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     

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.     

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.     

Theory of Hydrogen-Maser Auto-Tuning Systems Based on the Frequency or the Phase Method

A theoretical analysis of auto-tuning systems for actively operated hydrogen (H) masers is presented. Tuning procedures based on changes in the frequency or the phase of oscillation are considered and compared. The analysis takes into account the basic results of sampling theory. The condition which should be satisfied when the reference frequency source is perturbed by white or flicker phase noise is specified. It is shown that the phase method should give better results than the frequency method when the reference source is a good quartz crystal oscillator.     

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.     

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     

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.     

The state of the art of flicker frequency noise in BAW and SAW quartz resonators

Experimental results of the last 15 years are reviewed. Noise properties of crystal filters and oscillators are reported, along with practical measurements. It is shown that the additional phase fluctuations are compensated by frequency fluctuations and vice versa. With the assistance of these theoretical results the flicker and white frequency noise coefficients, h(-1) and h(0), respectively, are plotted versus unloaded Q and carrier frequency f(0) for the measured and published crystal oscillator noise characteristics. The dependence of h(-1) approximately 10(-12.75) Q(2) (u) is verified.     

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.     

An X-band, high power dielectric resonator oscillator for future military systems

A 9.0-GHz dielectric resonator oscillator (DRO), generating a CW output power of 2.5 W at room temperature, has been designed and fabricated using a high-power GaAs MESFET and a dielectric resonator (DR) in a parallel feedback configuration. The oscillator exhibited a frequency stability of better than 130 ppm, without any temperature compensation, over the range -50 degrees C to +50 degrees C. The output power varied from +35 dBm (3.2 W) at -50 degrees C to +33 dBm (2 W) at +50 degrees C. The single-sideband phase noise levels were measured and found to be -105 and -135 dBc/Hz, at 10- and 100-kHz carrier offset frequencies, respectively. The oscillator output was then fed into a single-stage high-power MESFET amplifier, resulting in a total RF power output of 6.5 W. The overall DC to RF conversion efficiency of the 6.5-W unit was approximately 15.3%     

Broad tuning ultra low phase noise dielectric resonator oscillators using SiGe amplifier and ceramic-based resonators

This paper describes the design of very low noise, tunable, X-band dielectric resonator oscillators (DROs) demonstrating phase-noise performance of -135 dBc/Hz at 10 kHz offset. SiGe transistors are used for the oscillator sustaining amplifiers that offer a circulating power of 12 dBm and a gain of 5.4 dB per stage as well as a low flicker noise corner of 40 kHz. A variety of resonator configurations utilising BaTiO₃ resonators are presented demonstrating unloaded Qs from 10 000 to 22 000. These resonators are optimised and coupled to the amplifiers for minimum phase noise where Q_L/Q₀ = 1/2, and hence S₂₁ = -6 dB. To incorporate tuning with low additional phase noise, a phase shifter is also investigated. The theory for the low noise oscillator design is included; experimental results demonstrate close correlation with the theory.     

The use of thermosensitive quartz sensor for thermal regulation at cryogenic temperatures: application to microwave sapphire resonator references

We demonstrated the use of thermosensitive quartz resonator oscillator as a thermal sensor for temperature control at the liquid nitrogen temperature. The high sensitivity of the quartz enables an efficient thermal regulation at ambient temperature as well as liquid nitrogen temperature. LC-cut quartz oscillator phase noise measurements show that the temperature measurement resolution is not limited by the intrinsic noise of the sensor and that a resolution of 10 muK can be achieved. This thermal regulation is applied to control a microwave temperature-compensated sapphire resonator oscillator at a temperature above 77 K, enabling the achievement of a flicker floor of 9.10(-13 ) at 9 GHz.     

New phase-noise model for crystal oscillators: application to the Clapp oscillator

Leeson's is the basic model for predicting oscillator noise. A mathematical analysis of this "heuristic" model has been proposed. Both models do not detail the relative importance of the amplifier transfer function associated to its own noise with regard to that of the resonator. In this paper, an improved version of those previous models is presented. The phase noise generated by the amplifier and the one generated by the resonator are differentiated without considering their origins, such as the conversion of amplitude modulation noise into phase modulation noise. The power spectral densities of phase noise at various points of the oscillator loop are calculated from their respective correlation functions. As a consequence, the influence of the inner amplifier and resonator noises on the resulting oscillator noise is predictable. The model is especially attractive to the makers of widely used quartz oscillators. The resulting oscillator noise is easily obtained from the oscillator open-loop noise. An example of the phase-noise modeling of the Clapp quartz crystal oscillator is simulated and discussed.     

Estimations of frequency and its drift rate

This paper presents an analysis of frequency and its drift rate estimation by the difference method, the least-squares method, and the Kalman filter. Error formulas are derived for all five noise processes: white phase, flicker phase, white frequency, flicker frequency, and random walk frequency. The error formulas show the relationship between the estimate error and the noise spectral density coefficients, the same interval τ, and the data number N. Because of the existence of some nonstationary noise processes, a large data number may not yield a good estimation. One should choose an appropriate sample interval and data number so as to control the estimate error. An optimal solution based on the Kalman filter is presented     

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.     

Direct conversion RF front-end with a low-power consumption technique for 2.4 GHz ISM band

The implementation and performance measurements of RF front-end are presented. The low-power RF front-end designed in TSMC 0.18 mm process for 2.4 GHz ISM band direct conversion is presented. The proposed RF front-end is comprised of the folded mixer, fully differential low-noise amplifier (LNA) and interstage matching network. Gilbert-cell mixers using the folded technique and current reused LNA are designed for low power consumption. The folded mixers are implemented by using PMOS devices in the switching stage of mixers with a resonating inductor for low flicker noise. The proposed RF front-end consumes 7.2 mW from the 1.2 V supply and a conversion gain of 23 dB is achieved. The third-order intercept point (IIP3) is 210.5 dBm, and the proposed RF front-end has good linearity. By using PMOS devices and the folded technique, low flicker noise of 10 dB at 10 kHz is achieved, and thus the proposed RF front-end can be used in the direct conversion receiver for narrow bandwidth.     

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.     

On the flicker noise of ferrite circulators for ultra-stable oscillators

The flicker noise of the ferrite circulator is a critical element in ultra-stable microwave oscillators, in which the signal reflected from the input of the reference cavity is exploited to stabilize the frequency. This paper explains why the circulator noise must be measured in isolation mode, proposes a measurement scheme, and provides experimental results. The observed flicker spans from -162 to -170 dB[rad2]/Hz at 1 Hz off the 9.2 GHz carrier, and at +19 dBm of input power. In the same conditions, the instrument limit is below -180 dB[rad2]/Hz. Experiments also give information on the mechanical stability of the microwave assembly, which is in the range of 10(-11) m. The measurement method can be used as the phase detector of a corrected oscillator; and, in the field of solid-state physics, it can be used for the measurement of random fluctuations in magnetic materials.     

Reduction of quartz crystal oscillator flicker-of-frequency and white phase noise (floor) levels and acceleration sensitivity via use of multiple resonators

Through the use of N series-connected quartz crystal resonators in an oscillator circuit, a 10 log N reduction in both flicker-of-frequency noise and white phase-noise (floor) levels has been demonstrated. The reduction in flicker noise occurs as a result of the uncorrelated short-term frequency instability in each of the resonators, and the reduction in noise floor level is a simple result of the increase in net, allowable crystal drive level. This technique has been used in 40-, 80-, and 100-MHz AT-, BT-, and SC-cut crystal oscillators using low flicker-of-phase noise modular amplifier sustaining stages, and four series connected crystals. Total (four crystal) power dissipations of up to 30 mW have been utilized. State-of-the-art, flicker-of-frequency noise levels have been obtained with noise-floor levels (80 MHz) as low as -180 dBc/Hz. Four- to five-fold reduction in acceleration sensitivities has been determined     

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