Simulation of mutually coupled oscillators using nonlinear phase macromodels

Design of integrated RF circuits requires detailed insight in the behavior of the used components. Unintended coupling and perturbation effects need to be accounted for before production, but full simulation of these effects can be expensive or infeasible. In this paper we present a method to build nonlinear phase macromodels of voltage controlled oscillators. These models can be used to accurately predict the behavior of individual and mutually coupled oscillators under perturbation at a lower cost than full circuit simulations. The approach is illustrated by numerical experiments with realistic designs

Rigorous analytical/graphical injection locking analysis of two-port negative resistance oscillators

Abstract-In this paper, we present a simple but rigorous nonlinear analysis for understanding and predicting steady-state operation and injection locking in two-port nonlinear negative-resistance oscillators (such as the Colpitts, Pierce, etc., topologies commonly used in RFICs). Key advances of our approach include the use of vector-based nonlinear feedback analysis and treatment of amplitude and frequency components in a coupled way. We develop rigorous and insightful graphical approaches for output voltage estimation and injection lock range prediction. We validate our analytical approach against transient and harmonic balance simulations. I. INTRODUCTION Oscillators are building blocks in analog, RF and mixed-signal systems. When perturbed by external signals, they often exhibit interesting and practically useful behaviors such as injection locking A common approach for predicting injection locking is to use SPICE-level transient simulation. However, computationally, transient simulation can be extremely inaccurate and inefficient for oscillators (see, e.g., Recent work In this paper, we generalize the technique of [18] to apply to arbitrary two-port nonlinear feedback oscillators. We use the new approac

Macromodelling Oscillators Using Krylov-Subspace Methods

Abstract-We present an efficient method for automatically extracting unified amplitude/phase macromodels of arbitrary oscillators from their SPICE-level circuit descriptions. Such comprehensive oscillator macromodels are necessary for accuracy when speeding up simulation of higherlevel circuits/systems, such as PLLs, in which oscillators are embedded. Standard MOR techniques for linear time invariant (LTI) and varying (LTV) systems are not applicable to oscillators on account of their fundamentally nonlinear phase behavior. By employing a cancellation technique to deflate out the phase component, we restore the validity and efficacy of Krylov-subspace-based LTV MOR techniques for macromodelling oscillator amplitude responses. The nonlinear phase response is re-incorporated into the macromodel after the amplitude components have been reduced. The resulting unified macromodels predict oscillator waveforms, in the presence of any kind of input or interference, at far lower computational cost than full SPICE-level simulation, and with far greater accuracy compared to existing macromodels. We demonstrate the proposed techniques on LC and ring oscillators, obtaining speedups of 30-120× with no appreciable loss of accuracy, even for small circuits

Periodically Disturbed Oscillators

By controlling the timing of events and enabling the transmission of data over long distances, oscillators can be considered to generate the "heartbeat" of modern electronic systems. Their utility, however, is boosted significantly by their peculiar ability to synchronize to external signals that are themselves periodic in time. Although this fascinating phenomenon has been studied by scientists since the 1600s, models for describing this behavior have seen a disconnect between the rigorous, methodical approaches taken by mathematicians and the design-oriented, physically-based analyses carried out by engineers. While the analytical power of the former is often concealed by an inundation of abstract mathematical machinery, the accuracy and generality of the latter are constrained by the empirical nature of the ensuing derivations. We hope to bridge that gap here. In this thesis, a general theory of electrical oscillators under the influence of a periodic injection is developed from first principles. Our approach leads to a fundamental yet intuitive understanding of the process by which oscillators lock to a periodic injection, as well as what happens when synchronization fails and the oscillator is instead injection pulled. By considering the autonomous and periodically time-varying nature that underlies all oscillators, we build a time-synchronous model that is valid for oscillators of any topology and periodic disturbances of any shape. A single first-order differential equation is shown to be capable of making accurate, quantitative predictions about a wide array of properties of periodically disturbed oscillators: the range of injection frequencies for which synchronization occurs, the phase difference between the injection and the oscillator under lock, stable vs. unstable modes of locking, the pull-in process toward lock, the dynamics of injection pulling, as well as phase noise in both free-running and injection-locked oscillators. The framework also naturally accommodates superharmonic injection-locked frequency division, subharmonic injection-locked frequency multiplication, and the general case of an arbitrary rational relationship between the injection and oscillation frequencies. A number of novel insights for improving the performance of systems that utilize injection locking are also elucidated. In particular, we explore how both the injection waveform and the oscillator's design can be modified to optimize the lock range. The resultant design techniques are employed in the implementation of a dual-moduli prescaler for frequency synthesis applications which features low power consumption, a wide operating range, and a small chip area. For the commonly used inductor-capacitor (LC) oscillator, we make a simple modification to our framework that takes the oscillation amplitude into account, greatly enhancing the model's accuracy for large injections. The augmented theory uniquely captures the asymmetry of the lock range as well as the distinct characteristics exhibited by different types of LC oscillators. Existing injection locking and pulling theories in the available literature are subsumed as special cases of our model. It is important to note that even though the veracity of our theoretical predictions degrades as the size of the injection grows due to our framework's linearization with respect to the disturbance, our model's validity across a broad range of practical injection strengths are borne out by simulations and measurements on a diverse collection of integrated LC, ring, and relaxation oscillators. Lastly, we also present a phasor-based analysis of LC and ring oscillators which yields a novel perspective into how the injection current interacts with the oscillator's core nonlinearity to facilitate injection locking.</p

Design of monolithic microwave integrated circuits for 60 GHz band

Potreba za bežicnim komunikacioniom linkovima velikih brzina prenosa podataka je podstaknuta ekspanzijom prenosivih uređaja i multimedijalnih servisa, uz pogodnost da priroda korišcenja dozvoljava a ponekad i zahteva ogranicen domet. Problem kapaciteta komunikacionih linkova i sve veceg broja korisnika se može rešiti prelaskom u opseg ucestanosti od 30 do 300 GHz, koji se naziva i milimetarski opseg. Visoka radna ucestanost pruža mogucnost korišcenja kanala velikog kapaciteta, kao i fizicki malih antenskih nizova za fokusiranje i prostornu lokalizaciju prijemnog i predajnog snopa. Milimetarski opseg nalazi primene i u ostalim oblastima, kao što su industrijske, medicinske i bezbednosne. U komercijalnim primenama od interesa je opseg ucestanosti oko 60 GHz, koji je dodeljen za nelicenciranu upotrebu širom sveta. Razvoj CMOS i BiCMOS tehnologija je omogucio da se sistemi u 60 GHz-om opsegu mogu integrisati u standardnim procesima. Pored viših radnih ucestanosti, skaliranje tehnologija uvodi i tehnološka ogranicenja koja degradiraju performanse ukoliko se njihov uticaj zanemari. Zanemareni efekti mogu doprineti vecim gubicima, koji povecavaju faktor šuma prijemnika i degradiraju efikasnost predajnika, ali i parazitnim preslušavanjima koja rezultuju neželjenim spektralnim komponentama. Stoga je potrebno razmotriti kvalitativne i kvantitativne pokazatelje uticaja tehnoloških ogranicenja na performanse i prilagoditi postupak projektovanja. Kriticni blokovi za domet primopredajnika su malošumni pojacavac na prijemnoj strani i pojacavac snage na predajnoj strani. U okviru teze predstavljen je postupak projektovanja malošumnog pojacavaca i pojacavaca snage za rad u 60 GHz-om opsegu i širokopojasnog delitelja ucestanosti. Uvedene su nove smernice projektovanja koje uzimaju u obzir tehnološka ogranicenja. Pokazano je da se pravilnim particionisanjem elektromagnetskog modela može postici dobro slaganje rezultata simulacije i merenja. Projektovana kola su fabrikovana u IHP Microelectronics korišcenjem 0.25 mm SiGe:C BiCMOS procesa (fT/fmax = 200 GHz). Parametri fabrikovanih kola su izmereni i verifikovani na stopicama cipa, upotrebom mikrotalasnih sondi...The need for high capacity wireless data links is driven by expansion of mobile devices and multimedia services, with the advantage that a typical use case allows, and sometimes demands, a limited range. Problems of limited communication link capacity and growing number of users can be solved by moving to frequency range of 30 - 300 GHz, also known as millimeter range. High operating frequency allows the use of high capacity channels, and physically small antenna arrays for beam steering and spatial localization. Millimeter region of spectrum is also suitable for industrial, scientific and security applications. Unlicensed 60 GHz band is available worldwide, and is attractive for commercial applications. Development of CMOS and BiCMOS technologies has enabled the integration of complete 60 GHz systems in standard processes. Technology scaling enables the use of higher operating frequencies, but imposes new design constraints which may degrade the performance if their effect is neglected. Neglected effects may contribute to higher losses, which increase the noise figure of receiver and degrade transmitter efficiency, and also to parasitic coupling which results in undesired spectral components. Therefore, qualitative and quantitative measure of technology constraints impact on performance degradation needs to be evaluated, and applied to circuit design process. Critical blocks for transceiver range are low noise amplifier on receiver, and power amplifier on transmitter side. Design procedures for 60 GHz low noise and power amplifiers, and wideband frequency divider are presented in this thesis. Guidelines for technology constraints aware design are used in the presented design flow. Good agreement of experimental and simulation results is achieved by proper electromagnetic model partitioning. Designed circuits have been fabricated in IHP Microelectronics 0.25 mm SiGe:C BiCMOS process (fT/fmax = 200 GHz). Test chip parameters have been measured and verified on-wafer by using microwave probes..

Measurement techniques for the characterization of radio frequency gallium nitride devices and power amplifiers

The rapid growth of mobile telecommunications has fueled the development of the fifth generation (5G) of standards, aiming to achieve high data rates and low latency. These capabilities make use of new regions of spectrum, wider bandwidths and spectrally efficient modulations. The deployment of 5G relies on the development of radio-frequency (RF) technology with increased performance. The broadband operation at high-power and high-frequency conditions is particularly challenging for power amplifiers (PA) in transmission stages, which seek to concurrently maximize linearity and energy efficiency. The properties of Gallium Nitride (GaN) allow the realization of active devices with favorable characteristics in these applications. However, GaN high-electron mobility transistors (HEMTs) suffer from spurious effects such as trapping due to physical defects introduced during the HEMT growth process. Traps dynamically capture and release mobile charges depending on the applied voltages and temperature, negatively affecting the RF PA performance. This work focuses on the development of novel measurement techniques and setups to investigate trapping behavior of GaN HEMTs and PAs. At low-frequency (LF), charge dynamics is analyzed using pulsed current transient characterizations, identifying relevant time constants in state-of-the-art GaN technologies for 5G. Instead, at high-frequency, tailored methods and setups are used in order to measure trapping effects during the operation of HEMTs and PAs in RF modulated conditions. These RF characterizations emulate application-like regimes, possibly involving the control of the device’s output load termination. Therefore, an innovative wideband active load pull (WALP) setup is developed, using the acquisition capabilities of standard vector-network-analyzers. Moreover, the implications of performing error-vector-magnitude characterizations under wideband load pull conditions are studied. Finally, an efficient implementation of a modified-Volterra model for RF PAs is presented, making use of a custom vector-fitting algorithm to simplify the nonlinear memory operators and enable their realization in simulation environments

Reports to the President

A compilation of annual reports for the 1988-1989 academic year, including a report from the President of the Massachusetts Institute of Technology, as well as reports from the academic and administrative units of the Institute. The reports outline the year's goals, accomplishments, honors and awards, and future plans