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.     

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.     

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.     

Phase noise in capacitively coupled micromechanical oscillators

Phase noise in capacitively coupled microresonator-based oscillators is investigated. A detailed analysis of noise mixing mechanisms in the resonator is presented, and the capacitive transduction is shown to be the dominant mechanism for low-frequency 1/f-noise mixing into the carrier sidebands. Thus, the capacitively coupled micromechanical resonators are expected to be more prone to the 1/f-noise aliasing than piezoelectrically coupled resonators. The analytical work is complemented with simulations, and a highly efficient and accurate simulation method for a quantitative noise analysis in closed-loop oscillator applications is presented. Measured phase noise for a microresonator-based oscillator is found to agree with the developed analytical and simulated noise models.     

High spectral purity microwave oscillator: design using conventional air-dielectric cavity

We report exceptionally low PM noise levels from a microwave oscillator that uses a conventional air-dielectric cavity resonator as a frequency discriminator. Our approach is to increase the discriminator's intrinsic signal-to-noise ratio by use of a high-power carrier signal to interrogate an optimally coupled cavity, while the high-level of the carrier is suppressed before the phase detector. We developed and tested an accurate model of the expected PM noise that indicates, among other things, that a conventional air-dielectric resonator of moderate Q will exhibit less discriminator noise in this approach than do more esoteric and expensive dielectric resonators tuned to a high-order, high-Q mode and driven at the dielectric's optimum     

Frequency stability of high-overtone bulk-acoustic resonators

The results of phase noise measurement for high-overtone bulk-acoustic resonators (HBARs) for use in high-performance oscillators, operating at 640 MHz with insertion losses of 10-15 dB and unmatched Qs greater than 110 K are reported. Noise measurements made on these resonators with input drive levels of 16 dBm have shown self-noise levels of S(y)(f=100 Hz)=8.0x10(-26) for 1/f noise which represents state-of-the-art for a UHF resonator.     

Tunable microwave resonators and oscillators using magnetostatic waves

The status of magnetostatic wave (MSW) straight-edge resonators (SERs) and their applications in tunable oscillator circuits are reviewed. The resonators are based on magnetostatic waves propagating in high-Q cavities fabricated in thin ferrimagnetic yttrium iron garnet (YIG) films. The resonance frequency of these resonators can be tuned using a bias magnetic field. The theory of operation and design criteria for the straight-edge resonators are described with emphasis on the effect of the resonator parameters on the tuning range, power handling, and phase noise performance. The use of the SER as the frequency-selective element in oscillator circuits is reported. Examples of tunable oscillators are included.     

Cooled, ultrahigh Q, sapphire dielectric resonators for low-noise, microwave signal generation

Ultra-high Q, X-band resonators, used in a frequency discriminator for stabilization of a low-noise signal generator, can provide a means of obtaining significant reduction in phase noise levels. Resonator unloaded Qs on the order of 500 K can be obtained in sapphire dielectric resonator (DR) operating on a low-order (i.e. TE(01)) mode at 77 K and employing high-temperature superconducting (HTS) films installed in the DR enclosure covers. Rigorous analysis for the determination of resonator frequency, modes, and unloaded Q have been carried out using mode matching techniques. Trade-off studies have been performed to select resonator dimensions for the optimum mode yielding highest unloaded Q and widest spurious mode separation. Field distributions within the resonator have been computed to enable practical excitation of the required mode. The results of both analysis and prototype device evaluation experiments are compared for resonators fabricated using enclosures consisting of conventional, metal sidewalls and covers employing HTS films as a function of cover conductivity.     

High-temperature superconducting resonators

Preliminary measurements on high-T(c) superconducting resonators are reported and why they are attractive candidates for incorporation in low-noise oscillators is discussed. Some of the important contributions to oscillator noise are reviewed and how they depend on the resonator parameters is shown. A preliminary YBaCu (3)O(7)/LaAlO(3) resonator with a Q of 9x10(4) at 6.9 GHz and 7x10(4) at 3.5 GHz has been fabricated. The temperature sensitivity, power dependence, and residual phase noise are discussed. An upper-limit on the coefficient of the 1/f component of fractional-frequency fluctuations has been measured to be -204 dB at 60 K.     

Microwave oscillators incorporating cryogenic sapphire dielectricresonators

Progress is reported on efforts to develop a commercially-viable high purity X-band signal source incorporating a cryogenic sapphire dielectric resonator. The resonator design is of the whispering gallery type to take advantage of the excellent electromagnetic field confinement offered by this geometry. Complications resulting from the high spurious mode density of this type of resonator have been eliminated by developing a very accurate and complete mode analysis program which fully incorporates the dielectric anisotropies of the sapphire ring. This program allows the design of a window in the frequency domain where no unwanted modes exist, with accurate placement of the desired mode at the center of this region. Preliminary evaluation of the phase noise properties of simple oscillators incorporating these resonators have been performed. For example, in a dual-oscillator comparison of two oscillators operating near 13 GHz phase noise values of L(f)=-55 dBc/Hz, -145 dBc/Hz and -161 dBc/Hz were obtained for offset frequencies of 1 Hz, 1 kHz and 10 kHz, respectively     

Doubly rotated quartz resonators with a low amplitude-frequencyeffect: the LD-cut

This article deals with a crystal quartz cut with virtually no amplitude-frequency effect (also called "isochronism defect" or "anisochronism"). The cut, called LD-cut (Low isochronism Defect), is set in a BVA-type structure for later use in an Ultra-Stable Oscillator (USO). Various design parameters are presented, along with the properties of the resonator. The resonance frequencies of various modes, the temperature dependence, the motional parameters and the phase noise in relation to the power supplied to the resonator are mainly studied. These properties are compared to those of the SC-cut resonators     

A Frequency-Lock System for Improved Quartz Crystal Oscillator Performance

The intrinsic noise of the best quartz crystal resonators is significantly less than the noise observed in oscillators employing these resonators Several problem areas common to traditional designs are pointed out and a new approach is suggested for their solution. Two circuits are described which frequency lock a spectrally pure quartz crystal oscillator to an independent quartz crystal resonator. The performance of the composite system is predicted based on the measured performance of its components.     

Noise and Sensitivity of Aluminum Kinetic Inductance Detectors for Sub-mm Astronomy

Kinetic inductance detectors are based upon high Q superconducting resonators. We have measured the electrical Noise Equivalent Power (NEP) of 100 nm thick 1/4λ coplanar waveguide Aluminum resonators at 100 mK using phase readout and radius readout. We find that the phase NEP is independent of the Q factor of the resonator, limited by excess noise in the KID and given by NEP at 100 Hz. It increases with roughly f ^−0.5 at lower frequencies. The amplitude NEP is strongly Q factor dependent, limited by the setup noise, nearly frequency independent and as low as NEP for a high Q resonator (Q=454.000). For lower Q resonators the amplitude NEP increases to values equal to or even larger than the phase readout.      

High Q printed helical resonators for oscillators and filters

High Q compact printed helical resonators which operate from around 1.8 to 2 GHz are described. These consist of a multilayer printed circuit board (PCB) incorporating a printed helical transmission line. Loss in the via hole is reduced by ensuring that the standing wave current at this point is near zero. This ensures a significant increase in Q. Further increased energy storage per unit volume is achieved due to the 3-D helical nature of the resonator. Unloaded Qs of 235 and 195 have been obtained on low loss PCBs with dielectric constants of 2.2 and 10.5, respectively. Two applications for these resonators are described in this paper. The first is the design of a compact low noise oscillator where the ratio of QL/Q0, and hence insertion loss, is adjusted for low noise. The 2-GHz oscillator demonstrates a phase noise of -120 dBc/Hz at 10 kHz which is predicted exactly by the theory. The second is a three-section filter designed to offer the response required by the front end filter of a modern GSM mobile telephone. In the filter design three helical resonators are coupled together to produce a completely printed triplate bandpass filter.     

Linear frequency tuning of SAW resonators

Frequency tuning in SAW (surface acoustic wave) resonator-stabilized oscillators is normally accomplished via utilization of a voltage-controlled phase shifter. The design of abrupt junction varactor diode-inductor networks which employ impedance transformation techniques to obtain linear frequency tuning of two-port SAW resonators is reported. The approach is similar to that previously developed for linear tuning of bulk wave, quartz crystal resonators. This technique uses varactor diode parallel inductance to provide a linear reactance versus voltage network, which is effectively connected in series with the resonator motional impedance in order to tune the effective resonator center frequency. Typical tuning ranges are significantly larger than those achievable using the phase shifter approach, and are on the order of 400 ppm for the 320-MHz resonator used.     

Design and properties of STW asynchronous resonators on quartz

In a surface transverse wave (STW) asynchronous resonator, grating phase shifters are placed between interdigital transducers and reflectors to obtain the incident and reflected waves in phase, and the resonance frequency is located near the center frequency of the reflectors. In this paper, the scattering matrix method is used for design of such resonators with one dominant longitudinal mode. At a frequency of about 509.5 MHz, insertion loss, and loaded and unloaded quality factors of about 6 dB, 5,300 and 11,000, respectively, were obtained. The measured and calculated parameters of this resonator are in good agreement. Design guidelines and comparison of synchronous and asynchronous resonators are presented. Compared to synchronous resonators, low spurious signals' level, location of the resonance frequency near the center frequency of the reflectors, and simple design method make the asynchronous resonators more attractive for manufacture and practical applications.     

Noise in microelectromechanical system resonators

Microelectromechanical system (MEMS) and nanoelectromechanical system (NEMS) based resonators and filters, ranging in frequencies from kHz to GHz, have been proposed. The question of how the stabilities of such resonators scale with dimensions is examined in this paper, with emphasis on the noise characteristics. When the dimensions of a resonator become small, instabilities that are negligible in macro-scale devices become prominent. The effects of fluctuations in temperature, adsorbing/desorbing molecules, outgassing, Brownian motion, Johnson noise, drive power and self-heating, and random vibration are explored. When the device is small, the effects of fluctuations in the numbers of photons, phonons, electrons and adsorbed molecules can all affect the noise characteristics. For all but the random vibration-induced noise, reducing the dimensions increases the noise. At submicron dimensions, especially, the frequency noise due to temperature fluctuations, Johnson noise, and adsorption/desorption are likely to limit the applications of ultra-small resonators.     

Scattering analysis of two-port SAW resonators

Linear equations derived from the scattering matrix approach to the two-port resonator were solved, and analytical expressions for the normalized SAW amplitudes were obtained. Asynchronous and synchronous resonators were analyzed numerically. It was shown that the output of the two-port resonator is a sum of two signals. In the case of the asynchronous resonator, these signals are in phase at a resonance frequency; for the synchronous resonator, they are in phase quadrature, which causes the higher insertion loss of the synchronous resonator     

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.