Pair Of Complex Poles Research Articles

Revisiting O(N) σ model at unphysical pion masses and high temperatures

Roy-equation analysis on lattice data of ππ scattering phase shifts at mπ=391 MeV reveals that the lowest f0 meson becomes a bound state under this condition. In addition, there is a pair of complex poles below threshold generated by crossing symmetry [X.-H. Cao , ]. We use the N/D method to partially recover crossing symmetry of the O(N) σ model amplitude at leading order of 1/N expansion, and qualitatively reproduce the pole structure and pole trajectories with varying pion masses as revealed by Roy-equation analyses. The σ pole trajectory with varying temperature is also discussed and found to be similar to its properties when varying mπ. As the temperature increases, the complex σ poles firstly move from the second Riemann sheet to the real axis becoming two virtual state poles, and then one virtual state pole moves to the first sheet turning into a bound state pole and finally tends to the pion pole position at high temperature which is as expected from the chiral symmetry restoration. Our results provide further evidence that the lowest f0 state extracted from experiments and lattice data plays the role of the σ meson in the spontaneous breaking of chiral symmetry. Finally, we also briefly discuss the problems of the effective potential in the situation when mπ and the temperature become large. Published by the American Physical Society 2024

Probing the singularities of the Landau-Gauge gluon and ghost propagators with rational approximants

We employ Padé approximants in the study of the analytic structure of the four-dimensional SU(2) Landau-gauge gluon and ghost propagators in the infrared regime. The approximants, which are model independent, serve as fitting functions for the lattice data. We carefully propagate the uncertainties due to the fitting procedure, taking into account all possible correlations. For the gluon-propagator data, we confirm the presence of a pair of complex poles at {p}_{textrm{pole}}^2 = [(−0.37 ± 0.05stat± 0.08sys) ± i (0.66 ± 0.03stat± 0.02sys)] GeV2, where the first error is statistical and the second systematic. The existence of this pair of complex poles, already hinted upon in previous works, is thus put onto a firmer basis, thanks to the model independence and to the careful error propagation of our analysis. For the ghost propagator, the Padés indicate the existence of a single pole at p2 = 0, as expected. In this case, our results also show evidence of a branch cut along the negative real axis of p2. This is corroborated with another type of approximant, the D-Log Padés, which are better suited to studying functions with a branch cut and are applied here for the first time in this context. Due to particular features and limited statistics of the gluon-propagator data, our analysis is inconclusive regarding the presence of a branch cut in the gluon case.

Control based on a hybrid predictor for linear unstable delayed systems with a pair of complex conjugate poles

This paper presents a methodology to design a hybrid predictor of continuous signals to solve the stabilization problema of unstable linear systems with time delay, specifically systems with an unstable pole and a pair of stable conjugate complex poles. Among the main contributions of this work is to guarantee the existence of the predictor device, regardless of the size of the delay. To solve the stabilization problem, the necessary and sufficient conditions are obtained for a Proportional-Integral (PI) controller that can guarantee the stability of the system using the designed predictor. The performance of this control strategy is evaluated by means of a numerical simulation.

Integrated Approach to Design and Implementation of a Single-Phase Current Regulator With Antiwindup Mechanism

An ac-regulated single-phase inverter operating in the stationary frame is designed to accurately track a sinusoidal reference signal at a designated frequency. To achieve such a control objective, resonant controllers with a conjugate set of marginally stable poles are required. The explicit implementation of marginally stable dynamics is prone to wind up in the event of the control signal entering a nonlinear saturation condition, resulting in a degraded or even an unstable dynamic response. This article proposes an integrated approach to the design and implementation of a resonant controller for a single-phase current regulator with an intrinsic antiwindup mechanism. The proposed method utilizes a disturbance observer to embed a pair of complex poles into the controller, leading to accurate tracking of a sinusoidal reference signal. Simultaneously, by using the observer architecture with a set of desired closed-loop poles as the performance specification, the implementation form remains completely stable. Furthermore, the closed-loop performance of the proposed resonant control system is analyzed to assess the impact of unmodeled dynamics. Experimental results are presented to demonstrate the efficacy of the proposed approach.

Partial Pole Placement using Static Output Feedback

For many dynamical systems it is required to specifically shift individual poles, especially when these poles are lightly damped or even unstable. To achieve that, a preferably large number of effectors and measurements are installed leading to multivariable control problems. In this paper, a novel control approach is presented for placing either a single pole or a conjugate complex pole pair at a predefined location using rank-one static output feedback. Rank-one feedback can be interpreted as blending inputs and outputs to define a single input and single output loop with a desirable root locus along which the pole is moved. The corresponding controller synthesis is reduced to an unconstrained optimization problem in a single variable that aims at minimizing the feedback gain. Although the approach is derived for a single pole or conjugate complex pole pair, it is easily extended to multiple poles. To this end, a repeated design and superposition of rank-one feedback gains is proposed. It is further shown how residual system dynamics as well as subsequently designed gains can be efficiently decoupled from each other in order to avoid undesired interactions and spillover effects. The effectiveness of the proposed control approach is demonstrated by means of a numerical example.

Design and Analysis of Three-Stage Amplifier for Driving pF-to-nF Capacitive Load Based on Local Q-Factor Control and Cascode Miller Compensation Techniques

This paper presents a new frequency compensation approach for three-stage amplifiers driving a pF-to-nF capacitive load. Thanks to the cascode Miller compensation, the non-dominant complex pole frequency is extended effectively, and the physical size of the compensation capacitors is also reduced. A local Q-factor control (LQC) loop is introduced to alter the Q-factor adaptively when loading capacitance CL varies significantly. This LQC loop decides how much damping current should be injected into the corresponding parasitic node to control the Q-factor of the complex-pole pair, which affects the frequency peak at the gain plot and the settling time of the proposed amplifier in the closed-loop step response. Additionally, a left-half-plane (LHP) zero is created to increase the phase margin and a feed-forward transconductance stage is paralleled to improve the slew rate (SR). Simulated in 0.13-µm CMOS technology, the amplifier is verified to handle a 4-pF-to-1.5-nF (375× drivability) capacitive load with at least 0.88-MHz gain-bandwidth (GBW) product and 42.3° phase margin (PM), while consuming 24.0-µW quiescent power at 1.0-V nominal supply voltage.

Enhanced-Selectivity High-Linearity Low-Noise Mixer-First Receiver With Complex Pole Pair Due to Capacitive Positive Feedback

A mixer-first receiver (RX) with enhanced selectivity and high dynamic range is proposed, targeting to remove surface acoustic-wave-filters in mobile phones and cover all frequency bands up to 6 GHz. Capacitive negative feedback across the baseband (BB) amplifier serves as a blocker bypassing path, while an extra capacitive positive feedback path offers further blocker rejection. This combination of feedback paths synthesizes a complex pole pair at the input of the BB amplifier, which is upconverted to the RF port to obtain steeper RF bandpass filter roll-off and reduced distortion. This paper explains the circuit principle and analyzes RX performance. A prototype chip fabricated in 45-nm partially depleted silicon on insulator (SOI) technology achieves high out-of-band linearity (input-referred third-order intercept point (IIP3) = 39 dBm and input-referred second-order intercept point (IIP2) = 88 dB) combined with sub-3-dB noise figure. Desensitization due to a 0-dBm blocker is only 2.2 dB at 1.4 GHz.

Probing the unitarity of the renormalizable theory of massive conformal gravity

The presence of an unstable massive spin-2 ghost state in the renormalizable theory of massive conformal gravity leads to a pair of complex poles appearing in the first sheet of the energy plane. Here we show that the positions of these poles are gauge dependent, which makes the theory unitary.

A 0.02 mm<formula formulatype="inline"><tex Notation="TeX">$^{2}$</tex></formula> 59.2 dB SFDR 4th-Order SC LPF With 0.5-to-10 MHz Bandwidth Scalability Exploiting a Recycling SC-Buffer Biquad

This paper reports a switched-capacitor (SC)-buffer Biquad that can be recycled efficiently as an ultra-compact low-pass filter (LPF) in nanoscale CMOS. It incorporates only passive-SC networks and open-loop unity-gain buffers; both are friendlier to technology downscaling than most conventional Biquads that use high-gain amplifiers and closed-loop negative feedback. Complex-pole pairs with independent Q factors are recursively realized in one clock period, while ensuring low crosstalk effect between the formations of each pole. Nonlinearity and parasitic effects are inherently low due to no internal gain. The fabricated 65 nm CMOS prototype is a 1x-recycling SC-buffer Biquad that is equivalent to a 4th-order Butterworth LPF with 75% buffer utilization. It occupies a die size of only 0.02 mm $^{2}$ and exhibits 20x bandwidth tunability (0.5 to 10 MHz), linear with the clock rate. At 10 MHz bandwidth, the in-band IIP3 is +17.6 dBm and input-referred noise is 19.5 nV/ $\surd$ Hz; they correspond to 59.2 dB SFDR and 0.013 fJ figure-of-merit which are favorably comparable with the recent art. The 1 dB compression point $({\rm P}_{1{\rm dB}})$ conforms to the out-of-band blocker profile of the LTE standard at a 20 dB front-end gain.

Regulation quality for frequency response of turbine regulating system of isolated hydroelectric power plant with surge tank

Aiming at the isolated hydroelectric power plant (HPP) with surge tank, this paper studies the regulation quality for frequency response of turbine regulating system under load disturbance. Firstly, the complete mathematical model of turbine regulating system is established and a fifth order frequency response under step load disturbance is derived. Then, the method of primary order reduction and secondary order reduction, for this complete fifth order system of frequency response, is proposed based on dominant poles. By this method, the complete fifth order system is solved and the regulation quality for frequency response is studied. The results indicate that the complete fifth order system always has a pair of dominant conjugate complex poles and three non-dominant poles. The primary fourth order equivalent system, which is obtained by primary order reduction, keeps the dominant poles almost unchanged, therefore it can represent and replace the complete fifth order system and it is obviously superior to other fourth order systems. The primary fourth order equivalent system is superimposed by two second-order subsystems, one of them is corresponding to two non-dominant real poles (i.e. head wave) and the other one is corresponding to a pair of dominant conjugate complex poles (i.e. tail wave), respectively. In the fluctuation process of frequency response, head wave decays very fast and works mainly in the beginning period while tail wave decays very slowly, fluctuates periodically and works throughout the period. The secondary order reduction of complete fifth order system can be conducted by using the second order system of tail wave, which is the main body of frequency response, to represent the fluctuation characteristics. The most important dynamic performance index that evaluates the regulation quality, i.e. settling time, is derived from the fluctuation equation of tail wave. The different characteristic parameters of turbine regulating system have different influences on the change rules of head wave, tail wave and settling time.

A LDO Regulator With Weighted Current Feedback Technique for 0.47 nF–10 nF Capacitive Load

A Weighted Current Feedback (WCF) technique for output capacitorless low-dropout (OCL-LDO) regulator is presented in this paper. Through feedback of a weighted current, the WCF permits smart management of the output impedance as well as the gain from the inter-gain stage. Based on the Routh-Hurwitz stability criterion, the WCF can avoid the right-half plane (RHP) pole and push the left-half plane (LHP) non-dominant complex pole pair to a higher frequency. Besides, it provides good regulator loop gain and fast transient response. Validated by UMC 65 nm CMOS process, the simulation and measurement results have shown that the WCF LDO regulator can operate at a load capacitance (C L ) range from 470 pF to 10 nF with only 3.8 pF compensation capacitor. At a supply of 0.75 V and a quiescent current of 15.9 μA, the proposed circuit can support a maximum load current (I L ) of 50 mA. When I L switches from 0 to 50 mA in 100 ns, the output can settle within 400 ns for the whole C L range. For a case of single capacitor (C L 470 pF), the settling time is only 250 ns. The comparison results have shown that the WCF LDO regulator offers a comparable or better transient figure-of-merit (FOM) and additional merit to drive wide load capacitance range.

LQ 제어기에 의한 극배치 방법

This paper studies the problem of pole placement by an LQ controller for system having two distinct real poles. Using the so-called Pole's Moving Range (PMR) drawn in the s-plane and relational equations between closed-loop system poles and weighting matrices, we calculate the state weighting matrix to move two distinct real poles to a pair of complex poles. By numerical examples, we show that the proposed method is applied to improve system performance.

Identification of Mechanical Systems through Kautz Filter

This paper presents a novelty approach to estimate the impulse response function (IRF) in lightly damped structures by using classical covariance method. The contribution of the present paper is to employ a Kautz filter to reduce the number of terms in the identification process of a finite impulse response (FIR) model. The Kautz filter is an orthogonal function that includes complex pole pair. So, the method incorporates a priori knowledge into the process that is essential to reach better results and to minimize the number of coefficients in the FIR model. For this reason, the present approach can be classified as a kind of “grey-box” methodology. The numerical and experimental applications of the method confirmed that by considering a priori parametric information the problem can be determined more easily. Moreover, the procedure proposed increased the convergence speed, and, as a consequence the consuming computational cost is lower.

Positive width function and energy indeterminacies in ammonia molecule

AbstractA recently published methodology based on the semiclassical path integral theory was applied in a double well structure and gave the analytic form of the system's Green's function. This type of potential can describe the ammonia molecule as far as the motion of the nitrogen atom perpendicular to the hydrogen plane is discussed. Because of the fact that a double well describes a bound system and correspondingly stationary states (constructed by the symmetric and antisymmetric superposition of the eigenstates of the two unperturbed wells), it was expected that the energy spectrum would be real, in a form of doublets due to the splitting effect that takes place. However, the result was a pair of complex poles, which had a clearly positive imaginary part for each member. The present work explains the role of the imaginary parts of the complex poles as the decay rate of quantities defined as the energy indeterminacies, which are directly related to the fact that energy is not well determined in a classically forbidden region of motion. These quantities come as a function of (dκ)/dE, which is the derivative of the classical action inside the potential barrier, with respect to energy. The major contribution comes from the turning points, and then the imaginary parts are responsible, not only for the conservation of energy, but for the correct sign of time as well. In this way, a different approach for the tunneling process is adopted, in which the entry or exit of the particle from the potential barrier takes place inside a neighborhood of the turning point, as though the latter was broadened and fluctuating. The magnitude of the previously mentioned decay rate is equal to ω/π, where ω is the frequency of the classical oscillations inside one well. In contrast, the inversion frequency is generated by the part of the complex pole that is unrelated to (dκ)/dE and is much smaller in magnitude than the classical frequency, since it is given as ω/π exp(−κ). In this way, the period of the energy fluctuations is much smaller than the internal period of the system produced by the oscillating communication of the two classically allowed regions of motion. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007

A dual complex pole-zero cancellation frequency compensation with gain-enhanced stage for three-stage amplifier

A dual complex pole-zero cancellation (DCPC) frequency compensation technique with gain enhanced stage (GES) for three-stage amplifier is proposed in this paper. It uses one pair of complex zeros to cancel one pair of complex poles, resulting in feature that the frequency response of three-stage amplifier exhibits that of a single-pole system. Meanwhile, the effective transconductance of output stage can be greatly increased by several times which are equal to gain of GES, and the power dissipation can be decreased when a GES is introduced. Thus the gain-bandwidth (GBW) is expected to be increased about 10 times compared to the conventional nested miller compensation (NMC) approach. Moreover, this technique requires only one very small compensation capacitor even when driving a large load capacitor. A GBW of 1.23 MHz, DC gain of 111 dB, PM of 86° and power dissipation of 0.29 mW can be achieved for a load capacitor of 500 pF with a single Miller compensation capacitor of 14 pF at a ± 1 V supply in a standard 0.6-?m CMOS technology.

A fully balanced pseudo-differential OTA with common-mode feedforward and inherent common-mode feedback detector

A pseudo-differential fully balanced fully symmetric CMOS operational transconductance amplifier (OTA) architecture with inherent common-mode detection is proposed. Through judicious arrangement, the common-mode feedback circuit can be economically implemented. The OTA achieves a third harmonic distortion of -43 dB for 900 mV/sub pp/ at 30 MHz. The OTA, fabricated in 0.5-μm CMOS process, is used to design a 100-MHz fourth-order linear phase filter. The measured filter's group delay ripple is 3% for frequencies up to 100 MHz, and the measured dynamic range is 45 dB for a total harmonic distortion of -46 dB. The filter consumes 42.9 mW per complex pole pair while operating from a ±1.65-V power supply.

Simulation of general linear dielectric properties in TLM

AbstractThe simulation of linear dispersive dielectric materials in time‐domain TLM requires the inclusion of frequency‐dependent material properties in the scattering process. For media having frequency dependencies described by a single pole or a pair of complex poles, for example Debye, Drude or Lorentz, it is straightforward to develop individual algorithms on a case‐by‐case basis. However, this approach lacks generality and when applied to the modelling of media displaying more complicated frequency dependencies, somewhat lengthy calculations need to be evaluated each time a new material is required. To address this difficulty, this paper describes methods for obtaining the iteration algorithm for general linear isotropic dielectric media. The results obtained using different 𝒵‐transform methods are compared and an example of a frequency‐dependent structure is simulated. Copyright © 2002 John Wiley & Sons, Ltd.

Improved design criteria of gain-boosted CMOS OTA with high-speed optimizations

A comprehensive study on gain-boosted regulated cascode operational transconductance amplifiers (OTA) is discussed. These amplifiers are usually good for power optimized high-speed designs. However, location of an additional pole-zero pair in the transfer function makes the transient response much slower than expected. A new design is proposed along with the systematic approach which get rid of this pole-zero pair and deliberately puts a pair of complex poles to make the design faster.

Delay approximation for synchronous filter topologies

It is shown that the original definition of e developed by Euler can be used as the basis of a delay approximation where all the poles have the same value. Furthermore, it is demonstrated that by splitting the Euler function into complex pole pairs, by the addition of an artificial variable β, an additional degree of freedom can be introduced. Through optimisation of the value of β it is shown that either the group delay or step response can be optimised. This delay approximation, when compared to a standard Bessel approximation, is shown to provide acceptable performance for many applications. Furthermore, it offers the considerable practical benefit of being realisable as a cascade of identical building block elements when appropriate technologies (e.g. second-order active filter blocks) are used.

A proposed z-plane criterion to expedite transient-performance analyses

A simple and insightful performance criterion is described with reference to the position of a pair of complex-conjugate poles in the z-plane. Introduced as the half-cycle decay factor, this criterion is a relative stability measure that is determined directly in the z-plane without reference to a corresponding damping ratio in the s-plane. Use of the proposed criterion expedites various analysis and design procedures, and this property is illustrated. The utilization is presented with several control system applications. One example presents a time-scaling procedure as required to implement an observer-the complex-pole pairs are moved in a manner that maintains the half-cycle decay factor for each complex pair at a fixed value. Other examples are considered in which the system model is characterized by a single pair (or single dominant pair) of complex-conjugate poles. In this situation specific conditions are described for which the half-cycle decay factor can be employed in expressions to evaluate percent overshoot and settling time in response to a step input. Finally, it is shown that the concept can be applied in either the z-plane or the s-plane using either discrete-time models or continuous models, respectively.