Characterizing Frequency Stability Measurements Having Multiple Data Gaps.

Time series measurements with data gaps (dead times) prevent accurate computations of frequency stability variances such as the Allan variance (AVAR) and its square-root the Allan deviation (ADEV). To extract frequency distributions, time-series data must be sequentially ordered and equally spaced. Data gaps, particularly large ones, make ADEV estimates unreliable. Gap imputation by interpolation, zero-padding, or adjoining live segments, all fail in various ways. We have devised an algorithm that fills gaps by imputing an extension of preceding live data and explaining its advantages. To demonstrate the effectiveness of the algorithm, we have implemented it on 513-length original datasets and have removed 30% (150 values). The resulting data is consistent with the original in all three major criteria: the noise characteristic, the distribution, and the ADEV levels and slopes. Of special importance is that all ADEV measurements on the imputed dataset lie within 90% confidence of the statistic for the original dataset.

Phase noise measurements with a cryogenic power-splitter to minimize the cross-spectral collapse effect.

The cross-spectrum noise measurement technique enables enhanced resolution of spectral measurements. However, it has disadvantages, namely, increased complexity, inability of making real-time measurements, and bias due to the "cross-spectral collapse" (CSC) effect. The CSC can occur when the spectral density of a random process under investigation approaches the thermal noise of the power splitter. This effect can severely bias results due to a differential measurement between the investigated noise and the anti-correlated (phase-inverted) noise of the power splitter. In this paper, we report an accurate measurement of the phase noise of a thermally limited electronic oscillator operating at room temperature (300 K) without significant CSC bias. We mitigated the problem by cooling the power splitter to liquid helium temperature (4 K). We quantify errors of greater than 1 dB that occur when the thermal noise of the oscillator at room temperature is measured with the power splitter at temperatures above 77 K.

Oscillator PM Noise Reduction From Correlated AM Noise.

We demonstrate a novel technique for reducing the phase modulation (PM) noise of an oscillator in a steady-state condition as well as under vibration. It utilizes correlation between PM noise and amplitude modulation (AM) noise that can originate from the oscillator's loop components. A control voltage proportional to the correlated AM noise is generated and utilized in a feedforward architecture to correct for the steady state as well as the vibration-induced PM noise. An improvement of almost 10-15 dB in PM noise is observed over one decade of offset frequencies for a 635-MHz quartz-MEMS oscillator. This corresponds to more than a factor of five reductions in vibration sensitivity.

Heat and Humidity in the City: Neighborhood Heat Index Variability in a Mid-Sized City in the Southeastern United States.

Daily weather conditions for an entire city are usually represented by a single weather station, often located at a nearby airport. This resolution of atmospheric data fails to recognize the microscale climatic variability associated with land use decisions across and within urban neighborhoods. This study uses heat index, a measure of the combined effects of temperature and humidity, to assess the variability of heat exposure from ten weather stations across four urban neighborhoods and two control locations (downtown and in a nearby nature center) in Knoxville, Tennessee, USA. Results suggest that trees may negate a portion of excess urban heat, but are also associated with greater humidity. As a result, the heat index of locations with more trees is significantly higher than downtown and areas with fewer trees. Trees may also reduce heat stress by shading individuals from incoming radiation, though this is not considered in this study. Greater amounts of impervious surfaces correspond with reduced evapotranspiration and greater runoff, in terms of overall mass balance, leading to a higher temperature, but lower relative humidity. Heat index and relative humidity were found to significantly vary between locations with different tree cover and neighborhood characteristics for the full study time period as well as for the top 10% of heat index days. This work demonstrates the need for high-resolution climate data and the use of additional measures beyond temperature to understand urban neighborhood exposure to extreme heat, and expresses the importance of considering vulnerability differences among residents when analyzing neighborhood-scale impacts.

An integrated low phase noise radiation-pressure-driven optomechanical oscillator chipset.

High-quality frequency references are the cornerstones in position, navigation and timing applications of both scientific and commercial domains. Optomechanical oscillators, with direct coupling to continuous-wave light and non-material-limited f × Q product, are long regarded as a potential platform for frequency reference in radio-frequency-photonic architectures. However, one major challenge is the compatibility with standard CMOS fabrication processes while maintaining optomechanical high quality performance. Here we demonstrate the monolithic integration of photonic crystal optomechanical oscillators and on-chip high speed Ge detectors based on the silicon CMOS platform. With the generation of both high harmonics (up to 59 th order) and subharmonics (down to 1/4), our chipset provides multiple frequency tones for applications in both frequency multipliers and dividers. The phase noise is measured down to -125 dBc/Hz at 10 kHz offset at ~400 µW dropped-in powers, one of the lowest noise optomechanical oscillators to date and in room-temperature and atmospheric non-vacuum operating conditions. These characteristics enable optomechanical oscillators as a frequency reference platform for radio-frequency-photonic information processing.

State-of-the-art RF signal generation from optical frequency division.

We present the design of a novel, ultralow-phase-noise frequency synthesizer implemented with extremely-low-noise regenerative frequency dividers. This synthesizer generates eight outputs, viz. 1.6 GHz, 320 MHz, 160 MHz, 80 MHz, 40 MHz, 20 MHz, 10 MHz and 5 MHz for an 8 GHz input frequency. The residual single-sideband (SSB) phase noises of the synthesizer at 5 and 10 MHz outputs at 1 Hz offset from the carrier are -150 and -145 dBc/Hz, respectively, which are unprecedented phase noise levels. We also report the lowest values of phase noise to date for 5 and 10 MHz RF signals achieved with our synthesizer by dividing an 8 GHz signal generated from an ultra-stable optical-comb-based frequency division. The absolute SSB phase noises achieved for 5 and 10 MHz signals at 1 Hz offset are -150 and -143 dBc/Hz, respectively; at 100 kHz offset, they are -177 and -174 dBc/Hz, respectively. The phase noise of the 5 MHz signal corresponds to a frequency stability of approximately 7.6 × 10(-15) at 1 s averaging time for a measurement bandwidth (BW) of 500 Hz, and the integrated timing jitter over 100 kHz BW is 20 fs.

Ultra-low-noise regenerative frequency divider.

We designed ultra-low-noise regenerative divide-by- 2 circuits that operate at input frequencies of 10, 20, and 40 MHz. We achieved output-referred single-sideband residual phase noise equal to -164 dBc/Hz at 10 Hz offset and estimated residual Allan deviation, σ(y)(τ) less than 3 × 10(-15)τ(-1) for a single divider, which is, to our knowledge, the lowest noise of any divider ever reported at these frequencies. To measure such a low noise, we also built a cross-spectrum measurement system that has a noise floor of -175 dBc/Hz at 10 Hz offset from the carrier frequency. The low noise of the divider and the measurement system are achieved by using custom-built mixers/phase detectors that use 2N2222A bipolar junction transistors (BJTs) in a conventional double-balanced diode ring.

Fast ThêoBR: a method for long data set stability analysis.

ThêoBR is a high-confidence statistic that evaluates frequency stability at long τ values. However, for real-world data sets that contain thousands of points or more, the calculation of ThêoBR can take hours, days, or even weeks on a typical PC. To make the calculation of ThêoBR faster for these data sets, a method of averaging points together within the data set is developed. The error introduced by this technique is analyzed and compared with the exact value, and a correction formula is developed to minimize this error for FM noise types. Finally, the technique is applied to real data sets and determines stability at the longest τ values in seconds as opposed to weeks.

Vibration-induced PM and AM noise in microwave components.

The performance of microwave components is sensitive to vibrations to some extent. Aside from the resonator, microwave cables, and connectors, bandpass filters, mechanical phase shifters, and some nonlinear components are the most sensitive. The local oscillator is one of the prime performance-limiting components in microwave systems ranging from simple RF receivers to advanced radars. The increasing present and future demand for low acceleration sensitive oscillators, approaching 10(-13)/g, requires a reexamination of sensitivities of basic nonoscillatory building-block components under vibration. The purpose of this paper is to study the phase-modulation (PM) noise performance of an assortment of oscillatory and nonoscillatory microwave components under vibration at 10 GHz. We point out some challenges and provide suggestions for the accurate measurement of vibration sensitivity of these components. We also study the effect of vibration on the amplitude-modulation (AM) noise.

ThêoH and Allan deviation as power-law noise estimators.

A spectral interpretation using the frequency sensitivity of the Allan variance (Avar) and Thêo-Hybrid (ThêoH) is used to determine falpha noise, or "power-law noise." ThêoH has narrower chi-square confidence than Avar; consequently, ThêoH provides significantly better determination of falpha noise types at long term. Furthermore, ThêoH has even narrower confidence than chi-square. Because the algorithms used to calculate these confidence intervals are computationally intensive, we have constructed an empirical formula that approximates confidence intervals as the percent error for ThêoH.

Merits of PM noise measurement over noise figure: a study at microwave frequencies.

This paper primarily addresses the usefulness of phase-modulation (PM) noise measurements versus noise figure (NF) measurements in characterizing the merit of an amplifier. The residual broadband (white PM) noise is used as the basis for estimating the NF of an amplifier. We have observed experimentally that many amplifiers show an increase in the broadband noise of 1 to 5 dB as the signal level through the amplifier increases. This effect is linked to input power through the amplifier's nonlinear intermodulation distortion. Consequently, this effect is reduced as linearity is increased. We further conclude that, although NF is sometimes used as a selection criteria for an amplifier for low-level signal, NF yields no information about potentially important close-to-carrier 1/f noise of an amplifier nor broadband noise in the presence of a high-level signal, but a PM noise measurements does. We also have verified experimentally that the single-sideband PM noise floor of an amplifier due to thermal noise is -177 dBc/Hz, relative to a carrier input power of 0 dBm.

Enhancements to GPS operations and clock evaluations using a "total" Hadamard deviation.

We describe a method based on the total deviation approach whereby we improve the confidence of the estimation of the Hadamard deviation that is used primarily in global positioning system (GPS) operations. The Hadamard-total deviation described in this paper provides a significant improvement in confidence indicated by an increase of 1.3 to 3.4 times the one degree of freedom of the plain Hadamard deviation at the longest averaging time. The new Hadamard-total deviation is slightly negatively biased with respect to the usual Hadamard deviation, and tau values are restricted to less than or equal to T/3, to be consistent with the usual Hadamard's definition. We give a method of automatically removing bias by a power-law detection scheme. We review the relationship between Kalman filter parameters and the Hadamard and Allan variances, illustrate the operational problems associated with estimating these parameters, and discuss how the Hadamard-total variance can improve management of present and future GPS satellite clocks.

High spectral purity microwave oscillator: design using conventional air-dielectric cavity.

We report exceptionally low PM noise levels from a microwave oscillator that uses a conventional air-dielectric cavity resonator as a frequency discriminator. Our approach is to increase the discriminator's intrinsic signal-to-noise ratio by use of a high-power carrier signal to interrogate an optimally coupled cavity, while the high-level of the carrier is suppressed before the phase detector. We developed and tested an accurate model of the expected PM noise that indicates, among other things, that a conventional air-dielectric resonator of moderate Q will exhibit less discriminator noise in this approach than do more esoteric and expensive dielectric resonators tuned to a high-order, high-Q mode and driven at the dielectric's optimum