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.     

Suppression of smeared spectrum ECM signal

Abstract

Three electronic counter‐countermeasures (ECCM) techniques for suppressing smeared spectrum (SMSP) jamming, a new electronic counter measures (ECM) technique, are presented. The analytical representations of the SMSP ECM signal in the time domain and the frequency domain are first derived, and then the differences between the SMSP jamming signal and the radar linear frequency modulation (LFM) signal are analyzed. Based on the differences, a jamming suppression system specifically for SMSP jamming interference excision is designed, which applies three different signal processing tools, i.e. fractional Fourier transform (FRFT), Fourier transform (FT) and atomic decomposition (AD). The jamming suppression performance of the presented methods is evaluated through simulations. The simulation results show that the presented methods can successfully suppress SMSP jamming.     

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.     

Characterization of Frequency Stability: A Transfer Function Approach and Its Application to Measurements via Filtering of Phase Noise

Frequency stability of high-quality signal sources is characterized in the Fourier frequency domain by the spectral density Sy(f) of the fractional instantaneous frequency deviation y(t), and in the time domain by the Allan variance ?y2(?). Two well-known types of measuring apparatus used to evaluate these parameters are analog spectrum analyzers and digital electronic counters, respectively. A detailed analysis of the structure of the relation between ?y2(?) and Sy(f) shows that it is possible to define a variance, i.e., a time-domain measure, by its transfer function in the Fourier frequency domain, even when no corresponding measurement sequence exists in the time domain. Two different kinds of variance are then defined, which possess different properties for white and flicker phase noises. One of these variances is an estimate of the Allan variance. These variances may be measured by a suitable filtering of phase noise at the output of a phase detector.     

Digital Frequency Multiplier for Spectrum Measurement of Periodic Signals

Frequency multipliers find applications in the Fourier and Walsh spectrum measurements of periodic signals. Earlier digital frequency multipliers use two counters: 1) An upcounter which is partitioned into a fractional counter of kbits in cascade with an integral counter. This determines the period of the input signal by the number of clock pulses that are accumulated in a period of the signal. 2) A downcounter which is next fed from the same clock, and which is periodically preset to the contents of the integral counter whenever the downcounter reaches zero. In this process an error is introduced in the output frequency because the fractional counter contents are ignored in the frequency multiplication phase. To minimize this error, a high clock frequency is required so that the fractional count is small compared with the integral count. The maximum output pulse frequency is limited by the speed of the counters used. A new method is described which also uses the contents of the fractional counter. The clock frequency is reduced substantially and the maximum output pulse frequency is limited by the settling time of a D/A converter: If the settling time is 200 ns, the maximum output frequency is ten times that of earlier methods.     

VOR信号量值溯源技术研究

基于相位发生器和调频调幅设备建立了甚高频全向信标(VOR)标准信号发生装置,将VOR相位量值溯源至国家相位基准,解决了传统基于直接数字信号合成方法难以实现量值溯源的问题。对VOR标准信号发生装置的不确定度进行了评定,VOR相位扩展不确定度小于±0.020°(k=2),VOR调幅深度不确定度为±0.2%(k=2)。基于该标准信号发生装置可以对商用VOR信号发生和解调设备提供校准。     

High-accuracy Fourier analysis based on synchronous samplingtechniques

The lack of synchronization between the sampling rate and the signal frequency represents the main source of errors in the frequency analysis of periodic signals performed by means of digital techniques. Several algorithms have been proposed in the literature to reduce these errors, at the cost of an increment in the computational burden of the instrument. However, the complete elimination of these errors can be achieved only when the sampling rate is synchronized to the fundamental frequency of the signal to be analyzed. It is shown how this can be achieved. The results of the fast Fourier transform (FFT) of multifrequency signals under synchronous sampling conditions are given. The accuracy of the measurements is discussed     

Improvements in data reduction in direct pulse heating calorimetry

This paper describes improvements introduced in data reduction in direct heating pulse specific heat experiments. In calculations of specific heat, it is necessary to calculate the first derivative of the recorded temperature data as a function of time. The error induced by different numerical differentiation techniques can represent a significant part of the overall measurement error. Thus, different digital filtering techniques, differentiation, and smoothing algorithms were applied and tested to examine their influence on the minimization of errors induced by noise, which is unavoidable in measured signals. A minimum square error criterion was applied in designing digital filters, with arbitrary prescribed magnitude characteristics. Attention was paid to applications when one or more structural phase transitions in the specimen material occur within the temperature range covered by the experiment. The cases where the frequency spectrum of induced noise overlaps with the spectrum of temperature transient signals originating from phase transitions were analyzed in detail. The effectiveness of the methods of extracting the final specific heat data from a noisy signal using different digital filtering techniques is demonstrated.Paper presented at the Fourth International Workshop on Subsecond Thermophysics, June 27–29, 1995, Köln, Germany.     

调频初相位补偿的广义Warblet变换时频分析

信号时频分析的长时间窗时频分析法通常可提高输出信噪比和频率分辨率,但对于调频信号,会降低线谱时频能量聚集度并影响瞬时频率估计。对于调频信号广义Warblet变换(Generalized Warblet Transform,GWT),具有较短时傅里叶变换(Short Time Fourier Transform,STFT)更优的时频分析性能,但在长时间窗分析时,调频初相位估计误差会使算法性能下降甚至失效。针对该问题,提出调频初相位补偿的GWT(Frequency Modulation Initial Phase CompensationGWT,FMIPC-GWT)时频分析方法。在调频参数估计时将一半时间窗长所经过的相位补偿到调频初相位中,提高调频参数估计的准确性以增加瞬时频率估计精度。仿真和实验数据验证了,相比STFT法和GWT法,FMIPC-GWT法对于非线性调频信号时频分析性能更优。FMIPC-GWT法在调频信号线谱检测与瞬时频率估计等方面具有应用前景。     

A low-cost frequency multiplier for synchronous sampling ofperiodic signals

The theory of digital signal processing indicates clearly that the measurements performed on periodic signals by means of digital techniques are affected by an error due to the nonsynchronization between the sampling frequency and the signal frequency. The authors present a low-cost device, based on a frequency multiplier, that allows the generation of sampling pulses synchronized with the signal frequency. The behavior of this device is analyzed in order to assure its ability to work with input signals in the frequency range typical of the mains. As an example of the application of this device, the results of the Fourier analysis of a multifrequency signal are given, showing the high accuracy that can be attained     

Logarithmic cyclic frequency domain profile for automatic modulation recognition

Cyclostationary techniques have been applied widely to the problem of recognising communication modulation schemes. As these techniques are processing intensive, much effort has been invested in researching algorithms that can reduce the number of computational steps required, with fast Fourier transform approaches predominating. A novel approach to improve the extent of the cyclic frequency (a) is proposed. By using the constant Q transform (CQT), a logarithmic form of the spectral correlation function (SCF) can be produced. This allows the a-axis to be extended, which can be advantageous when the receiver bandwidth cannot be well matched to the signal frequency and bandwidth using a priori knowledge of spectrum allocation. It is found that a CQT-based SCF can form the basis of a logarithmic cyclic frequency domain profile algorithm without loss of sensitivity compared with the conventional, linear form.     

测量低信噪比电压的数字相敏解调算法及性能分析

本文研究了低信噪比正弦电压幅值及相位测量用的数字相敏解调（ＤＰＳＤ）算法，给出了ＤＰＳＤ算法的主要参数（数据长度、取样频率、Ａ／Ｄ转换器位数）与低信噪比电压测量的性能指标（测量精度、频率分辨力、动态储备及最小可测电压）之间的关系。对纳伏电压的实际测量表明，理论分析与测量结果是一致的。本文研究结果可以用于数字式相敏解调程序的设计及应用     

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.     

Measurement of static and vibration-induced phase noise in UHF thin-film resonator (TFR) filters

Measurements of the static phase noise and vibration sensitivity of thin-film resonator (TFR) filters operating at 640 and 2110 MHz have been made. They show that the short-term frequency instability of the filters is small compared with that induced in the oscillator signal by the sustaining stage amplifier PM (phase modulation) noise. In-oscillator measurement of filter performance under vibration indicates that fractional frequency vibration sensitivities (δf ₀/f₀) are on the order of several parts in 10^-9/g. Because the percentage bandwidth and order (number of poles) of the filters was fairly constant, so was the product of the center frequency and group delay. Thus, the fractional frequency vibration sensitivity of the filters can be expressed alternatively as carrier signal phase sensitivity to vibration. The τ-ω₀ product for the filters that were tested was on the order of 300 rad, so that the equivalent phase sensitivity to vibration was approximately 1 grad/g     

Secondary standard for PM and AM noise at 5, 10, and 100 MHz

A practical implementation of a portable secondary standard for phase modulation (PM) and amplitude modulation (AM) noise at 5, 10, and 100 MHz is described. The accuracy of the standard for both PM and AM noise is +0.14 dB, and the temperature coefficient is less than 0.02 dB/K. The noise floor S_φ (10 kHz) of the standard for PM noise measurements is less than -190 dBC relative to 1 rad²/Hz at 5, 10, and 100 MHz. The noise floor for AM measurements depends on the configuration. A calibrated level of PM and AM noise of approximately -130±0.2 dB relative to 1 rad² /Hz (for Fourier frequencies from approximately 1 Hz to 10% of the carrier frequency) is used to evaluate the accuracy versus Fourier frequency. Similar PM/AM noise standards are under test at 10 GHz. This new standard can also be used as an alternative to the normal method of calibrating the conversion sensitivity of the PM/AM detector for PM/AM measurements. Some types of time-domain measurement equipment can also be calibrated     

A simple analysis of the Dick effect in terms of phase noise spectral densities

In cold-atom frequency standards based on the Ramsey double interaction method, the phase noise of the interrogating signal appears as a random "end-to-end phase difference", thereby introducing frequency noise in the loop. This phenomenon is analyzed in this paper in the Fourier frequency domain, using phase noise power spectral densities S(phi)(f). In continuously operated standards, the excess noise thus introduced is servoed out in the long term to become eventually smaller than the atomic shot noise, whereas in standards with pulsed operation the phase noise around even harmonics of the pulse rate is down-converted by aliasing to base band. This latter mechanism is referred to in the literature as Dick effect. In this paper, a model of the frequency control servo system is proposed, in which the input signal is the (known) local oscillator (LO) phase noise S(phi)(f) and the output signal is the (unknown) phase noise S(phi)(f) of the standard in closed loop operation. The level of excess white frequency noise added by aliasing on the stabilized LO through the Dick effect can be related analytically to the characteristics of the free LO phase noise. From this, the stability limitation (with slope tau(-1/2)) typical of the Dick effect can then be obtained by the usual conversion formulas based on the power law model.     

Additive noise effect in digital phase detection

The characteristic polynomials associated with the algorithms used in digital phase detection are used to investigate the effects of additive noise on phase measurements. First, it is shown that a loss factor eta can be associated with any algorithm. This parameter describes the influence of the algorithm on the global signal-to-noise ratio (SNR). Second, the variance of the phase error is shown to depend mainly on the global SNR. The amplitude of a modulation of this variance at twice the signal frequency depends on a single parameter beta. The material presented here extends previously published results, and as many as 19 algorithms are analyzed.     

基于CCD探测器的全视场层析成像方法研究

由正弦信号驱动PZT调制参考镜以实现参考光相位调制,CCD光探测器的曝光时间为正弦驱动信号的四分之一周期,利用频率-同步探测技术,在一个参考光调制周期共提取四帧全视场参考光与样品反射和散射光干涉图像.为了获得最优的参考光信号调制参数,一种基于PID控制器的闭环控制技术与数字移相相结合的方法用于调制系统,采用50Hz的理想正弦曲线的数字离散量来控制PZT的调制幅度,数字移相电路调整PZT的振动相位来保证最优调制参数的获得.CCD(频率f=200Hz)由软件驱动,采用积分算法,实现了由CCD探测器提取微弱全视场层析信号的方法.     

Advanced noise reduction techniques for ultra-low phase noise optical-to-microwave division with femtosecond fiber combs

We report what we believe to be the lowest phase noise optical-to-microwave frequency division using fiber-based femtosecond optical frequency combs: a residual phase noise of -120 dBc/Hz at 1 Hz offset from an 11.55 GHz carrier frequency. Furthermore, we report a detailed investigation into the fundamental noise sources which affect the division process itself. Two frequency combs with quasi-identical configurations are referenced to a common ultrastable cavity laser source. To identify each of the limiting effects, we implement an ultra-low noise carrier-suppression measurement system, which avoids the detection and amplification noise of more conventional techniques. This technique suppresses these unwanted sources of noise to very low levels. In the Fourier frequency range of ～200 Hz to 100 kHz, a feed-forward technique based on a voltage-controlled phase shifter delivers a further noise reduction of 10 dB. For lower Fourier frequencies, optical power stabilization is implemented to reduce the relative intensity noise which causes unwanted phase noise through power-to-phase conversion in the detector. We implement and compare two possible control schemes based on an acousto-optical modulator and comb pump current. We also present wideband measurements of the relative intensity noise of the fiber comb.     

Quantization noise and its reduction in lensless Fourier digital holography

Digital holography is an imaging technique that enables recovery of topographic 3D information about an object under investigation. In digital holography, an interference pattern is recorded on a digital camera. Therefore, quantization of the recorded hologram is an integral part of the imaging process. We study the influence of quantization error in the recorded holograms on the fidelity of both the intensity and phase of the reconstructed image. We limit our analysis to the case of lensless Fourier off-axis digital holograms. We derive a theoretical model to predict the effect of quantization noise and we validate this model using experimental results. Based on this, we also show how the resultant noise in the reconstructed image, as well as the speckle that is inherent in digital holography, can be conveniently suppressed by standard speckle reduction techniques. We show that high-quality images can be obtained from binary holograms when speckle reduction is performed.