need of correlation.

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arXiv2005

Low flicker-noise dc amplifier for 50 Ohm sources

This article analyzes the design of a low-noise amplifier intended as the input front-end for the measurement of the low-frequency components (below 10 Hz) of a 50 Ohm source. Low residual flicker is the main desired performance. This feature can only be appreciated if white noise is sufficiently low, and if an appropriate design ensures dc stability. An optimal solution is proposed, in which the low-noise and dc-stability features are achieved at a reasonable complexity. Gain is accurate to more than 100 kHz, which makes the amplifier an appealing external front-end for fast Fourier transform (FFT) analyzers.

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arXiv2005

The Leeson effect - Phase noise in quasilinear oscillators

Time, and equivalently frequency, is the most precisely measured physical quantity. It is therefore inevitable that virtually all domains of engineering and physics need reference oscillators. The oscillator noise can be decomposed into amplitude noise and phase noise. The latter, far more important, affects timing, for it is related to precision and accuracy of measurements. The oscillator, inherently, turns the phase noise of the internal parts into frequency noise. This is a necessary consequence of the Barkhausen condition, which states that the loop gain must be of one, with zero phase, for stationary oscillation. There follows that oscillator phase noise, which is the integral of the frequency noise, diverges in the long run. This is the Leeson effect. The topics covered can be divided into three parts. Chapter 1 addresses language and general physical mechanisms. Chapter 2 aims at understanding the inside of commercial oscillators through the analysis of the specifications. Chapter 3 and 4 focus on the use of the Laplace transform to describe the oscillator and its phase noise. Since spring 2004, I had the opportunity to give some seminars on noise in oscillators at the Jet Propulsion Laboratory, at the IEEE Frequency Control Symposium, at the FEMTO-ST Laboratory, and at the Universite' Henri Poincare'. These seminars had the purpose to provide a TUTORIAL, as opposed to a report on advanced science, addressed to a variety of people including technicians, PhD students, and senior scientists. This booklet derives from these seminars, and from numerous discussions with colleagues.

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arXiv2004

On the measurement of frequency and of its sample variance with high-resolution counters

A frequency counter measures the input frequency $\barν$ averaged over a suitable time $τ$, versus the reference clock. High resolution is achieved by interpolating the clock signal. Further increased resolution is obtained by averaging multiple frequency measurements highly overlapped. In the presence of additive white noise or white phase noise, the square uncertainty improves from $\smash{σ^2_ν\propto1/τ^2}$ to $\smash{σ^2_ν\propto1/τ^3}$. Surprisingly, when a file of contiguous data is fed into the formula of the two-sample (Allan) variance $\smash{σ^2_y(τ)=\mathbb{E}\{\frac12(\bar{y}_{k+1}-\bar{y}_k) ^2\}}$ of the fractional frequency fluctuation $y$, the result is the \emph{modified} Allan variance mod $σ^2_y(τ)$. But if a sufficient number of contiguous measures are averaged in order to get a longer $τ$ and the data are fed into the same formula, the results is the (non-modified) Allan variance. Of course interpretation mistakes are around the corner if the counter internal process is not well understood.

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