Effects of noisy and modulated interferers on the free-running oscillator spectrum

A new methodology for the prediction of oscillator phase dynamics under the effect of an interference signal is presented. It is based on a semianalytical formulation in the presence of a noisy or modulated interferer, using a realistic oscillator model extracted from harmonic-balance simulations. The theoretical analysis of the phase process enables the derivation of key mathematical properties, used for an efficient calculation of the interfered-oscillator spectrum. The resulting quasi-periodic spectrum is predicted, as well as the impact of the interferer phase noise and modulation over each spectral component, in particular over the one at the fundamental frequency. It is demonstrated that under some conditions, the phase noise at this component is pulled to that of the interference signal. Resonance effects at multiples of the beat frequency are also predicted. In addition, the effects of interferer phase and amplitude modulation on the oscillator phase dynamics have been studied and compared. For that analysis, efficient simulation techniques have been developed. The analyses have been validated with experimental measurements in an FET-based oscillator at 2.5 GHz, obtaining excellent agreement.This work was supported in part by the Spanish Ministry of Economy and Competitiveness and the European Regional Development Fund (ERDF/FEDER) under research projects TEC2014-60283-C3-1-R and TEC2017-88242-C3-1-R, in part by the Juan de la Cierva Research Program under Grant IJCI-2014-19141, and in part by the Parliament of Cantabria through the project Cantabria Explora under Grant 12.JP02.6406

Cavity optoelectromechanical regenerative amplification

Cavity optoelectromechanical regenerative amplification is demonstrated. An optical cavity enhances mechanical transduction, allowing sensitive measurement even for heavy oscillators. A 27.3 MHz mechanical mode of a microtoroid was linewidth narrowed to 6.6\pm1.4 mHz, 30 times smaller than previously achieved with radiation pressure driving in such a system. These results may have applications in areas such as ultrasensitive optomechanical mass spectroscopy

Injection locking of an electro-optomechanical device

The techniques of cavity optomechanics have enabled significant achievements in precision sensing, including the detection of gravitational waves and the cooling of mechanical systems to their quantum ground state. Recently, the inherent non-linearity in the optomechanical interaction has been harnessed to explore synchronization effects, including the spontaneous locking of an oscillator to a reference injection signal delivered via the optical field. Here, we present the first demonstration of a radiation-pressure driven optomechanical system locking to an inertial drive, with actuation provided by an integrated electrical interface. We use the injection signal to suppress drift in the optomechanical oscillation frequency, strongly reducing phase noise by over 55 dBc/Hz at 2 Hz offset. We further employ the injection tone to tune the oscillation frequency by more than 2 million times its narrowed linewidth. In addition, we uncover previously unreported synchronization dynamics, enabled by the independence of the inertial drive from the optical drive field. Finally, we show that our approach may enable control of the optomechanical gain competition between different mechanical modes of a single resonator. The electrical interface allows enhanced scalability for future applications involving arrays of injection-locked precision sensors.Comment: Main text: 10 pages, 7 figures. Supplementary Information: 5 pages, 4 figure

Review of Injected Oscillators

Oscillators are critical components in electrical and electronic engineering and other engineering and sciences. Oscillators are classified as free-running oscillators and injected oscillators. This chapter describes the background necessary for the analysis and design of injected oscillators. When an oscillator is injected by an external periodic signal mentioned as an injection signal, it is called an injected oscillator. Consequently, two phenomena occur in the injected oscillators: (I) pulling phenomena and (II) locking phenomena. For locking phenomena, the oscillation frequency of the injection signal must be near free-running oscillation frequency or its sub-/super-harmonics. Due to these phenomena are nonlinear phenomena, it is tough to achieve the exact equation or closed-form equation of them. Therefore, researchers are scrutinizing them by different analytical and numerical methods for accomplishing an exact inside view of their performances. In this chapter, injected oscillators are investigated in two main subjects: first, analytical methods on locking and pulling phenomena are reviewed, and second, applications of injected oscillators are reviewed such as injection-locked frequency dividers at the latter. Furthermore, methods of enhancing the locking range are introduced

Stochastic analysis of cycle slips in injection-locked oscillators and analog frequency dividers

A detailed investigation of cycle slips in injection-locked oscillators (ILOs) and analog frequency dividers is presented. This nonlinear phenomenon gives rise to a temporal desynchronization between the injected oscillator and the input source due to noise perturbations. It involves very different time scales so even envelope-transient-based Monte Carlo analyses may suffer from high computational cost. The analysis method is based on an initial extraction of a reduced-order nonlinear model of the injected oscillator based on harmonic-balance simulations. This model has been improved with a more accurate description of oscillation dependence on the input source either at the fundamental frequency or, in the case of a frequency divider, at a given harmonic frequency. The reduced-order model enables an efficient stochastic analysis of the system based on the use of the associated Fokker-Planck equation in the phase probability density function. Several methods for the solution of the associated Fokker-Planck equation are compared with one of them being applicable under a wider range of system specifications. The analysis enables the prediction of the parameter-space regions that are best protected against cycle slips. The technique has been applied to two microwave ILOs and has been validated through commercial software envelope simulations in situations where the computational cost of the envelope simulations was acceptable, and through measurements. The measurement procedure of the cycle slipping phenomenon has been significantly improved with respect to previous work.This work was supported by the Spanish Ministry of Economy and Competitiveness under Contract TEC2011-29264-C03-01

Analysis of the high frequency substrate noise effects on LC-VCOs

La integració de transceptors per comunicacions de radiofreqüència en CMOS pot quedar seriosament limitada per la interacció entre els seus blocs, arribant a desaconsellar la utilització de un únic dau de silici. El soroll d’alta freqüència generat per certs blocs, com l’amplificador de potencia, pot viatjar pel substrat i amenaçar el correcte funcionament de l’oscil·lador local. Trobem tres raons importants que mostren aquest risc d’interacció entre blocs i que justifiquen la necessitat d’un estudi profund per minimitzar-lo. Les característiques del substrat fan que el soroll d’alta freqüència es propagui m’és fàcilment que el de baixa freqüència. Per altra banda, les estructures de protecció perden eficiència a mesura que la freqüència augmenta. Finalment, el soroll d’alta freqüència que arriba a l’oscil·lador degrada al seu correcte comportament. El propòsit d’aquesta tesis és analitzar en profunditat la interacció entre el soroll d’alta freqüència que es propaga pel substrat i l’oscil·lador amb l’objectiu de poder predir, mitjançant un model, l’efecte que aquest soroll pot tenir sobre el correcte funcionament de l’oscil·lador. Es volen proporcionar diverses guies i normes a seguir que permeti als dissenyadors augmentar la robustesa dels oscil·ladors al soroll d’alta freqüència que viatja pel substrat. La investigació de l’efecte del soroll de substrat en oscil·ladors s’ha iniciat des d’un punt de vista empíric, per una banda, analitzant la propagació de senyals a través del substrat i avaluant l’eficiència d’estructures per bloquejar aquesta propagació, i per altra, determinant l’efecte d’un to present en el substrat en un oscil·lador. Aquesta investigació ha mostrat que la injecció d’un to d’alta freqüència en el substrat es pot propagar fins arribar a l’oscil·lador i que, a causa del ’pulling’ de freqüència, pot modular en freqüència la sortida de l’oscil·lador. A partir dels resultats de l’anàlisi empíric s’ha aportat un model matemàtic que permet predir l’efecte del soroll en l’oscil·lador. Aquest model té el principal avantatge en el fet de que està basat en paràmetres físics de l’oscil·lador o del soroll, permetent determinar les mesures que un dissenyador pot prendre per augmentar la robustesa de l’oscil·lador així com les conseqüències que aquestes mesures tenen sobre el seu funcionament global (trade-offs). El model ha estat comparat tant amb simulacions com amb mesures reals demostrant ser molt precís a l’hora de predir l’efecte del soroll de substrat. La utilitat del model com a eina de disseny s’ha demostrat en dos estudis. Primerament, les conclusions del model han estat aplicades en el procés de disseny d’un oscil·lador d’ultra baix consum a 2.5GHz, aconseguint un oscil·lador robust al soroll de substrat d’alta freqüència i amb característiques totalment compatibles amb els principals estàndards de comunicació en aquesta banda. Finalment, el model s’ha utilitzat com a eina d’anàlisi per avaluar la causa de les diferències, en termes de robustesa a soroll de substrat, mesurades en dos oscil·ladors a 60GHz amb dues diferents estratègies d’apantallament de l’inductor del tanc de ressonant, flotant en un cas i connectat a terra en l’altre. El model ha mostrat que les diferències en robustesa són causades per la millora en el factor de qualitat i en l’amplitud d’oscil·lació i no per un augment en l’aïllament entre tanc i substrat. Per altra banda, el model ha demostrat ser vàlid i molt precís inclús en aquest rang de freqüència tan extrem. el principal avantatge en el fet de que està basat en paràmetres físics de l’oscil·lador o del soroll, permetent determinar les mesures que un dissenyador pot prendre per augmentar la robustesa de l’oscil·lador així com les conseqüències que aquestes mesures tenen sobre el seu funcionament global (trade-offs). El model ha estat comparat tant amb simulacions com amb mesures reals demostrant ser molt precís a l’hora de predir l’efecte del soroll de substrat. La utilitat del model com a eina de disseny s’ha demostrat en dos estudis. Primerament, les conclusions del model han estat aplicades en el procés de disseny d’un oscil·lador d’ultra baix consum a 2.5GHz, aconseguint un oscil·lador robust al soroll de substrat d’alta freqüència i amb característiques totalment compatibles amb els principals estàndards de comunicació en aquesta banda. Finalment, el model s’ha utilitzat com a eina d’anàlisi per avaluar la causa de les diferències, en termes de robustesa a soroll de substrat, mesurades en dos oscil·ladors a 60GHz amb dues diferents estratègies d’apantallament de l’inductor del tanc de ressonant, flotant en un cas i connectat a terra en l’altre. El model ha mostrat que les diferències en robustesa són causades per la millora en el factor de qualitat i en l’amplitud d’oscil·lació i no per un augment en l’aïllament entre tanc i substrat. Per altra banda, el model ha demostrat ser vàlid i molt precís inclús en aquest rang de freqüència tan extrem.The integration of transceivers for RF communication in CMOS can be seriously limited by the interaction between their blocks, even advising against using a single silicon die. The high frequency noise generated by some of the blocks, like the power amplifier, can travel through the substrate, reaching the local oscillator and threatening its correct performance. Three important reasons can be stated that show the risk of the single die integration. Noise propagation is easier the higher the frequency. Moreover, the protection structures lose efficiency as the noise frequency increases. Finally, the high frequency noise that reaches the local oscillator degrades its performance. The purpose of this thesis is to deeply analyze the interaction between the high frequency substrate noise and the oscillator with the objective of being able to predict, thanks to a model, the effect that this noise may have over the correct behavior of the oscillator. We want to provide some guidelines to the designers to allow them to increase the robustness of the oscillator to high frequency substrate noise. The investigation of the effect of the high frequency substrate noise on oscillators has started from an empirical point of view, on one hand, analyzing the noise propagation through the substrate and evaluating the efficiency of some structures to block this propagation, and on the other hand, determining the effect on an oscillator of a high frequency noise tone present in the substrate. This investigation has shown that the injection of a high frequency tone in the substrate can reach the oscillator and, due to a frequency pulling effect, it can modulate in frequency the output of the oscillator. Based on the results obtained during the empirical analysis, a mathematical model to predict the effect of the substrate noise on the oscillator has been provided. The main advantage of this model is the fact that it is based on physical parameters of the oscillator and of the noise, allowing to determine the measures that a designer can take to increase the robustness of the oscillator as well as the consequences (trade-offs) that these measures have over its global performance. This model has been compared against both, simulations and real measurements, showing a very high accuracy to predict the effect of the high frequency substrate noise. The usefulness of the presented model as a design tool has been demonstrated in two case studies. Firstly, the conclusions obtained from the model have been applied in the design of an ultra low power consumption 2.5 GHz oscillator robust to the high frequency substrate noise with characteristics which make it compatible with the main communication standards in this frequency band. Finally, the model has been used as an analysis tool to evaluate the cause of the differences, in terms of performance degradation due to substrate noise, measured in two 60 GHz oscillators with two different tank inductor shielding strategies, floating and grounded. The model has determined that the robustness differences are caused by the improvement in the tank quality factor and in the oscillation amplitude and no by an increased isolation between the tank and the substrate. The model has shown to be valid and very accurate even in these extreme frequency range.Postprint (published version

Multi-Loop-Ring-Oscillator Design and Analysis for Sub-Micron CMOS

Ring oscillators provide a central role in timing circuits for today?s mobile devices and desktop computers. Increased integration in these devices exacerbates switching noise on the supply, necessitating improved supply resilience. Furthermore, reduced voltage headroom in submicron technologies limits the number of stacked transistors available in a delay cell. Hence, conventional single-loop oscillators offer relatively few design options to achieve desired specifications, such as supply rejection. Existing state-of-the-art supply-rejection- enhancement methods include actively regulating the supply with an LDO, employing a fully differential or current-starved delay cell, using a hi-Z voltage-to-current converter, or compensating/calibrating the delay cell. Multiloop ring oscillators (MROs) offer an additional solution because by employing a more complex ring-connection structure and associated delay cell, the designer obtains an additional degree of freedom to meet the desired specifications. Designing these more complex multiloop structures to start reliably and achieve the desired performance requires a systematic analysis procedure, which we attack on two fronts: (1) a generalized delay-cell viewpoint of the MRO structure to assist in both analysis and circuit layout, and (2) a survey of phase-noise analysis to provide a bank of methods to analyze MRO phase noise. We distill the salient phase-noise-analysis concepts/key equations previously developed to facilitate MRO and other non-conventional oscillator analysis. Furthermore, our proposed analysis framework demonstrates that all these methods boil down to obtaining three things: (1) noise modulation function (NMF), (2) noise transfer function (NTF), and (3) current-controlled-oscillator gain (KICO). As a case study, we detail the design, analysis, and measurement of a proposed multiloop ring oscillator structure that provides improved power-supply isolation (more than 20dB increase in supply rejection over a conventional-oscillator control case fabricated on the same test chip). Applying our general multi-loop-oscillator framework to this proposed MRO circuit leads both to design-oriented expressions for the oscillation frequency and supply rejection as well as to an efficient layout technique facilitating cross-coupling for improved quadrature accuracy and systematic, substantially simplified layout effort

Integrated turnkey soliton microcombs operated at CMOS frequencies

While soliton microcombs offer the potential for integration of powerful frequency metrology and precision spectroscopy systems, their operation requires complex startup and feedback protocols that necessitate difficult-to-integrate optical and electrical components. Moreover, CMOS-rate microcombs, required in nearly all comb systems, have resisted integration because of their power requirements. Here, a regime for turnkey operation of soliton microcombs co-integrated with a pump laser is demonstrated and theoretically explained. Significantly, a new operating point is shown to appear from which solitons are generated through binary turn-on and turn-off of the pump laser, thereby eliminating all photonic/electronic control circuitry. These features are combined with high-Q $Si_3N_4$ resonators to fully integrate into a butterfly package microcombs with CMOS frequencies as low as 15 GHz, offering compelling advantages for high-volume production.Comment: Boqiang Shen, Lin Chang, Junqiu Liu, Heming Wang and Qi-Fan Yang contributed equally to this wor