David A. Howe

Noise figure vs. PM noise measurements: a study at microwave frequencies

This paper addresses two issues: (i) it compares the usefulness of phase-modulation (PM) noise measurements vs. noise figure (NF) measurements in characterizing the merit of an amplifier, and (ii) it reconciles a general misunderstanding in using -174 dBc/Hz (relative to carrier input power of 0 dBm) as thermal noise level. The residual broadband (white PM) noise is used as the basis for estimating the noise figure (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 amplifiers nonlinear intermodulation distortion. Consequently, this effect is reduced as linearity is increased. It is important to note that NF is sometimes used as a selection criteria for an amplifier but yields no information about potentially important close-to-carrier 1/f noise of an amplifier, whereas PM and amplitude modulation (AM) noise measurements do. We have verified theoretically and experimentally that the single-sideband PM (and AM) noise floor due to thermal noise is -177 dBc/Hz, relative to a carrier input power of 0 dBm.

Wavelet variance, Allan variance, and leakage

Wavelets have recently been a subject of great interest in geophysics, mathematics and signal processing. The discrete wavelet transform can be used to decompose a time series with respect to a set of basis functions, each one of which is associated with a particular scale. The properties of a time series at different scales can then be summarized by the wavelet variance, which decomposes the variance of a time series on a scale by scale basis. The wavelet variance corresponding to some of the recently discovered wavelets can provide a more accurate conversion between the time and frequency domains than can be accomplished using the Allan variance. This increase in accuracy is due to the fact that these wavelet variances give better protection against leakage than does the Allan variance. >

Sub-femtosecond absolute timing jitter with a 10 GHz hybrid photonic-microwave oscillator

We present an optical-electronic approach to generating microwave signals with high spectral purity. By circumventing shot noise and operating near fundamental thermal limits, we demonstrate 10 GHz signals with an absolute timing jitter for a single hybrid oscillator of 420 attoseconds (1 Hz–5 GHz).

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 discriminators 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 dielectrics optimum power.

A collapse of the cross-spectral function in phase noise metrology

Cross-spectral analysis is a mathematical tool for extracting the power spectral density of a correlated signal from two time series in the presence of uncorrelated interfering signals. We demonstrate and explain a set of amplitude and phase conditions where the detection of the desired signal using cross-spectral analysis fails partially or entirely in the presence of a second uncorrelated signal. Not understanding when and how this effect occurs can lead to dramatic under-reporting of the desired signal. Theoretical, simulated and experimental demonstrations of this effect as well as mitigating methods are presented.

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 amplifiers 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

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 59th 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.

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 /spl tau/ values are restricted to less than or equal to T/3, to be consistent with the usual Hadamards 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.

Microwave Optoelectronic Oscillator with Optical Gain

Optoelectronic oscillators (OEO) are unique compared to radio-frequency (RF) oscillators in that they do not fundamentally require a RF gain element in order to satisfy the amplitude threshold condition for oscillation. All of the energy required for oscillation can be obtained from the optical carrier. This, however, was not initially possible, due to the inefficiency and power limitations on the optical components used in the OEO. Recent improvements driven by the need for optical-RF links have improved modulator and detector technology. Electro-optic modulators (EOM) with ultra-low half-wave voltage (Vpi), and high optical power capabilities, when coupled with high-power photodetectors, have achieved optical links with gain. With sufficient gain from the photonic components in the OEO, the RF loop amplifier becomes unnecessary. Eliminating this amplifier removes one of the major noise contributing elements of the oscillator. Here we present designs and phase noise results of several OEOs, operating at RF frequencies up to 10 GHz, constructed with only optical gain.

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

We present the design of a novel, ultralow-phasenoise frequency synthesizer implemented with extremely-lownoise 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 opticalcomb- 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.