小型化铷原子频标数字锁频环路设计与实现

设计并实现了一种用于铷原子频标的小型化锁频环路。采用数字锁相倍频技术,实现了10MHz信号的45.5645833次倍频。再经过一级15次倍频后获得频率为6834.6875MHz的铷原子频标微波探寻信号。通过数字电路技术实现了455.645833MHz信号的小调频。测量并分析了455.645833MHz信号的相位噪声,结果表明电路系统对铷频标频率稳定度的贡献为3.2×10^-12τ^-1/2。测量了利用该电路得到的铷频标的短期频率稳定度,结果为5×10^-12τ^-1/2（1s≤τ≤100s）,明显高于一般商品小型化铷原子频标。     

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.     

Predicting phase noise in crystal oscillators

In order to predict the phase noise in crystal oscillators an enhanced phase-noise model has been built. With this model, the power spectral densities of phase fluctuations can be computed in different points of the oscillator loop. They are calculated from their correlation functions. The resonator-caused noise as well as the amplifier-caused noise are taken into account and distinguished. To validate this enhanced model, the behavior of a batch of 10 MHz quartz crystal oscillators is observed and analyzed. The tested batch has been chosen in a facility production. Their associated resonators have been selected according to the value of their resonant frequency and their motional resistance. Open-loop and closed-loop measurements are given. The phase noise of the overall oscillator working in closed loop is provided by the usual active method. Theoretical and experimental results are compared and discussed.     

微波、毫米波相位噪声测试系统的研制

提出了首先对微波、毫米波信号进行下变频,再利用锁相环提取被测试信号相位噪声的相位噪声提取方法,采用现代谱分析技术对提取出的相位噪声信号在频率中进行分析,并利用"反卷积"技术实现测试系统的误差校正,研制实现了微波、毫米波相位噪声测试系统.实验测试结果表明该系统具有测试灵敏度高和被测信号频率范围广的优点,证明了它具有较大的应用价值.     

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.     

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     

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     

Residual phase noise measurements of VHF, UHF, and microwavecomponents

The results of residual phase noise measurements on a number of VHF, UHF, and microwave amplifiers, both silicon (Si) bipolar junction transistor (BJT) and gallium arsenide (GaAs) field effect transistor (FET) based, electronic phase shifters, frequency dividers and multipliers, etc., which are commonly used in a wide variety of frequency source and synthesizer applications are presented. The measurement technique has also been used to evaluate feedback oscillator components, such as the loop and buffer amplifiers, which can play important roles in determining an oscillator's output phase noise spectrum (often in very subtle ways). While some information has previously been published related to component residual phase noise properties, it generally focused on the flicker noise levels of the devices under test, for carrier offset frequencies less than 10 kHz. The work reported herein makes use of an extremely low noise, 500 MHz surface acoustic wave resonator oscillator (SAWRO) test source for residual phase noise measurements, both close-to-and far-from-the-carrier. Using this SAWRO-based test source at 500 MHz, we have been able to achieve a measurement system phase noise floor of -184 dBc/Hz, or better, for carrier offset frequencies greater than 10 kHz, and a system flicker phase noise floor of -150 dBc/Hz, or better, at 1 Hz carrier offset. The paper discusses the results of detailed residual phase noise measurements performed on a number of components using this overall system configuration. Several interesting observations related to the residual phase noise properties of moderate to high power RF amplifiers, i.e., amplifiers with 1 dB gain compression points in the range of +20 to +33 dBm, are highlighted     

一种明显提高相位测距分辨率的方法

本文从原理和实验两方面提出了一种明显提高相位测距分辨率的方法.应用差频模拟锁相环(APLL)专用集成电路KD080H,作者设计制作出一种环路噪声带宽小于1Hz的晶体分频APLL,并成功用于相位检测频率1.5kHz的相位测距系统.实验表明,在光电信号频率为15MHz,晶体滤波器带宽500Hz,所得信号信噪比仅为40dB的条件下,测距分辨率可优于0.5mm,比应用中心频率1.5kHz带宽50Hz的有源滤波器测距系统的分辨率提高约7倍.该方法还具有结构简单,成本低,使用方便等优点.     

An ultralow noise microwave oscillator based on a high-Q liquidnitrogen cooled sapphire resonator

Two liquid nitrogen-cooled sapphire loaded cavities (SLC's) operating at about 80 K have been successfully constructed, Both cavities were designed to operate on the whispering gallery (WG) E_{12, 1, δ} mode at a resonant frequency of 8.95 GHz. The first SLC was used as the frequency-determining element in a loop oscillator, while the second was used as a frequency discriminator to measure oscillator phase noise. The single sideband phase noise of a free running loop oscillator incorporating the first SLC was measured as -133 dBc/Hz at an offset frequency of 1 kHz, and was limited by the SLC Q-factor and the amplifier flicker phase noise. By using specially designed feedback electronics the oscillator phase noise was reduced to -156 dBc/Hz and -162 dBc/Hz at 1 and 10 kHz offset, respectively. This measurement was shown to be limited by the electronic flicker noise imposed by the phase detector in the feedback electronics, To our knowledge the phase noise and resonator Q-factor of 6×10⁷ represent the best results ever measured at liquid nitrogen temperatures or above     

Enhancing time-stamp counter phase modulation measurements

This paper demonstrates that digital signal processing techniques can enhance the quality of phase modulation measurements produced by a time-stamp (phase digitizing) frequency counter. A typical time-stamp counter utilizes a digital divider to reduce signal frequency to the desired sample rate. Unfortunately, division also reduces phase modulation to the point where useful information may be obscured by counter measurement uncertainty (jitter). An analogy between an analog-to-digital converter (ADC) and a time-stamp counter predicts that the counter induced modulation can be modeled as random noise which is white in phase. The noise magnitude is directly related to the instrument's resolution specification. Fourier analysis, subject to some restrictions, can compute the power spectra of phase or frequency modulation, revealing even low level responses. A number of techniques can be used to reduce the amount of counter induced noise that appears on time domain plots of phase and frequency modulation. Experimental data, generated by a prototype counter, illustrates the type of results that can be expected from Fourier analysis and various noise reduction techniques     

用于原子重力仪的扫频频率源系统

原子重力测量实验中,需要通过扫频频率源来实现主从Raman激光的线性啁啾,进而补偿原子在自由下落过程中产生的多普勒频移,实现当地重力加速度g的测量。针对传统扫频频率源体积大、发热量大的问题,通过AD9959数字芯片设计了一款扫频频率源,可用作原子喷泉扫频控制和Raman光锁相环鉴频鉴相本振参考。最终通过实验测得：该扫频信号源的相位噪声为-112 dB@1 kHz,频率稳定度为1.38×10^-11@1 s,对原子重力仪灵敏度影响为2.81×10^-9 g/Hz^1/2,600 s积分时间对原子重力仪实验影响为1.15×10^-10 g。该系统具有低噪声、高稳定度的特点,可满足搬运式原子重力仪分辨力10^-10 g需求。研究结果为原子重力仪从原理样机向工程化可搬运实验测试仪器发展提供了一定参考。     

Oscillator frequency stability improvement by means of negative feedback

A novel, simple method is proposed to increase the frequency stability of an oscillator. An additional negative feedback is used in combination with the positive loop of the harmonic oscillator to decrease the phase sensitivity to fluctuations of parameters other than the resonator. The main advantage of the proposed correction approach is that it does not require expensive external elements such as mixers or resonators. The validity of the method is theoretically demonstrated on a Colpitts oscillator using the control system theory approach and numerical simulations, and is experimentally verified with phase noise measurements of an actual oscillator-mockup. It is shown that the medium-term frequency stability can be easily improved by a factor of ten.     

Design of asynchronous phase detection algorithms optimized for wide frequency response

In many fringe pattern processing applications the local phase has to be obtained from a sinusoidal irradiance signal with unknown local frequency. This process is called asynchronous phase demodulation. Existing algorithms for asynchronous phase detection, or asynchronous algorithms, have been designed to yield no algebraic error in the recovered value of the phase for any signal frequency. However, each asynchronous algorithm has a characteristic frequency response curve. Existing asynchronous algorithms present a range of frequencies with low response, reaching zero for particular values of the signal frequency. For real noisy signals, low response implies a low signal-to-noise ratio in the recovered phase and therefore unreliable results. We present a new Fourier-based methodology for designing asynchronous algorithms with any user-defined frequency response curve and known limit of algebraic error. We show how asynchronous algorithms designed with this method can have better properties for real conditions of noise and signal frequency variation.     

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.     

脉冲调制下相噪测量的环路设计和定标方法研究

在窄脉冲调制下相位噪声测量的定标过程中,通过采用PRF滤波器提取主谱线技术,对主载频差拍频率的波形进行了还原,使定标过程较之传统方法简便快捷。在脉冲调制状态下的锁相环路设计中,采用PRF滤波器消除PRF谱线,避免锁相环路难以锁定或者偏锁,另外通过提高环路增益等方法解决由于窄脉冲调制造成的环路锁定能力降低。应用以上技术的脉冲调制波相位噪声现场测量装置分别以不同的环路带宽对不同占空比下的脉冲调制波源的相位噪声进行了测量,证明了上述方法的可行性。     

A Heterodyne Low-Level Signal Phase Meter Operating over 1 MHz to 300 MHz

After giving a brief summary of the main devices allowing the measurement of phase shifts between two sine signals in the approximate range 1 Hz-1 GHz, we propose a new apparatus for measuring phase shift. The principle of this apparatus uses a heterodyne technique in association with a phase-locked loop which brings about frequency translation of the measured signals. The intermediate frequency which is obtained is small with respect to the frequencies studied conveying a high degree of selectivity to the apparatus. This allows measurements to be made on signal with noise or low-level signal while also maintaining good accuracy. For a system operating from 1-300 MHz, we have obtained phase linearity of ± 1°, resolution of 0.1°. In obtaining the accuracy of ± 5°, the sensitivity is -86 dBm in the 1-30-MHz frequency range; with 300 MHz the sensitivity reached is -68 dBm.     

Suppression of phase-noise interference due to closely spaced data and calibration signals

At high frequencies, phase noise, which occurs at frequencies surrounding a data frequency, may seriously interfere with the measurement of nearby signals. Our motivation for removing phase noise was based on our use of simultaneous data and calibration signals, which were closely spaced in frequency. We found that by measuring the source phase noise, we are able to effectively remove phase-noise interference from the measured data and calibration signals. In order to accomplish this phase-noise suppression, a normalization procedure has been developed so that signals on differing measurement channels can be compared. Using this phase-noise suppression procedure and a prototype measurement system, we were able to improve magnitude measurements by 36 dB. We were able to improve phase measurements by a factor of 70. We propose that this procedure can significantly improve measurement accuracy in many situations where two closely spaced signals, which have a common source, must be measured with high accuracy. This procedure can also be used to monitor, and thereby remove, other types of interference besides just phase noise.     

Microwave generation with photonic frequency octupling using a DPMZM in a Sagnac loop

A photonic microwave signal generation scheme with frequency octupling is proposed and experimentally demonstrated. The scheme is based on bi-directional use of a dual-parallel Mach–Zehnder modulator (DPMZM) in a Sagnac loop. The two sub-modulators in the DPMZM are driven by two low-frequency signals with a π/2 phase difference, and the dc biases of the modulator are all set at the maximum transmission points. Due to the velocity mismatch of the modulator, only the light wave along the clockwise direction is effectively modulated by the drive signals to generate an optical signal with a carrier and ±4th order sidebands, while the modulation of the light wave along the counterclockwise direction is far less effective and can be ignored. By properly adjusting the polarization of the light wave output from the Sagnac loop, the optical carrier can be significantly suppressed at a polarizer, and then an optical signal with only ±4th order sidebands is generated. In the experiment, a pure 24-GHz microwave signal without additional phase noise from the optical system is generated using a 3-GHz local oscillator signal. As no electrical or optical filter is used, the photonic frequency octupler is of good frequency tunability.     

High-Q whispering gallery traveling wave resonators for oscillator frequency stabilization

Usually a frequency-stabilized standing wave resonator-oscillator incorporating a resonator as a frequency discriminator requires a circulator to separate the injected and reflected wave, A ferrite circulator is a noisy device and can limit the phase noise or frequency stability. Moreover, we show that the noise in a circulator varies, and detailed low noise measurements are necessary to choose an appropriate quiet circulator. Thus, by realizing a configuration that does not require a circulator, an improvement in performance and reliability can be obtained. A solution to this problem is to design a high-Q whispering gallery traveling wave (WGTW) resonator. This device naturally separates the injected and reflected wave in the same way as a ring cavity at optical frequencies, without degrading the frequency discrimination. Q-factor measurements of a WGTW sapphire resonator are presented, along with a derivation of critical parameters to maximize the frequency discrimination. New measurements of noise in ferrite circulators and isolators have also been made, which is followed with a discussion on oscillator design.