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.     

Phase noise measurements in dual-mode SC-cut crystal oscillators

This paper describes the phase-noise characteristics and the analysis model of an SC-cut dual-mode oscillator. The C mode phase-noise sideband levels of -124 dBc at 10 Hz and -154 dBc at 10 kHz have been demonstrated using a dual-mode oscillator that simultaneously excited the C and B mode of a 10-MHz, third overtone, SC-cut crystal resonator. Based on Leeson's model, a phase-noise analysis model for dual-mode oscillators has been proposed also. Actual phase-noise levels of the C mode in dual-mode oscillation corresponded well to results calculated from the proposed model.     

A simple method for SC-cut resonator design

Presents a design method utilizing simple semi-empirical equations for round, plano-convex SC-cut resonators. These equations were developed on the basis of experimental results, collected over a long period, relating SC-cut resonator design and performance covering a wide range of frequencies, radii of curvature, and plate diameters. The equations make possible the design of fundamental, third overtone, and fifth overtone resonators. An example calculation of resonator parameters and comparison with experimental results are also presented     

Two-Stage Self-Limiting Series Mode Type Quartz-Crystal Oscillator Exhibiting Improved Short-Term Frequency Stability

A simplified model of the transistor sustaining stage employed in common quartz-crystal oscillators is presented. Examination of the model, including associated noise sources, provides an explanation for general differences observed in the output-frequency spectra of several types of widely used self-limiting crystal oscillator circuits. A self-limiting quartz-crystal oscillator circuit configuration is described that has been specifically designed to exhibit simultaneously each of the three important circuit characteristics necessary for improved oscillator short-term frequency/phase stability: large value of oscillator resonator loaded Q, adequate suppression of 1/f flicker-of-phase type noise, and improvement in oscillator ultimate signal-to-noise ratio. Several models of the oscillator circuit have been constructed employing high quality third overtone 5-MHz AT- and BT-cut quartz resonators. Measurement of oscillator short-term frequency stability using conventional phase lock and sampling techniques confirm attainment of substantial improvement in oscillator short-term frequency stability when compared to conventional self-limiting oscillator circuits.     

A temperature insensitive quartz microbalance

Mass deposition onto a microbalance is generally accompanied by a temperature change. By measuring a single frequency only, it is not possible to separate the frequency change due to mass change from that due to temperature change. In the temperature insensitive microbalance technique, measurements of two frequencies, the fundamental mode and third overtone frequencies of an SC-cut resonator, yield two equations with two unknowns. This allows the separation of mass change effects from temperature change effects. Dual mode excitation can be used for highly accurate resonator self-temperature sensing over wide temperature ranges. SC-cut resonators are also thermal transient compensated. These unique properties allowed the development of a temperature compensated microbalance that is highly sensitive to mass changes, which can be used in rapidly changing thermal environments, over wide temperature ranges, and which requires neither temperature control nor a thermometer other than the resonator. To demonstrate the performance of this microbalance, SC-cut resonators were coated with thin polymethylmethacrylate (PMMA) photoresist films then placed into a UV-ozone cleaning chamber that initially was at about 20 degrees C. When the UV lamp was turned on, the UV-ozone removed PMMA from the surfaces while the chamber temperature rose to about 60 degrees C. The frequency changes due to mass changes could be accurately determined, independently of the frequency changes due to temperature changes.     

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.     

Dynamic measurement of amplitude-frequency effect of VHF resonators

Dynamic amplitude-frequency effect measurements made of VHF quartz resonators indicate the presence of two separate mechanisms, the relative contribution of which varies for different cuts. For the SC-cut a step-change in drive level leads to a frequency shift with very short time constant (1 ms) that is presumably the classic direct nonlinear elastic effect. Others such as AT-, BT-, and LD-cuts show only a much longer time constant (200 ms), presumably a thermally related indirect nonlinear elastic effect. Near the SC-cut, resonators exhibit a combination of both short- and long-time-constant frequency changes. In some cases the two mechanisms produce frequency shifts in opposite directions. This behavior is problematic for some amplitude-frequency-effect measurement approaches because the measured shift depends on the timing of those measurements. It is not surprising that the SC-cut response shows only the direct nonlinear elastic effect, but it is unexpected that the AT- and BT-cuts appear not to show such effect. These results raise a question as to what amplitude-frequency effect criterion is appropriate to use, as well as whether it is proper to determine nonlinear elastic constants from AT-cut resonator measurements that assume the effect is not thermally related.     

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     

High-frequency overtone TCXO based on mixing of dual crystal oscillators

To implement a high-stability and high-frequency overtone temperature-compensated crystal oscillator (TCXO) conveniently, an improved design of the novel overtone TCXO is described in this paper. A 120-MHz TCXO based on mixing of dual crystal oscillators is implemented. It utilizes a 100-MHz AT-cut 5th-overtone crystal oscillator mixed with a 20-MHz AT-cut voltage-controlled crystal oscillator (VCXO). The 120-MHz mixed product is filtered to produce the output signal. The total frequency deviation of 20-MHz and 100-MHz crystal oscillators is compensated by adjusting the output frequency of the 20-MHz oscillator to produce the stable 120-MHz output frequency. In this work, verifying experimental results of the compensation are presented. The stability of the experimental 120-MHz overtone TCXO with microprocessor temperature compensation achieves +/-2 X 10(-7) over the temperature range from -30 degrees C to +70 degrees C. A phase noise level of -133 dBc/Hz at 1 kHz offset has been initially measured for the prototype TCXO. The experimental result demonstrates this approach can conveniently implement the high-frequency overtone temperature compensation with a relatively high stability, and it is available for a wider frequency range as well.     

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.     

Extremely low phase noise UHF oscillators utilizing high-overtone, bulk-acoustic resonators

High-overtone, bulk acoustic resonators (HBAR) have been designed that exhibit 9-dB insertion loss and loaded Q values of 80000 at 640 MHz with out-of-phase resonances occurring every 2.5 MHz. These resonators have been used as ovenized frequency-control elements in very low phase noise oscillators. The oscillator sustaining stage circuitry incorporates low-1/f noise modular RF amplifiers, Schottky-diode ALC, and a miniature 2-pole helical filter for suppression of HBAR adjacent resonant responses. Measurement of oscillator output signal flicker-of-frequency noise confirms that state-of-the-art levels of short-term frequency stability have been obtained. Sustaining stage circuit contribution to resulting oscillator flicker-of-frequency noise is 7-10 dB below that due to the resonators themselves. At 16-dBm resonator drive, an oscillator output signal white phase noise floor level of -175 dBc/Hz is achieved.     

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).     

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.     

Force-frequency effect of Y-cut langanite and Y-cut langatate

Most recently, langasite and its isomorphs (LGX) have been advanced as potential substitutes for quartz, owing to their extremely high-quality (Q) factors. At least twice higher Q value of LGX than that of quartz has been reported. High Q translates into potentially greater stability. In order to make such materials practical, the environmental sensitivities must be addressed. One of such sensitivities is the force-frequency effect, which relates the sensitiveness of a resonator to shock and vibration via the third-order (non-Hookean) elastic constants. In this paper, we report measured force-frequency coefficients of a Y-cut langanite (LGN) resonator and a Y-cut langatate (LGT) resonator as a function of the azimuthal angle, which is the angle between the crystalline X-axis of a resonator plate and the direction of in-plane diametric force applied to the periphery of the resonator. It was found that the LGN and the LGT behave like AT-cut quartz in the polarity of the frequency changes and the existence of zero-coefficient angle. The maximum magnitudes of the coefficients of the LGN and the LGT are five and seven times smaller than that of stress-compensated cut (SC-cut) quartz, respectively (or, 7 and 10 times smaller comparing to AT-cut quartz). The coefficients of planar-stress, which represent the superposition of a continuous distribution of periphery stresses, also were obtained as 0.52/spl times/10/sup -15/ m/spl middot/s/N and 0.38/spl times/10/sup -15/ m/spl middot/s/N for the LGN and the LGT, respectively.     

A micromachined vibration isolation system for reducing the vibration sensitivity of surface transverse wave resonators

A micromachined system has been developed for reducing the vibration sensitivity of surface transverse wave (STW) resonators. The isolation system consists of a support platform for mounting the STW resonator, four support arms, and a support rim. The entire isolation system measures 8 mm by 9 mm by 0.4 mm without the resonator mounted on the platform. The system acts as a passive vibration isolation system, decreasing the magnitude of high frequency (>1.2 kHz) vibrations. Finite element analysis is used to analyze the acceleration sensitivity of the mounted resonator. The isolation system is then modeled as a damped mass-spring system and the transmissibility of vibration from the support rim to the support platform is calculated. Multiplying the acceleration sensitivity of the resonator by the transmissibility results in the expected system vibration sensitivity. The isolation systems are fabricated using two sided bulk etching of (110) oriented silicon wafers. STW resonators were mounted on the isolation systems, and the isolated units were mounted on commercial hybrid oscillator substrates. Vibration sensitivity measurements were taken for vibrations with frequencies ranging from 100 Hz to 5 kHz. The measured data show that the system performs as expected with a low frequency (<500 Hz) vibration sensitivity of 1.8×10^-8/g and a high frequency roll off of 12 dB/octave     

Measurement of static and vibration-induced phase noise in UHF thin-film resonator (TFR) filters

Measurements of the static phase noise and vibration sensitivity of thin-film resonator (TFR) filters operating at 640 and 2110 MHz have been made. They show that the short-term frequency instability of the filters is small compared with that induced in the oscillator signal by the sustaining stage amplifier PM (phase modulation) noise. In-oscillator measurement of filter performance under vibration indicates that fractional frequency vibration sensitivities (δf ₀/f₀) are on the order of several parts in 10^-9/g. Because the percentage bandwidth and order (number of poles) of the filters was fairly constant, so was the product of the center frequency and group delay. Thus, the fractional frequency vibration sensitivity of the filters can be expressed alternatively as carrier signal phase sensitivity to vibration. The τ-ω₀ product for the filters that were tested was on the order of 300 rad, so that the equivalent phase sensitivity to vibration was approximately 1 grad/g     

Isolated electrodeless high-frequency quartz crystal microbalance for immunosensors

This paper presents a contactless technique to measure shear bulk wave resonance frequencies of an isolated quartz crystal in a flow cell. The line antenna placed outside the cell generates and detects the resonance frequencies in a wireless-electrodeless manner. It is revealed that this mechanism relies on the quasistatic electric field. A 0.3-mm-thick AT-cut quartz was used, and its overtone resonance frequencies up to 80 MHz were measured in liquids. Exact vibrational analysis was carried out for a triple-layered resonator system consisting of the adsorbed material layer, the electrode film, and the quartz plate. It predicts higher frequency sensitivity to the adsorbed material at higher modes when the electrode layer is removed. The 13th overtone (72-MHz resonance frequency) was used to detect human immunoglobulin G with concentrations between 0.1 and 20 microg/mL captured by protein A immobilized on one side of the crystal. The real-time measurement of the frequency response yielded the equilibrium constant KA=5.21 x 10(7) M(-1).     

Thermal transient model of a crystal resonator employing thickness-shear vibrations

This paper presents an improved model of thermally induced frequency transients in vacuum-enclosed thickness-shear mode quartz crystal resonators. The response times to temperature changes for different parts of the resonator and resulting thermal dynamic coefficients are examined and are related to Ballato's coefficient through a function defined by the resonator design, dependent on thermal response times only. A method is worked out for response time calculations for the different contributions to the static and dynamic temperature behavior of general and anharmonic modes. The model has been used to examine thermally induced frequency transients of the AT-cut resonator h(513) anharmonic mode excited by the modulational method within an ovenized Colpitts oscillator. A good agreement is shown between the predicted curves and experimental data over a variety of temperature ranges.     

Doubly rotated quartz resonators with a low amplitude-frequencyeffect: the LD-cut

This article deals with a crystal quartz cut with virtually no amplitude-frequency effect (also called "isochronism defect" or "anisochronism"). The cut, called LD-cut (Low isochronism Defect), is set in a BVA-type structure for later use in an Ultra-Stable Oscillator (USO). Various design parameters are presented, along with the properties of the resonator. The resonance frequencies of various modes, the temperature dependence, the motional parameters and the phase noise in relation to the power supplied to the resonator are mainly studied. These properties are compared to those of the SC-cut resonators