Nonlinear Design Technique for High-Power Switching-Mode Oscillators

A simple nonlinear technique for the design of high-efficiency and high-power switching-mode oscillators is presented. It combines existing quasi-nonlinear methods and the use of an auxiliary generator (AG) in harmonic balance. The AG enables the oscillator optimization to achieve high output power and dc-to-RF conversion efficiency without affecting the oscillation frequency. It also imposes a sufficient drive on the transistor to enable the switching-mode operation with high efficiency. Using this AG, constant-power and constant-efficiency contour plots are traced in order to determine the optimum element values. The oscillation startup condition and the steady-state stability are analyzed with the pole-zero identification technique. The influence of the gate bias on the output power, efficiency, and stability is also investigated. A class-E oscillator is demonstrated using the proposed technique. The oscillator exhibits 75 W with 67% efficiency at 410 MHz

Analysis and elimination of hysteresis and noisy precursors in power amplifiers

Power amplifiers (PAs) often exhibit instabilities leading to frequency division by two or oscillations at incommensurate frequencies. This undesired behavior can be detected through a large-signal stability analysis of the solution. However, other commonly observed phenomena are still difficult to predict and eliminate. In this paper, the anomalous behavior observed in a Class-E PA is analyzed in detail. It involves hysteresis in the power-transfer curve, oscillation, and noisy precursors. The precursors are pronounced bumps in the power spectrum due to noise amplification under a small stability margin. The correction of the amplifier performance has required the development of a new technique for the elimination of the hysteresis. Instead of a trial-and-error procedure, this technique, of general application to circuit design, makes use of bifurcation concepts to suppress the hysteresis phenomenon through a single simulation on harmonic-balance software. Another objective has been the investigation of the circuit characteristics that make the noisy precursors observable in practical circuits and a technique has been derived for their elimination from the amplifier output spectrum. All the different techniques have been experimentally validated

Envelope domain formulation for the analysis of the nonlinear transient dynamics of coupled oscillators

A reduced-order envelope-domain formulation of coupled-oscillator systems based on realistic nonlinear models of the oscillator elements is presented for the first time to our knowledge. The formulation, based on numerical models of the transistor-based oscillators, enables an accurate prediction of the nonlinear dynamics of the coupled system, including the oscillation build-up, the locked and unlocked states, and the oscillator ON?OFF switching. To increase the applicability of the method, both admittance- and impedance-type models are extracted through harmonic balance simulations, under a voltage and current excitation, respectively, at the node/branch where the oscillator is connected to the coupled system. They are used to derive a nonlinear differential-equation system able to describe the transient dynamics of the entire structure. Because the oscillators are coupled through current injection, the impedance-based formulation is formally different from the admittance one, so it requires a dedicated derivation. For illustration, the method has been applied to exhaustively investigate the nonlinear dynamics of a system of three FET-based oscillators at 5 GHz. Very good agreement has been obtained with both circuit-level envelope transient (when applicable) and with measurements.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

Analysis of the transient dynamics of microwave oscillators

A semi-analytical method for the global prediction and understanding of the transient dynamics of oscillator circuits is presented. It covers both the linear and nonlinear transient stages, which are related with the circuit generalized eigenvalues, here introduced for the first time. The transient model relies on the application of the implicit-function theorem to the harmonicbalance system, in order to derive a reduced-order nonlinear differential equation from a given observation node. This requires the extraction of a nonlinear admittance function, depending on the voltage excitation and oscillation frequency, which is done with a forcing auxiliary generator. The linearization of this admittance function for each excitation amplitude provides a sequence of linear ordinary differential equations, describing the system dynamics in the vicinity of each point of the transient trajectory, which can be reconstructed from the expression of the solution increment at each time step. The sequence of differential equations provides a set of generalized eigenvalues, responsible for the acceleration or deceleration of the oscillation growth and capable to detect spurious transient frequencies. The concept of escape time, or time required by the transient trajectory to go through a certain interval of amplitude values, is also introduced, for the first time to our knowledge. The method has been successfully applied to analyze the transient dynamics of several FET oscillators, including dual-frequency oscillators and switched oscillators.This work was supported by the Spanish Ministry of Economy and Competitiveness and the European Regional Development Fund (ERDF/FEDER) under Project TEC2014-60283-C3-(1/2)-R and Project TEC2017-88242-C3-(1/2)-R

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

Analysis of the transient dynamics of coupled-oscillator systems

A realistic reduced-order formulation of systems containing several transistor-based oscillators, such as coupledoscillator networks, is presented. The formulation is able to predict the oscillation build-up and other transient effects for the first time to our knowledge. The individual oscillator models are constructed from a nonlinear admittance function extracted from circuit-level harmonic-balance simulations. These models are used to derive a nonlinear differential-equation system able to describe the transient behavior of the entire structure. For illustration, the method has been applied to a coupled-oscillator system at 5 GHz, obtaining very good agreement with circuit-level envelope transient (when applicable) and with measurements.This 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

Nonlinear microwave simulation techniques

The design of high performance circuits with short manufacturing cycles and low cost demands reliable analysis tools, capable to accurately predict the circuit behaviour prior to manufacturing. In the case of nonlinear circuits, the user must be aware of the possible coexistence of different steady-state solutions for the same element values and the fact that steady-state methods, such as harmonic balance, may converge to unstable solutions that will not be observed experimentally. In this contribution, the main numerical iterative methods for nonlinear analysis, including time-domain integrations, shooting, harmonic balance and envelope transient, are briefly presented and compared. The steady-state methods must be complemented with a stability steady-state analysis to verify the physical existence of the solution. This stability analysis can also be combined with the use of auxiliary generators to simulate the circuit self-oscillation and predict qualitative changes in the solution under the continuous variation of a parameter. The methods will be applied to timely circuit examples that are demanding from the nonlinear analysis point of view.This work has been supported by the Spanish Government under contract TEC2014-60283-C3-1-R and the Parliament of Cantabria (12.JP02.64069)

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

Growth-rate function for the nonlinear analysis of the transient dynamics of microwave oscillators

In this paper, a new technique is presented for the analysis of the transient dynamics of microwave oscillators. The technique makes use of a nonlinear admittance function that can be identified in commercial Harmonic Balance software. This function is included in a time-frequency domain equation governing the transient dynamics. The equation provides the growth rate function of the first harmonic amplitude, which allows an exhaustive analysis of the transient speed from the neighborhood of the dc solution to the oscillation establishment, with no need for a numerical integration, as in time domain or envelope-transient methods. The technique has been applied to predict the length of the transient towards the oscillating state of a FET oscillator at 5 GHz.This work has been supported by the Spanish Ministry of Economy and Competitiveness under project TEC2014-60283-C3-1-R and the Parliament of Cantabria (12.JP02.64069). The authors would like to thank S. Pana, University of Cantabria, for her assistance with the manufacturing process

A Kerr-microresonator optical clockwork

Kerr microresonators generate interesting and useful fundamental states of electromagnetic radiation through nonlinear interactions of continuous-wave (CW) laser light. Using photonic-integration techniques, functional devices with low noise, small size, low-power consumption, scalable fabrication, and heterogeneous combinations of photonics and electronics can be realized. Kerr solitons, which stably circulate in a Kerr microresonator, have emerged as a source of coherent, ultrafast pulse trains and ultra-broadband optical-frequency combs. Using the f-2f technique, Kerr combs support carrier-envelope-offset phase stabilization for optical synthesis and metrology. In this paper, we introduce a Kerr-microresonator optical clockwork based on optical-frequency division (OFD), which is a powerful technique to transfer the fractional-frequency stability of an optical clock to a lower frequency electronic clock signal. The clockwork presented here is based on a silicon-nitride (Si$_3$N$_4$) microresonator that supports an optical-frequency comb composed of soliton pulses at 1 THz repetition rate. By electro-optic phase modulation of the entire Si$_3$N$_4$ comb, we arbitrarily generate additional CW modes between the Si$_3$N$_4$ comb modes; operationally, this reduces the pulse train repetition frequency and can be used to implement OFD to the microwave domain. Our experiments characterize the residual frequency noise of this Kerr-microresonator clockwork to one part in $10^{17}$, which opens the possibility of using Kerr combs with high performance optical clocks. In addition, the photonic integration and 1 THz resolution of the Si$_3$N$_4$ frequency comb makes it appealing for broadband, low-resolution liquid-phase absorption spectroscopy, which we demonstrate with near infrared measurements of water, lipids, and organic solvents