Cryogenic monolithic sapphire-rutile temperature compensated resonator oscillator

We have tested a new temperature-compensated sapphire resonator as frequency determining element for high-stability microwave oscillator. Temperature compensation has been obtained by coating the sapphire resonator with a thin rutile film. A 2-/spl mu/m rutile thickness is sufficient to reach turnover temperature higher than 40 K, and a 2/spl times/10/sup -12/ short-term frequency stability has been obtained.     

Analysis of the rutile-ring method of frequency-temperature compensating a high-Q whispering gallery sapphire resonator

The rutile-ring method of dielectrically frequency-temperature compensating a high-Q whispering gallery (WG) sapphire resonator is presented. Two and three-dimensional finite element (FE) analysis has been implemented to design and analyze the performance of such resonators, with excellent agreement between theory and experiment. A high-Q factor of 30 million at 13 GHz, and compensation temperature of 56 K was obtained. It is shown the frequency-temperature compensation can occur either because the rutile adds a small perturbation to the sapphire resonator or because of a mode interaction with a resonant mode in the rutile. The characteristics of both of these methods are described, and it is shown that for high frequency stability, it is best to compensate perturbatively     

Development of a high stability cryogenic sapphire dielectricresonator

The development of a new design of cryogenic sapphire dielectric resonator is reported. The temperature dependence of the resonant frequency and width is discussed. Preliminary results of a prototype oscillator referenced to this resonator are given     

Temperature-compensated sapphire resonator for ultra-stableoscillator capability at temperatures above 77 K

We report on the design and test of a whispering gallery sapphire resonator for which the dominant (WGH_n11) microwave mode family shows frequency-stable, compensated operation for temperatures above 77 K. The resonator makes possible a new ultra-stable oscillator (USO) capability that promises performance improvements over the best available crystal quartz oscillators in a compact cryogenic package. A mechanical compensation mechanism, enabled by the difference between copper and sapphire expansion coefficients, tunes the resonator to cancel the temperature variation of sapphire's dielectric constant. In experimental tests, the WGH₈₁₁ mode showed a frequency turnover temperature of 87 K in agreement with finite element calculations. Preliminary tests of oscillator operation show an Allan Deviation of frequency variation of 1.4-6×10^-12 for measuring times 1 s ⩽τ⩽100 s with unstabilized resonator housing temperature and a mode Q of 2×10⁶. We project a frequency stability 10^-14 for this resonator with stabilized housing temperature and with a mode Q of 10⁷     

Microwave oscillators incorporating cryogenic sapphire dielectricresonators

Progress is reported on efforts to develop a commercially-viable high purity X-band signal source incorporating a cryogenic sapphire dielectric resonator. The resonator design is of the whispering gallery type to take advantage of the excellent electromagnetic field confinement offered by this geometry. Complications resulting from the high spurious mode density of this type of resonator have been eliminated by developing a very accurate and complete mode analysis program which fully incorporates the dielectric anisotropies of the sapphire ring. This program allows the design of a window in the frequency domain where no unwanted modes exist, with accurate placement of the desired mode at the center of this region. Preliminary evaluation of the phase noise properties of simple oscillators incorporating these resonators have been performed. For example, in a dual-oscillator comparison of two oscillators operating near 13 GHz phase noise values of L(f)=-55 dBc/Hz, -145 dBc/Hz and -161 dBc/Hz were obtained for offset frequencies of 1 Hz, 1 kHz and 10 kHz, respectively     

High-Q sapphire-rutile frequency-temperature compensated microwave dielectric resonators

A sapphiro-rutile composite resonator was constructed from a cylindrical sapphire monocrystal with two thin disks of monocrystal rutile held tightly against the ends. Because rutile exhibits low loss and an opposite temperature coefficient of permittivity to sapphire, it is an ideal material for compensating the frequency-temperature dependence of a sapphire resonator. Most of the electromagnetic modes in the composite structure exhibited turning points (or compensation points) in the frequency-temperature characteristic. The temperatures of compensation for the WG quasi TM modes were measured to be below 90 K with Q-factors of the order of a few million depending on the mode. For WG quasi TE modes, the temperatures of compensation were measured to be between 100 to 160 K with Q-factors of the order of a few hundreds of thousands, depending on the mode. The second derivatives of the compensation points were measured to be of the order 0.1 ppm/K(2 ), which agreed well with the predicted values.     

Designs of a microwave TE011 mode cavity for a space borne H-maser.

Method of Lines and Finite Element Analysis investigations have been performed to optimize parameters in a TE011 mode cavity resonator suitable for a spaceborne hydrogen maser. We report on designs that were explored to find a global maximum in the important design parameters for the microwave cavity used in a hydrogen maser. The criteria sought in this exercise were both the minimization of the total volume of the cavity and the maximization of the product of the z-component of the magnetic energy filling factor and the cavity TE011 mode Q-factor (Q.eta). Different configurations were studied. They were a sapphire tube in a copper cylinder, a sapphire tube in a copper cylinder with Bragg reflectors, and spherical copper cavities both empty and sapphire-lined on the inside cavity surface. At 320 K, the simulations resulted in an optimum product Q.eta = 4.9 x 10(4), with an inner cavity radius of 80 mm and unity aspect ratio. This represents a 54% improvement over an earlier design. The expected increase in the product Q . eta) with the inclusion of Bragg reflectors to the sapphire tube was not achieved. Moreover, the z-component of the magnetic energy filling factor was greatly reduced due to an increase in the radial magnetic field. The sapphire-lined spherical cavity showed no better performance than an equivalent-sized empty copper spherical cavity. For the empty cavity the simulations resulted in the product Q.eta = 4.4 x 10(4). The empty spherical cavity resonator is not suitable for the spaceborne hydrogen maser as the total volume in this case is 33% larger than that of the optimized sapphire tube resonator.     

Compact, high-Q, zero temperature coefficient, TE011 sapphire-rutile microwave distributed Bragg reflector resonators

Some novel new resonator designs based on the distributed Bragg reflector are presented. The resonators implement a TE₀₁₁ resonance in a cylindrical sapphire dielectric, which is confined by the addition of rutile and sapphire dielectric reflectors at the end faces. Finite element calculations are utilized to optimize the dimensions to obtain the highest Q-factors and zero frequency-temperature coefficient for a resonator operating near 0°C. We show that a Q-factor of 70,000 and 65,000 can be achieved with and without the condition of zero frequency-temperature coefficients, respectively     

Designs of a microwave TE/sub 011/ mode cavity for a space borne H-maser

Method of lines and finite element analysis investigations have been performed to optimize parameters in a TE/sub 011/ mode cavity resonator suitable for a spaceborne hydrogen maser. We report on designs that were explored to find a global maximum in the important design parameters for the microwave cavity used in a hydrogen maser. The criteria sought in this exercise were both the minimization of the total volume of the cavity and the maximization of the product of the z-component of the magnetic energy filling factor and the cavity TE/sub 011/ mode Q-factor (Q/spl middot//spl eta/). Different configurations were studied. They were a sapphire tube in a copper cylinder, a sapphire tube in a copper cylinder with Bragg reflectors, and spherical copper cavities both empty and sapphire-lined on the inside cavity surface. At 320 K, the simulations resulted in an optimum product Q/spl middot//spl eta/ = 4.9 /spl times/ 10/sup 4/, with an inner cavity radius of 80 mm and unity aspect ratio. This represents a 54% improvement over an earlier design. The expected increase in the product Q/spl middot//spl eta/ with the inclusion of Bragg reflectors to the sapphire tube was not achieved. Moreover, the z-component of the magnetic energy filling factor was greatly reduced due to an increase in the radial magnetic field. The sapphire-lined spherical cavity showed no better performance than an equivalent-sized empty copper spherical cavity. For the empty cavity the simulations resulted in the product Q/spl middot//spl eta/ = 4.4 /spl times/ 10/sup 4/. The empty spherical cavity resonator is not suitable for the spaceborne hydrogen maser as the total volume in this case is 33% larger than that of the optimized sapphire tube resonator.     

High performance distributed Bragg reflector microwave resonator

A new resonator device structure is described that achieves Q-factors well above those currently realizable for conventional room temperature microwave structures. The new structure consists of a microwave cavity, for which the enclosure walls consist of distributed Bragg reflectors (DBR) made of low-loss sapphire. For this configuration, most of the resonant field resides in empty space, with small field strengths in the thin layers of sapphire which comprise the DBR structure. The physical structure takes the form of interpenetrating concentric rings and plates of low-loss sapphire contained in a cylindrical metal enclosure. The theoretical analysis of the DBR resonant structure allows the positions and dimensions of the component rings and plates to be precisely determined for a specified resonant frequency. The resonator Q can be accurately calculated, and plots of the resonant fields clearly show the physical mechanism leading to the observed efficiency of this resonator structure. Experimental results are given for resonators designed at 9.0 and 13.2 GHz. The measured unloaded Q's at room temperature are over 650000 and 450000, respectively.     

Frequency locking of a pulsed single-longitudinal-mode laser in a coupled-cavity resonator

The performance of a novel resonator that couples a grazing-incidence and a linear cavity is reported. The coupling secures single-longitudinal mode, TEM(00), higher-efficiency and lower-threshold operation. By use of Ti:sapphire as the gain medium, a slope efficiency of 23% and a 100-nm tuning range are reported. A model is explained that fully predicts the mode behavior of the resonator and that can be used to optimize the cavity for single-mode operation. We have developed computer control of the cavity, which is simple in design and is used to lock the <200-MHz bandwidth mode to +/-40 MHz. A 4.8-GHz scan has also been demonstrated.     

High-Q whispering gallery traveling wave resonators for oscillator frequency stabilization

Usually a frequency-stabilized standing wave resonator-oscillator incorporating a resonator as a frequency discriminator requires a circulator to separate the injected and reflected wave, A ferrite circulator is a noisy device and can limit the phase noise or frequency stability. Moreover, we show that the noise in a circulator varies, and detailed low noise measurements are necessary to choose an appropriate quiet circulator. Thus, by realizing a configuration that does not require a circulator, an improvement in performance and reliability can be obtained. A solution to this problem is to design a high-Q whispering gallery traveling wave (WGTW) resonator. This device naturally separates the injected and reflected wave in the same way as a ring cavity at optical frequencies, without degrading the frequency discrimination. Q-factor measurements of a WGTW sapphire resonator are presented, along with a derivation of critical parameters to maximize the frequency discrimination. New measurements of noise in ferrite circulators and isolators have also been made, which is followed with a discussion on oscillator design.     

Temperature-compensated cryogenic Fabry-Perot cavity

We show that temperature compensation based on differential thermal expansion between sapphire and fused silica can be used to create a Fabry-Perot cavity with an exceptionally low coefficient of thermal expansion at low temperatures. We describe the design of such a cavity that utilizes shaped fused silica mirrors and a sapphire spacer. The geometry of the fused silica mirror was designed using a finite element model to have a small platform, giving a frequency temperature turning point of 16.6 K. The measured turning point was 16.2 K and the curvature was 6 x 10(-10) K(-2), both of which were consistent with the model.     

Whispering-gallery mode technique applied to the measurement of the dielectric properties of Langasite between 4 K and 300 K

We report new measurements of dielectric properties of Lanthanum gallium silicate (Langasite or LGS) conducted with the whispering-gallery mode technique at microwave frequencies and between 4.2 K and 300 K. The real part of the permittivity tensor of LGS presents two components having temperature coefficients of opposite sign. This unique property enables the design of a temperature compensated resonator that may be useful in building stable microwave oscillators or filters. We report also the first measurements of the two independent components of the imaginary part of the permittivity tensor. It appears LGS is a relatively high-loss dielectric material compared with sapphire or quartz.     

Microwave oscillators incorporating high performance distributed Bragg reflector microwave resonators

We previously demonstrated a new resonator device structure that achieves Q-factors well above those currently realisable. The new structure consists of a microwave cavity, where the enclosure walls consist of distributed Bragg reflectors (DBRs) in three dimensions, made of low-loss sapphire. Theoretical analysis has demonstrated that the resonator's performance is critically dependent upon accurate alignment of the DBR components, thereby maintaining the desired symmetry of the resonant structure. Breaking of the symmetry causes mixing of the high performance Bragg reflected mode with low-Q hybrid cavity modes. The fabrication tolerances required to achieve the expected resonator performance are met with a precise but simple alignment tool. A pair of these resonators have been built at 9.0 GHz, and have demonstrated unloaded Qs in excess of 700,000 at room temperature. These resonators are incorporated into simple two-port feedback oscillator circuits. Phase noise measurements were performed on the two free-running oscillators.     

Optimization of an ultra low-phase noise sapphire--SiGe HBT oscillator using nonlinear CAD

In this paper, the electrical and noise performances of a 0.8 /spl mu/m silicon germanium (SiGe) transistor optimized for the design of low phase-noise circuits are described. A nonlinear model developed for the transistor and its use for the design of a low-phase noise C band sapphire resonator oscillator are also reported. The best measured phase noise (at ambient temperature) is -138 dBc/Hz at 1 kHz offset from a 4.85 GHz carrier frequency, with a loaded Q/sub L/ factor of 75,000.     

Ultra temperature-stable bulk-acoustic-wave resonators with SiO2 compensation layer

This paper describes temperature compensated bulk acoustic-wave resonators (BAR) with temperature coefficient of frequency (TCF) less than 1 ppm/degrees C at above 3 GHz. The temperature compensation is produced from the unique physical property of silicon dioxide's positive TCF, unlike most other materials that have negative TCF. Two types of resonators have been explored: film bulk acoustic resonator (FBAR) composed of Al/ZnO/Al/SiO2 on a surface micromachined cantilever that is released by XeF2 vapor etching and high-overtone acoustic resonator (HBAR) composed of an Al/ZnO/Al resonator on a bulk micromachined SiO2/Si/SiO2 supporting substrate.     

Measurement and analysis of a microwave oscillator stabilized by a sapphire dielectric ring resonator for ultra-low noise

Phase-noise measurements are presented for a microwave oscillator whose frequency is stabilized by a whispering gallery mode sapphire ring resonator with Q of 2x10(5). The nature of the mode, which involves little metallic conduction, allows nearly full use of the very low dielectric loss in sapphire. Several mode families have been identified with good agreement with calculated frequency predictions. Waveguide coupling parameters have been characterized for the principal (lowest frequency) mode family, for n=5 to n =10 full waves around the perimeter. For a 5-cm wheel resonator in a 7.6-cm container, Q-values of above 10(5) were found at room temperature for all of the modes in this sequence. Coupling Q-values for the same modes ranged from 10(4) (n =5) to 10(5) (n=10) for a WR112 waveguide port at the center of the cylinder wall of the containing can. Phase noise measurements for a transistor oscillator locked to the n=10 (7.84-GHz) mode showed a 1/f(3) dependence for low offset frequencies, and a value of L(f)=-55 dB/Hz at an offset of 10 Hz from the carrier. The oscillator shows phase noise below the previously reported for any X-band source.     

Sensitivity and optimization of a high-Q sapphire dielectric motion-sensing transducer

A high-Q sapphire dielectric motion sensing transducer that operates at microwave frequencies has been developed. The device uses cylindrical whispering gallery modes of quality factor greater than 10 (5) at room temperature and greater than 10(8) at 4 K. The tuning coefficient of the transducer resonance frequency with respect to displacement was measured to be of the order of a few MHz/mum. An electromagnetic model that predicts the resonant frequency and tuning coefficient has been developed and was verified by experiment. We implemented the model to determine what aspect ratio and what dielectric mode is necessary to maximize the sensitivity. We found that the optimum mode type was a TM whispering gallery mode with azimuthal mode number of about 7 for a resonator of 3 cm in diameter. Also, we determined that the tuning coefficients were maximized by choosing an aspect ratio that has a large diameter with respect to the height. By implementing a microwave pump oscillator of SSB phase noise -125 dBc/Hz at 1 kHz; offset, we have measured a sensitivity of order 10 (-16) m/ radicalHz. We show that this can be improved with existing technology to 10(-18) m/ radicalHz, and that in the near future this may be further improved to 10(-19) m/ radicalHz.     

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.