Analysis and simulation methods for free-running, injection-locked and super-regenerative oscillators

RESUMEN: En los últimos años, muchos esfuerzos han sido dedicados al desarrollo de técnicas complementarias para el análisis de circuitos autónomos de microondas. Estas técnicas están pensadas para su uso en combinación con balance armónico, ampliamente usado para el análisis a frecuencias de microondas. De hecho, balance armónico sufre de restricciones cuando se utiliza para el análisis de circuitos autónomos, en su mayoría debidos a su falta de sensibilidad a las propiedades de estabilidad de la solución que se genera o se extingue mediante bifurcaciones. En esta tesis doctoral se presentan nuevos métodos de simulación y análisis para la caracterización y modelado de osciladores libres, sincronizados y superregenerativos. Todos los resultados obtenidos mediante los nuevos métodos de simulación y análisis han sido comparados satisfactoriamente con otras técnicas de simulación y con medidas.ABSTRACT: In the last years, numerous efforts have been devoted to the development of complementary analysis tools for autonomous microwave circuits. They are intended to be applied in combination with the harmonic-balance (HB) method, widely used at microwave frequencies. In fact, HB suffers from a number of shortcomings when dealing with autonomous circuits, mostly due the fact that it is insensitive to the stability properties of the solution, generated and extinguished through bifurcation phenomena. Here, new simulation and analysis methodologies for the characterization and modeling of free-running, injection-locked and super-regenerative oscillators have been proposed to overcome these problems when using commercial software. Results from the different new analysis methodologies have been successfully compared with independent simulations and with measurements

Transformaciones en los procesos productivos agrícolas en La Cañada de Huamuxtitlán, Guerrero y su relación con la generación de vulnerabilidad

La Cañada de Huamuxtitlán es un espacio naturalmente privilegiado para la agricultura, desde tiempos precolombinos se ha utilizado para este fin, los grupos que se asentaron en este valle implementaron tecnología tradicional, y pudieron utilizar el río Tlapaneco para una agricultura de riego; desde entonces, la zona ha sido aprovechada por su suelo fértil, propicio para la agricultura y ha dado pie a la construcción de una microrregión inserta en la región Montaña de Guerrero. El riego es la principal actividad económica del valle. El uso y conocimiento del río es muy importante para asegurar una continuidad de la vida económica y cultural de dos municipios, conformándose un territorio específico y dinámico. Sin embargo, en la última década, se han ido configurando algunas transformaciones en los procesos productivos agrícolas y la introducción de nuevos cultivos que han traído como consecuencia la generación de vulnerabilidad social y ambiental

Systematic methodology for the global stability analysis of nonlinear circuits

A new methodology for the detection of Hopf, flip, and turning-point bifurcations in nonlinear circuits analyzed with harmonic balance (HB) is presented. It enables a systematic determination of bifurcation loci in terms of relevant parameters, such as input power, input frequency, and bias voltages, for instance. It does not rely on the use of continuation techniques and is able to globally provide the entire loci, often containing multivalued sections and/or disconnected curves, in a single simulation. The calculation of Hopf and flip bifurcations is based on the extraction of a small-signal admittance/impedance function from HB and the calculation of its zeros through a geometrical procedure. The method is ideally suited for the investigation of the global stability properties of power amplifiers and other nonlinear circuits. The turning-point locus, associated with either jump phenomena or synchronization, is obtained by taking into account the annihilation/generation of steady-state solutions that is inherent to this type of bifurcation. A technique is also presented for the exhaustive calculation of oscillation modes in multidevice oscillators and oscillators loaded with multiresonance networks. The new methodologies are illustrated through their application to a power amplifier and a multimode oscillator.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

Analysis of superregenerative oscillators in nonlinear mode

Superregenerative oscillators in a nonlinear mode are investigated in detail using methodologies based on envelope transient, complemented with additional algorithms. A maximum-detection technique is applied to obtain the input-power threshold for nonlinear operation under different implementations of the quench signal. A mapping procedure enables the prediction of hangover and self-oscillation effects. It is based on the detection of the sequence of local maxima in the envelope amplitude after the application of a single input pulse. Using a contour-intersection method, and depending on the analysis time interval, it is possible to quantify the hangover effects and obtain the oscillation boundary, in terms of any two significant parameters. Then, a compact time-variant behavioral model is derived, valid in the absence of hangover and self-oscillation effects. It consists of a single time-variant Volterra kernel and is applicable provided that the amplitude transitions occur outside the sensitivity interval. Various methodologies are tested in a practical FET-based oscillator at 2.7 GHz. The prototype has been manufactured and measured, obtaining good agreement with the analysis results.This work was supported by the Spanish Ministry of Economy and Competitiveness and the European Regional Development Fund (ERDF/FEDER) under the research project TEC2017-88242-C3-1-R

Envelope-domain analysis and modeling of super-regenerative oscillators

An envelope-domain methodology for the numerical modeling of super-regenerative oscillators (SROs) is presented. The main advantage is its generality of application to transistor-based oscillators with arbitrary topology. Initially, a stability analysis of the nonoscillatory steady-state solution, forced by the quench signal, is performed. It is based on the calculation of a linear-time-variant (LTV) transfer function, obtained by linearizing the circuit envelope-domain equations about the nonoscillatory regime. Under moderate quench frequencies, it will be possible to estimate the SRO normalized envelope and sensitivity function from the detected dominant pair of complex-conjugate poles. In the general case, the SRO oscillatory response is modeled with a numerical method, valid under linear operation with respect to the input signal. This is based on the calculation of the LTV impulse response from a time-frequency transfer function obtained under a small-signal sinusoidal excitation. The LTV impulse response enables a straightforward determination of the sensitivity time interval and time distance to the envelope maximum. An integral expression, in terms of the LTV transfer function, will provide the SRO response to any small-signal input with any arbitrarily carrier frequency and modulation. The methodology has been successfully validated through its application to an SRO at 2.7 GHz, which has been manufactured and measured.This work was supported by the Spanish Ministry of Economy and Competitiveness and the European Regional Development Fund (ERDF/FEDER) under Research Project TEC2014-60283-C3-1-R and Research Project TEC2017-88242-C3-1-

Caracterización morfológica y morfométrica de la carta Toluca

Se presenta la interpretación de los mapas morfológicos y morfométricos elaborados de la carta Toluca E14A38, escala 1:50 000. La cartografía elaborada permite conocer como los procesos endógenos y exógenos relacionados con el origen, evolución, dinámica en la zona de estudio, así como caracterizar las principales formas del relieve. La metodología está sustentada en el análisis sistémico bajo el enfoque de la geomorfología aplicada, en donde se obtiene cartografía morfológica y morfométrica con la cual se extrae y agrupan los rasgos generales de la expresión del relieve

Simulation method for complex multivalued curves in injection-locked oscillators

A new methodology is presented for the efficient harmonic-balance simulation of injection-locked oscillators with complex multivalued and disconnected curves. It is illustrated through its application to high-order subharmonically injection-locked oscillators. A graphical technique is applied to analyze the oscillator-phase sensitivity with respect to the input signal, required for the injection-locked operation. The intricate synchronized-solution curves are obtained with the new method, which enables a global exploration of all the coexistent periodic solutions. These solutions can belong to different curve sections, in a multivalued response, or to disconnected synchronization curves. The method is based on the calculation of a series of phase-dependent outer-tier admittance functions, which provide the oscillator response to the injection signal. Coexistent solutions are simultaneously obtained through a contour-plot intersection, without the need for continuation techniques. The method is illustrated through application to an oscillator synchronized to low-frequency sinusoidal signal by means of a nonlinear-transmission line. The analysis and design techniques have been successfully validated through comparison with independent simulations and measurements.This work was supported by the Spanish Ministry of Economy and Competitiveness under the research project TEC2014-60283-C3-1-R, the European Regional Development Fund (ERDF/FEDER) and Juan de la Cierva Research Program IJCI-2014-19141 and by the Parliament of Cantabria under the project Cantabria Explora 12.JP02.64069

Noise analysis of super-regenerative oscillators in linear and nonlinear modes

A rigorous analysis of noise effects in super-regenerative oscillators (SROs), operating in both linear and nonlinear modes, is presented. For operation in the linear mode, two different analysis methods are presented. One is based on the calculation of linear-time variant (LTV) transfer function with respect to the input signal and the noise sources. The second method is based on a compact semianalytical formulation of the pulsed oscillator under the effect of the quench signal. The compact formulation also enables the analysis of the SRO in the nonlinear mode. It constitutes a fully new mathematical description of SROs, with general applicability, as it is not restricted to a particular oscillator topology. It relies on a numerical nonlinear black-box model of the stand-alone free-running oscillator, extracted from harmonic-balance simulations. This model is introduced into an envelope-domain formulation of the SRO at the fundamental frequency. Both the method based on LTV transfer functions and the semianalytical formulation take into account the cyclostationary nature of the SRO response to the noise sources. In the nonlinear mode, the variances of the amplitude and phase are calculated linearizing the formulation of the pulsed steady-state solution. The particular time variation of the phase variance is explained in detail and related to the onset and extinction of the oscillation in the presence of an RF input signal. The new analysis methods have been validated with both independent circuit-level simulations and measurements.This work was supported by the Spanish Ministry of Economy and Competitiveness and the European Regional Development Fund (ERDF/FEDER) under Project TEC2017-88242-C3-1-R

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

Cyclostationary noise analysis of superregenerative oscillators

A rigorous analysis of noise effects in super regenerative oscillators (SRO) operating in linear mode is presented. The analysis takes into account the cyclostationary nature of the SRO response to the noise sources, due to the effect of the quench signal. It is based on the determination of envelope-domain linear-time-variant (LTV) transfer function with respect to each noise source, plus the application of a detailed stochastic analysis of the SRO output. Initially, the autocorrelation of the output signal is calculated, which varies at two different time scales, and is periodic with respect to the quench signal, so it can be expressed in terms of the frequency-dependent harmonic components of the LTV transfer functions. This enables the calculation of the output spectral density, depending on these harmonic components. Once the spectral density is known, the signal-to-noise ratio can be obtained in a straightforward manner. The analysis method has been validated with both independent circuit-level simulations and measurementsThis work was supported by the Spanish Ministry of Science, Innovation and Universities and the European Regional Development Fund (ERDF/FEDER) under the research project TEC2017-88242-C3-1-R