Phase Noise Spectral Density Research Articles

Multiple-access ultrastable frequency dissemination based on optical frequency combs via a fiber link.

We demonstrate an optical fiber-based, multiple-access frequency transmission using two optical frequency combs. The experimental results using the Allan deviation analysis show that with the phase compensation technique, the frequency instabilities at the remote site are 8.7 × 10-15/1 s and 1.0 × 10-17/103 s, and at the accessing node along the fiber link, the frequency instabilities are 6.9 × 10-15/1 s and 1.1 × 10-17/103 s. Similarly, the power spectral density of phase noise was analyzed in the frequency domain. These experimental results demonstrate that the compensation scheme improved the performance by two to three orders of magnitude. Thus, the proposed frequency transmission technique has potential application for disseminating ultrastable frequency references in the optical fiber network.

VHF crystal oscillator noise Part 2. Experimental and calculated data

Problem statement. The noise of radar local oscillator reference oscillation sources often prevails among the noise of the local oscillator signals. At long ranges, this leads to significant distortion of the results of processing weak reflected signals in radars. One of the ways to reduce the noise of the local oscillator signals is the use of VHF crystal oscillators with a low noise level. Goal. To obtain equations for the power spectral density of phase noise, as well as for random deviations of the oscillation phase of a model of a VHF crystal oscillator. Results. Equations for the power spectral density of phase noise, as well as for random deviations of the oscillation phase of a model of a VHF crystal oscillator are obtained. Practical significance. These theoretical and practical results obtained allow a more selective approach to the selection of parameters of high-frequency crystal oscillators for use as sources of local oscillator oscillations.

On the stability & phase locking to a system reference of an optoelectronic oscillator with large delay

Delay line oscillators based on photonic components, offer the potential for realization of phase noise levels up to 3 orders of magnitude lower than achievable by conventional microwave sources. Fibreoptic-based delay lines can realize the large delay required for low phase noise systems whilst simultaneously achieving insertion loss levels that can be compensated with available microwave and photonic amplification technologies. Multimode operation is an artefact of the delay line oscillator and introduces modulational instability into phase-locked control loops. An optoelectronic oscillator (OEO) with large delay under proportional integral control by a phase-locked loop (PLL) is modelled, providing the first report of the location of all the infinity of poles of the PLL-OEO system function. The first experimental observation of giant phase modulated oscillation of a free OEO and spontaneous giant phase modulated oscillation of a PLL-OEO are also reported and explained respectively as a source and manifestation of modulational instability. Nevertheless, the analysis and experimental observations, including a prototype 10 GHz PLL-OEO phase noise spectral density achieving - 80dBc/Hz {text{at}} 10 Hz and - 145dBc/Hz {text{at}} 10 kHz, demonstrate that stable phase lock operation and optimum phase noise performance is achievable provided full account of the multimode nature of the OEO is taken in the phase lock analysis.

Oscillators Based on Step-Impedance and Slow Wave Transmission Lines for Sensing Applications

This work investigates the capabilities of oscillators based on step-impedance and slow wave structures to sense dielectric constants. The material under test (MUT) is placed over the structure and the objective is to achieve a high sensitivity of the oscillation frequency with the advantage of low phase noise, enabled by the high quality factor of the structure. With the aid of simplified analytical models, we will initially study the variation of the resonance frequency of a istep-impedance transmission line with the dielectric constant of the MUT, paying attention to the influence of the number of line sections. The study includes the derivation of analytical expressions for the sensitivity of the resonance frequency. Next, the structure will be connected to the oscillator active core, which will be modeled with a numerical nonlinear admittance function extracted from harmonic-balance (HB) simulations. The resulting semianalytical formulation will provide insight into the variation of the oscillation frequency and amplitude with the dielectric constant of the MUT, as well as the variation of the phase-noise spectral density. It will also enable a versatile test and optimization of the various structures to achieve high sensitivity with low phase noise. The methods have been successfully applied to an field-effect transistor (FET)-based oscillator at about 2 GHz.

Phase Noise Spectral Density Measurement of Broadband Frequency-Modulated Radar Signals

In continuous-wave (CW) radar systems, such as frequency-modulated (FMCW), frequency-stepped (FSCW), or orthogonal frequency-division multiplexing (OFDM) radar systems, the range and velocity uncertainty are significantly impaired by phase noise decorrelation. Therefore, radar designers require accurate knowledge of their synthesizers’ phase noise profiles to assess and predict radar performance. However, commercial phase noise analyzers cannot determine phase noise during modulation, and this may differ notably from phase noise in the pure CW mode. Recent methods for FMCW phase noise analysis usually require comprehensive <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${a}$ </tex-math></inline-formula> <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">priori</i> knowledge of modulation parameter and are prone to systematic deviations. To overcome these issues, we propose a new approach based on differential analysis of subsequent time-domain measurements. This method retains, statistical phase noise information while reducing systematic influences. For the first time, less <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${a}$ </tex-math></inline-formula> <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">priori</i> signal knowledge is required, and the method works for nearly any kind of broadband signal modulation. The concept requires only a digitizer (e.g., an oscilloscope) and some digital signal processing. The proposed method is first experimentally tested with different phase-locked-loop (PLL)-based synthesizer phase noise profiles. The obtained phase noise profiles agree perfectly with the results of an established measurement system. After this proof of basic functionality, the unique phase noise analysis capability for BB modulated signals is demonstrated with PLL-generated FMCW signals. The results reveal a significant phase noise difference between the different setups and clearly show the capability and benefit of the novel phase noise spectral density measurement concept.

Comparison of modified Woo’s solar phase scintillation model with ESA’s BepiColombo superior solar conjunction measurement data for X-band and Ka-band

Solar phase scintillation is of major interest in deep space mission operations for designing a communications system capable of transmitting signals when the path is close to the Sun, but also for improving the navigation under these conditions. The basis of this work is Woo’s solar phase scintillation theory which reported a useful model for the spectral power density of phase scintillations of a signal traveling through a medium close to the Sun. In this paper, Woo’s solar phase scintillation formula is used for the simulation of the spectral density of phase fluctuations induced by the Sun on coherent signals (uplink and downlink carriers are coherently related by a fractional ratio implemented by the spacecraft’s transponder), for the two downlink frequency bands supported by the ESA deep space mission BepiColombo. In particular, the model has been compared to measurement data collected at low Sun Earth Probe (SEP) angles during the superior solar conjunction campaign in March 2021 (in its cruise phase to Mercury). The comparison shows a good match between the phase noise spectral densities of the modified formula and measurement data, therefore, confirming that the formula can be used for the planning and verification of the future near Sun measurements.

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.

Mathematical models of noise characteristics of high-speed digital-to-analog converters of radar signal generators

A mathematical model of the power spectral density of phase noise of high-speed digital-to-analog converters in one side frequency band of tuning is obtained. Calculated using the developed mathematical model of the power spectral density of phase noise of high-speed digital-to-analog converters from Analog Devices in the efficiency mode in the NRZ baseband showed a small error in comparison with the experimental characteristics. It is shown that in the 2 × NRZ oversampling mode, the phase noise level of the high-speed DAC is 7-8 dBc/Hz lower than in the main NRZ operation mode.

DIRECT DIGITAL SYNTHESIZER IN A NEW MATHEMATICAL BASIS

The principles of the construction and operation of a digital synthesizer for direct frequency synthesis with acceleration of computational operations by using a residual class system (RNS) are considered. The specifics of the implementation of the operation of direct and inverse transformations from the positional number system to the number system of the residual classes are described. A mathematical model of a synthesizer with a phase accumulator in the system of residual classes is considered. The ways of designing a digital synthesizer of direct synthesis with a phase accumulator in the RNS system and a sinusoidal DAC are considered. In traditional schemes, the conversion of residuals to the value of an analog signal occurs in several stages, where conversion to a binary system is one of the stages. This procedure degrades the speed of the RNS system, adding additional constraints and increasing the waiting time for the conversion result. Methods of converting from RNS to binary number system for basic operations are considered. A DDS design with a phase accumulator in the residual class system and a converter to an analog signal form without using a slow ROM is proposed. The problems of efficient use of the synthesizer crystal area and reduction of delays in the formation of the output signal are considered. A study of one of the main functional blocks of a direct digital frequency synthesizer, a digital-to-analog converter, has been carried out. The architecture of a direct digital frequency synthesizer with a DAC direct conversion from a non-positional number system to an analog signal is proposed. The main sources of noise generation in digital computational synthesizers of the proposed type are investigated. A mathematical model is proposed for calculating the power spectral density of phase noise, which will allow analyzing the noise characteristics in synthesizers built on the indicated principles.

300 GHz wave generation based on a Kerr microresonator frequency comb stabilized to a low noise microwave reference.

In this Letter, we experimentally demonstrate low noise 300 GHz wave generation based on a Kerr microresonator frequency comb operating in the soliton regime. The spectral purity of a 10 GHz GPS-disciplined dielectric resonant oscillator is transferred to the 300 GHz repetition rate frequency of the soliton comb through an optoelectronic phase-locked loop. Two adjacent comb lines beat on a uni-traveling carrier photodiode emitting the 300 GHz millimeter-wave signal into a waveguide. In an out-of-loop measurement, we measure the 300 GHz power spectral density of phase noise to be -88dBc/Hz, -105dBc/Hz at 10 kHz, and 1 MHz Fourier frequency, respectively. Phase-locking error instability reaches 2×10-15 at 1 s averaging time. Such a system provides a promising path to the realization of compact, low power consumption millimeter-wave oscillators with low noise performance for out-of-the-laboratory applications.

Analysis of high-order sub-harmonically injection-locked oscillators

AbstractHigh-order sub-harmonically injection-locked oscillators have recently been proposed for low phase-noise frequency generation, with carrier-selection capabilities. Though excellent experimental behavior has been demonstrated, the analysis/simulation of these circuits is demanding, due to the high ratio between the oscillation frequency and the frequency of the input source. This work provides an analysis methodology that covers the main aspects of the circuit behavior, including the detection of the locking bands and the prediction of the phase-noise spectral density. Initially, the oscillator in the presence of a multi-harmonic input source is described with a reduced-order envelope-domain formulation, at the oscillation frequency, based on an oscillator-admittance function extracted from harmonic-balance simulations. This allows deriving an expression for the oscillation phase shift with respect to the input source, and the average of this phase shift is shown to evolve continuously in the distinct synchronization bands obtained when varying a tuning voltage. This property can be used to detect the locking bands in circuit-level envelope-domain simulations, which, as shown here, can be done through different Fourier decompositions and sampling rates. The phase noise of the high-order sub-harmonic injection-locked oscillator under an arbitrary periodic input waveform is investigated in detail. The frequency response to the noise sources is described with a semi-analytical formulation, relying on the oscillator-admittance function in injection-locked conditions. The input noise is derived from the timing jitter of the injection source and the phase-noise response is shown to exhibit a low-pass characteristic, which initially follows the up-converted input noise and then the oscillator own noise sources. A method is proposed to identify the key parameters of the derived phase-noise spectrum from envelope-domain simulations. The various analysis methodologies have been applied to a prototype at 2.7 GHz at the sub-harmonic order N = 30 which has been manufactured and measured.

Wireless-Coupled Oscillator Systems With an Injection-Locking Signal

A detailed analysis of wireless-coupled oscillator systems under the effect of an injection-locking signal is presented. The injection source of high spectral purity is introduced at a single node and enables a reduction of the phase-noise spectral density. Under this injection source, the behavior of the coupled system is qualitatively different from the one obtained in free-running conditions. Two cases are considered: bilateral synchronization, in which an independent source is connected to a particular system oscillator, coupled to the other oscillator elements, and unilateral synchronization, in which one of these elements is replaced by an independent source that cannot be influenced by the rest. The two cases are illustrated through the analysis of a wireless-coupled system with a star topology, such that the injection signal is introduced at the central node. The investigation involves an insightful analytical calculation of the coexisting steady-state solutions, as well as a determination of their stability and bifurcation properties and phase noise. The injection signal stabilizes the system in a large and continuous distance interval, enabling a more robust operation than in autonomous (noninjected) conditions. A coupled system operating at 2.45 GHz has been manufactured and experimentally characterized, obtaining a very good agreement between simulations and measurements.

High-detectivity optical heterodyne method for wideband carrier-envelope phase noise analysis of laser oscillators.

Broadband characterization of the carrier-envelope phase (CEP) noise spectral density of free-running mode-locked lasers is essential for advanced low-noise optical frequency comb designs. Here we present a direct method that utilizes an optical heterodyne beat between a pair of repetition-rate-locked mode-locked lasers for CEP noise characterization, without requiring an f-2f interferometer or nonlinear optical conversion steps. A proof-of-principle experiment in a femtosecond Yb-fiber laser achieves CEP noise spectral density characterization with >270 dB dynamic range over a Fourier frequency range from 5mHz to 8MHz. The measurement noise floor is well below 1 μrad/√Hz, enabling dependable detection down to a quantum-limited noise floor. The method can resolve various noise mechanisms that cause specific CEP noise spectral shapes. The underlying mechanisms are further analyzed in terms of spurious temporal correlation to distinguish between technical and stochastic noise signatures. Moreover, a Hadamard deviation analysis reveals a varying degree of frequency stability in the measured CEP time series.

Analysis of Output Loading Effects in Autonomous Circuits

A methodology is presented to analyze the impact of the termination load on the oscillation frequency and output power of autonomous circuits. Variations of this load can also lead to an extinction of the oscillation signal, due to their effect on the impedance seen by the active device(s). The new methodology enables an efficient analysis and mitigation of the pulling effects, in the case of undesired output mismatch, as well as an efficient oscillator synthesis in large-signal conditions, for specified values of oscillation frequency and output power. The method is based on the calculation of constant-amplitude and constant-frequency contours, traced in the Smith chart. Oscillation extinctions and some forms of hysteresis can be predicted through the inspection of these contours. However, the stability properties will generally depend on the frequency characteristic of the termination impedance. In an oscillator synthesis, the selected impedance, providing the specified values of oscillation frequency and output power, must be implemented in order to guarantee a stable solution. The dependence of the phase-noise spectral density on the particular implementation is predicted, combining an analysis based on the variance of the phase deviation with the conversion-matrix approach.

アンダーサンプリングを用いたフルディジタル位相雑音計測におけるノイズフロアの推定とその特性

This paper describes phase noise floor level of digital phase noise measurement. It has estimated the noise floor level of phase noise from ENOB of the analog to digital converter and sampling frequency. We have discussed phase noise measurement using normal sampling based on sampling theorem and under sampling which samples longer sampling period than the signal under the test. We compared the phase noise spectral density of noise floor between normal sampling and under sampling. As a result, measurement results are in good agreement in both methods.

Acousto-optic pulse picking scheme with carrier-frequency-to-pulse-repetition-rate synchronization.

We introduce and experimentally validate a pulse picking technique based on a travelling-wave-type acousto-optic modulator (AOM) having the AOM carrier frequency synchronized to the repetition rate of the original pulse train. As a consequence, the phase noise characteristic of the original pulse train is largely preserved, rendering this technique suitable for applications requiring carrier-envelope phase stabilization. In a proof-of-principle experiment, the 1030-nm spectral part of an 74-MHz, carrier-envelope phase stable Ti:sapphire oscillator is amplified and reduced in pulse repetition frequency by a factor of two, maintaining an unprecedentedly low carrier-envelope phase noise spectral density of below 68 mrad. Furthermore, a comparative analysis reveals that the pulse-picking-induced additional amplitude noise is minimized, when the AOM is operated under synchronicity. The proposed scheme is particularly suitable when the down-picked repetition rate is still in the multi-MHz-range, where Pockels cells cannot be applied due to piezoelectric ringing.

Low-power Ka band injection-locked frequency dividers using distributed LC tanks

This article presents low-power injection-locked frequency dividers (ILFD) operating in the Ka band. To achieve low-power operation, we use two circuit techniques to reduce the effects of the capacitance and resistance. To achieve a high oscillation frequency by reducing the effective capacitance, a distributed LC tank with a split auxiliary negative-gm cell is used. To achieve a high loop gain for a given power, we reduce the gate resistance by modifying the foundry-provided transistor layout. Two versions of the divider, which have different inductor implementations, are fabricated in 1-poly 9-metal 65-nm low-power RFCMOS. When biased at 1 V and 1 mA, the ILFD shows successful injection locking at 34 GHz with −35 dBm input power. When biased at 1.2 V and 3 mA, the input frequency ranges from 32.3 to 34.6 GHz at 5 dBm input power. Good phase noise spectral density of −126.6 and −132.0 dBc/Hz at a 1-MHz offset is achieved. © 2015 Wiley Periodicals, Inc. Microwave Opt Technol Lett 57:1379–1383, 2015

Optical injection locking of monolithically integrated photonic source for generation of high purity signals above 100 GHz.

A monolithically integrated photonic source for tuneable mm-wave signal generation has been fabricated. The source consists of 14 active components, i.e. semiconductor lasers, amplifiers and photodetectors, all integrated on a 3 mm(2) InP chip. Heterodyne signals in the range between 85 GHz and 120 GHz with up to -10 dBm output power have been successfully generated. By optically injection locking the integrated lasers to an external optical comb source, high-spectral-purity signals at frequencies >100 GHz have been generated, with phase noise spectral density below -90 dBc/Hz being achieved at offsets from the carrier greater than 10 kHz.

Quasi-planar K-band push-push low phase noise oscillator stabilized by cavity resonator

The results of developing a K-band (24 GHz) push-push low phase noise transistor oscillator have been presented. This oscillator is stabilized by a rectangular resonant metallic cavity. The power level of output signal is −9.5 dBm, the fundamental harmonic suppression is 21 dB. Single sideband (SSB) phase noise spectral density of −98 dBc/Hz at 10 kHz and −128 dBc/Hz at 100 kHz offset from the carrier frequency is at the level of dielectric resonator oscillators (DRO) scaled to the same frequency. The oscillator features a compact size, low cost quazi-planar design and it is built using commercially available off the shelf parts.

Phase noise of self-sustained optomechanical oscillators

In this paper we present a theory that predicts the phase noise characteristics of self-sustained optomechanical oscillators. By treating the cavity optomechanical system as a feedback loop consisting of an optical cavity and a mechanical resonator, we analytically derive the transfer functions relating the amplitude and phase noise of all the relevant dynamical quantities from the quantum Langevin equations, and obtain a closed-form expression for the phase noise spectral densities contributed from thermomechanical noise, photon shot noise, and low-frequency technical laser noise. We numerically calculate the phase noise for various situations and perform a sample calculation for an experimentally demonstrated system. We also show that the presented model reduces to the well-known Leeson's phase noise model when the amplitude noise and the amplitude to phase noise intertransfers are ignored. This paper not only addresses the practical questions about oscillator phase noise characteristics but also presents a theoretical framework for studying cavity optomechanical systems with large oscillation amplitude.