John G. Hartnett

Complex permittivity of some ultralow loss dielectric crystals at cryogenic temperatures

Whispering gallery modes were used for very accurate permittivity and dielectric loss measurements of ultralow loss isotropic and uniaxially anisotropic single crystals. Several materials including sapphire, YAG, quartz, and SrLaAlO4 were measured. The total absolute uncertainty in the real part of permittivity tensor components was estimated to be ±0.1%, limited principally by the uncertainty in sample dimensions. Imaginary parts of permittivities were measured with uncertainties of about 10%, limited by the accuracy of Q-factor measurements of whispering gallery modes. It has been observed that, for most crystals, dielectric losses can be approximated by a power function of absolute temperature only in limited temperature ranges. At temperatures between 4-50 K, losses are often affected by impurities, which are always present in real crystals.

Lithium tantalate - a high permittivity dielectric material for microwave communication systems

Lithium tantalate single crystal is characterized by very low thermal expansion and exhibits excellent electro-optical, piezoelectric and pyroelectric properties. We have studied the real part of relative permittivity (/spl epsi//sub r/) perpendicular to the crystal axis and the loss tangent of LiTaO/sub 3/ over the temperature range from 15 K to room temperature at a frequency of 11.4 GHz. The /spl epsi//sub r/ and tan/spl delta/ were determined by measurements of the resonance frequency and the unloaded Q-factor of a TE/sub 011/ mode cylindrical cavity containing the sample under test. The permittivity of LiTaO/sub 3/ was found to change from 38.9 to 41.1 and the loss tangent increased from 1.1 /spl times/ 10/sub -4/ to 6.5 /spl times/ 10/sub -4/ over the temperature range from 15 K to 295 K. Due to the low losses and high permittivity this material can be used in many microwave applications.

Invited Article: Design techniques and noise properties of ultrastable cryogenically cooled sapphire-dielectric resonator oscillators

We review the techniques used in the design and construction of cryogenic sapphire oscillators at the University of Western Australia over the 18 year history of the project. We describe the project from its beginnings when sapphire oscillators were first developed as low-noise transducers for gravitational wave detection. Specifically, we describe the techniques that were applied to the construction of an interrogation oscillator for the PHARAO Cs atomic clock in CNES, in Toulouse France, and to the 2006 construction of four high performance oscillators for use at NMIJ and NICT, in Japan, as well as a permanent secondary frequency standard for the laboratory at UWA. Fractional-frequency fluctuations below 6 x 10(-16) at integration times between 10 and 200 s have been repeatedly achieved.

Microwave characterisation of BaCe2Ti5O15 and Ba5Nb4O15 ceramic dielectric resonators using whispering gallery mode method

A microwave dielectric ceramic resonators based on BaCe2Ti5015 and Ba5Nb4O15 have been prepared by conventional solid state ceramic route. The dielectric resonators (DRs) have high dielectric constant 32 and 40 for BaCe2Ti5O15 and Ba5Nb4O15, respectively. The whispering gallery mode (WGM) technique was employed for the accurate determination of the dielectric properties in the microwave frequency range. The BaCe2Ti5O15 and Ba5Nb4O15 have quality factors (Q×F) of 30,600 and 53,000 respectively. The quality factor is found to depend on the azimuthal mode numbers. The temperature coefficient of resonant frequency (τf) of BaCe2Ti5O15 and Ba5Nb4O15 have been measured accurately using different resonant modes and are +41 and +78 ppm/K, 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/sup 2/, which agreed well with the predicted values.

Cryogenic sapphire oscillator with exceptionally high long-term frequency stability

The authors report on the development of a sapphire cryogenic microwave resonator oscillator with long-term fractional frequency stability of 2×10−17√τ for integration times τ>103s and a negative drift of about 2.2×10−15∕day. The short-term frequency instability of the oscillator is highly reproducible and also state of the art: 5.6×10−16 for an integration time of τ≈20s.

Ultra-low-phase-noise cryocooled microwave dielectric-sapphire-resonator oscillators

Two nominally identical ultra-stable microwave oscillators are compared. Each incorporates a sapphire resonator cooled to near 6 K in an ultra-low vibration cryostat using a pulse-tube cryocooler. The phase noise for a single oscillator is measured at −105 dBc/Hz at 1 Hz offset on the 11.2 GHz carrier. The oscillator fractional frequency stability, after subtracting a linear frequency drift of 3.5×10-14/day, is characterized by 5.3×10-16τ-1/2+9×10-17 for integration times 0.1s<τ<1000s and is limited by a flicker frequency noise floor near 1×10-16.

Frequency-temperature compensation in Ti/sup 3+/ and Ti/sup 4+/ doped sapphire whispering gallery mode resonators

A new method of compensating the frequency-temperature dependence of high-and monolithic sapphire dielectric resonators near liquid nitrogen temperature is presented. This is achieved by doping monocrystalline sapphire with Ti(3+) ions. This technique offers significant advantages over other methods.

Ultra-Stable Very-Low Phase-Noise Signal Source for Very Long Baseline Interferometry Using a Cryocooled Sapphire Oscillator

The design and implementation of a novel frequency synthesizer based on low phase-noise digital dividers and a direct digital synthesizer is presented. The synthesis produces two low noise accurate tunable signals at 10 and 100 MHz. We report the measured residual phase noise and frequency stability of the syn thesizer and estimate the total frequency stability, which can be expected from the synthesizer seeded with a signal near 11.2 GHz from an ultra-stable cryocooled sapphire oscillator (cryoCSO). The synthesizer residual single-sideband phase noise, at 1-Hz offset, on 10and 100-MHz signals was -135 and -130 dBc/Hz, respectively. The frequency stability contributions of these two sig nals was σ_y = 9 × 10^-15 and σ_y = 2.2 × 10^-15, respectively, at 1-s integration time. The Allan deviation of the total fractional frequency noise on the 10- and 100-MHz signals derived from the synthesizer with the cry oCSO may be estimated, respectively, as σ_y ≈ 3.6 × 10^-15 τ^-1/2 + 4 × 10^-16 and σ_y ≈ s 5.2 × 10^-2 × 10^-16 τ^-1/2 + 3 × 10^-16, respectively, for 1 ≤ τ <; 10⁴s. We also calculate the coherence function (a figure of merit for very long baseline interferometry in radio astronomy) for observation frequencies of 100, 230, and 345 GHz, when using the cry oCSO and a hydrogen maser. The results show that the cryoCSO offers a significant advantage at frequencies above 100 GHz.

Ultra-Low Vibration Pulse-Tube Cryocooler Stabilized Cryogenic Sapphire Oscillator With

A low maintenance long-term operational cryogenic sapphire oscillator has been implemented at 11.2 GHz using an ultra-low-vibration cryostat and pulse-tube cryocooler. It is currently the worlds most stable microwave oscillator employing a cryocooler. Its performance is explained in terms of temperature and frequency stability. The phase noise and the Allan deviation of frequency fluctuations have been evaluated by comparing it to an ultra-stable liquid-helium cooled cryogenic sapphire oscillator in the same laboratory. Assuming both contribute equally, the Allan deviation evaluated for the cryocooled oscillator is σ<i>y</i> ≈ 1 × 10^-15τ^-1/2 for integration times 1 <; τ <; 10 s with a minimum σ<i>y</i> = 3.9 × 10^-16 at τ = 20 s. The long term frequency drift is less than 5×10^-14/day. From the measured power spectral density of phase fluctuations, the single-sideband phase noise can be represented by <i>L</i>_φ(<i>f</i>) = 10^-14.0/<i>f</i>⁴+10^-11.6/<i>f</i>³+10^-10.0/<i>f</i>²+10^-10.2/<i>f</i>+ 10^-11.0 rad²/Hz for Fourier frequencies 10^-3 <; <i>f</i> <; 10³ Hz in the single oscillator. As a result, <i>L</i>_φ ≈ -97.5 dBc/Hz at 1-Hz offset from the carrier.