1/f noise in etched groove surface acoustic wave (SAW) resonators

Measurements of 1/f (or flicker) frequency fluctuations in SAW resonators fabricated with etched groove reflectors on single crystal quartz have shown that the observed noise levels vary inversely with device size. These measurements were made on sixteen 450 MHz resonators of four different sizes. The 1/f noise levels were also evaluated on twenty-eight other SAW resonators ranging in frequency from 401 to 915 MHz. This additional data provides valuable information on the dependence of the flicker noise levels on resonator frequency. A model based an localized, independent velocity fluctuations in the quartz is proposed which correctly fits the observed size and frequency dependence of the measured 1/f noise levels. This model suggests that the velocity fluctuations originate in small regions (much less than ~5 mum in diameter) randomly distributed throughout the quartz with an average separation of about 5 mum between independent (incoherent) sources. The magnitude of the localized fractional velocity fluctuations, Deltav/v, averaged over a 5 micron cube is on the order of 1x10 (-9).     

Modeling of a short-term stability measuring system of quartz crystal resonators

A new numerical model of a short-term stability measuring system of quartz crystal resonators is presented. It is based on the phase bridge method using a pair of resonators driven by a low-noise source. The output signal, obtained with a phase detector, is proportional to the phase difference introduced by the resonators. The numerical transfer function of each bridge path is given by the model. The output spectral density of the phase fluctuations is computed from these transfer functions and the numerical approximation of the low-noise source. The model was applied to third overtone, SC-cut, 10 MHz BVA quartz crystal resonators. It enables the rejection of the source noise versus the resonant frequency of quartz crystal resonators to be quantified.     

Phase noise measurements of 10-MHz BVA quartz crystal resonators

In this paper, we review a new piece of equipment that allows one to characterize the phase noise of crystal resonators using a phase bridge system with carrier suppression. This equipment allows one to measure the inherent phase stability of quartz crystal resonators in a passive circuit without the noise usually associated with an active oscillator. We achieved a system noise floor of approximately -150 dBc/Hz at 1 Hz and -160 dBc/Hz, at 10 Hz. A SPICE characterization of the carrier suppression system is given. An investigation of the phase modulation (PM) noise in 10 MHz BVA, SC-cut quartz crystal resonator pairs is presented.     

Frequency performances of a miniature optically pumped cesium beam frequency standard

The optically pumped cesium beam clock named Cs IV is operated with a new short Ramsey cavity satisfying strict requirements on the microwave leakage level. The most relevant characteristics of the device are presented. Cs IV is presently driven by standard electronics coming from a HP 5061 B clock that provides a sinusoidal modulation of the interrogation microwave signal and a microwave power stability of about 1% at a temperature of 20+/-1 degrees C. The short- and medium-term frequency stability measurement gives sigma(y)(1 day)=2x10(-14): this value holds up to 3 days. The accuracy evaluation results in an uncertainty of 10(-12), and the repeatability is evaluated to 3x10(-13). It appears that the flicker floor is beginning at 2x10(-14) and is mainly due to both the power fluctuations of the free running microwave interrogating signal and the fluctuations of the external static magnetic field. The accuracy is limited by the lack of knowledge of the end-to-end cavity phase shift.     

Short-Term Frequency Stability of Relaxation Crystal Oscillators

Due to the need for stable frequency rectangular wave signals, various relaxation quartz crystal oscillators were designed. Therefore it is of interest to have data on their short-term frequency stability. The generally accepted definitions of measures for short-term frequency stability and measurement procedures are reviewed in this paper. Measurement results for the short-term frequency stability of quartz crystal multivibrators in time and frequency domains show a high spectral purity of the multivibrator output signal. The single-sideband-to-carrier phase noise has values lower than -90 and -120 dB on the offset frequencies of 1 and 10 Hz, respectively. The white phase noise is about -160 dB. The power law spectral density model of fractional frequency fluctuations for the quartz multivibrators is established and a discussion on the noise sources is given.     

Doubly rotated resonators for sensing the properties of liquids

When a doubly rotated resonator is operated in a liquid, the displacement of the surface is partly out of the plane of the plate of the resonator. The out-of-plane component of the displacement propagates a damped compressional wave into the liquid, and the in-plane component propagates a damped shear wave. In this paper, we report the measurements of the series resonant frequency and the motional arm resistance of doubly rotated quartz resonators (theta approximately 35 degrees and phi = 7 degrees) in liquids to compare with singly rotated AT-cut resonators (theta approximately 35 degrees and phi = 0 degrees). A modified Butterworth-Van Dyke (BVD) equivalent circuit model is suggested to analyze doubly rotated cut resonators under liquid loading.     

Predicting phase noise in crystal oscillators

In order to predict the phase noise in crystal oscillators an enhanced phase-noise model has been built. With this model, the power spectral densities of phase fluctuations can be computed in different points of the oscillator loop. They are calculated from their correlation functions. The resonator-caused noise as well as the amplifier-caused noise are taken into account and distinguished. To validate this enhanced model, the behavior of a batch of 10 MHz quartz crystal oscillators is observed and analyzed. The tested batch has been chosen in a facility production. Their associated resonators have been selected according to the value of their resonant frequency and their motional resistance. Open-loop and closed-loop measurements are given. The phase noise of the overall oscillator working in closed loop is provided by the usual active method. Theoretical and experimental results are compared and discussed.     

Reduction of quartz crystal oscillator flicker-of-frequency and white phase noise (floor) levels and acceleration sensitivity via use of multiple resonators

Through the use of N series-connected quartz crystal resonators in an oscillator circuit, a 10 log N reduction in both flicker-of-frequency noise and white phase-noise (floor) levels has been demonstrated. The reduction in flicker noise occurs as a result of the uncorrelated short-term frequency instability in each of the resonators, and the reduction in noise floor level is a simple result of the increase in net, allowable crystal drive level. This technique has been used in 40-, 80-, and 100-MHz AT-, BT-, and SC-cut crystal oscillators using low flicker-of-phase noise modular amplifier sustaining stages, and four series connected crystals. Total (four crystal) power dissipations of up to 30 mW have been utilized. State-of-the-art, flicker-of-frequency noise levels have been obtained with noise-floor levels (80 MHz) as low as -180 dBc/Hz. Four- to five-fold reduction in acceleration sensitivities has been determined     

On the flicker noise of ferrite circulators for ultra-stable oscillators

The flicker noise of the ferrite circulator is a critical element in ultra-stable microwave oscillators, in which the signal reflected from the input of the reference cavity is exploited to stabilize the frequency. This paper explains why the circulator noise must be measured in isolation mode, proposes a measurement scheme, and provides experimental results. The observed flicker spans from -162 to -170 dB[rad2]/Hz at 1 Hz off the 9.2 GHz carrier, and at +19 dBm of input power. In the same conditions, the instrument limit is below -180 dB[rad2]/Hz. Experiments also give information on the mechanical stability of the microwave assembly, which is in the range of 10(-11) m. The measurement method can be used as the phase detector of a corrected oscillator; and, in the field of solid-state physics, it can be used for the measurement of random fluctuations in magnetic materials.     

Broad tuning ultra low phase noise dielectric resonator oscillators using SiGe amplifier and ceramic-based resonators

This paper describes the design of very low noise, tunable, X-band dielectric resonator oscillators (DROs) demonstrating phase-noise performance of -135 dBc/Hz at 10 kHz offset. SiGe transistors are used for the oscillator sustaining amplifiers that offer a circulating power of 12 dBm and a gain of 5.4 dB per stage as well as a low flicker noise corner of 40 kHz. A variety of resonator configurations utilising BaTiO₃ resonators are presented demonstrating unloaded Qs from 10 000 to 22 000. These resonators are optimised and coupled to the amplifiers for minimum phase noise where Q_L/Q₀ = 1/2, and hence S₂₁ = -6 dB. To incorporate tuning with low additional phase noise, a phase shifter is also investigated. The theory for the low noise oscillator design is included; experimental results demonstrate close correlation with the theory.     

Measurement of the Short-Term Stability of Quartz Crystal Resonators and the Implications for Crystal Oscillator Design and Applications

A new technique is presented which makes it possible to measure the inherent short-term stability of quartz crystal resonators in a passive circuit. Comparisons with stability measurements made on crystal controlled oscillators indicate that noise in the electronics of the oscillators very seriously degrades the inherent stability of the quartz resonators for times less than 1 s. A simple model appears to describe the noise mechanism in crystal controlled oscillators and points the way to design changes which should improve their short-term stability by two orders of magnitude. Calculations are outlined which show that with this improved short-term stability it should be feasible to multiply a crystal controlled source to 1 THz and obtain a linewidth of less than 1 Hz. In many cases, this improved short-term stability should also permit a factor of 100 reduction in the length of time necessary to achieve a given level of accuracy in frequency measurements.     

Quantum 1/f effect in resonant biochemical piezoelectric and MEMS sensors

Piezoelectric sensors used for the detection of chemical agents and as electronic nose instruments are based on bulk and surface acoustic wave resonators. Adsorption of gas molecules on the surface of the polymer coating is detected by a reduction of the resonance frequency of the quartz disk, subject also to fundamental quantum 1/f frequency fluctuations. The quantum 1/f limit of detection is given by the quantum 1/f formula for quartz resonators. Therefore, for quantum 1/f optimization and for calculation and improvement of the fundamental sensitivity limits, we must avoid closeness of the crystal size to the phonon coherence length, which corresponds to the maximum error and minimal sensitivity situation, as shown here. Adsorbed masses below the pg range can be detected. Microelectromechanical system (MEMS) resonators have provided a possibility for the nanominiaturization of these sensors. Essential for integrated nanotechnology, these resonant silicon bars (fingers) are excited magnetically or electrically through external applied forces, since they are not piezoelectric or magnetostrictive. The application of the quantum 1/f theory to these systems is published here for the first time. It provides simple formulas that yield much lower quantum 1/f frequency fluctuations for magnetic excitation, in comparison with electrostatically driven MEMS resonators.     

A Digital Instrument for Light Flicker Effect Evaluation

The voltage waveform in an electric power system usually presents a fluctuation due to the intermittent operation of nonlinear devices. In some cases, the frequency and width of these voltage variations can produce a physiologically irritating phenomenon due to luminance fluctuations of the lighting (flicker effect). In addition to the visual inconvenience, some of the electrical equipment can be strongly disturbed. The International Electrotechnical Commission standardized the implementation of a flickermeter based on the simulation of the process of physiological visual perception to supply information about the human reaction to voltage amplitude modulation. A standard parameter (i.e., the flicker severity index P_st) is obtained from the cumulated probability function of the instantaneous perception. In this paper, a different measurement approach for the flicker effect evaluation is proposed. It is based on the calculation of the luminous variation perception function by processing digital samples of the acquired voltage. The choice of this technique is motivated by the aim of simplifying the flickermeter implementation and reducing the hardware requirements. A prototype of the instrument has been implemented, and the performance has been evaluated, by means of direct comparison with standard flickermeters. In this paper, the main results are also reported.     

The use of thermosensitive quartz sensor for thermal regulation at cryogenic temperatures: application to microwave sapphire resonator references

We demonstrated the use of thermosensitive quartz resonator oscillator as a thermal sensor for temperature control at the liquid nitrogen temperature. The high sensitivity of the quartz enables an efficient thermal regulation at ambient temperature as well as liquid nitrogen temperature. LC-cut quartz oscillator phase noise measurements show that the temperature measurement resolution is not limited by the intrinsic noise of the sensor and that a resolution of 10 muK can be achieved. This thermal regulation is applied to control a microwave temperature-compensated sapphire resonator oscillator at a temperature above 77 K, enabling the achievement of a flicker floor of 9.10(-13 ) at 9 GHz.     

Development of a 10 MHz oscillator working with an LGT crystal resonator: preliminary results

Presently, to our knowledge, measurement of the noise of langatate (LGT) crystal oscillators has not previously been reported. First results of such a measurement are given in this paper. They have been obtained from 10 MHz resonator prototypes tested with a dedicated electronics. The main steps of the resonator manufacturing are described in this paper. Good quality factors, close to 1.4 10(6), have already been achieved on the 5th overtone of the thickness shear mode of LGT Y cuts, even if the energy trapping should still be optimized. The motional parameters of these resonator prototypes are quite different from those of usual quartz crystal resonators. As a consequence, dedicated sustaining electronics have been designed. The explored options are reported to justify the implemented one. Moreover, the high thermal sensitivity of LGT crystal resonators (parabolic f-T curve) requires that particular attention be paid to the oven thermal stability. This important feature is also pointed out in the paper. The preliminary version of the resulting system exhibits a relative frequency stability of 6 10(-12).     

Investigations on LGS and LGT crystals to realize BAW resonators

The LGS family are promising materials for the design of high quality bulk acoustic wave resonators. We have manufactured many plano-convex 10 MHz 5th overtone Y-cut resonators using langasite (LGS, La₃Ga₅SiO₁₄) and langatate (LGT, La₃Ga_5.5Ta_0.5O₁₄) crystals. We observed that the quality factor strongly depends on the polishing method, the supplier of the material, and on the energy trapping. For quartz crystals, we have found that resulting IR spectra exhibit absorption peaks more or less deep, linked to defects. These predominant criteria are not surprising, but they have to be defined in manner similar to that used for quartz crystal. A satisfying machining and polishing method has been first applied to elaborate high Q resonators, and a comparison between samples of LGS and LGT materials from different suppliers is established. In addition, LGT resonators are characterized by their motional parameters and frequency-temperature curves. Nevertheless, one of the main results is that the measured Q × f product is not the expected one. We present results of Q-factor versus radius of curvature: it appears that an optimization should be performed and that this last one cannot be directly transposed from that of quartz crystal resonator. Currently, the best resonator that we have made has a Q × f product of 1.4 × 10¹³ on its 5th overtone (1.7 × 10¹³ on its 9th overtone). This result is slightly higher than the similar parameter obtained on a state-of-the-art SC-cut quartz crystal resonator working at the same frequency.     

Quartz crystal oscillator at very low temperature

The most significant results concerning quartz crystal resonators and semiconductors properties at liquid helium temperature are presented. A cryogenic quartz oscillator is realized with these elements and some values of its frequency stability are given.     

Relationship of AM to PM noise in selected RF oscillators

We have studied the amplitude modulation (AM) and phase modulation (PM) noise in a number of 5 MHz and 100 MHz oscillators to provide a basis for developing models of the origin of AM noise. To adequately characterize the AM noise in high performance quartz oscillators, we found it necessary to use two-channel cross-correlation AM detection. In the quartz oscillators studied, the power spectral density (PSD) of the f(-1) and f(0) regions of AM noise is closely related to that of the PM noise. The major difference between different oscillators of the same design depends on the flicker noise performance of the resonator. We therefore propose that the f(-1) and f(0) regions of AM and PM noise arise from the same physical processes, probably originating in the sustaining amplifier.     

Employing stochastic models for prediction of arc furnace reactive power to improve compensator performance

The time-varying nature of electric arc furnace (EAF) gives rise to voltage fluctuations, which produce the effect known as flicker. the ability of a static var compensator (SVC), a widely used method for flicker reduction, is limited by delays in reactive power measurements and thyristor ignition. to improve the SVC performance in flicker compensation, a technique for the prediction of EAF reactive power for a half cycle ahead is presented. this technique is based on a new procedure for stochastic modelling of EAF reactive power at an SVC bus. this procedure uses huge field data, collected from eight arc furnaces, to determine the most suitable signal among several candidate signals in view of eaf reactive power prediction. in addition, appropriate orders of autoregressive moving average models are found for reactive power time series. for this purpose, various model adequacy checking methods and some other stochastic analysis methods have been applied on data records. the performance of the compensator in the case of employing predicted fundamental reactive power of an EAF is compared with that of the conventional method by using three new indices that have been defined based on concepts of flicker frequencies and the power spectral density.     

SAW oscillator frequency stability at high temperatures

A broad overview of various factors affecting the frequency stability of surface-acoustic-wave (SAW) resonators is given. Two major causes of rapid degradation in the long-term frequency stability are the presence of a chromium interface between aluminum and quartz, and moderate to high drive levels in SAW devices with pure aluminum fingers, resulting in metal migration in the region of high thin-film stresses. On the other hand, devices with copper-doped aluminum electrodes maintained excellent long-term stability, even when operating at 175 degrees C and at moderately high drive levels. Experimental data on both the long-term and short-term frequency stabilities of SAW devices at 25 degrees C and 175 degrees C for moderate to high drive levels are presented. Results obtained for the frequency stabilities of SAW devices with pure aluminum and copper-doped aluminum electrodes are compared. It is shown that the short-term frequency stability of SAW devices with copper-doped aluminum electrodes is a few parts in 10(10), even at 175 degrees C and for moderately large drive levels. Overall, the best short-term frequency stability is found to be for a gate time of 0.1 s.