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.     

High Q-factor distributed bragg reflector resonators with reflectors of arbitrary thickness

The Bragg reflection technique improves the Q-factor of a resonator by reducing conductor and dielectric losses. This is achieved by designing a low-loss inner resonant region (usually free space) surrounded by an outer anti-resonant region made of distributed Bragg reflector layers. In this paper we develop a simple non-Maxwellian model and apply it to design three distinct cylindrical Bragg resonators based on the same set of single-crystal sapphire plates and rings by changing only the dimension of the cavity that supports the structure. To accomplish this, the simple model allows an arbitrary thickness for either the horizontal or the cylindrical dielectric reflectors by relaxing the condition that they must be lambda/4 thick. The model also allows for higher-order field variations in both the resonant and the anti-resonant regions. The resonators were constructed and experimental results were compared with the simple model and the rigorous method of lines analysis. For the fundamental mode, an unloaded Q-factor of 234,000 at 9.7 GHz was obtained. This is larger than that for a whispering gallery mode resonator. The resonator also exhibited a greatly reduced spurious mode density when compared to an overmoded whispering gallery mode resonator.     

Simple design rules for optimal design of dielectric temperature-compensated sapphire resonators

It has been shown that the use of two dielectric crystals with opposite temperature coefficient of permittivity allows the realization of a resonator with a zero temperature coefficient of frequency. By using sapphire and rutile materials, which have low-loss tangents, some compensated resonators with very high Q-factors have been realized. In this work we develop rules that greatly simplify the design of a dielectric-compensated resonator. We show that the optimum design for compensation at a specific temperature may be determined by simply selecting the aspect ratio of the sapphire resonator.     

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     

HTS Surface Wave Resonators

A novel class of surface wave high-temperature superconductivity (HTS) resonators was investigated. The resonator consists of HTS film and one or two dielectric plates. One of the dielectric plates may be the HTS film substrate. Theoretical analysis of the resonator structure was carried out using the partial region method, with the 20 lowest waves being considered in every region. The resonant frequencies, quality of oscillations, and the field and current distributions were calculated. It was shown that there is a high-density and homogeneous microwave current flowing on the film surfaces. Experimental measurements carried out in the 3-cm wavelength range demonstrate good agreement with simulated data.     

HTS Surface Wave Resonators

A novel class of surface wave high-temperature superconductivity (HTS) resonators was investigated. The resonator consists of HTS film and one or two dielectric plates. One of the dielectric plates may be the HTS film substrate. Theoretical analysis of the resonator structure was carried out using the partial region method, with the 20 lowest waves being considered in every region. The resonant frequencies, quality of oscillations, and the field and current distributions were calculated. It was shown that there is a high-density and homogeneous microwave current flowing on the film surfaces. Experimental measurements carried out in the 3-cm wavelength range demonstrate good agreement with simulated data.     

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.     

Low-Pressure Microwave Discharge in a Plasmatron with a Rectangularly Shaped Resonator

The author presents results of measurements of certain electrophysical characteristics that determine the operation of a microwave plasmatron based on a rectangularly shaped resonator with partial filling of the resonant volume with a plasma. It is established that the distributions of the microwave field and the local electrical conductivity of the plasma along the length of the discharge region are of a periodic character with alternating maxima and minima, and the change in the values of the temperature decreases continuously from the site of input of microwave energy to the resonator.     

Use of a piezoelectric SQUIGGLE motor for positioning at 6 K in a cryostat

The piezoelectric SQUIGGLE^® motor model SQ-110C from New Scale Technologies, Inc., has been used in a cryostat as part of a mechanism to accurately deform a cylindrical superconducting microwave resonator in order to change its resonant frequency. This paper describes the practical setup for testing and using the piezo motor in a cryostat, and comments on the performance of the motor at temperatures from room temperature to 6 K.     

Dielectric constant measurement of low loss liquids using stacked multi ring resonator

The concept of dielectric constant measurement has been extended and applied in agriculture, pharmaceutical and food industry for quality control of liquids. Dielectric analysis of material at microwave frequencies can be done using novel shielded stacked multi-ring resonator (SMRR). The dielectric constant of liquids and paste has been calculated using SMRR with greater accuracy than the planar resonator, boxed resonator and stacked resonator. SMRR contains a ring resonator with fed patch and parasitic patch with different numbers and sizes of rings. The dimensions of rings on the parasitic patch are optimized to achieve Quality factor Q greater than 100 and return loss less than ?2 dB. Due to dual resonance in novel SMRR, structure losses are reduced by 50% than planar resonator structure. The behavior of SMRR structure at the 2.45 GHz frequency is studied with E field and H field. 3D model is designed in Computer Simulation Technology Microwave Studio (CST MWS) using TLM (Transmission Line Modeling) solver. Electromagnetic field analysis as well as impedance bandwidth of SMRR using CST MWS 3D model prove that electromagnetic coupling in SMRR structure increases thus improves quality factor. In SMRR quality factor increases and losses reduce help us to predict the complex permittivity of material for quality analysis.     

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     

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.     

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.     

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     

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.     

HighQsapphire loaded superconducting cavities and application to ultrastable clocks

This paper describes the microwave properties of a sapphire loaded super conducting cavity resonator. We report measurements of energy confinement, evanescent field scale lengths, and radiation losses. We report high quality factors, in excess of 10⁹at cryogenic temperatures, for a resonator based on a sapphire element mounted inside a superconducting cavity. Resonators of this type have potentially valuable applications as ultrahigh stability oscillators, high Q filters and as low phase noise frequency sources.     

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.     

Properties of regular polygons of coupled microring resonators

The resonant properties of a closed and symmetric cyclic array of N coupled microring resonators (coupled-microring resonator regular N-gon) are for the first time determined analytically by applying the transfer matrix approach and Floquet theorem for periodic propagation in cylindrically symmetric structures. By solving the corresponding eigenvalue problem with the field amplitudes in the rings as eigenvectors, it is shown that, for even or odd N, this photonic molecule possesses 1 + N/2 or 1+N resonant frequencies, respectively. The condition for resonances is found to be identical to the familiar dispersion equation of the infinite coupled-microring resonator waveguide with a discrete wave vector. This result reveals the so far latent connection between the two optical structures and is based on the fact that, for a regular polygon, the field transfer matrix over two successive rings is independent of the polygon vertex angle. The properties of the resonant modes are discussed in detail using the illustration of Brillouin band diagrams. Finally, the practical application of a channel-dropping filter based on polygons with an even number of rings is also analyzed.     

Demonstrating high-power 30-GHz free-electron maser operation on a resonant load

An effective narrow-band free-electron maser (FEM) with reversed axial guide magnetic field, based on a corrugated high-selectivity Bragg resonator with a jump in the ripple phase, has been constructed and tested. The FEM operates at 30 GHz with characteristics of the output radiation (power, pulse duration, spectrum width) and stability of the generation regime that allow the device to be used in testing electrodynamic components for future electron-positron supercolliders. Experiments have been performed with a high-Q resonator operating on a resonant load, which can be used to model the degradation of an accelerating structure of the CLIC collider (CERN) as a result of thermal fatigue caused by the multiply repeated (∼10⁵ cycles) action of microwave pulses.     

Frequency-temperature compensation of piezoelectric resonators by electric DC bias field

Electromechanical resonators have been widely used in signal processing and frequency control applications. It has been found that the resonant frequency of most resonator devices is highly temperature dependent, as temperature variation leads to materials properties change as well as resonator dimension change, which result in the undesirable shift of the resonance frequency. In this paper, we present a new frequency tuning method in which direct current (DC) bias field is used to control the resonance frequency of the piezoelectric resonator that is subjected to ambient temperature variations. It has been found that, depending on the polarity, the application of a DC bias field can reduce or increase the resonance frequency of the resonator. The experimental results demonstrate that the DC bias field tuning can achieve fairly good temperature compensation within a certain temperature range, and that the mechanical Q factor of the resonator is quite stable under different DC bias fields.