闪烁噪声的自相关函数及其表征

闪烁噪声是一种非平稳随机过程,其功率谱密度函数在频率低端（ｆ＝０）发散,无法直接利用Ｗｉｅｎｅｒ－Ｋｈｉｎｔｃｈｉｎｅ关系得到它的自相关函数,本文采用“降阶－积分”方法,得到了频率源中闪烁调频噪声的自相关函数的解析表达式。根据这一结果,分析了频率稳定度的表征原理,指出了频率稳定度表征的实质是将非平稳过程转化为平稳过程并求取时间平均。最后,通过时域分析得到了闪烁噪声的Ａｌｌａｎ方差表达式。     

闪烁噪声的自动关函数及其表征

闪烁噪声是一种非平衡随机过程，其功率谱密度函数在频率低端（f=0)发散，无法直接利用Wiener-Khintchine关系得到它的自相关函数，本文采用“降价－积分”方法，得到了频率源中闪烁调频噪声的自相关函数的解析表达式，根据这一结果，分析了频率稳定度的表征原理，指出了频率稳定度表征的实质是将非平稳过程转化为平衡过程并求取时间平均，最后，通过时域分析得到了闪烁噪声的Allan方差表达式。     

振荡器稳定度时域-频域参数转换的新方法

依据相位起伏谱密度至阿伦方差的转换公式,提出了一种由阿伦方差至相位起伏谱密度转换基本数学模型,考虑到转换结果的不唯一性,采用相位起伏谱密度的通用幂律模型,给出了转换方法的约束最大似然解,并结合正则化方法消除模型求解过程中的病态特性.计算表明,由该方法转换所得的相位起伏谱密度与真实谱密度数据能很好地吻合;此外,还分析了正则化因子的选择与输入阿伦方差参数的选择对反演性能的影响.     

原子干涉仪灵敏度的阿伦方差分析

针对分析原子干涉仪灵敏度时,采用哪种阿伦方差容易出现混淆的问题,系统地给出了阿伦方差、重叠阿伦方差和修正阿伦方差三种形式在时域和频域中的详细推导,分析了它们对五类典型噪声的分辨能力,指出修正阿伦方差具有更加适合评估原子干涉仪长期稳定性的特点。基于修正阿伦方差在频域中的表达式,文中还首次给出了存在测量死区的原子干涉仪灵敏度与噪声功率谱之间的传递函数,通过分析其特点,指出了提高原子干涉仪灵敏度的两条具体途径,为原子干涉仪技术的进一步发展和评价奠定了更加扎实的理论基础。     

NIM频率稳定度测量系统

本文作者按国际建议所推荐,在时域,以双取样标准偏差来表征随机频率不稳定度:在傅里叶频域,推荐以 Y(t)的单边谱密度 S_y(f)表征频率稳定度的方法所建立的测量系统,及其近期已取得的进展。     

变形高阶差分方差—用于相位噪声测量的一种新型方差

本文提出一种用于相位噪声测量的新型方差——变形高阶差分方差,其传递函数具有无旁瓣、谐波少等优点。文中导出了该方差的传递函数 H_c(f)、采样函数h_c(t)及等效带宽B_N。利用变形高阶差分方差可将时域测量结果折算为频域表征。     

基于虚拟仪器的频率稳定度测试方法研究

频率稳定度是整机系统、频率源、多种两端口频率控制和变换部件设计中必须认真考虑的重要性能指标，是时间频率标准的主要参数。频率稳定度按观测域的不同．分为时域频率稳定度（以下简称“频率稳定度”）和频域频率稳定度（通称“相位噪声”）。本文基于LabVIEW的虚拟仪器设计理念．对虚拟仪器下时域频率稳定度的测量系统建设进行探讨。     

相位噪声测试结果的分析与应用

本文简单介绍了相位噪声测量的各种方法,主要对相位噪声测试结果的正确分析与应用方法进行了介绍,并就工程技术人员关心的相位噪声与阿伦方差和时域抖动的换算方法进行了描述。     

石英谐振器和振荡器内的噪声机制(英文)

本文把振荡器内的噪声分为两大类:其一是附加噪声,是由热噪声引起的,又可分为内附加噪声和外附加噪声两种;其二是参数噪声,来源于振荡器参数的变化。文中给出了这些噪声与输出信号的相位谱密度及阿仑方差之间的定量关系式。文章介绍了石英谐振器噪声特性的测量系统,从理论和实验上给出了相对频率起伏的谱密度与谐振器无载Q值的关系。文中还介绍了一种新型的SC切割晶体,其频率温度效应可减少两个数量级。     

阿伦方差公式的扩充

阿伦方差是评定振荡器频率随机波动的一个特征值。有人对阿伦方差的引出、推证、表达及其发展已作比较系统的论述。本文对频域参数α作进一步扩充,从而推得一组阿伦方差表达式。     

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.     

Characterization of Frequency Stability: Effect of RF Filtering

This paper shows that the RF filtering of a signal generated by an oscillator affects the characterization of the frequency stability in a manner that differs from the filtering of the phase of this signal. The effect on both the frequency domain and the time domain measurement is considered. It is shown that the spectral density of the phase fluctuations of the filtered signal is a function of the spectral densities of the amplitude fluctuations and of the phase fluctuations of the original signal. The corresponding expression for the two-sample variance (Allan variance) is then also a function of these two contributions. Detailed calculation is made for the case of a signal with frequency stability limited by white phase noise and filtered by a first-order, low-pass filter. It is found that the frequency stability is improved by more filtering if the cutoff frequency, fc, is higher than the signal frequency, f0, as is the case for phase filtering. However, the stability will degrade with more filtering if fc < f0. An optimum frequency stability is reached when fc = f0/?2. Experimental measurements confirm these theoretical predictions.     

Characterization of Frequency Stability: Uncertainty Due to the Autocorrelation of the Frequency Fluctuations

We considered the general sampling form for the estimate of the Allan variance which is the proposed measure of frequency stability in the time domain, and we defined a variable proportional to the difference between the average fractional frequency fluctuations over the time interval ? to derive the autocorrelation coefficient of the process to which the variable belongs. Calculations of the variance of the estimated Allan variance proved that it may be convergent to its true value with infinite sample number for considered spectral densities of frequency noise. We also applied the results to estimations of frequency measurements to know the influence of the autocorrelation of the process considered. In order to obtain some direct estimates of the confidence of the estimate, distributions of the estimate were plotted by means of computer simulations, and were compared with the chi-square distribution. Those results suggested that for white-and flicker-phase noises (and white-frequency noise) we have to take into account the autocorrelation of the process, while for flicker-or random-walk-frequency noise we may regard the process as a nearly independent (and Gaussian) one.     

Frequency Multiplication Effects on Oscillator Instability

The effects which frequency multiplication produces on the power spectral density of an oscillator is examined as a function of the multiplication ratio and the power spectral density of the phase noise process. In addition, the power spectral density (PSD) of the multiplied-up oscillation is interconnected with the frequency standard L(f). It is explicitly demonstrated how errors are introduced when one attempts to define the rms fractional frequency deviation ?f(?)/f0 and the Allan variance ?2y(?) using the measurement of L(f). Finally, the genesis of spectral spreading of the PSD due to frequency multiplication is demonstrated in such a way that this interesting and important phenomena can be grasped by the practicing engineer.     

Characterization of Frequency Stability: Uncertainty due to the Finite Number of Measurements

We consider the characterization of the frequency stability of signal generators by means of the Allan variance of their fractional frequency fluctuations. As the number m of measurements is always finite, one can only get an estimate of this variance, which is a random function of m. We calculate the variance of the Allan variance for commonly encountered spectral densities of frequency fluctuations and deduce the relative uncertainty in the evaluation of frequency stability, as a function of m. The theory is experimentally checked for white noise of phase and flicker noise of frequency. The main hypothesis of the calculations, i.e., the Gaussian character of frequency fluctuations is verified. The m dependence of the uncertainty (one sigma) in the evaluation of frequency stability agrees with the predicted value.     

Frequency stability characterization from the filtered signal of aprecision oscillator in the presence of additive noise

The authors present a generalized theory to express the frequency stability characterization of a precision oscillator when its signal, perturbed by additive noise, is filtered. The general expressions for the power spectral density of the amplitude and phase fluctuations of the filtered signal are calculated as functions of the oscillator amplitude and phase fluctuations, the additive noise, and the filter characteristics. The results obtained for the phase fluctuations of the filtered signal are used to characterize the frequency stability of the oscillator. The contribution of white additive noise to the generalized Allan variance is expressed in terms of a parameter, the equivalent bandwidth. The contributions of other types of noise are also calculated. For the first-order low-pass filter, the contributions of all types of additive, amplitude, phase, and frequency noise are given. Experimental results show excellent agreement with the theoretical predictions     

Short-Term Frequency Stability of the Rb87 Maser

Measurements of the short-term stability of the Rb87 maser are reported here. The measurements were made as a function of the maser power output and of the receiver cutoff frequency. The experimental data are compared to theoretical results obtained from an approximate theory. In this theory the transfer function of the maser for thermal noise is derived, and the spectral density of the phase fluctuations is calculated. An analytical expression for the "Allan variance" is also given. A comparison of the stability of the Rb87 maser with existing frequency standards shows its superiority for averaging times less than 1 s. We obtain ?f/f ? 1.3 × 10-3 ?-1. A stability of 5 × 10-12 for ? ?1000 s is also reported.     

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).