Pulsed-waveform generator based on coupled oscillators

Waveform sharpening in nonlinear transmissionlines (NLTL) is analyzed in detail and applied to the design of apulse-generator based on two coupled oscillators. The maximumpropagation frequency through the NLTL is calculated with arealistic numerical technique, which enables an optimized design.By coupling two NLTL oscillators terminated in grounded stubsof different length, three design parameters are available, whichenables a flexible mechanism for pulse formation. A reducedordermodel is proposed for the efficient determination of thetuning voltage in one of the oscillator elements. The analysis anddesign techniques have been applied to a prototype at 0.8 GHz.Spanish project TEC20 11-29264-C03-01 for financial support

Analysis of self-injection locked oscillators for motion sensing applications

Self-injection locked oscillators have been recently proposed for motion sensing applications demonstrating a good experimental performance. Here a detailed investigation of the system dynamics is presented using a realistic model of the oscillator circuit under the injection of the reflected signal, which is phase modulated due to the target motion. The instability effects observed for some distance values are studied by means of a perturbation method and the results are validated through comparison with full circuit-level simulations and with measurements. The regular operation ranges are efficiently determined through a bifurcation analysis in terms of the distance to the target and the antenna gain. The modulation effect is analyzed with a reduced-order envelope transient formulation that copes with the accuracy problems associated with the small values of the modulation frequency. Very good agreement has been obtained with the experimental results.The authors would like to thank to Spanish Ministry of Economy and Competitiveness for their financial support under the research project TEC2014-60283-C3-1-R and Juan de la Cierva Research Program IJCI-2014-19141 and the Parliament of Cantabria for financial support under the project Cantabria Explora 12.JP02.64069

Analysis of a frequency divider by two based on a differential nonlinear transmission line

A recently proposed frequency divider by two, based on differential nonlinear transmission line, acting like a reflective distributed resonator, is analyzed in-depth. The flip bifurcation locus of a single cell is obtained analytically, which enables an understanding of the divider behavior and an initial estimation of its element values. The possibility to modify the division threshold and bandwidth through the proper selection of an additional linear capacitor is demonstrated. The influence of the number of cells on the division bandwidth and on the generated standing wave at the subharmonic frequency is also investigated. The techniques have been applied to two frequency divider with 1.5 and 2.2 GHz input frequency.Spanish project TEC2011-29264-C03-01 for financial support

Stability analysis of wireless coupled-oscillator circuits

Distributed synchronization of sensor networks can be achieved by coupling the oscillator signals of the sensor nodes. Previous works describe the coupling effects in an idealized manner, with constant scalar coefficients. Here a realistic analysis of the coupled-system dynamics is presented for the first time to our knowledge, taking into account the antenna gains and propagation effects on the amplitude and phase values of the equivalent current sources, injecting the oscillator elements. The new formulation provides the synchronized oscillation frequency and amplitude and phase distributions of the coupled system. Distinct oscillation modes, with different phase shifts between the oscillator elements, are identified, associated with the system symmetry. The stability properties of these modes change with the distance between the oscillator elements. The possibility to impose in-phase operation by tuning of the oscillator elements is demonstrated. Good agreement is obtained between simulation and measurements.The authors would like to thank to Spanish Ministry of Economy and Competitiveness for their financial support under the research project TEC2014-60283-C3-1-R, the European Regional Development Fund (ERDF/FEDER), Juan de la Cierva Research Program IJCI-2014-19141 and the Parliament of Cantabria for financial support under the project Cantabria Explora 12.JP02.64069

Oscillation modes in symmetrical wireless-locked systems

Time synchronization of multiple elements of a wireless network can be achieved through the wireless coupling of their oscillator circuits. Most previous works on wireless locking of oscillators analyze the system in an idealized manner, representing the oscillator elements with phase models and describing the propagation effects with constant scalar coefficients and time delays. Here, a realistic analysis of the wireless system is presented, which relies on the extraction of the oscillator models from harmonic-balance (HB) simulations and takes into account the antenna gains and propagation effects. The most usual network configurations, corresponding to ring, fully connected, and star topologies, are investigated in detail. In symmetric conditions, the oscillation modes are detected through an eigenvalue/eigenvector calculation of an equivalent coupling matrix. For each particular mode, the system is analyzed in the following manners: by means of an analytical formulation, able to provide all the coexistent solutions, and through a circuit-level HB simulation of an equivalent system with a reduced number of oscillator elements. The stability properties are determined by means of a perturbation system of general application to any coupled structure. A specific formulation is also derived to predict the impact of discrepancies between the oscillator elements. All the results have been validated with independent circuit-level simulations and measurements.This work was supported in part by the Spanish Ministry of Economy and Competitiveness under the research project TEC2017-88242-C3-1-R, in part by the European Regional Development Fund (ERDF/FEDER), in part by Juan de la Cierva Research Program under IJCI-2014-19141, and in part by the Parliament of Cantabria under the project Cantabria Explora 12.JP02.64069

Optimized design of frequency dividers based on varactor-inductor cells

This paper presents an in-depth analysis of a recently proposed frequency divider by two, which is based on a parallel connection of varactor-inductor cells, in a differential operation at the subharmonic frequency. The analytical study of a single-cell divider enables the derivation of a real equation governing the circuit at the frequency-division threshold. This equation is used for a detailed investigation of the impact of the circuit elements on the input-amplitude threshold and the frequency bandwidth. Insight provided by the analytical formulation enables the derivation of a thorough synthesis methodology for multiple-cell dividers, usable in harmonic balance with an auxiliary generator at the divided frequency. Two different applications of this topology are demonstrated: a dual-phase divider and a dual-band frequency divider. The former is obtained by using Marchand balun to deliver 180 ° phase-shifted signals to the two dividers. On the other hand, the dual-band divider is based on a novel configuration which combines cells with parallel varactors and cells with series varactors. Departing from the optimization procedure of the single-band divider, a simple synthesis method is presented to center the two division bands at the desired values. The techniques have been applied to three prototypes at 2.15 GHz, 1.85 GHz, and 1.75 GHz/3.95 GHz, respectively.This work was supported by the Spanish Ministry of Science and Innovation under project TEC2014-60283-C3-1-R and by the Parliament and University of Cantabria under the project Cantabria Explora 12-JP02-640.6

Analysis of two coupled NLTL-based oscillators

A system of two coupled oscillators based on nonlinear transmission lines (NLTL) is proposed for pulsed-shaping applications. The maximum propagation frequency through the NLTL is calculated and optimized with a realistic numerical method. With additional design considerations, this is used to increase the waveform steepening capabilities of the NLTL and obtain an oscillator based on the shockwave concept. Coupling two of these oscillators with slightly different characteristics various pulse shapes can be achieved through composition of the individual waveforms. The coupled-system behavior is understood with the aid of a new reduced-order formulation, which takes into account the differences between the oscillator elements. The formulation is extended for stability and phase-noise analysis. It provides valuable insight into the impact of the individual oscillator characteristics on the coupled-system dominant poles and unsymmetrical stable phase-shift range. It also explains the variation of the spectral density with the phase shift, as well as the mechanisms for the phase noise corners observed when increasing the offset frequency. A more realistic analysis of the coupled system is also carried out with the conversion-matrix approach, using cyclostationary noise sources. The analysis and design techniques have been applied to several prototypes at 0.8 GHz.This work was supported by the Spanish Ministry of Science and Innovation under project TEC2011-29264-C03-01

Wireless injection locking of oscillator circuits

An in-depth investigation of the global behavior of wireless injection-locked oscillator circuits is presented. This kind of operation has been proposed for motion-sensing applications, in which each oscillator is also self-injection locked by the signal reflected by the target, with the overall system behaving in an autonomous manner. The analysis is based on a realistic description of the effect of the self-injection and mutual-injection signals, and the oscillator behavior, described with a reduced-order model, extracted from harmonic balance. As will be shown, sinusoidal dependences on the oscillation frequency, associated with the signal propagation, may give rise to turning points in the solution curves, whereas the mutual synchronization of the oscillator circuits inherently gives rise to a coexistence of solutions with different phase shifts. The investigation includes fundamental aspects such as the bifurcation phenomena and phase-noise variation with the distance and antenna gain. The aim is to develop a useful methodology for the efficient analysis and reliable prediction of the behavior of these promising systems. All the results obtained with the new formulation, for easy application, have been carefully validated with costly circuit-level simulations of the whole system. For experimental validation, a prototype operating at 2.45 GHz has been manufactured and measured.This work was supported by the Spanish Ministry of Economy and Competitiveness under the research project TEC2014-60283-C3-1-R and Juan de la Cierva Research Program IJCI-2014-19141 and by the Parliament of Cantabria under the project Cantabria Explora 12.JP02.64069

Phase-sensitivity analysis of injection-locked mutually coupled oscillators

A system of two injection-locked mutually-coupled oscillators intended for sensing applications is analyzed with the aid of a semi-analytical formulation, based on realistic oscillator models, extracted from harmonic-balance simulations. Two different configurations are compared. In the first configuration, only one oscillator is connected to the synchronizing source, whereas the second oscillator is tuned by a capacitive element. Explicit expressions for the synchronization bandwidth and the phase sensitivity versus the tuning element are derived, which should be useful for an optimized design. The system stability properties and their dependence on the coupling-network elements and injection amplitude are also investigated. In the second configuration, the two oscillators are injection locked by the synchronizing source. Results are validated with costly harmonic-balance simulations at circuit level and with experimental measurements.The authors would like to thank to Spanish Ministry of Economy and Competitiveness for their financial support under the research project TEC2014-60283-C3-1-R and Juan de la Cierva Research Program IJCI-2014-19141 and by the Parliament of Cantabria under the project Cantabria Explora 12.JP02.64069

Wireless-coupled oscillator systems with an injection-locking signal

A detailed analysis of wireless-coupled oscillator systems under the effect of an injection-locking signal is presented. The injection source of high spectral purity is introduced at a single node and enables a reduction of the phase-noise spectral density. Under this injection source, the behavior of the coupled system is qualitatively different from the one obtained in free-running conditions. Two cases are considered: bilateral synchronization, in which an independent source is connected to a particular system oscillator, coupled to the other oscillator elements, and unilateral synchronization, in which one of these elements is replaced by an independent source that cannot be influenced by the rest. The two cases are illustrated through the analysis of a wireless-coupled system with a star topology, such that the injection signal is introduced at the central node. The investigation involves an insightful analytical calculation of the coexisting steady-state solutions, as well as a determination of their stability and bifurcation properties and phase noise. The injection signal stabilizes the system in a large and continuous distance interval, enabling a more robust operation than in autonomous (noninjected) conditions. A coupled system operating at 2.45 GHz has been manufactured and experimentally characterized, obtaining a very good agreement between simulations and measurements.This work was supported 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