Optimized design of harmonic-injection dividers

A new formulation is presented for the efficient harmonic-balance analysis of the division bandwidth of frequency dividers by a high order. The procedure is based on some mathematical properties of the solution curve under low-amplitude of the input generator. Through a simple fitting technique, it is possible to determine the variation of the synchronization bandwidth versus any design parameter, while keeping constant the central frequency of the division band. The procedure also enables a prediction of the frequency-division interval for any value of the input-generator amplitude within the region of linear behavior with respect to the input source. It has been applied to the optimization of the input matching network in a frequency divider by 10, which uses a nonlinear transmission line (NLTL) as a feedback network.Spanish project TEC2011-29264-C03-01 for financial support

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

Analysis of output loading effects in autonomous circuits

A methodology is presented to analyze the impact of the termination load on the oscillation frequency and output power of autonomous circuits. Variations of this load can also lead to an extinction of the oscillation signal, due to their effect on the impedance seen by the active device(s). The new methodology enables an efficient analysis and mitigation of the pulling effects, in the case of undesired output mismatch, as well as an efficient oscillator synthesis in large-signal conditions, for specified values of oscillation frequency and output power. The method is based on the calculation of constant-amplitude and constant-frequency contours, traced in the Smith chart. Oscillation extinctions and some forms of hysteresis can be predicted through the inspection of these contours. However, the stability properties will generally depend on the frequency characteristic of the termination impedance. In an oscillator synthesis, the selected impedance, providing the specified values of oscillation frequency and output power, must be implemented in order to guarantee a stable solution. The dependence of the phase-noise spectral density on the particular implementation is predicted, combining an analysis based on the variance of the phase deviation with the conversion-matrix approach.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

Wireless injection locking of Zero-IF self-oscillating mixers

The recently introduced Zero-IF self-oscillating mixers (SOMs) enable a direct frequency conversion, of interest for the implementation of compact and low consumption radio frequency identification (RFID) tags, among other applications. In previous works, the Zero-IF SOM is placed in only one of the terminals of the wireless link, the other one being based on a conventional scheme. In this article, a system made up of two wirelessly locked Zero-IF SOMs, operating as a frequency upconverter and downconverter, will be analyzed to evaluate its potential for low-cost short-range communications. A complete formulation describing the system under antenna and propagation effects will be presented, which, as a particular case, is able to predict the behavior of the previously proposed Zero-IF SOM, locked by an independent signal. The formulation based on oscillator models extracted from harmonic balance allows deriving design criteria for an optimum and robust performance and can predict the maximum communication range, as well as the stability properties and phase-noise behavior. The operation under modulated conditions is analyzed with a novel envelope-transient formulation, accounting for the time differentiation caused by the propagation effects. The methods have been applied to a system of two Zero-IF SOMs operating at 900 MHz.This work was supported in part by the Spanish Ministry of Science and Innovation under Grant PID2020-116569RB-C31 and in part by MCIN/AEI and the European Regional Development Fund (MCIN/AEI/10.13039/501100011033/“ERDF A way of making Europe”) under Grant TEC2017-88242-C3-1-R. An earlier version of this paper was presented at the IEEE MTT-S International Microwave Symposium (IMS 2021), Atlanta, GA, USA, June 20–25, 2021 [DOI: 10.1109/IMS19712.2021.9574961]

Nonlinear analysis of oscillator mutual injection locking through inductor coupling

This work presents an in-depth investigation of the nonlinear behavior of two mutually injection-locked oscillators through inductor coupling. An analytical formulation, solved through an innovative procedure, facilitates the understanding of the qualitative transformations in the system solutions when increasing the coupling factor. The analysis demonstrates that, in a manner similar to the unilaterally injection-locked oscillators, families of disconnected/connected curves are obtained when increasing this factor, although the patterns, associated with distinct operation modes, are more complex. Then, an accurate numerical method to predict the behavior of coupled transistor-based oscillators is presented, based on nonlinear admittance models of the individual oscillators. Mathematical conditions are derived to solve the coupled system through a two-level contour-intersection technique. In this way, all the solutions coexisting for a given set of element and parameter values are calculated simultaneously, in an exhaustive manner. The cases of two coupled oscillators at the fundamental frequency and at 1:3 frequency ratio are considered. Possible applications include the oscillator phase-noise reduction and the implementation of sensors using the phase shift between the two oscillator elements.This work was supported in part by the Spanish Ministry of Economy and Competitiveness and the European Regional Development Fund (ERDF/FEDER) under research project TEC2017-88242-C3-1-R

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

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

Efficient simulation of solution curves and bifurcation loci in injection-locked oscillators

A new method is presented for the two-level harmonic-balance analysis of multivalued synchronized solution curves in injection-locked oscillators. The method is based on the extraction of a nonlinear admittance function, which describes the circuit response from the input source terminals. It does not require any optimization or parameter switching procedures, this constituting a significant advantage compared with previous analysis techniques. With additional mathematical conditions, it enables a straightforward determination of the turning point and Hopf bifurcation loci that delimit the stable injection-locked operation bands. The codimension two bifurcation point at which the turning point and Hopf bifurcation loci merge is analyzed in detail, as well as the saddle-connection locus. As it is shown, a second intersection of the saddle-connection locus with the turning point locus acts as a boundary between synchronization points and points associated with jumps and hysteresis. The likely observation of chaotic solutions in the neighborhood of the saddle-connection locus is discussed too. The techniques have been validated by application to several injection-locked oscillators, obtaining good agreement with the experimental results.This work was supported by the Spanish Ministry of Economy and competitiveness under contract TEC2011-29264-C03-01 and the predoctoral fellowship for researchers in training of the University of Cantabria and the Regional Ministry of Education of the Government of Cantabria