A new method for the determination of the locking range of oscillators

A time-domain method for the determination of the injection-locking range of oscillators is presented. The method involves three time dimensions: the first and the second are warped time scales used for the free-running frequency and the external excitation, respectively and the third is to account for slow transients to reach a steady-state regime. The locking range is determined by tuning the frequency of the external excitation until the oscillator locks. The locking condition is determined by analyzing the Jacobian matrix of the system. The method is advantageous in that the computational effort is independent of the presence of widely separated time constants in the oscillator. Numerical results for a Van Der Pol oscillator are presented

Review of Injected Oscillators

Oscillators are critical components in electrical and electronic engineering and other engineering and sciences. Oscillators are classified as free-running oscillators and injected oscillators. This chapter describes the background necessary for the analysis and design of injected oscillators. When an oscillator is injected by an external periodic signal mentioned as an injection signal, it is called an injected oscillator. Consequently, two phenomena occur in the injected oscillators: (I) pulling phenomena and (II) locking phenomena. For locking phenomena, the oscillation frequency of the injection signal must be near free-running oscillation frequency or its sub-/super-harmonics. Due to these phenomena are nonlinear phenomena, it is tough to achieve the exact equation or closed-form equation of them. Therefore, researchers are scrutinizing them by different analytical and numerical methods for accomplishing an exact inside view of their performances. In this chapter, injected oscillators are investigated in two main subjects: first, analytical methods on locking and pulling phenomena are reviewed, and second, applications of injected oscillators are reviewed such as injection-locked frequency dividers at the latter. Furthermore, methods of enhancing the locking range are introduced

An effective method for the determination of the locking range of an injection-locked frequency divider

The paper proposes a methodology for the determination of the locking range of an Injection-Locked Frequency Divider. The technique involves the use of the Warped Multi-time scale model and is applicable to oscillators in general. The ability to determine, in an efficient manner, the locking ranges of Injection Locked Frequency Dividers is of great importance to design engineers as ILFDs are suitable for lower-power wireless applications

Design of CMOS integrated frequency synthesizers for ultra-wideband wireless communications systems

Ultra¬wide band (UWB) system is a breakthrough in wireless communication, as it provides data rate one order higher than existing ones. This dissertation focuses on the design of CMOS integrated frequency synthesizer and its building blocks used in UWB system. A mixer¬based frequency synthesizer architecture is proposed to satisfy the agile frequency hopping requirement, which is no more than 9.5 ns, three orders faster than conventional phase¬locked loop (PLL)¬based synthesizers. Harmonic cancela¬tion technique is extended and applied to suppress the undesired harmonic mixing components. Simulation shows that sidebands at 2.4 GHz and 5 GHz are below 36 dBc from carrier. The frequency synthesizer contains a novel quadrature VCO based on the capacitive source degeneration structure. The QVCO tackles the jeopardous ambiguity of the oscillation frequency in conventional QVCOs. Measurement shows that the 5¬GHz CSD¬QVCO in 0.18 µm CMOS technology draws 5.2 mA current from a 1.2 V power supply. Its phase noise is ¬120 dBc at 3 MHz offset. Compared with existing phase shift LC QVCOs, the proposed CSD¬QVCO presents better phase noise and power efficiency. Finally, a novel injection locking frequency divider (ILFD) is presented. Im¬plemented with three stages in 0.18 µm CMOS technology, the ILFD draws 3¬mA current from a 1.8¬V power supply. It achieves multiple large division ratios as 6, 12, and 18 with all locking ranges greater than 1.7 GHz and injection frequency up to 11 GHz. Compared with other published ILFDs, the proposed ILFD achieves the largest division ratio with satisfactory locking range

Analysis, simulation and design of nonlinear RF circuits

The PhD project consists of two parts. The first part concerns the development of Computer Aided Design (CAD) algorithms for high-frequency circuits. Novel Padébased algorithms for numerical integration of ODEs as arise in high-frequency circuits are proposed. Both single- and multi-step methods are introduced. A large part of this section of the research is concerned with the application of Filon-type integration techniques to circuits subject to modulated signals. Such methods are tested with analog and digital modulated signals and are seen to be very effective. The results confirm that these methods are more accurate than the traditional trapezoidal rule and Runge-Kutta methods. The second part of the research is concerned with the analysis, simulation and design of RF circuits with emphasis on injection-locked frequency dividers (ILFD) and digital delta-sigma modulators (DDSM). Both of these circuits are employed in fractional-N frequency synthesizers. Several simulation methods are proposed to capture the locking range of an ILFD, such as the Warped Multi-time Partial Differential Equation (WaMPDE) and the Multiple-Phase-Condition Envelope Following (MPCENV) methods. The MPCENV method is the more efficient and accurate simulation technique and it is recommended to obviate the need for expensive experiments. The Multi-stAge noise Shaping (MASH) digital delta-sigma modulator (DDSM) is simulated in MATLAB and analysed mathematically. A novel structure employing multimoduli, termed the MM-MASH, is proposed. The goal in this design work is to reduce the noise level in the useful frequency band of the modulator. The success of the novel structure in achieving this aim is confirmed with simulations

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

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

Stochastic analysis of cycle slips in injection-locked oscillators and analog frequency dividers

A detailed investigation of cycle slips in injection-locked oscillators (ILOs) and analog frequency dividers is presented. This nonlinear phenomenon gives rise to a temporal desynchronization between the injected oscillator and the input source due to noise perturbations. It involves very different time scales so even envelope-transient-based Monte Carlo analyses may suffer from high computational cost. The analysis method is based on an initial extraction of a reduced-order nonlinear model of the injected oscillator based on harmonic-balance simulations. This model has been improved with a more accurate description of oscillation dependence on the input source either at the fundamental frequency or, in the case of a frequency divider, at a given harmonic frequency. The reduced-order model enables an efficient stochastic analysis of the system based on the use of the associated Fokker-Planck equation in the phase probability density function. Several methods for the solution of the associated Fokker-Planck equation are compared with one of them being applicable under a wider range of system specifications. The analysis enables the prediction of the parameter-space regions that are best protected against cycle slips. The technique has been applied to two microwave ILOs and has been validated through commercial software envelope simulations in situations where the computational cost of the envelope simulations was acceptable, and through measurements. The measurement procedure of the cycle slipping phenomenon has been significantly improved with respect to previous work.This work was supported by the Spanish Ministry of Economy and Competitiveness under Contract TEC2011-29264-C03-01