Analysis of injection-locked pulsed waveform oscillators

The injection-locked behaviour of a high efficiency pulsed waveform oscillator is analyzed in detail. The design is based on a closed-loop configuration, loaded with a short nonlinear transmission line (NLTL). A new technique is provided to predict the effect of the circuit elements on the synchronization bandwidth, which enables an overall optimization of the oscillator design, considering efficiency, pulse width and locking interval. The phase-noise minimum in free-running conditions, obtained for particular values of the design parameters, is investigated through the use of phase sensitivity functions. The impact of this minimum on the noise spectrum in injection-locked conditions is also studied. The techniques have been applied to a pulsed-waveform oscillator at 0.9 GHz

Oscillator stabilization through feedback with slow wave structures

This article presents a new formulation to predict the steady-state, stability, and phase-noise properties of oscillator circuits, including either a self-injection network or a two-port feedback network for phase-noise reduction. The additional network contains a slow wave structure that stabilizes the oscillation signal. Its long delay inherently gives rise to multivalued solutions in some parameter intervals, which should be avoided for a reliable operation. Under a two-port feedback network, the circuit is formulated extracting two outer-tier admittance functions, which depend on the node-voltage amplitudes, phase shift between the two nodes, and excitation frequency. Then, the effect of the slow wave structure is predicted through an analytical formulation of the augmented oscillator, which depends on the numerical oscillator model and the structure admittance matrix. The solution curves are obtained in a straightforward manner by tracing a zero-error contour in the plane defined by the analysis parameter and the oscillation frequency. The impact of the slow-wave structure on the oscillator stability and noise properties is analyzed through a perturbation method, applied to the augmented oscillator. The phase-noise dependence on the group delay is investigated calculating the modulation of the oscillation carrier. The various analysis and design methods have been applied to an oscillator at 2.73 GHz, which has been manufactured and measured, obtaining phase-noise reductions of 13 dB, under a one-port load network, and 18 dB, under a feedback network.This work was supported by the Spanish Ministry of Economy ans Competitiveness through the European Regional Development Fund(ERDf)/ Fondo Europeo de Desarrollo Regional (FEDER) and under Project TEC2017-88242-C3-(1/2)-R

Phase-noise reduction in self-injection locked oscillators using slow-wave structures

An analysis of self-injection locked oscillators using a slow-wave structure for phase-noise reduction is presented. This structure is the key component of a feedback network, added to an existing oscillator and providing a stable self-injection locking signal. The unit cell of the slow-wave structure is based on a recently proposed configuration, made up of an open-ended stub and a Schiffman section. A tuning capacitor is introduced as an additional parameter, enabling an adjustment of the structure response at the desired oscillation frequency. The circuit solutions are analyzed by means of a semi-analytical formulation that incorporates the results of an electromagnetic simulation of the structure. The formulation enables a prediction of multivalued parameter regions, inherent to the long delay, which are more controllable than in the case of continuous transmission lines. An analytical derivation of the phase-noise spectral density is presented, which relates the phase-noise reduction with respect to the original freerunning oscillator to the group delay of the self-injection network. The analysis and synthesis method has been applied to an oscillator at 2.75 GHz.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

Phase-noise reduction through an external high-Q network using a black-box oscillator model

A method is presented to minimize the phase noise of an existing oscillator when connected to an external high-Q network. It relies on the experimental extraction of a reducedorder model of the original free-running oscillator, which involves a characterization of its pulling effects. With this model it is possible to predict the solution curves, stability properties and phase-noise of the augmented oscillator. It enables the optimization of the high-Q network to maximize the phase-noise reduction at a stable operation point in a single valued section of the solution curve. The method has been applied to (VCO) MiniCircuits ROS-3000-819+ (2-3GHz) obtaining a phase-noise reduction of about 10 dB with respect to the free-running values.Work supported by the Spanish Ministry of Science and Innovation (ERDF/FEDER) project TEC2017-88242-C3-1-R

Subharmonically injection-locked oscillator using a nonlinear transmission line

This work describes a first realization of an oscillator driven through a nonlinear transmission line (NLTL). In this way, the oscillator is able to synchronize to a sinusoidal injection source of much lower frequency. This can be understood as the result of two processes: high harmonic generation in the NLTL and frequency multiplication plus mixing in the oscillator device. The concept can be applicable in ultrawideband signal oscillators where synchronization should enable a fast oscillation start-up and facilitate the modulation process. As an example, it has been used here to obtain a pulsed-envelope oscillator at 6 GHz injected with a sinusoidal signal in the order of 100 MHz. The operation bands have been analyzed with a Poincaré map technique, allowing the detection of the bifurcation phenomena that delimit the stable synchronization ranges. For an understanding of the phase-noise spectrum, this spectrum is analyzed at higher injection frequencies with the conversion matrix approach. Very good results have been obtained in comparison with measurements.Spanish project TEC2011-29264-C03-01 for financial support

Analysis of chirped oscillators under injection signals

An in-depth investigation of the response of chirped oscillators under injection signals is presented. The study confirms the oscillator capability to detect the input-signal frequencies, demonstrated in former works. To overcome previous analysis limitations, a new formulation is presented, which is able to accurately predict the system dynamics in both locked and unlocked conditions. It describes the chirped oscillator in the envelope domain, where two time scales are used, one associated with the oscillator control voltage and the other associated with the beat frequency. Under sufficient input amplitude, a dynamic synchronization interval is generated about the input-signal frequency. In this interval, the circuit operates at the input frequency, with a phase shift that varies slowly at the rate of the control voltage. The formulation demonstrates the possibility of detecting the input-signal frequency from the dynamics of the beat frequency, which increases the system sensitivity. All the results have been validated with both full 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 research projects TEC2014-60283-C3-1-R and TEC2017-88242-C3-1-R

Stability and oscillation analysis at circuit level and through semi-analytical formulations

Harmonic balance provides steady-state solutions only and has significant shortcomings when addressing oscillatory regimes. As a result, complementary methodologies are required both to ensure the stability of the solution obtained and to design/simulate oscillator circuits. The complexity of the stability analysis increases with the number of active elements and the intricacy of the topology, so there can be uncertainties in the case of complex structures. On the other hand, as recently demonstrated oscillators enable a compact and low-cost implementation of RFID readers and radar systems, which comes at the expense of a more complex performance, very difficult/impossible to simulate with commercial HB. This work presents a review of recent advances on stability and oscillation analysis at circuit level and through semi-analytical formulations. At circuit level, a method for the stability analysis of complex microwave systems is presented, based on the calculation of the characteristic determinant, extracted from the commercial simulator through a judicious partition of the system into simpler blocks. This determinant will be used for the first time to obtain the stability boundaries through a contour-intersection method, able to provide multivalued and disconnected curves. At a semi-analytical level, a realistic numerical model of the standalone oscillator, extracted from HB simulations, is introduced in an analytical formulation that describes the oscillator interaction with other elements. Here it will be applied to a self-injection locked radar, in which the oscillator is injected by its own signal after this signal undergoes propagation and reflection effects. A procedure to determine the stability properties considering the time delay of the signal envelope is presented for the first time. Using the same self-injection concept, a new stabilization method to reduce the phase-noise of an existing oscillator with minimum impact on its original frequency is described.This work was supported by a project under Grant TEC2017-88242-C3-1–

Advances in the simulation of autonomous microwave circuits

Advances in the simulation of nonlinear microwave circuits of autonomous nature are presented, covering three relevant aspects: potential instability of power amplifiers under output mismatch effects, design of dual-band frequency dividers, with interest in multi-band communication systems, and oscillator phase-noise analysis. The instability under mismatch effects is predicted through the calculation of a 3-port scattering matrix, at three relevant sideband frequencies, which is obtained by linearizing the circuit about the large-signal steady-state solution. The dual-band divider is based on a parallel configuration, using two types of inductor-varactor cells, as well as a simultaneous design/optimization of two identical circuits, each operating at one of the two frequency bands. Finally, a new phase-noise analysis method able to predict the near-carrier spectral density in the presence of near-critical poles is described.Work funded by the Spanish Ministry of Economy and Competitiveness (TEC2014-60283-C3-1-R), ERDF/FEDER and the Parliament of Cantabria (12.JP02.64069)

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

Two-scale envelope-domain analysis of injected chirped oscillators

The response of chirped oscillators under the injection of independent signals, for spectrum sensing in cognitive radio, and under self-injection, for radio frequency identification, is analyzed in detail. The investigation is performed by means of a semianalytical formulation, based on a realistic modeling of the free-running oscillator, extracted from harmonic-balance simulations or from experimental measurements, through a new characterization technique. In the new formulation, the oscillator is linearized about a free-running solution that varies with the control voltage. This enables its application to oscillators having a frequency characteristic that deviates from the linear one. In the case of injection by independent signals, the two-scale envelope-domain formulation will enable an efficient handling of the difference between the slow chirp frequency and the beat frequency. The input carriers can be detected from their dynamic synchronization intervals or, at lower input-power levels, from the dynamics of the beat frequency. Noise perturbations are introduced into the formulation, which enables an estimation of the minimum detectable signal. In the case of a self-injected oscillator for radio frequency identification, an insightful formulation is derived to predict the propagation and tag-resonance effects on the instantaneous oscillation frequency. The tag-resonance signature gives rise to a distinct modulation of the oscillation frequency during the chirp period, which can be detected from the variation of the oscillator bias current. The analysis methods are illustrated through their application to a chirped oscillator, operating in the band 2-3 GHz.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-R and Project TEC2017-88242-C3-1-