Phase Noise Power Spectral Density Research Articles

High-speed digital-to-analogue converters phase noise modelling

The paper presents a mathematical model of the phase noise power spectral density of a high-speed digital-to-analogue converter. The shapes of the envelopes of the spectrum of the output signal in RFZ3, RFZ4 operating modes are given. The phase noise transfer coefficients for RFZ3, RFZ4 operating modes are obtained. The modelling of the power spectral density of phase noises in the studied operating modes was carried out. The analysis of the received dependences is carried out. It is concluded that RFZ3, RFZ4 modes of operation allow to obtain a lower level of PSD phase noise for images n = 1, 3, 4, 5, which indicates the possibility of generating high-frequency signals with a frequency that is 5-11 times higher than the generated frequency in NRZ mode without noise degradation.

Hybrid synthesizer with two PLLs and DDS Part 2. Fine tuning circuit and main PLL

The use of a direct digital synthesizer (DDS) with a frequency converter in the frequency shift circuit of a hybrid synthesizer of high-frequency oscillations can significantly reduce its phase noise. This version of the frequency synthesizer (FS) has not been previously considered in known publications. There is a need to perform an analysis of existing circuits of hybrid FS with PLL to identify the elements that make the greatest contribution to the phase noise of the output oscillations, develop and experimentally test a FS with a low level of phase noise power spectral density. The performed calculations and experiments show that the use of a frequency shift circuit with frequency conversion based on a DDS operating in the first Nyquist zone in a hybrid frequency synthesizer makes it possible to minimize the effect of DDS phase noises on the FS phase noises. In this case, at frequencies of detuning from the carrier, where the flicker noise of the PFD of PLL circuits in cascade connection prevails, the contribution of the flicker noise of the PLL chips to the noise of the output oscillation of the FS will be equivalent. It is convenient to estimate the phase noise of the FS at the equivalent frequency, determined by the frequency of the phase detector and the division factor in the feedback circuit of the second (main) PLL ring. Taking into account the results of the first part of this work, the calculated relations obtained allow us to design hybrid frequency synthesizers with DDS and PLL with a low level of phase noise. The expressions obtained in the work for the phase noise of a hybrid FS and its components also make it possible to estimate the potentially achievable levels of FS phase noise and can be used in calculating the characteristics of oscillation sources and signal synthesizers.

Mitigation of noise in Josephson parametric oscillator by injection locking

Injection locking is a well-established technique widely used in optics as well as solid-state devices for efficient suppression of noise. We present the spectroscopic characterization of the effect of the injection-locking signal (ILS) in mitigating the phase noise of a Josephson parametric oscillator, whose output oscillating phase undergoes indeterministic switching between the bistable states with symmetry θ→θ+π. With the injection of a weak locking signal, we measure the phase noise power spectral density of the self-sustained oscillator output state for different locking signal strengths. We observed suppression of phase noise by injection locking. As the ILS strength surpasses more than a few photons, the output state stays completely pinned to the locking phase of the ILS, and the random telegraphic noise due to switching of the states is significantly suppressed.

A Novel Approach for Modeling and Digital Generation of RF Signals Distorted by Bandlimited Phase Noise

In radar and communication systems, phase noise is one of the main causes of performance degradation. Phase noise increases the uncertainty in radar measurements and limits the achievable data rates in communication systems. When radio frequency (RF) signals distorted by bandlimited phase noise are modeled, the phase noise power spectral density (PSD) is usually approximated by a scalar root-mean-square (RMS) phase error derived from a simple integration of the PSD. This disregards the close-to-carrier noise excess. In this article, we show that this convention simplification describes the real behavior of phase noise inadequately. In addition, we present a simulation of realistic phase noise behavior. The novel additive colored noise (ACN) model requires a representative phase noise PSD of the phase-locked loop (PLL) signal generator phase noise to be modeled. The developed ACN approach is validated by comparing the measured PSD of different PLL signal generators with the respective simulated RF signals distorted by phase noise. As a simple metric for assessing the quality of the phase noise models, we use the influence of phase noise on carrier frequency estimation. It is shown that the novel approach shows a significant improvement in the agreement between the simulated and measured precision compared to standard additive white Gaussian noise (AWGN) models. The results show that advanced phase noise models, as proposed in this paper, are necessary to adequately model and predict the performance of radar and communication systems.

Detailed Analysis and Modeling of Phase Noise and Systematic Phase Distortions in FMCW Radar Systems

In coherent continuous-wave (CW) radar systems, such as frequency-modulated CW (FMCW) radar systems, measurement precision is distorted by phase noise and systematic phase errors during radar signal generation. Unfortunately, to date, these phase distortions have typically been modeled based on many simplifications, often leading to overoptimistic predictions of radar performance. For example, phase noise is regularly considered based on additive white Gaussian noise (AWGN) models, ignoring its colored spectral property. Systematic errors are also frequently not properly separated from stochastic distortions, or not precisely measured and modeled. To overcome these issues, an advanced CW radar and frequency synthesizer model is proposed, analyzed, and experimentally verified in this paper. It is shown how systematic phase errors can be measured and how the influence of phase distortions on radar measurement can be accurately predicted. The proposed modeling approach was investigated for range correlation and range precision. The key metrics are the phase noise power spectral density (PSD) for range correlation and the variance of the frequency estimate for range precision. A 24-GHz FMCW radar system was used for the experimental verification. Long-range radar targets with distances of 38 to 880 m were created with an analog fiber optical link. Therefore, a precise and systematic evaluation of all effects was possible. The proposed phase distortion modeling approach realistically represented the range-dependent radar measurement effects. This enables the most precise simulation of and prediction for FMCW radar performance to date.

Coherent fibre link for synchronization of delocalized atomic clocks.

Challenging experiments for tests in fundamental physics require highly coherent optical frequency references with suppressed phase noise from hundreds of kHz down to μHz of Fourier frequencies. It can be achieved by remote synchronization of many frequency references interconnected by stabilized optical fibre links. Here we describe the path to realize a delocalized optical frequency reference for spectroscopy of the isomeric state of the nucleus of Thorium-229 atom. This is a prerequisite for the realization of the next generation of an optical clock - the nuclear clock. We present the established 235 km long phase-coherent stabilized cross-border fibre link connecting two delocalized metrology laboratories in Brno and Vienna operating highly-coherent lasers disciplined by active Hydrogen masers through optical frequency combs. A significant part (up to tens of km) of the optical fibre is passing urban combined collectors with a non-negligible level of acoustic interference and temperature changes, which results in a power spectral density of phase noise over 105 rad2· Hz-1. Therefore, we deploy a digital signal processing technique to suppress the fibre phase noise over a wide dynamic range of phase fluctuations. To demonstrate the functionality of the link, we measured the phase noise power spectral density of a remote beat note between two independent lasers, locked to high-finesse stable resonators. Using optical frequency combs at both ends of the link, a long-term fractional frequency stability in the order of 10-15 between local active Hydrogen masers was measured as well. Thanks to this technique, we have achieved reliable operation of the phase-coherent fibre link with fractional stability of 7 × 10-18 in 103 s.

Phase Noise Monitoring in Cascaded Systems for High-Resolution Automotive Radar Sensors

The trend toward a higher degree of automation in modern cars demands radar sensors providing a significantly increased angular resolution. This is achieved by increasing the number of transmit and receive channels, which is most commonly done by cascading several radar monolithic microwave integrated circuits (MMICs). As for single MMIC radar solutions, the phase noise (PN) contained in the transmit signal is one of the most dominant signal distortions limiting detection sensitivity and range also in cascaded radar systems. In this work, we present a novel method to estimate the mean PN power spectral density (PSD) of two radar MMICs in operation. This estimation result is used to detect whether the frequency-generating circuit of the involved MMICs generate PN out of specification. Different to most of the existing methods, the proposed approach is based on an application relevant frequency modulated continuous wave (FMCW) signal, which is actually used to perform a radar measurement, instead of a continuous wave (CW) signal. Finally, the presented concept is verified based on simulations and with the help of measurement data.

Frequency domain analysis of optoelectronic oscillators utilizing optical and RF resonators with arbitrary transfer functions

Optoelectronic oscillators (OEOs) have attracted much attention for producing ultra-low phase-noise microwave/millimeter-wave oscillations. Traditional delay-based OEOs usually suffer from strong spurious peaks in their phase noise power spectral densities and possible mode-hopping phenomena. Some methods have been proposed in the literature such as using multi-loop architectures or injection locking to other OEOs or radio frequency (RF) oscillators to reduce these spurious peaks. In other approaches, optical filters/resonators other than optical fibers have been proposed to reduce or suppress these peaks and prevent the mode-hopping phenomenon, such as whispering gallery mode resonators (WGMRs), fiber Bragg gratings, and other forms of microwave photonic filters. Usually, approximate single-purpose approaches have been presented to analyze OEOs utilizing such resonators. Here a general framework for analyzing the performance of OEOs implementing RF and optical filters/resonators with arbitrary linear transfer functions is presented. Consequently, it can consider, for example, the most general dispersion models of the fibers as well as any OEO architecture using a combination of different optical resonators. It can also consider the noise transfer between any sidebands of the RF or optical signals and any kind of amplitude noise to phase noise transfers and vice versa. The non-idealities of the electro-optic modulators such as the chirping and finite extinction ratios can also be taken into account. The validity of the new approach is verified by comparing its results with those previously published in the literature. In particular, the case of a WGMR plus delay line OEO is considered for comparisons.

Cascaded Microwave Frequency Transfer over 300-km Fiber Link with Instability at the 10−18 Level

Comparing and synchronizing atomic clocks between distant laboratories with ultra-stable frequency transfer are essential procedures in many fields of fundamental and applied science. Existing conventional methods for frequency transfer based on satellite links, however, are insufficient for the requirements of many applications. In order to achieve high-precision microwave frequency transfer over a thousand kilometers of fiber and to construct a fiber-based microwave transfer network, we propose a cascaded system for microwave frequency transfer consisting of three 100-km single-span spooled fiber links using an improved electronic phase compensation scheme. The transfer instability measured for the microwave signal reaches 1.1 × 10−14 at 1 s and 6.8 × 10−18 at 105 s, which agrees with the root-sum-square of each span contribution. It is feasible to extend the length of the fiber-based microwave frequency transfer up to 1200 km using 4 stages of our cascaded system, which is still sufficient to transfer modern cold atom microwave frequency standards. Moreover, the transfer instability of 9.0 × 10−15 at 1 s and 9.0 × 10−18 at 105 s for a 100-MHz signal is achieved. The residual phase noise power spectral density of the 300-km cascaded link measured at 100-MHz is also obtained. The rejection frequency bandwidth of the cascaded link is limited by the propagation delay of one single-span link.

All-passive multiple-place optical phase noise cancellation

We report on the realization of delivering coherent optical frequency to multiple places based on passive phase noise cancellation over a bus topology fiber network. This technique mitigates any active servo controller on the main fiber link and at arbitrary access places as opposed to the conventional technique, in which an active phase compensation circuit has to be adopted to stabilize the main fiber link. Although the residual fiber phase noise power spectral density in the proposed technique turns out to be a factor of seven higher than that of in the conventional multiple-access technique when the access place is close to the end of the fiber link, it could largely suppress the phase noise introduced by the servo bumps, improve the response speed and phase recovery time, and minimize hardware overhead in systems with many stations and connections without the need for active servo circuits including phase discriminators and active compensators. The proposed technique could considerably simplify future efforts to make precise optical frequency signals available to many users, as required by some large-scale science experiments.

Power spectral density analysis of relative comb-line phase jitter in a twin-soliton molecule

Investigation on the relative phase evolution between two bounded optical solitons is essential for its potential applications in development of larger telecommunication capacity of optical fiber transmission lines, resolution improvement in advancing ultrafast characterization approaches and development of all-optical information storage. Here we characterized relative comb-line phase jitter power spectral density (PSD) of a soliton molecule pair generated from a passively mode-locked Er:fiber laser. Through tracking the intensity difference between two selected wavelengths in one certain spectral interference fringe, the relative comb-line phase noise PSD is measured by balanced detection. The estimated measurement resolution is at 10−14 rad2/Hz level and the estimated integrated phase noise from 10 MHz to 100 Hz is 2.04 mrad. The estimated relative linewidth is far below 1 mHz. Comparison between phase noise PSD and intensity noise PSD indicates that AM–PM conversion plays an important role in relative phase jitter dynamics between the two solitons. Our spectral interference fringe tracking technique is attractive for its simplicity and shows potential in ultra-high resolution in phase noise measurement, providing an ultra-sensitive alternative approach for relative phase noise stabilization of optical soliton molecules, two independent mode-locked lasers and optical length stabilization of interferometers.

Algorithm for designing low-noise frequency synthesizers for remote sensing systems

Frequency synthesizer is an important component of radar tracking system for remote sensing. Synthesizers generate wideband radio frequency signals with high frequency resolution. Parameters of radar depend on the synthesizers phase noise. This paper presents algorithm for structural design of signal generators based on various synthesis methods: direct, indirect and hybrid ones. Specialized software based on presented algorithm was developed in this work. Software allows calculating frequency ratios in the structure of synthesizers, selecting optimal parameters which can provide low phase noise level. Also software allows performing mathematical modelling and analysis of phase noise power spectral density (PSD) of frequency synthesizers. Presented algorithm and software can be useful for developers of remote sensing radio systems.

Low-noise hybrid frequency synthesizers based on direct digital and direct analog synthesis

The research of the possibility of using hybrid frequency synthesizers based on direct digital and direct analog methods of frequency synthesis as heterodynes of modern spectrum analyzers constructed according to the superheterodyne scheme is presented. The main advantages of such synthesizers over traditionally used heterodyne schemes based on direct digital and indirect frequency synthesis methods are shown. The requirements for the heterodynes of the first mixing stages of spectrum analyzers are presented. A block diagram of a wideband heterodyne generating a frequency range from 4000 MHz to 8000 MHz with a step not exceeding 1 Hz is proposed. Formulas for calculating the main frequency ratios in the structure of the heterodyne have been developed. A mathematical model of phase noise power spectral density (PSD) depending on the offset frequency from the carrier is developed. The noise characteristics of the proposed scheme are studied using the model. It is determined that at the output frequency of the heterodyne equal to 4521,4 MHz, the level of phase noise PSD is: minus 90 dBc/Hz at the offset frequency equal to 100 Hz; minus 140 dBc/Hz at the offset frequency equal to 100 kHz. It is shown that the hybrid synthesizer based on direct digital and direct analog synthesis methods has an advantage in the level of phase noise from 5 to 30 dB over the low-noise heterodynes of modern spectrum analyzers at frequencies above 1 kHz from the carrier. Additional advantages of the proposed scheme are a simple architecture, low power consumption and high frequency tuning speed due to the absence of phaselocked loops in the structure of the heterodyne.

Phase Noise in Modular Millimeter Wave Massive MIMO

This paper investigates the effect of oscillator phase noise on a multiuser millimeter wave (mmWave) massive MIMO uplink as we scale up the number of base station antennas, fixing the load factor, defined as the ratio of the number of simultaneous users to the number of base station antennas. We consider a modular approach in which the base station employs an array of subarrays, or “tiles.” Each tile supports a fixed number of antennas, and can therefore be implemented using a separate radio frequency integrated circuit (RFIC), with synchronization across tiles accomplished by employing a phased locked loop in each tile to synthesize an on-chip oscillator at the carrier frequency by locking on to a common lower frequency reference clock. Assuming linear minimum mean squared error (LMMSE) multiuser detection, we provide an analytical framework that can be used to specify the required power spectral density (PSD) mask for phase noise for a target system performance. Our analysis for the phase noise at the output of the LMMSE receiver indicates two distinct effects: self-noise for each user which is inversely proportional to the number of tiles, and cross-talk between users which is insensitive to the number of tiles, and is proportional to the load factor. These analytical predictions, verified by simulations for a 140 GHz system targeting a per-user data rate of 10 Gbps, show that tiling is a robust approach for scaling. Numerical results for our proposed design approach yield relatively relaxed specifications for phase noise PSD masks.

Regenerative Talbot Laser for Generating Tunable Pulse Train With a Low Phase Noise

We propose and demonstrate an improved Talbot laser including a regenerative RF feedback loop. This architecture greatly enhances both amplitude and noise performances of the pulsed laser, while preserving the broadband tunability of its repetition rate. The phase noise power spectral density of the associated RF signal is found to be independent of the repetition rate. For a 4.9 GHz repetition rate, the timing jitter is as low as 54 fs (integrated between 10 kHz and 100 MHz offset frequency). This architecture paves the way towards tunable high performances coupled opto-electronic microwave oscillators.

Comparison of Optical Frequency Comb and Sapphire Loaded Cavity Microwave Oscillators

The single-sideband phase noise power spectral density and Allan deviation of a portable microwave oscillator system based on an optical frequency comb stabilized to an ultra-low expansion Fabry-Perot reference cavity is characterized at carrier frequencies of 4.0, 8.0, and 16.0 GHz. Compared to industry standard sapphire loaded cavity oscillators, the photonic microwave oscillator shows superior phase noise at offset frequencies $3.0 \times 10^{-14}$ obtains at an averaging time of 400 ms.

Evaluation of Fiber Noise Induced in Ultrastable Environments

Phase noise induced by environmental disturbance was greatly reduced when the optical fiber was installed in an ultrastable environment. In this paper, the optical fiber length was 10 m, and the reduction in the phase noise power spectral density was approximately 70 and 30 dB at Fourier frequencies of 10 mHz and 10 Hz, respectively. To evaluate faint fiber noise, we developed a modified Mach–Zehnder heterodyne interferometer with reduced optical path length fluctuation. The Allan deviation calculated from the phase noise was $7 \times 10^{-20}$ at a 1-s averaging time and reached $2 \times 10^{-21}$ at a 10 000-s averaging time (measurement bandwidth: 500 Hz). In addition, we revealed the frequency bands in which fiber noise is reduced by selectively removing the environmental stabilization measures of evacuation, vibration isolation, acoustic shielding, and temperature stabilization from an ultrastable environment.

Influence of the Parameters of Schottky Barriers of AlGaN/GaN/SiC HEMT Transistors on the Phase Noise of Microwave Generators

Microwave HEMT transistors based on gallium nitride (a novel wide-band-gap material) allow us to construct advanced radioelectronic systems. Therefore, the determination of the relation between the parameters of the transistor structure and the characteristics of microwave generators based on HEMT transistors is a relevant problem. The connection between the capacitance parameters of gate–drain Schottky barriers of AlGaN/GaN/SiC transistors and the phase noise power spectral density of microwave generators based on these transistors is analyzed. A set of power 6-finger transistors of the X band with a gate length of 0.25 μm, plated holes connecting the source region to the backside of the crystal, and field plates are studied. The C–V characteristics of most crystals are found to have a peak in the region of transition from enhancement to depletion in the measurements performed at frequencies f < 500 kHz. The height of this peak increases with a reduction in the measurement frequency. A rigid correlation between the height of the characteristic capacitance peak in the C–V curves and the power spectral density of the phase noise of the microwave generator based on the corresponding transistor crystal from the studied set is revealed. This correlation may be attributed to the presence of trap centers both in the barrier AlGaN layer and the structure interfaces.

Fully-correlated multi-mode pumping for low-noise dual-frequency VECSELs.

We report a fully-correlated multi-mode pumping architecture optimized for dramatic noise reduction of a class-A dual-frequency Vertical External Cavity Surface Emitting Laser (VECSEL). Thanks to amplitude division of a laser diode, the two orthogonally polarized modes emitted by the VECSEL oscillating at 852 nm are separately pumped by two beams exhibiting fully in-phase correlated intensity noises. This is shown to lead to very strong and in-phase correlations between the two lasing modes intensities. As a result, the phase noise power spectral density of the RF beat note generated by the two modes undergoes a drastic reduction of about 10 to 20 dB throughout the whole frequency range from 10 kHz to 20 MHz and falls below the detection floor above a few MHz. A good agreement is found with a model which uses the framework of rate equations coupled by cross-saturation. The remaining phase noise is attributed to thermal effects and additional technical noises and lies mainly within the bandwidth of a phase-locked-loop.

Highly Efficient Environment for FMCW Radar Phase Noise Simulations in IF Domain

One of the most dominant signal distortions in a frequency modulated continuous wave (FMCW) radar system is the phase noise (PN) contained in the transmit signal. It has significant impact on the detection sensitivity and range. In this brief, we present a system simulator that directly generates the intermediate frequency (IF) signal of an FMCW radar system, without any computations in the radio frequency (RF) domain. Thus, the simulation can be performed up to about 30 times faster than a corresponding RF simulation, for an arbitrarily shaped input PN power spectral density (PSD). As a major contribution of this brief, an analytical expression for the average PSD of the residual cyclostationary part of the IF signal, which depends on the so-called decorrelated phase noise, is derived. Finally, the simulations are compared with the analytical average PSD as well as with measurement results, and excellent conformance can be observed.