Cross-spectrum analysis is a commonly used technique for the detection of phase and amplitude noise of a signal in the presence of interfering uncorrelated noise. Recently, we demonstrated that the phase-inversion (anti-correlation) effect due to amplitude noise leakage can cause complete or partial collapse of the cross-spectral function. In this paper, we discuss the newly discovered effect of anti-correlated thermal noise that originates from the common-mode power divider (splitter), an essential component in a cross-spectrum noise measurement system. We studied this effect for different power splitters and discuss its influence on the measurement of thermal-noise limited oscillators. We provide theory, simulation and experimental results. In addition, we expand this study to reveal how the presence of ferrite-isolators and amplifiers at the output ports of the power splitters can affect the oscillator noise measurements. Finally, we discuss a possible solution to overcome this problem.

We describe operational challenges and progress of optical frequency-comb dividers (OFDs) that synthesize RF signals from the optical domain. Our priorities include: (1) ultra-low phase-noise, (2) continuous operation, and (3) broadly low Allan deviation.

We discuss frequency synthesizer needs and recent phase noise results of a multi-level frequency divider that are consistent with the phase noise of new high-accuracy optical atomic standards. Optical atomic standards achieve extremely low frequency uncertainties in less than hundreds of seconds due to their unprecedented phase stability and accuracy. The desire for low white-FM noise that ordinarily required days of averaging for laboratory standards to attain full accuracy has been shifted to a need for low flicker-FM noise to maintain long-term frequency uncertainty with only seconds of averaging. This imposes new requirements for low levels of phase noise realizable by laser stabilization by a hi-Q optical cavity of a phase-coherent optical frequency comb. The multi-level frequency divider serves as a tool for synthesizing many low-phase noise frequencies.

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.

A new scheme for reducing the phase-modulated (PM) noise of an oscillator from correlation between amplitude-modulated (AM) and PM noise is presented. Experimental results of this correlation effect are also presented. An improvement of almost 10 dB in the PM noise is reported for frequency offsets with strong correlation.

We discuss techniques for measuring the correlation between phase-modulated (PM) and amplitude-modulated (AM) noise in an oscillator and report results of such correlation in a few selected oscillators of similar size, weight, power consumption and vibration sensitivity.

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 [1-2]. Not understanding when and how this effect occurs can lead to dramatic under-reporting of the desired signal.

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. A set of conditions is demonstrated and explained 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 and simulated demonstrations of this effect are presented.

We present phase-noise measurements in support of terahertz electronics. By combining even-harmonic mixers with a 2.5 GHz frequency comb, we achieve a phase-noise measurement system in waveguide (WR1.5) by use of cross-spectral and digital phase-noise measurement techniques. At 670 GHz an upper bound of this system's noise floor is found to be -20, -40, and -60 dBc/Hz at 1, 100, and 10000 Hz offsets, respectively. In addition, a commercial, low-phase-noise, 670 GHz source is measured at offset frequencies from 0.1 Hz to 1 MHz.

Current methods for measuring the vibration sensitivity of microwave devices are limited primarily by choice of cables connecting a stationary platform to a vibrating actuator. We experimentally compare the current ("conventional") method with a new ("modified") common-arm counter propagating (CACP) technique for evaluation of two-port devices. We demonstrate that a CACP method reduces the vibrational noise floor of an optimized measurement system at 10 GHz by up to 25 dB. Common-mode disturbances from the vibration of cables and circulators contained in the measurement loop are rejected to first order. The CACP method enables accurate measurement of devices with low vibration sensitivity. The sensitivity measurement of such devices is normally limited by a conventional measurement system's noise floor. Our system is based on similar work at optical frequencies by Nelson et al. [2]

We implement an ultra-low-noise frequency divider chain from 8 GHz to 5 MHz that utilizes custom-built regenerative frequency divide-by-2 circuits. The single-sideband (SSB) residual phase-noise of this regenerative divider at 5 MHz output is -163 dBc/Hz at 10 Hz offset frequency. This level is achieved with custom-built mixers that use 2N2222A bipolar junction transistors in a conventional double-balanced diode ring. We report absolute phase-noise of radio-frequency (RF) signals at 10 MHz and 5 MHz obtained by dividing an 8 GHz signal generated from ultra-stable optical comb-based frequency division. The absolute SSB phase-noise for a 10 MHz and 5 MHz signal at 1 Hz offset is -143 dBc/Hz and -150 dBc/Hz, and at 100 kHz offset is -174 dBc/Hz and -177 dBc/Hz, respectively.

We present phase-noise measurements in support of terahertz electronics. Using digital phase-noise measurement techniques and an even-harmonic mixer, we achieve a phase-noise measurement system in waveguide (WR1.5). At 670 GHz an upper bound of this system's noise floor is found to be -20, -40, and -60 dBc/Hz at 1, 100, and 10000 Hz offsets, respectively. In addition, a commercial, low-phase-noise, 670 GHz source is measured at offset frequencies from 0.1 Hz to 1 MHz.

We measure and analyze effects of nonlinear mixing of phase-noise modulation (PM) and amplitude-noise modulation (AM) in an oscillating signal by real-time correlations measured in the cross power spectral density (CPSD). We outline sensitive measurements of PM-AM correlation coefficients by means of a time-averaged CPSD measurement technique. Separate but simultaneous PM and AM measurements using a two-channel cross-correlation spectrum analyzer, quantifies the relevant effects of intermodulation mixing with excellent sensitivity compared to traditional 3IM measurements and the scatter-plot correlation technique. Time-averaged cross-spectrum measurements provide good estimates of correlation coefficients as a function of Fourier frequency (f). We use normalized PM-AM CPSD measurements of a 645 MHz quartz-MEMs oscillator as an example and find that 1/f PM-AM CPSD is exactly correlated, even for very widely differing levels of PM and AM noise, in which individual PSDs of PM and AM differ by >40 dB (or, greater than a factor of 10,000). We also verify that white-PM noise has uncorrelated PM-AM CPSD.

A digital phase/amplitude modulation (PM/AM) noise-measurement system (DNMS) implementing field-programmable gate array (FPGA)-based digital down-converters (DDCs), and 250 MHz analog-to-digital converters (ADCs) is reported. Performance in the first, baseband Nyquist region shows white phase-noise floors of less than -180 dBc/Hz. With proper pre-filtering of the input signals to prevent undesired aliasing, high-bandwidth track-and-hold amplifiers (THA) extend the operating range of the DNMS to microwave frequencies. Preliminary testing with an 18 GHz THA shows residual white phase-noise floors at 10 GHz of less than -160 dBc/Hz.

Building optical fiber-based systems presents different challenges than free-space architectures due to the inherent vibration sensitivity of the fiber and the associated components. A survey of the vibration sensitivity of an assortment of commonly used fiber-based optical components is presented to identify problematic parts of a fiber-based design. The measurement of vibration sensitivity is challenging due to the difficulty of separating the sensitivity of the components from the measurement apparatus itself. The noise introduced by the interconnecting fibers bridging between the stationary measurement system and the vibrating device under test can dominate and mask the noise of the device being measured. We propose and demonstrate a novel technique to measure the vibration sensitivity of fiber-based optical components. It uses a common-arm counter-propagating frequency-shifted interferometer that cancels the vibration-induced phase noise of the interconnecting fibers. The proposed technique improves the vibration-induced phase noise floor by more than 30 dB compared to a conventional frequency-shifted Mach-Zehnder interferometer and allows measurement of low vibration sensitive devices.

Frequency-difference-of-arrival (FD to monitor and track an emitter’s location by o frequency shifts of the carrier durin transmissions. This specific application need frequency-stability levels: the short τon-av measurements and the sampling time measurements, denoted by τs. We show the a “dynamic” ThêoH for τon frequency measurem transmissions while powered off, the em oscillator frequency will change due to pow variations, vibration, stress, and other freque If we regard long-term frequency instability on an oscillator's expected or designated fre dominant error of frequency prediction is like due to frequency drift and/or random walk F non-stationary behavior or disturbances. variance is devised, called “Psi-variance,” t statistical properties similar to those of th From this, we compute the power spectral de fluctuations, Sy(f), from which phase noise, L(f

For common FM noise in oscillators, discontinuous measurements with dead-time, small sample statistics, and an assumed /spl chi//sup 2/ distribution, the RMS frequency fluctuations vs. time-interval may be the only reportable measure of frequency stability. We show in a group of simulation trials that in a typical experimental scenario, the RMS frequency stability can seriously underestimate true flicker frequency (FLFM) and random-walk frequency (RWFM) noise and can have larger long-term uncertainty with respect to the zero dead-time Allan deviation and should not be reported as Allan deviation.

Direct observation of phase-modulation (PM) noise is often difficult due to the high dynamic range that exists between the carrier and the modulated sidebands. A common tool used to reduce the dynamic range is the phase detector, which removes the carrier and down-converts its noise sidebands to baseband. The double balanced mixer (DBM) is the most widely used phase detector for high-resolution PM noise detection at most carrier frequencies. For Fourier offset frequencies close to the carrier, the residual flicker phase noise of the DBM is often the limiting factor of a PM noise measurement system. Careful evaluation of the phase detector under various operating conditions can lead to the optimization of a PM noise measurement system's sensitivity. This paper describes a survey of residual PM noise measurements for a variety of DBMs at 5 MHz. In order to attain quality measurements, careful attention is devoted to the reduction of ground loops during PM noise measurements. The input powers to the local oscillator (LO) and reference frequency (RF) ports of the mixers are varied to determine the optimal operating point of these devices.

We propose and demonstrate a novel technique to measure the vibration sensitivity of fiber-based optical components. It uses a common-arm counterpropagating frequency-shifted interferometer that reduces the vibration-induced phase noise of the interconnecting fibers feeding the signal to and from the vibrating device under test. The noise introduced by the vibrating fibers can be excessive, and measurements of a given device cannot be made with assurance. The proposed technique improves the vibration-induced phase noise floor by more than 30 dB compared to a conventional frequency-shifted Mach-Zehnder interferometer and allows measurement of low vibration sensitive devices. A phase sensitivity of 1 mrad/g at 192 Terahertz (THz) is achieved with this method. We also present results of vibration sensitivity of an assortment of commonly used fiber-based optical devices.

The measurement of close-to-carrier phase modulation (PM) noise of state-of-the-art oscillators is always challenging. Quite often the residual noise of the phase detector used in these measurements is higher than the noise of the source at Fourier offset frequencies between 5 and 100 Hz. A conventional double balanced mixer using 2N2222A transistors as the nonlinear components of a diode ring was constructed for use as a phase detector. Residual single-sideband PM noise measurements at 5 MHz for this device have shown a low flicker noise floor of L(10 Hz) = -2163 dBc/Hz. When this mixer design is implemented in a dual-channel measurement system, a cross-correlated PM noise floor of better than L(10 Hz) = 2170 dBc/Hz is expected.