On the 1/f frequency noise in ultra-stable quartz oscillators

The frequency flicker of an oscillator, which appears as a 1/f3 line in the phase noise spectral density, and as a floor on the Allan deviation plot, originates from two basic phenomena, namely, (1) the 1/f phase noise turned into 1/f frequency noise via the Leeson effect, and (2) the 1/f fluctuation of the resonator natural frequency. The discussion on which is the dominant effect, thus on how to improve the stability of the oscillator, has been going on for years without giving a clear answer. This article tackles the question by analyzing the phase noise spectrum of several commercial oscillators and laboratory prototypes, and demonstrates that the fluctuation of the resonator natural frequency is the dominant effect. The investigation method starts from reverse engineering the oscillator phase noise in order to show that if the Leeson effect was dominant, the resonator merit factor Q would be too low as compared to the available technology.     

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.     

One-port noise model of a crystal oscillator

This paper presents a one-port noise model of a crystal oscillator combined with equivalent impedances of a resonator and linearized feedback amplifier. Based on the noise conversion technique, we translate the thermal additive and flicker noise of both the resonator and amplifier into the oscillator signal amplitude and phase. The generic transformation coefficients for the noise are derived, and the power spectral density (psd) function of the oscillator signal phase is analyzed in detail. The remarkable property of the model is demonstrated by determining the separate contribution of each noise source to the oscillator performance. Some important rules for shaping the phase psd are noted. The consistency with Leeson's model also is reported.     

Precision close-to-carrier phase noise simulation of BAW oscillators

Based on a commercial simulation tool, the influence of BAW resonator noise on the resulting oscillator phase noise is revisited. The parametric model of the resonator uses experimental data, and includes an f(-2) noise not often considered in measurements, in addition to its flicker noise.     

差分振子时间历程在微弱调制信号检测中的应用

单一的差分振子仅可实现对周期信号中某一频率成分进行检测,对于强噪声背景下的边频带,尽管可以利用多个差分振子组成差分阵列进行逐个检测,进而确定边频带的间隔,但这种做法无疑会带来巨大的计算量。在对调制信号进行Hilbert变换包络分析时,所得到的时域信号是原始调制信号中的低频分量,亦是调制波信号,若该低频分量仍然包含较强的噪声成分,传统的频谱分析将会失效。此时,我们可借助差分振子时间历程对含较强的噪声的包络进行检测。因此,提出基于差分振子时间历程的微弱调制信号检测方法,即首先对信号进行Hilbert包络解调,然后利用差分振子时间历程对含较强的噪声的幅值包络进行检测,并成功应用于风机早期故障检测中。     

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.     

Transient response of a resonator fiber optic gyro with triangular wave phase modulation

We present an in-depth analysis of the transient response of a resonator fiber optic gyro based on triangular wave phase modulation. Unusual effects have been observed in the process of tracking the resonant frequency of an optical fiber ring resonator (OFRR). There is a distortion phenomenon, unlike the ideally square wave or a pure DC output of the OFRR, but signal overshoot or undershoot occurs. A deep analysis of the influence of the nonideal square wave or pure DC output on gyro performance is fully developed for the first time, to the best of our knowledge. Further analysis shows that this is the transient response process after modulation by the triangular wave, and the process is related both to the parameters of the OFRR and the modulation frequency of the triangular wave. By sampling the steady-state signal of the distortion square wave, or by oversampling the distortion signal to get a number of data, and then accumulating and averaging these data to be demodulated, the distortion's effect can be considerably decreased.     

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     

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     

A high-quality 120 GHz millimeter-wave generation without laser phase noise

A 120-GHz millimeter-wave system using two lasers and two Mach–Zehnder modulation (MZM) with frequency 8-tupling of the radio frequency local oscillator’s signal frequency is proposed and demonstrated. The first MZM is the even-order harmonic modulations output and then optical filter filters the 0-order wave. The second MZM is the single sideband suppression output. In the system, two light components with the same phase noise are generated. The millimeter wave can avoid the laser phase noise. It has simplified the system, so the fibre dispersion is reduced.     

Direct bidirectional angle-insensitive imaging of the flow signal intensity in Doppler optical coherence tomography

We introduce a new method, to our knowledge, for direct detection of flow signal intensity by stationary target rejection. In our system, two delay lines are constructed with identical scanning speed and ranging depth. One delay line is used for depth ranging as well as phase modulation, and the other one acts as a full-range retroreflector (FRRR). The signal from this FRRR carries the overall features of local phase modulation, and it is used as the local oscillator for coherent demodulation. With this setup, stationary targets can be rejected at a 4-kHz high-pass cutoff frequency of the filter that follows the demodulator, compared with 20 kHz for conventional fixed-frequency demodulation. This technique features angle insensitivity and provides flow direction as well by implementing standard in-phase and quadrature detection. Besides the direct directional detection of flow signal intensity, flow speed information can be acquired with postprocessing.     

Extremely low phase noise UHF oscillators utilizing high-overtone, bulk-acoustic resonators

High-overtone, bulk acoustic resonators (HBAR) have been designed that exhibit 9-dB insertion loss and loaded Q values of 80000 at 640 MHz with out-of-phase resonances occurring every 2.5 MHz. These resonators have been used as ovenized frequency-control elements in very low phase noise oscillators. The oscillator sustaining stage circuitry incorporates low-1/f noise modular RF amplifiers, Schottky-diode ALC, and a miniature 2-pole helical filter for suppression of HBAR adjacent resonant responses. Measurement of oscillator output signal flicker-of-frequency noise confirms that state-of-the-art levels of short-term frequency stability have been obtained. Sustaining stage circuit contribution to resulting oscillator flicker-of-frequency noise is 7-10 dB below that due to the resonators themselves. At 16-dBm resonator drive, an oscillator output signal white phase noise floor level of -175 dBc/Hz is achieved.     

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.     

Characterization technique of optical whispering gallery mode resonators in the microwave frequency domain for optoelectronic oscillators

Optical Q factor measurements are performed on a whispering gallery mode (WGM) disk resonator using a microwave frequency domain approach instead of using an optical domain approach. An absence of hysteretic behavior and a better linearity are obtained when performing linewidth measurements by using a microwave modulation for scanning the resonances instead of the piezoelectric-based frequency tuning capability of the laser. The WGM resonator is then used to stabilize a microwave optoelectronic oscillator. The microwave output of this system generates a 12.48 GHz signal with -94 dBc/Hz phase noise at 10 kHz offset.     

Reduced transposed flicker noise in microwave oscillators using gaas-based feedforward amplifiers

Transposed flicker noise reduction and removal is demonstrated in 7.6 GHz microwave oscillators for offsets greater than 10 kHz. This is achieved by using a GaAs-based feedforward power amplifier as the oscillation-sustaining stage and incorporating a limiter and resonator elsewhere in the loop. 20 dB noise suppression is demonstrated at 12.5 kHz offset when the error correcting amplifier is switched on. Three oscillator pairs have been built. A transmission line feedback oscillator with a Qo of 180 and two sapphire-based, dielectric resonator oscillators (DROs) with a Qo of 44,500. The difference between the two DROs is a change in the limiter threshold power level of 10 dB. The phase noise rolls-off at (1/f)(2) for offsets greater than 10 kHz for the transmission line oscillator and is set by the thermal noise to within 0-1 dB of the theoretical minimum. The noise performance of the DROs is within 6-12 dB of the theory. Possible reasons for this discrepancy are presented.     

HF and VHF Source Stabilization Technique Incorporating Q-Multiplied Quartz Crystal Resonator

A new approach is described for the desiga of HF/VHF crystal-controlled frequency sources exhibiting theoretical short-term stability unattainable through the use of conventional quartz oscillator design. The signal generator design uses the concept of AFC stabilization of a conventional quartz oscillator (VCXO) by means of a crystal-controlled highly selective active frequency reference. The AFC reference is a phase-shift type frequency discriminator that employs a product detector and an active Q-multiplied quartz crystal resonator. The extremely selective transmission response, large group delay, and power gain exhibited by the resonator, together with resonator phase noise levels comparable to that exhibited by the oscillator-maintaining circuit, provide the principal means for prediction of superior output signal spectral purity. Models of the resonators have been designed and constructed at 30 and 80 MHz, exhibiting 3-dB bandwidths of 30 and 160 Hz, respectively. Based on actual measurement of VHF Q-multiplied crystal resonator performance characteristics, approximately 16 dB improvement in VHF crystal-controlled frequency source spectral purity at low and moderate modulation rates is possible, compared to that attainable using the best available VHF quartz oscillator circuit designs.     

Relationship of AM to PM noise in selected RF oscillators

We have studied the amplitude modulation (AM) and phase modulation (PM) noise in a number of 5 MHz and 100 MHz oscillators to provide a basis for developing models of the origin of AM noise. To adequately characterize the AM noise in high performance quartz oscillators, we found it necessary to use two-channel cross-correlation AM detection. In the quartz oscillators studied, the power spectral density (PSD) of the f(-1) and f(0) regions of AM noise is closely related to that of the PM noise. The major difference between different oscillators of the same design depends on the flicker noise performance of the resonator. We therefore propose that the f(-1) and f(0) regions of AM and PM noise arise from the same physical processes, probably originating in the sustaining amplifier.     

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     

调相信号的数字化解调

通过单周期正弦波曲线模型的滑动拟合法,获得正弦序列的瞬时频率信息,使用对瞬时频率的积分运算,实现了正弦载波相位调制信号波形的精确解调.在调制信号是方波的情况下,给出了相位解调的仿真结果和其它参数的波动情况;在1个实测调相曲线波形上进行的解调分析,给出了相位调制波形的解调结果;在调制信号也是正弦波的情况下,给出了解调失真的计算方法和结果.本方法用于评价载波为正弦波的调相信号时,具有准确度高、分辨力高的特点,可用于调相信号源及其解调设备的指标评价和计量测试.     

Expected quality factor of a simple tuned oscillator

A positive feedback system oscillating under self-sustained mode is shown to have an extremely high gain. Modeled as one port, the expected Q is much higher than the loaded Q-factor of the resonator. With just thermal noise present, random phase/frequency deviation is linear. Centered about the oscillator frequency omega/(0), noise frequency on both sides is more amplified with decreasing separation distance. Ultimately, frequency pulling may result in synchronous locking with hysteresis, which occurs because a real oscillator displays a truncated limiting curve. Once locked onto a signal, smaller levels are ignored. A new approach to the design and characterization of a simple tuned oscillator is offered: According to the phenomenon of injection locking, there exists an expected quality factor relating the shape of the truncated limiting curve to an ideal curve. In this paper, synthesis and innovative analytical methods of academic interest are revealed: 1) application of the transducer loss method is revised to establish a new method for oscillator characterization; 2) a transparent method of normalizing a two-port network in the presence of white noise is developed; and 3) in quartz crystal controlled oscillators, characterization of the noise originating from an equivalent noise-resistance determined from parameter of the quartz crystal is proposed. It is shown that the two-port model can also be approximated on a one-port basis. In conclusion, a sample of closed-form estimation of expected Q-factor order of magnitude of piezoelectric resonator oscillators is calculated.