Theoretical study of the Dick effect in a continuously operatedRamsey resonator

It is well established that passive frequency standards operated in pulsed mode may suffer a degradation of their frequency stability due to the frequency (FM) noise of the Local Oscillator (LO). In continuously operated frequency standards, it has been shown that a similar degradation of the frequency stability may arise, depending on the used modulation-demodulation scheme. In this paper, we report a theoretical analysis on the possible degradations of the frequency stability of a continuous fountain due to the LO FM noise. A simple model is developed to evaluate whether or not aliasing persists. This model is based on a continuous frequency control loop of a frequency standard using a Ramsey resonator. From this model, we derive a general formula, valid for all usual modulation-demodulation schemes, for the LO frequency fluctuations due to aliasing in closed loop operation. We demonstrate that in an ideal situation and for all usual modulation waveforms, no aliasing occurs if the half-period of modulation equals the transit time of atoms in the Ramsey resonator. We also deduce that in the same conditions, square-wave phase modulation provides the strongest cancellation of the LO instabilities in closed loop operation. Finally, we show that the “Dick formula” for the specific case of the pulsed fountain can be recovered from the model by a sampling operation     

A derivation of the long-term degradation of a pulsed atomic frequency standard from a control-loop model

The phase of a frequency standard that uses periodic interrogation and control of a local oscillator (LO) is degraded by a long-term random-walk component induced by downconversion of LO noise into the loop passband. The Dick formula for the noise level of this degradation is derived from an explicit solution of an LO control-loop model.     

Properties of an oscillator slaved to a periodically interrogated atomic resonator

In advanced atomic resonators, such as those using a fountain of cold cesium atoms or an ensemble of stored ions, the atomic medium is interrogated periodically, and the control signal of the slaved oscillator is updated at equally spaced time intervals. We analyze the properties of the output frequency of these frequency standards. We establish the equations that describe the time behavior of this frequency. We give the stability condition and the transient response of the frequency feedback loop, the response to systematic frequency changes of the free running oscillator, the frequency stability for given free-running oscillator noise and given optical detection noise, and the limitation of the frequency stability by down-conversion of the intrinsic oscillator frequency noise (Dick effect). We point out that a second integration in the feedback loop may not improve significantly the rejection of slow perturbations, unless a condition relative to the timing of the atom-field interaction is verified.     

Ultimate linewidth reduction of a semiconductor laser frequency-stabilized to a Fabry-Pérot interferometer

We report a theoretical dynamical analysis on effect of semiconductor laser phase noise on the achievable linewidth when locked to a Fabry-Perot cavity fringe using a modulation-demodulation frequency stabilization technique such as the commonly used Pound-Drever-Hall frequency locking scheme. We show that, in the optical domain, the modulation-demodulation operation produces, in the presence of semiconductor laser phase noise, two kinds of excess noise, which could be much above the shot noise limit, namely, conversion noise (PM-to-AM) and intermodulation noise. We show that, in typical stabilization conditions, the ultimate semiconductor laser linewidth reduction can be severely limited by the intermodulation excess noise. The modulation-demodulation operation produces the undesirable nonlinear intermodulation effect through which the phase noise spectral components of the semiconductor laser, in the vicinity of even multiples of the modulation frequency, are downconverted into the bandpass of the frequency control loop. This adds a spurious signal, at the modulation frequency, to the error signal and limits the performance of the locked semiconductor laser. This effect, reported initially in the microwave domain using the quasistatic approximation, can be considerably reduced by a convenient choice of the modulation frequency.     

Flicker noise measurement of HF quartz resonators

Frequency flicker of quartz resonators can be derived from the measurement of S(phi) (f), i.e., the power spectrum density of phase fluctuations phi. The interferometric method appears to be the best choice to measure the phase fluctuations of the quartz resonators because of its high sensitivity in the low power conditions, which is required for this type of resonator. Combining these two ideas, we built an instrument suitable to measure the frequency flicker floor of the quartz resonators, and we measured the stability of some 10-MHB high performance resonators as a function of the dissipated power. The stability limit of our instrument, described in terms of Allan deviation sigma(y)(tau), is of some 10(-14).     

Limitation of the frequency stability by local oscillator phase noise: new investigations and natural improvements

In frequency standards in which the atoms have a continuous interaction with the probe signal, local oscillator phase noise may limit medium term frequency stability. This spurious effect cannot be suppressed whenever there Is any truncation in the spectrum of the resonator response. Nevertheless, a simultaneous processing of the probe signal, similar to that of the NIST, and of the resonator response (by means of an appropriate demodulation) makes it possible to reduce this limiting effect. Previously achieved with a square wave frequency modulation, this result is now extended to various frequency modulations. An uncontrolled distortion in the demodulation waveform may significantly degrade the performance. For the case of a square wave phase modulation, the limiting effect also exists, but it is smaller than for a frequency modulation. When the phase noise of the local oscillator is naturally "not flat", it is possible to easily reduce the spurious effect: using the quasi-static approximation, one can calculate various optimized demodulation waveforms and the corresponding improvements. For the simplest optimized demodulation (f (M), 3f(M)), theoretical predictions are experimentally confirmed for flicker phase noise and flicker frequency noise.     

Analysis of light noise sources in a recycled Michelson interferometer with Fabry-Perot arms

We present a method by which the effect of laser field variations on the signal output of an interferometric gravitational wave detector is rigorously determined. Using the Laser Interferometer Gravitational Wave Observatory (LIGO) optical configuration of a power recycled Michelson interferometer with Fabry-Perot arm cavities as an example, we calculate the excess noise after the input filter cavity (mode cleaner) and the dependence of the detector strain sensitivity on laser frequency and amplitude noise, radio frequency oscillator noise, and scattered-light phase noise. We find that noise on the radio frequency sidebands generally limits the detector's sensitivity.     

Local oscillator limited frequency stability for passive atomic frequency standards using square wave frequency modulation

Atomic frequency standards using square wave frequency modulation effectively interrogate the atomic line by switching back and forth between two frequencies with equal atomic absorption values. For a symmetric absorption line, the slope of the responses will also be equal. In the quasistatic limit, this would seem to be an ideal interrogation process: the sign reversal of frequency slope can be removed by detection electronics to give an essentially unvarying sensitivity to local oscillator frequency variations. Such an interrogation would seem to eliminate L.O. aliasing and relieve stringent requirements on L.O. phase noise. Nevertheless, sign changes in the interrogation and detection processes mean that the sensitivity is actually zero at some point in the cycle. We derive consequences of this fact by an analysis in terms of the sensitivity function g(t). For white phase noise, we derive an optimal form for g(t) and show that the aliased noise always diverges as g(t) approaches a constant. For flicker phase noise, we find a limiting form that could, in principle, eliminate the aliasing effect; in practice, however, the improvement is limited by a slow dependence on available bandwidth. Finally, we derive optimized forms for any phase noise spectrum.     

The noise bandwidth of sampled data systems

The effect of aliasing on sampled noise power measurements is investigated. It is shown that although aliasing does not bias noise power measurements, it can significantly increase the measurement variance. The equivalent noise bandwidth (EENBW) of a sampled data system is defined by equating the mean and variance of the noise power measurement to those of a system with a rectangular spectral response. With this definition, which is shown to be consistent with that for analog systems, it follows that the ENBW is bounded by the smaller of the analog ENBW or half the sampling frequency. Practical examples of sampled-data systems are used to demonstrate the increased variance, integration time, and noise spectral density that accompany aliasing     

High performance photonic microwave frequency down-conversion using a dual-drive dual-parallel Mach-Zehnder modulator

Photonic microwave frequency down-conversion based on carrier suppression single sideband (CS-SSB) modulation via an integrated dual-drive dual-parallel Mach-Zehnder modulator (DP-MZM) is proposed. The MZM on the up path of the DP-MZM is used to generate SSB modulation signal, while the MZM on the bottom path of the DP-MZM is unmodulated. By adjusting the amplitude and phase of the unmodulated optical carrier, two optical carriers are cancelled out, which improves the performance of the system with reduced local oscillator (LO) power and large suppression of mixing spurious sidebands. The frequency down-conversion approach is theoretically analyzed and verified by simulation. Simulation results show that the power of frequency down-conversion signal is at least 39?dB higher than that of the mixing spurious sidebands. Besides, 9.5?dB gain, 2.8?dB noise figure (NF) and 1.9?dB spurious-free dynamic range (SFDR) improvements can be obtained compared with the previous OCS modulation frequency down-conversion scheme while the required LO power is 10?dB, 5?dB and 5?dB lower than that of the OCS modulation scheme, respectively.     

齿轮故障振动信号检波解调分析中的混频效应

在齿轮故障诊断中,振动信号解调分析是一种很有效的方法。本文在分析调幅调相信号检波解调分析原理的基础上,讨论了该类算法软件实现过程中产生的混频效应,指出信号在检波解调过程中经过非线性变换后将包含高频成分,有可能发生明显的混频,导致得出错误的解调信号。通过合理地选择采样频率及分析算法中低通滤波器的截止频率或采用较高的采样频率能有效地消除这种混频效应对解调的影响,最后以仿真数据及实验论证了这些结论。     

A low noise and ultra-narrow bandwidth frequency-locked loop based on the beat method

A novel frequency-locked loop (FLL) based on the beat method is proposed in this paper. Compared with other frequency feedback loops, this FLL is a digital loop with simple structure and very low noise. As shown in the experimental results, this FLL can be used to reduce close-in phase noise on atomic frequency standards, through which a composite frequency standard with ultra-low phase noise and low cost can be easily realized.     

Radio-frequency front-end for 5 GHz wireless local area network transceivers

A transceiver front-end for 5 GHz wireless local area network applications has been designed and implemented in a low-cost 46 GHz f_r pure-silicon bipolar technology. The transceiver front-end adopts a superheterodyne sliding-IF architecture and consists of a down-converter, an up-converter and an LO frequency synthesiser. By exploiting a 1 bit variable-gain low-noise amplifier, the down-converter is able to provide an excellent noise figure of 4 dB while ensuring an input 1 dB compression point of 210 dBm with a current consumption of 25 mA from a 3 V supply voltage. The transmitter front-end is implemented by means of a current-reuse variable-gain up-converter. The circuit provides an output 1 dB compression point of 5.3 dBm although consuming only 45 mA from a 3 V supply voltage. Moreover, a linear-in-dB gain control characteristic is achieved over a 35 dB dynamic range. The LO frequency synthesiser is implemented by means of an integer-N phase-locked loop. It features a phase noise of 2117 dBc/Hz at 1 MHz offset from the centre frequency of 4.1 GHz and exhibits a tuning range of 1.2 GHz, from 3.47 to 4.65 GHz. The LO frequency synthesiser draws 20 mA from a 3 V supply voltage.     

Diode laser phase noise influence on the ultimate performance of its frequency stabilization to a Mach-Zehnder interferometer fringe

We report a detailed investigation on the effect of semiconductor laser phase noise on the achievable frequency stability when locked to a Mach-Zehnder interferometer fringe. We show that the modulation-demodulation operation produces in the presence of laser phase noise two kinds of excess noise, which could be much above the shot noise limit, namely: conversion noise (PM-to-AM) and intermodulation noise. We show that in typical stabilization conditions, the frequency stability of the locked laser is limited by the intermodulation excess noise. This effect, reported initially in the microwave domain, can be considerably reduced by a convenient choice of the modulation frequency. To our knowledge, this is the first time such a phenomenon is reported in the optical domain.     

Conversion of 1/f fluctuations in crystal resonator within an inter resonance gap

This paper presents general relationships for transformation coefficients of BAW or SAW crystal resonator amplitude and phase fluctuations through the 1/f flicker noises of its motional and static equivalent parameters within the resonator inter resonance gap. Approximate functions of phase and amplitude power spectral densities are found based on Leeson's oscillator open loop model and are given with detailed consideration of Butler and Colpitts modes of operation with the assumption of full and zero inter noise correlation. It is also substantiated that a low-noise frequency region of crystal resonator operation exists in which the fluctuation influence of its motional inductance and capacity tend to zero in oscillators. Five examples are given as an illustration of a good agreement of the measured data with the prediction curves, giving a possibility of resonator power phase and amplitude spectral densities valuation at an arbitrary offset frequency from the carrier through the 1/f flicker noises of resonator parameters. Emphasis is laid in conclusion on the possible way of parameter spectral densities definition.     

IFOG中相位调制器的残余强度调制及其测量

利用开环正弦波调制解调方法,推导了铌酸锂相位调制器的残余强度调制(简称RIM)对干涉型光纤陀螺(简称IFOG)信号的影响,指出在调制频率漂移或光纤环渡越时间变化时RIM可导致陀螺的零偏和噪声增大.对典型条件的计算表明,0.01°/h的IFOG容许的最大RIM为13ppm,0.1°/h的中低精度IFOG则为81ppm.提出利用锁相放大器精确测量相位调制器RIM的方法,并对国产器件进行测量,结果表明,器件RIM指标可在中低精度IFOG中应用.     

The adiabatic anti-jitter circuit

The anti-jitter circuit (AJC) is able to reduce phase noise and spurious content of any frequency source at sideband frequencies above a defined cut-off frequency. By contrast, a phase-locked loop (PLL) can only reduce the intrinsic phase noise of its output oscillator closer to carrier lower than a defined cut-off frequency. The AJC has no output oscillator, but its phase noise performance can be assessed as if it had. This paper reports the invention of the adiabatic AJC (AAJC), giving the AJC improved power consumption, frequency range, and maximum frequency of operation. The term “adiabatic” is adopted to indicate that the core part of the new circuit does not require a power supply. It takes power from the input source directly to create the sawtooth waveform that has considerably reduced time jitter on the longer of its two ramp waveforms. Discrete models of the AJC are now operational at 30 MHz, which is twice the 15-MHz operation previously reported. The cut-off frequency of suppression has been maintained at a few kiloHertz. Noise analysis now shows performance comparable with an LC oscillator is possible. SPICE simulations show potential operation up to 5 GHz. The AAJC is also cascadable up to the intrinsic (shot) noise limit. Shot noise can be reduced by feedback     

Technical limitations to homodyne detection at audio frequencies

Homodyne detection relies on the beat between a relatively strong local oscillator (LO) field at the carrier frequency and a signal beam with sidebands centered around the carrier frequency. This type of signal detection, or signal readout, is widely used in quantum optics applications and is expected to be used in advanced interferometric gravitational wave detectors. We investigate experimentally the limitations to making such measurements in a laboratory environment at audio frequencies. We find that beam jitter noise, electronic noise of the photodetectors, and the LO intensity noise can limit the homodyne detection in this frequency band, and we discuss potential solutions.     

爆破振动信号3种经验模态分解差异性研究

为了准确评估冻结立井爆破对井壁产生的影响,采用井壁预埋法对大药量爆破下井壁的振动响应进行了监测。利用EMD、EEMD和CEEMD典型经验模态算法对井壁信号进行了分析,并结合时频谱对分解和重构效果进行了综合评价。分析结果表明:受测试环境影响,爆破信号中普遍含有噪声等干扰成分。EMD分解存在明显模态混叠和端点效应,EEMD分解虽对模态混叠现象有所改善,但去噪效果仍不理想,CEEMD分解对模态混叠和噪声消除方面均具有很好的处理效果。CEEMD重构信号时频谱能够深刻揭示爆破能量在时频域上的分布且对干扰成分不敏感,适合用于批量信号的预处理过程。分析结果对于爆破能量识别和振动损伤控制具有积极的现实意义。     

Spatially filtered wave-front sensor for high-order adaptive optics

Adaptive optics (AO) systems take sampled measurements of the wave-front phase. Because in the general case the spatial-frequency content of the phase aberration is not band limited, aliasing will occur. This aliasing will cause increased residual error and increased scattered light in the point-spread function (PSF). The spatially filtered wave-front sensor (SFWFS) mitigates this phenomenon by using a field stop at a focal plane before the wave-front sensor. This stop acts as a low-pass filter on the phase, significantly reducing the high-spatial-frequency content phase seen by the wave-front sensor at moderate to high Strehl ratios. We study the properties and performance of the SFWFS for open- and closed-loop correction of atmospheric turbulence, segmented-primary-mirror errors, and sensing with broadband light. In closed loop the filter reduces high-spatial-frequency phase power by a factor of 10(3) to 10(8). In a full AO-system simulation, this translates to a reduction by up to 625 times in the residual error power due to aliasing over a specific spatial frequency range. The final PSF (generated with apodization of the pupil) has up to a 100 times reduction in intensity out to lambda/2d.