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Derivation of Floquet Eigenvectors Displacement for Optimal Design of LC Tank Pulsed Bias Oscillators  [PDF]
Stefano Perticaroli, Nikend Luli, Fabrizio Palma
Circuits and Systems (CS) , 2011, DOI: 10.4236/cs.2011.24043
Abstract: The paper presents an approximated and compact derivation of the mutual displacement of Floquet eigenvectors in a class of LC tank oscillators with time varying bias. In particular it refers to parallel tank oscillators of which the energy restoring can be modeled through a train of current pulses. Since Floquet eigenvectors are acknowledged to give a correct decomposition of noise perturbations along the stable orbit in oscillator's space state, an analytical and compact model of their displacement can provide useful criteria for designers. The goal is to show, in a simplified case, the achievement of oscillators design oriented by eigenvectors. To this aim, minimization conditions of the effect of stationary and time varying noise as well as the contribution of jitter noise introduced by driving electronics are deduced from analytical expression of eigenvectors displacement.
CMOS Phase and Quadrature Pulsed Differential Oscillators Coupled through Microstrip Delay-Lines  [PDF]
Francesco Stilgenbauer, Stefano Perticaroli, Fabrizio Palma
Circuits and Systems (CS) , 2014, DOI: 10.4236/cs.2014.58020
Abstract:

An innovative solution to design phase and quadrature pulsed coupled oscillators systems through electromagnetic waveguides is described in this paper. Each oscillator is constituted by an LC differential resonator refilled through a couple of current pulse generator circuits. The phase and quadrature coupling between the two differential oscillators is achieved using delayed replicas of generated fundamentals from a resonator as driving signal of pulse generator injecting in the other resonator. The delayed replicas are obtained by microstrip-based delay-lines. A 2.4 - 2.5 GHz VCO has been implemented in a 150 nm RF CMOS process. Simulations showed at 1 MHz offset a phase noise of -139.9 dBc/Hz and a FOM of -189.1 dB.

Quadrature Oscillators Using Operational Amplifiers  [PDF]
Jiun-Wei Horng
Active and Passive Electronic Components , 2011, DOI: 10.1155/2011/320367
Abstract: Two new quadrature oscillator circuits using operational amplifiers are presented. Outputs of two sinusoidal signals with 90° phase difference are available in each circuit configuration. Both proposed quadrature oscillators are based on third-order characteristic equations. The oscillation conditions and oscillation frequencies of the proposed quadrature oscillators are orthogonally controllable. The circuits are implemented using the widely available operational amplifiers which results in low output impedance and high current drive capability. Experimental results are included. 1. Introduction Quadrature oscillator is used because the circuit provides two sinusoids with 90° phase difference, as, for example, in telecommunications for quadrature mixers and single-sideband generators or for measurement purposes in vector generators or selective voltmeters. Therefore, quadrature oscillators constitute an important unit in many communication and instrumentation systems [1–7]. Recently, several multiphase oscillators based on operational amplifiers were proposed [6–11]. Two-integrator loop technique was developed to realize quadrature oscillators using operational amplifiers [6]. In 1993 [7], Holzel proposed a new method for realizing quadrature oscillator, which consists of two all-pass filters and one inverter using operational amplifiers. Several multiphase oscillators using operational amplifiers were proposed in [8–11]. However, the quadrature output voltages cannot be obtained from [8–10]. The multiphase sinusoidal oscillator in [11] was constructed by cascading several first-order all-pass networks and unity-gain inverting networks. However, the block diagram of the quadrature oscillators in [11] was the same with [7]. In this paper, two new quadrature oscillator circuits using operational amplifiers are proposed. Outputs of two sinusoidal signals with 90° phase difference are available in each proposed circuit configuration. Both proposed quadrature oscillators are based on third-order characteristic equations. The oscillation conditions and oscillation frequencies of the proposed quadrature oscillators are orthogonally controllable. The circuits are implemented using the widely available operational amplifiers which results in low output impedance, high current drive capability (enabling the systems to drive a variety of loads), simplicity, and low cost. 2. Circuit Description Figure 1 shows the first proposed quadrature oscillator circuit. The characteristic equation of the circuit can be expressed as Figure 1: The first proposed quadrature
Phase and Quadrature Pulsed Bias LC-CMOS VCO  [PDF]
Stefano Perticaroli, Fabrizio Palma, Adriano Carbone
Circuits and Systems (CS) , 2011, DOI: 10.4236/cs.2011.21004
Abstract: Pulsed bias is an attempt to improve the performance of oscillators in integrated circuits as a result of architectural innovation. Given the relatively low value of resonator quality factor achievable on-chip, for a specified bias voltage level, pulsed bias may result in a lower power consumption and in an improvement of the spectral purity of the oscillation. The main drawback of this approach is the need to introduce a certain time delay in order to properly position pulses with respect to oscillation waveform. Delay accumulation requires further energy dissipation and introduce additional jitter. In this paper we present a new architecture capable to avoid unnecessary delay, based on the idea to apply the pulsed bias approach to a quadrature oscillator. A ?rst circuit-level implementation of this concept is presented with simulation results.
Cheon's anholonomies in Floquet operators  [PDF]
Manabu Miyamoto,Atushi Tanaka
Physics , 2007, DOI: 10.1103/PhysRevA.76.042115
Abstract: Anholonomies in the parametric dependences of the eigenvalues and the eigenvectors of Floquet operators that describe unit time evolutions of periodically driven systems, e.g., kicked rotors, are studied. First, an example of the anholonomies induced by a periodically pulsed rank-1 perturbation is given. As a function of the strength of the perturbation, the perturbed Floquet operator of the quantum map and its spectrum are shown to have a period. However, we show examples where each eigenvalue does not obey the periodicity of the perturbed Floquet operator and exhibits an anholonomy. Furthermore, this induces another anholonomy in the eigenspaces, i.e., the directions of the eigenvectors, of the Floquet operator. These two anholonomies are previously observed in a family of Hamiltonians [T. Cheon, Phys. Lett. A 248, 285 (1998)] and are different from the phase anholonomy known as geometric phases. Second, the stability of Cheon's anholonomies in periodically driven systems is established by a geometrical analysis of the family of Floquet operators. Accordingly, Cheon's anholonomies are expected to be abundant in systems whose time evolutions are described by Floquet operators. As an application, a design principle for quantum state manipulations along adiabatic passages is explained.
Current-Controlled CFTA Based Fractional Order Quadrature Oscillators  [PDF]
Tada Comedang, Pattana Intani
Circuits and Systems (CS) , 2016, DOI: 10.4236/cs.2016.713345
Abstract: This paper presents a study of fractional order quadrature oscillators based on current-controlled current follower transconductance amplifiers (CCCFTA). The design realisation and performance of the fractional order quadrature oscillators have been presented. The quadrature oscillators are constructed using three fractional capacitors of orders α = 0.5. The fractional capacitor is not available on the market or in the PSPICE program. Fortunately, the fractional capacitor can be realised by using the approximate method for the RC ladder network approximation. The oscillation frequency and oscillation condition can be electronically/orthogonally controlled via input bias currents. Due to high-output impedances, the proposed circuit enables easy cascading in current-mode (CM). The PSPICE simulation results are depicted, and the given results agree well with the anticipated theoretical outcomes.
Low Phase Noise Quadrature Oscillators Using New Injection Locked Technique
Chi Baoyong,Zhu Xiaolei,Wang Ziqiang,Wang Zhihua,
Chi Baoyong
,Zhu Xiaolei,Wang Ziqiang,and Wang Zhihua

半导体学报 , 2005,
Abstract: A low phase noise quadrature oscillator using the new injection locked technique is proposed.The incident signal is directly injected into the common-source connection of the sub-harmonic oscillator.In principle,the phase noise performance of the quadrature output is better than the sub-harmonic oscillator itself.The quadrature oscillator is implemented in a 0.25μm CMOS process.Measurements show the proposed oscillator could achieve a phase noise of -130dBc/Hz at 1MHz offset from 1.13GHz carrier while only drawing an 8.0mA current from the 2.5V power supply.
Floquet analysis of pulsed Dirac systems: A way to simulate rippled graphene  [PDF]
Tridev Mishra,Tapomoy Guha Sarkar,Jayendra N. Bandyopadhyay
Physics , 2014, DOI: 10.1140/epjb/e2015-60356-2
Abstract: The low energy continuum limit of graphene is effectively known to be modeled using Dirac equation in (2+1) dimensions. We consider the possibility of using modulated high frequency periodic driving of a two-dimension system (optical lattice) to simulate properties of rippled graphene. We suggest that the Dirac Hamiltonian in a curved background space can also be effectively simulated by a suitable driving scheme in optical lattice. The time dependent system yields, in the approximate limit of high frequency pulsing, an effective time independent Hamiltonian that governs the time evolution, except for an initial and a final kick. We use a specific form of 4-phase pulsed forcing with suitably tuned choice of modulating operators to mimic the effects of curvature. The extent of curvature is found to be directly related to $\omega^{-1}$ the time period of the driving field at the leading order. We apply the method to engineer the effects of curved background space. We find that the imprint of curvilinear geometry modifies the electronic properties, such as LDOS, significantly. We suggest that this method shall be useful in studying the response of various properties of such systems to non-trivial geometry without requiring any actual physical deformations.
Floquet topological system based on frequency-modulated classical coupled harmonic oscillators  [PDF]
Grazia Salerno,Tomoki Ozawa,Hannah M. Price,Iacopo Carusotto
Physics , 2015,
Abstract: We theoretically propose how to observe topological effects in a generic classical system of coupled harmonic oscillators, such as classical pendula or lumped-element electric circuits, whose oscillation frequency is modulated fast in time. Making use of Floquet theory in the high frequency limit, we identify a regime in which the system is accurately described by a Harper-Hofstadter model where the synthetic magnetic field can be externally tuned via the phase of the frequency-modulation of the different oscillators. We illustrate how the topologically-protected chiral edge states, as well as the Hofstadter butterfly of bulk bands, can be observed in the driven-dissipative steady state under a monochromatic drive. In analogy with the integer quantum Hall effect, we show how the topological Chern numbers of the bands can be extracted from the mean transverse shift of the steady-state oscillation amplitude distribution. Finally we discuss the regime where the analogy with the Harper-Hofstadter model breaks down.
Heating and thermal squeezing in parametrically-driven oscillators with added noise  [PDF]
Adriano A. Batista
Physics , 2012, DOI: 10.1103/PhysRevE.86.051107
Abstract: In this paper we report a theoretical model based on Green functions, Floquet theory and averaging techniques up to second order that describes the dynamics of parametrically-driven oscillators with added thermal noise. Quantitative estimates for heating and quadrature thermal noise squeezing near and below the transition line of the first parametric instability zone of the oscillator are given. Furthermore, we give an intuitive explanation as to why heating and thermal squeezing occur. For small amplitudes of the parametric pump the Floquet multipliers are complex conjugate of each other with a constant magnitude. As the pump amplitude is increased past a threshold value in the stable zone near the first parametric instability, the two Floquet multipliers become real and have different magnitudes. This creates two different effective dissipation rates (one smaller and the other larger than the real dissipation rate) along the stable manifolds of the first-return Poincare map. We also show that the statistical average of the input power due to thermal noise is constant and independent of the pump amplitude and frequency. The combination of these effects cause most of heating and thermal squeezing. Very good agreement between analytical and numerical estimates of the thermal fluctuations is achieved.
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