1/f frequency noise of 2-GHZ high-Q thin-film sapphire resonators

We present experimental results on intrinsic 1/f frequency modulation (FM) noise in high-overtone thin-film sapphire resonators that operate at 2 GHz. The resonators exhibit several high-Q resonant modes approximately 100 kHz apart, which repeat every 13 MHz. A loaded Q of approximately 20000 was estimated from the phase response. The results show that the FM noise of the resonators varied between S_y (10 Hz)=-202 dB relative (rel) to 1/Hz and -210 dB rel to 1/Hz. The equivalent phase modulation (PM) noise of an oscillator using these resonators (assuming a noiseless amplifier) would range from L(10 Hz)=-39 to -47 dBc/Hz     

Microwave regenerative frequency dividers with low phase noise

We demonstrate regenerative divide-by-two (halver) circuits with very low phase modulation (PM) noise at input frequencies of 18.4 GHz and 39.8 GHz. The PM noise of the 18.4 to 9.2 GHz divider pair was L(10 Hz)=-134 dB below the carrier in a 1 Hz bandwidth (dBc/Hz) and L(10 MHz)=-166 dBc/Hz, and the PM noise of the 39.8 GHz to 19.9 GHz divider pair was L(10 Hz)=-122 dBc/Hz and L(10 MHz)=-167 dBc/Hz.     

Interpreting anomalously low voltage noise in two-channel measurement systems

In this work we 1) analyze and give a theoretical explanation for the anomalously low cross-spectral density of voltage fluctuations that is observed when two thermal noise sources with matched intensities are coupled to the inputs of two-channel phase modulation (PM) or amplitude modulation (AM) noise measurement systems (NMS), 2) empirically evaluate spectral resolutions of different types of measurement systems, and 3) discuss noise measurement techniques involving cross-correlation signal processing. Our work shows that the statistical uncertainty, which sets the ultimate spectral resolution in the thermal noise limited regime, is approximately the same for both systems. However, in practical terms, the non-stationary nature of the noise, the temporal separation of calibration and measurement, and the difficulty of reproducing the calibrations for two measurements make it extremely difficult to resolve noise that is more than 10 dB below the noise floor in a single channel NMS. In a two-channel NMS, however, the calibrations of the two channels are carried out simultaneously, and one can take full advantage of a large number of averages and make reproducible noise measurements with resolution 10 dB below the noise floor of a single channel NMS     

Up-converted 1/f PM and AM noise in linear HBT amplifiers

In this paper we describe a technique to predict the 1/f phase modulation (PM) and 1/f amplitude modulation (AM) noise due to up-conversion of 1/f baseband current noise in microwave heterojunction bipolar transistor (HBT) amplifiers. We obtain an accurate model for the amplifier and find the expression for voltage gain in terms of DC bias, transistor parameters, and circuit components. Theoretical 1/f PM and AM noise sensitivities to 1/f baseband current noise are then found by applying the definitions of PM and AM noise to the gain expression of the amplifier. Measurements of PM and AM sensitivities at 500 MHz and 1 GHz were in good agreement with the values predicted by theory, verifying the validity of this technique. This method can be used to optimize amplifier design for low PM and AM noise. We show that the amplifier PM noise can be reduced by 9 dB by adjusting the value of the input coupling capacitor.     

Phase noise measurements of 10-MHz BVA quartz crystal resonators

In this paper, we review a new piece of equipment that allows one to characterize the phase noise of crystal resonators using a phase bridge system with carrier suppression. This equipment allows one to measure the inherent phase stability of quartz crystal resonators in a passive circuit without the noise usually associated with an active oscillator. We achieved a system noise floor of approximately -150 dBc/Hz at 1 Hz and -160 dBc/Hz, at 10 Hz. A SPICE characterization of the carrier suppression system is given. An investigation of the phase modulation (PM) noise in 10 MHz BVA, SC-cut quartz crystal resonator pairs is presented.     

AM noise impact on low level phase noise measurements

The influence of the source AM noise in microwave residual phase noise experiments is investigated. The noise floor degradation problem, caused by the parasitic detection of this type of noise by an imperfectly balanced mixer, is solved thanks to a refinement of the quadrature condition. The parasitic noise contribution attributable to the AM to PM (phase modulation) conversion occurring in the device under test is minimized through the development of a dedicated microwave source featuring an AM noise level as low as -170 dBc/Hz at 10 kHz offset from a 3.5 GHz carrier     

The Direct-Detection Noise-Measuring System and Its Threshold

This paper describes a typical direct-detection noise-measuring system, with particular attention given to the use of Schottky-barrier diodes as envelope detectors. The rise of threshold at low modulation frequencies encountered in these systems has been found to be mainly attributable to FM-to-AM conversion occurring in comparatively narrow-band detectors rather than to diode-flicker noise and thus is largely removable. A sensitivity improvement of 10-20 dB may result at low frequencies, yielding a noise-to-carrier ratio threshold range of about -150 to -155 dB/100 Hz at modulation frequencies from 100 Hz to 50 kHz for measurements of AM noise, and below 0.01 Hz/100 Hz for FM noise, of microwave oscillators at C band.     

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     

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.     

Ultralow-noise programmable voltage source

To avoid introducing additional noise sources while making low-frequency noise measurements, batteries are normally used instead of electronic power supplies. This paper presents an alternative solution by describing the design, construction, and testing of an ultralow-noise voltage source. Such a power supply can be computer controlled and has a typical noise level two orders of magnitude below that of similar commercial instruments. Some typical values of the spectral density of the voltage fluctuations at its output are: (10^-12, 10^-15, 10^-16) V²/Hz at (0.01, 0.1, and 1) Hz, respectively. These noise performances are almost independent of the supplied current, with a degradation of less than 3 dB up to 400 mA. A special algorithm for digital-to-analog conversion, using passive devices with 1% tolerance, ensures a resolution of 2.5 mV and an accuracy better than ±1.5 mV over the entire output range from 0 to 8 V     

Merits of PM noise measurement over noise figure: a study at microwave frequencies

This paper primarily addresses the usefulness of phase-modulation (PM) noise measurements versus noise figure (NF) measurements in characterizing the merit of an amplifier. The residual broadband (white PM) noise is used as the basis for estimating the NF of an amplifier. We have observed experimentally that many amplifiers show an increase in the broadband noise of 1 to 5 dB as the signal level through the amplifier increases. This effect is linked to input power through the amplifier's nonlinear intermodulation distortion. Consequently, this effect is reduced as linearity is increased. We further conclude that, although NF is sometimes used as a selection criteria for an amplifier for low-level signal, NF yields no information about potentially important close-to-carrier 1/f noise of an amplifier nor broadband noise in the presence of a high-level signal, but a PM noise measurements does. We also have verified experimentally that the single-sideband PM noise floor of an amplifier due to thermal noise is -177 dBc/Hz, relative to a carrier input power of 0 dBm.     

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     

Extremely low thermal noise floor, high power oscillators usingsurface transverse wave devices

This paper presents state-of-the-art results on 1-GHz surface transverse wave (STW) oscillators running at extremely high loop power levels. The high-Q single-mode STW resonators used in these designs have an insertion loss of 3.6 dB, an unloaded Q of 8000, a residual PM noise of -142 dBc/Hz at a 1-Hz carrier offset, and operate at an incident power of up to +31 dBm in the loop. Other low-Q STW resonators and coupled resonator filters (CRF), with insertion losses in the 5-9 dB range, can conveniently handle power levels in excess of two Watts. These devices were incorporated into voltage controlled oscillators (VCO's) running from a 9.6-V dc source and provide an RF output power of +23 dBm at an RF/dc efficiency of 28%. Their tuning range was 750 kHz and the PM noise floor was -180 dBc/Hz. The oscillators, stabilized with the high-Q devices and using specially designed AB-class power amplifiers, delivered an output power of +29 dBm and exhibited a PM noise floor of -184 dBc/Hz and a 1-Hz phase noise level of -17 dBc/Hz. The 1-Hz phase noise level was improved to -33 dBc/Hz using a commercially available loop amplifier. In this case, the output power was +22 dBm. In all cases studied, the loop amplifier was found to be the factor limiting the close-to-carrier oscillator phase noise performance     

Microwave interferometry: application to precision measurements and noise reduction techniques

A concept of interferometric measurements has been applied to the development of ultra-sensitive microwave noise measurement systems. These systems are capable of reaching a noise performance limited only by the thermal fluctuations in their lossy components. The noise floor of a real time microwave measurement system has been measured to be equal to -193 dBc/Hz at Fourier frequencies above 1 kHz. This performance is 40 dB better than that of conventional systems and has allowed the first experimental evidence of the intrinsic phase fluctuations in microwave isolators and circulators. Microwave frequency discriminators with interferometric signal processing have proved to be extremely effective for measuring and cancelling the phase noise in oscillators. This technique has allowed the design of X-band microwave oscillators with a phase noise spectral density of order -150 dBc/Hz at 1 kHz Fourier frequency, without the use of cryogenics. Another possible application of the interferometric noise measurements systems include “flicker noise-free” microwave amplifiers and advanced two oscillator noise measurement systems     

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。     

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.     

A new multilayer planar PVDF standard hydrophone and itsapplications

A new type of PVDF hydrophone, the multilayer planar PVDF hydrophone, is described. The hydrophone disturbs measured acoustic fields very little and has a high sensitivity. The noise-equivalent pressure of the hydrophone is 45 dB re 1 μ Pa per Hz bandwidth. The working frequency range of the hydrophone is 20 kHz~4 MHz. In the range 100 kHz~1 MHz, the hydrophone has a flat frequency response with sensitivity -205 dB ±1.5 dB (0 dB=1 V/μPa). In this range, the hydrophone has been used for five years as a standard one. Two other applications (measurements of noise spectra and ultrasonic imaging) are also reported     

Origin of 1/f PM and AM noise in bipolar junction transistor amplifiers

In this paper we report the results of extensive research on phase modulation (PM) and amplitude modulation (AM) noise in linear bipolar junction transistor (BJT) amplifiers. BJT amplifiers exhibit 1/f PM and AM noise about a carrier signal that is much larger than the amplifiers thermal noise at those frequencies in the absence of the carrier signal. Our work shows that the 1/f PM noise of a BJT based amplifier is accompanied by 1/f AM noise which can be higher, lower, or nearly equal, depending on the circuit implementation. The 1/f AM and PM noise in BJTs is primarily the result of 1/f fluctuations in transistor current, transistor capacitance, circuit supply voltages, circuit impedances, and circuit configuration. We discuss the theory and present experimental data in reference to common emitter amplifiers, but the analysis can be applied to other configurations as well. This study provides the functional dependence of 1/f AM and PM noise on transistor parameters, circuit parameters, and signal frequency, thereby laying the groundwork for a comprehensive theory of 1/f AM and PM noise in BJT amplifiers. We show that in many cases the 1/f PM and AM noise can be reduced below the thermal noise of the amplifier.     

A model for phase noise generation in amplifiers

In this paper, a model is presented for predicting the phase modulation (PM) and amplitude modulation (AM) noise in bipolar junction transistor (BJT) amplifiers. The model correctly predicts the dependence of phase noise on the signal frequency (at a particular carrier offset frequency), explains the noise shaping of the phase noise about the signal frequency, and shows the functional dependence on the transistor parameters and the circuit parameters. Experimental studies on common emitter (CE) amplifiers have been used to validate the PM noise model at carrier frequencies between 10 and 100 MHz     

Correlation between upper and lower sidebands

Experimental measurements supported by a simple model show that the upper and lower phase modulation (PM) noise sidebands are always equal and 100% correlated, independent of the noise power originating from multiplicative or additive processes. Similarly, we show that the upper and lower amplitude modulation (AM) noise sidebands are also equal and 100% correlated, independent of the noise power originating from multiplicative or additive processes, Moreover, the single sideband (SSB) PM noise is always equal to one-half the total PM noise. The same is true for the AM noise. Although the upper and lower PM or AM noise sidebands are equal and correlated for broadband additive noise, the phase between the AM and the PM sidebands varies randomly with time. These conclusions still hold even when the RF noise sidebands are not symmetric about the carrier.