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.     

Analysis of aging of piezoelectric crystal resonators

Aging of piezoelectric (quartz crystal) resonator has been identified as one of the most important quality control problems of quartz crystal products. Aging is defined as frequency change with time. Aging in quartz resonators can be due to several sources: mass transfer due to contamination inside the resonator enclosure, stress-strain in the resonator blank, quartz defect, etc. In this study, the stress-strain effect, which has been believed as a dominant factor contributing to aging, is studied. The stress-strain effect is caused mainly by the long-term viscoelastic properties of bonding adhesive that attach quartz crystal plate to the ceramic base package. With the available accelerating testing method under elevated temperatures, the stress-strain induced aging in the quartz crystal resonators can be investigated. Because of the miniaturized size of the resonator, a digital image analysis method called image intensity matching technique (IIMT) is applied to obtain deformation patterns in the quartz blank due to thermal load. Our preliminary results showed that the unsymmetric thermal deformations may be a dominant contributing factor to aging. For simulation purposes, finite-element analysis is used to investigate the deformation patterns (i.e., stress-strain distributions) and corresponding natural frequency shift in the piezoelectric resonators. The viscoelastic behavior of mounting adhesives is incorporated into the analysis to show the dominant effect of long-term behavior of stress-strain developed in the crystal resonators. Also, some geometrical aspects-such as uneven mounting supports due to distances, volumes and heights of the adhesives-are simulated in the model.     

HF and VHF Source Stabilization Technique Incorporating Q-Multiplied Quartz Crystal Resonator

A new approach is described for the desiga of HF/VHF crystal-controlled frequency sources exhibiting theoretical short-term stability unattainable through the use of conventional quartz oscillator design. The signal generator design uses the concept of AFC stabilization of a conventional quartz oscillator (VCXO) by means of a crystal-controlled highly selective active frequency reference. The AFC reference is a phase-shift type frequency discriminator that employs a product detector and an active Q-multiplied quartz crystal resonator. The extremely selective transmission response, large group delay, and power gain exhibited by the resonator, together with resonator phase noise levels comparable to that exhibited by the oscillator-maintaining circuit, provide the principal means for prediction of superior output signal spectral purity. Models of the resonators have been designed and constructed at 30 and 80 MHz, exhibiting 3-dB bandwidths of 30 and 160 Hz, respectively. Based on actual measurement of VHF Q-multiplied crystal resonator performance characteristics, approximately 16 dB improvement in VHF crystal-controlled frequency source spectral purity at low and moderate modulation rates is possible, compared to that attainable using the best available VHF quartz oscillator circuit designs.     

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.     

Resonant frequency function of thickness-shear vibrations of rectangular crystal plates

The resonant frequencies of thickness-shear vibrations of quartz crystal plates in rectangular and circular shapes are always required in the design and manufacturing of quartz crystal resonators. As the size of quartz crystal resonators shrinks, for rectangular plates we must consider effects of both length and width for the precise calculation of resonant frequency. Starting from the three-dimensional equations of wave propagation in finite crystal plates and the general expression of vibration modes, we obtained the relations between frequency and wavenumbers. By satisfying the major boundary conditions of the dominant thickness-shear mode, three wavenumber solutions are obtained and the frequency equation is constructed. It is shown the resonant frequency of thickness-shear mode is a second-order polynomial of aspect ratios. This conforms to known results in the simplest form and is applicable to further analytical and experimental studies of the frequency equation of quartz crystal resonators.     

Quartz crystal resonator g sensitivity measurement methods and recent results

A technique for accurate measurements of quartz crystal resonator vibration sensitivity is described. The technique utilizes a crystal oscillator circuit in which a prescribed length of coaxial cable is used to connect the resonator to the oscillator sustaining stage. A method is provided for determination and removal of measurement errors normally introduced as a result of cable vibration. In addition to oscillator-type measurements, it is also possible to perform similar vibration sensitivity measurements using a synthesized signal generator with the resonator installed in a passive phase bridge. Test results are reported for 40 and 50 MHz, fifth overtone AT-cut, and third overtone SC-cut crystals. Acceleration sensitivity (gamma vector) values for the SC-cut resonators were typically four times smaller (5x10(-10) per g) than for the AT-cut units. However, smaller unit-to-unit gamma vector magnitude variation was exhibited by the AT-cut resonators. Oscillator sustaining stage vibration sensitivity was characterized by an equivalent open-loop phase modulation of 10(-6) rad/g.     

Application of the photo-elastic method to measurement of dynamicstress distribution for NS-GT cut quartz crystal resonators

NS-GT cut quartz crystal resonators are widely used as a frequency standard element in consumer products and communication equipment. The vibration mode of the resonators was analyzed by the finite element method (FEM) because they have a complicated shape. As a result, an asymmetrical vibration mode at the main resonant frequency has been obtained by the FEM simulation. But, it is necessary to confirm the asymmetrical vibration mode experimentally because it is just a simulation. In this paper, stress distributions of the NS-GT cut quartz crystal resonators are measured experimentally by using a dynamic photo-elastic method when the resonators are vibrating in the resonant frequency; thereafter, vibration modes of the NS-GT cut resonators are estimated with the experimental data of the stress distributions. This experiment for the NS-GT cut quartz crystal resonators exposes the existence of a twisted asymmetrical vibration mode at the main resonant frequency, with the magnitude of the twisted vibration in proportion to thickness of the resonators     

An X-ray double crystal topographic assessment of defects in quartz resonators

This paper describes an X-ray double crystal topographic study of defects in eighteen quartz resonators designed to operate at 1.4 MHz. The types of defects found in quartz are described, together with their reported effects on resonator performance. The mode of operation of the bulk resonator and the technique of X-ray double crystal reflection topography are outlined. Topographs reveal the electrode structures and surface features of the resonators together with the presence of growth defects such as dislocation cells, sub-boundaries, growth striations and growth sector boundaries. Spurious flexure modes in two resonators are also shown. It is demonstrated that a correlation exists between the presence of growth striations (and probably sub-boundaries) and a higher equivalent series resistance of the resonators. It is shown that such defects change the contributions to the losses, possibly by changing the nature of the vibration pattern of the resonator.     

石英晶体振荡器加速度效应及敏感度的测试

石英晶体振荡器因其具有频率稳定度高的特点,作为标准频率源或脉冲信号源提供频率基准是目前其它类型的振荡器所不能替代的.而加速度对晶振输出频率影响的补偿问题目前还没有得到很好解决,加速度已成为当前影响晶体振荡器准确度的重要因素.本文简要介绍了加速度对晶体频率的影响,国内外加速度敏感度的测试方法及其改进方法,并以实验验证,取得了较好的效果.     

Is an oscillator-based measurement adequate in a liquid environment?

Oscillator-based measurements with quartz crystal resonators are analyzed. The investigations have shown that classical thickness monitors as well as many chemical vapor sensors based on a quartz crystal microbalance (QCM) work properly, even with simple oscillators. It was demonstrated that, for applications in a liquid environment, more sophisticated electronics are necessary. Also a comparison between the experimental results in liquids and the theoretical predictions is hardly possible without the knowledge of the oscillator behavior. As our solution, we present an automatic gain-controlled oscillator with two output signals, the oscillator frequency, and a signal that represents the damping of the quartz resonator. A calibration method is introduced, which allows one to calculate the series resonance frequency f/sub s/ and the series resistance R/sub s/ from these oscillator signals.     

A Frequency-Lock System for Improved Quartz Crystal Oscillator Performance

The intrinsic noise of the best quartz crystal resonators is significantly less than the noise observed in oscillators employing these resonators Several problem areas common to traditional designs are pointed out and a new approach is suggested for their solution. Two circuits are described which frequency lock a spectrally pure quartz crystal oscillator to an independent quartz crystal resonator. The performance of the composite system is predicted based on the measured performance of its components.     

A new method for continuous monitoring of series resonance frequency and simple determination of motional impedance parameters for loaded quartz-crystal resonators

A new electronic design for continuous motional series resonant frequency monitoring of loaded quartz crystal resonators is presented. Using this circuit, a low-cost method for a simple determination of equivalent circuit parameters of quartz crystal resonators is described. Measurements made with the proposed system on typical AT cut quartz crystals are in good agreement with those of an Impedance Analyzer.     

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.     

A 2*4 all optical decoder switch based on photonic crystal ring resonators

Based on photonic crystal ring resonators and nonlinear Kerr effect in this paper, we proposed a 2*4 all optical decoder switch. Our proposed structure has two logic input ports and one bias input port. This decoder switch has four output ports. Via these two logic input ports, we control the bias signal to transfer toward which output port. We employed numerical methods such as plane wave expansion and finite difference time domain methods for analyzing the proposed structure.     

The frequency-temperature analysis equations of piezoelectric plates with Lee plate theory

Frequency-temperature analysis theory of crystal plates based on the incremental field theory (IFT) and the Mindlin plate theory have been widely used in the vibration analysis of crystal resonators subject to temperature change. As one of the two major plate theories for the resonator analysis, the Lee plate theory based on the trigonometric series expansion of displacements has been extensively used for both analytical and numerical analyses of quartz resonators, and efforts have also been made in correcting and perfecting the theory for much broader applications. In this paper, the earlier frequency-temperature analysis equations based on the IFT is further extended to the trigonometric series expansion in a systematic manner. By incorporating the frequency-temperature analysis into the Lee plate theory, the complete analysis of crystal resonators can be made in a consistent way. The thickness-shear and flexural vibration equations have been compared with the Mindlin plate theory to demonstrate the similarity and consistency.     

Excitation of quartz lenses with clearances in a parallel field

Conclusions The quartz resonators described above can be used for investigating certain physical phenomena. Their main advantage consists in their translucence under oscillatory conditions to light, x-ray, and other radiations. For instance, by transmitting light rays through an oscillating quartz crystal it is possible to observe their diffraction on an ultrasonic grid, and by transmitting through that crystal x-rays it is possible to observe the relaxation of microstresses in a crystal lattice after the application of the exciting force is stopped. It would appear that this method may prove useful in investigating problems related to the pressure of light, and the excitation of quartz crystals by an UHF power transmitted through them. The possibility of making highly-sensitive detectors and instruments on this basis is not excluded.     

Influence of a magnetic field on quartz crystal resonators

The magnetic sensitivity of quartz crystal resonators is a consequence of the ferromagnetic properties of the metal used as support for the vibrating plate. Various magneto-mechanic interactions can contribute to the overall sensitivity, the most important of which is shown to be the change in Young's modulus of the spring material submitted to a magnetic field, which in turn modifies the stress in the quartz plate and then induces a change in the crystal resonant frequency. The experimental setup and procedure are described and a large number of experimental results obtained with resonators of different technologies are presented and discussed. A comparison between the magnetic behavior of identical resonators mounted with different materials definitely proves the responsibility of the supports in the magnetic sensitivity of resonators and gives interesting information on its reduction     

Multichannel quartz crystal microbalance

Arrays of quartz crystal resonators are fabricated on a single quartz wafer as a multichannel quartz crystal microbalance (MQCM). Three types of four-channel array of 10-MHz resonators are prepared and tested. Mechanical oscillation of each channel is entrapped within the channel almost completely, so that the interference between the channels via the quartz crystal plate is almost negligible. A mass change on each channel is quantitatively evaluated on the basis of Sauerbrey's law. Thus, each channel of a MQCM device can be used as an independent QCM. Influence from a longitudinal wave generated from another channel is also negligible compared to the influence from the wave from the monitored channel itself. The simultaneous oscillation of channels is also possible. The potential applicability of MQCM to the two-dimensional mapping of mass changes is demonstrated.     

An analysis of nonlinear vibrations of coupled thickness-shear and flexural modes of quartz crystal plates with the homotopy analysis method

We investigated the nonlinear vibrations of the coupled thickness-shear and flexural modes of quartz crystal plates with the nonlinear Mindlin plate equations, taking into consideration the kinematic and material nonlinearities. The nonlinear Mindlin plate equations for strongly coupled thickness- shear and flexural modes have been established by following Mindlin with the nonlinear constitutive relations and approximation procedures. Based on the long thickness-shear wave approximation and aided by corresponding linear solutions, the nonlinear equation of thickness-shear vibrations of quartz crystal plate has been solved by the combination of the Galerkin and homotopy analysis methods. The amplitude frequency relation we obtained showed that the nonlinear frequency of thickness-shear vibrations depends on the vibration amplitude, thickness, and length of plate, which is significantly different from the linear case. Numerical results from this study also indicated that neither kinematic nor material nonlinearities are the main factors in frequency shifts and performance fluctuation of the quartz crystal resonators we have observed. These efforts will result in applicable solution techniques for further studies of nonlinear effects of quartz plates under bias fields for the precise analysis and design of quartz crystal resonators.     

Linear frequency tuning of SAW resonators

Frequency tuning in SAW (surface acoustic wave) resonator-stabilized oscillators is normally accomplished via utilization of a voltage-controlled phase shifter. The design of abrupt junction varactor diode-inductor networks which employ impedance transformation techniques to obtain linear frequency tuning of two-port SAW resonators is reported. The approach is similar to that previously developed for linear tuning of bulk wave, quartz crystal resonators. This technique uses varactor diode parallel inductance to provide a linear reactance versus voltage network, which is effectively connected in series with the resonator motional impedance in order to tune the effective resonator center frequency. Typical tuning ranges are significantly larger than those achievable using the phase shifter approach, and are on the order of 400 ppm for the 320-MHz resonator used.