Z-domain Model Research Articles

Delta system transfer function model for IEMI time domain test

Intentional electromagnetic interference (IEMI) is a serious threat to the stable operation of computer and other intelligent terminal equipment. For testing research on IEMI, it is very important to build a stable and reliable test system model for accurate analysis of test data. In the time-domain test of IEMI, the z-domain discrete system transfer function is usually used to describe the response characteristics of the test system. However, with the change of sampling frequency, the parameters of the z-domain model should change accordingly, which leads to inconvenience in modeling the test system. In this paper, a δ-domain transfer function model of the test system is constructed by the transformation from z-domain. And the δ-domain model has better stability at high sampling rate and can be approximately equivalent to the system transfer function in the continuous-time domain.

Z-domain model procedure for heterodyne digital optical phase-locked loop

Although there are already some simulation tools modeling and s-domain modeling studied for heterodyne optical phase-locked loop (HOPLL), few studies about z-domain model of OPLL are reported. When the loop filter in HOPLL is implemented by digital circuit, the operation of HOPLL is controlled by digital signals which is called heterodyne digital optical phase-locked loop (HDOPLL) in this paper. It is easily deduced that the performance of HDOPLL can be analyzed more accurately by z-domain model. With a deep analysis, the problem about the nonlinear operation of optical related components can be circumvented, if the optical related components are grouped with phase frequency detector (PFD) during z-domain modeling. So the detail about the z-domain model procedure for HDOPLL is presented in the paper. Then for a case study, stability of HDOPLL is analyzed by an established z-domain model, and the correctness of z-domain model is verified by Simulink behavioral model of HDOPLL.

Modeling and analysis of all-optical 2-bit and 4-bit synchronous up counter using silicon waveguide based all-optical JK flip-flop in Z domain

Placing reliance on Silicon waveguide based OMRR, this paper has brought a simple design of optically pumped 2-bit and higher bit counters using optical J–K flip flop.The present paper has used the non-linerarity characteristic of OMRR. A Pump pulse is applied from the top which causes switching operation. The Counter Circuit has been achieved by using the delay line signal process approach. Circuit’s performance has been assessed vide exploration of Z-domain model. The validity and viability of the present model is determined by evaluating the performance parameters such as Free Spectral Range, Q-factor, Amplitude modulation, ON-OFF ratio, Extinction Ratio (ER), Fineness and Contrast Ratio during simulation.

Z-domain modeling of peak current mode control for full-bridge DC-DC buck converters

Traditional local-averaged state-space modeling for peak current mode (PCM) controls fails to explain the subharmonic oscillation phenomenon when the spectrum is higher than half of the switching frequency. To address this problem, this paper presents a small-signal modeling method in the z-domain, and builds a discrete linear model for the current loop of a full-bridge DC-DC converter. This discrete model is converted into a second-order continuous model that is able to represent the system performance with a wider frequency range. A frequency-domain analysis shows that this model can be used to explain the subharmonic oscillations and unstable characteristics. This provides an engineering guideline for the practical design of slope compensation. The effectiveness of the proposed modeling method has been verified by simulation and experimental results with a prototype working in the Buck mode.

Analysis of Digital PCM-Controlled Boost Converter With Trailing-Edge Modulation Based on z-Domain and Describing-Function Model

Digital trailing-edge modulated peak-current-mode (PCM) control scheme is commonly used in power converters, due to the similar excellent characteristics with its peer analog controller and being achieved easily in practice. However, the additional issues, such as time delays, quantization error, and resolution of the digital pulsewidth modulator (DPWM), in the digital controller, not only reduce the stability of the converter but also make the modeling and analysis more complicated. Taking the digital controlled boost converter as an example, this article presents a z-domain model of the whole converter system on the basis of a describing-function method by considering the effects of the abovementioned problems. The influences of time delays from analog-to-digital conversion (ADC) and DPWM and resolution from the DPWM module can be analyzed clearly according to the proposed model. And more importantly, the critical resolution between stable and unstable operations of the converter can be determined by checking the eigenvalues. Furthermore, the stability analysis based on the presented z-domain model is verified by the simulations and experiments.

Z-domain modeling approach of a multilayer sextuple-coupled micro-ring resonator with 1 × 5 input-output bus waveguides as optical filters.

This paper introduces the modeling approach of a new micro-ring resonator configuration composite of six asymmetrical rings with one input and five output bus waveguides. This multilayer sextuple-coupled micro-ring resonator (MSCMRR) is modelled in the z domain by practicing the delay line signal approach and Mason's gain formula. Both lateral coupling and vertical coupling are used to design this MSCMRR structure to confine it up to four layers. Performance analysis is carried out in a MATLAB platform with the graphical representation of performance parameters like free spectral range (FSR), group delay, dispersion, full width at half-maximum, etc. The optical couplers of the proposed model are also designed by the finite-difference time-domain (FDTD) method. Electric field propagation through the rings and the waveguides are also studied by FDTD. The proposed structure offers different values of high FSR with zero crosstalk at every output port that ensures the quality application of this proposed model as an optical add-drop filter in an optical communication network.

Modeling and Performance Analysis of Bragg Grating in Z-Domain

Z-domain model of fiber Bragg grating is developed, and its performance analysis is presented in this letter. The developed mathematical model is used for the evaluation of reflection and transmission response. Spectral characteristics in terms of bandwidth, peak transmittance, and side lobes formation is determined for a model of length 0.84 mm and is found to be in very close agreement with previously published fabrication result. A similar structure with different parameters is considered. The transmission response provides a wide full width half maximum (FWHM) bandwidth of 9.52 nm and a peak transmission of 0.067. The proposed model is extended to determine the transmission response for a very small incidence angle variation. Performance parameters, such as FWHM, stopband width, and optical density, are analyzed. Transmission response of the proposed model for different length combinations is evaluated.

Extracting cavity and pulse phases from limited data for coherent pulse stacking

Coherent pulse stacking (CPS) is a new time-domain coherent addition technique that stacks several optical pulses into a single output pulse, enabling high pulse energy and high average power. A Z-domain model targeting the pulsed laser is assembled to describe the optical interference process. An algorithm, extracting the cavity phase and pulse phases from limited data, where only the pulse intensity is available, is developed to diagnose optical cavity resonators. We also implement the algorithm on the cascaded system of multiple optical cavities, achieving phase errors less than 1.0° (root mean square), which could ensure the stability of CPS.

Design and performance analysis of optical microring resonator based J − K flip-flop

A simple design of optically pumped J−K flip-flop using a two GaAs–AlGaAs based optical microring resonator (OMRR) is introduced. The nonlinear property of a GaAs–AlGaAs based ring resonator is explored to use it as an optical switch. A high-intensity optical pump pulse is used for the switching operation of the OMRR. A theoretical model of the proposed J–K flip-flop circuit is developed by applying the delay line signal process approach. Z-domain model of the circuit is explored to analyze its performance. Various performance parameters—such as contrast ratio (CR), extinction ratio (ER), on-off ratio (Ton-off), and amplitude modulation (AM)—are determined from the simulation results obtained on MATLAB. The optimum values of CR, ER, Ton-off, and AM are calculated for the proposed model, which confirms the feasibility of the flip-flop.

Performance analysis of optical micro-ring resonator as all-optical reconfigurable logic and multiplexer in Z-domain

Performance and design methodology of [Formula: see text] multiplexer (MUX) and all-optical reconfigurable logic circuit using GaAs–AlGaAs-based optical micro-ring resonator (OMRR) are presented in current paper. Proposed design of reconfigurable logic circuit is capable to perform eight different logic operations. Performances of the logic circuits have been theoretically analyzed using Z-domain modeling. Numerical simulation results confirming the method are explained in the present paper. Proposed circuit is simple, compact, efficient as it have minimum number of OMRR, low operating power, high operating speed and high Q-factor. Different ‘figure of merits’ of the purposed model are calculated from the simulation results.

Performance of optical microring resonator as multiplexer and all-optical logic shifter in Z-domain

The performance of 4×1 multiplexer (MUX) and 8×1 multiplexer (MUX) using GaAs–AlGaAs based optical microring resonator (OMRR) is presented. The 4×1 MUX is designed with two OMRR and 8×1 MUX is designed with three OMRR. The proposed structure of 8×1 MUX is further used to design 8-bit logic shifter circuit. The nonlinear property of OMRR is used as an optical switch in all the optical logic circuits. The performance of 4×1 MUX, 8×1 MUX, and 8-bit logic shifter circuit is analyzed using Z-domain model. The various important parameters of the proposed model, such as on–off ratio [τon-off(dB)], full-width half maximum (FWHM), Q-factor, extinction ratio [ξER(dB)], contrast ratio [χCR(dB)] amplitude modulation [ηAM(dB)], are also analyzed.

Modeling and performance analysis of vertically coupled triple microring resonator in the Z domain.

A theoretical model of vertically coupled triple microring resonators (VCTMRRs) in the Z domain is presented in this work. Delay line signal processing approach in Z-domain modeling is used for the performance analysis of waveguide-based VCTMRRs. Overall transmittance of the VCTMRR is determined in the Z domain, and frequency response is evaluated in a MATLAB environment. Performance in terms of free spectral range (FSR) and crosstalk of VCTMRR with two symmetric rings is compared with previously published results, and found to be in close agreement. VCTMRR architectures with different ring length combinations have been considered for the analysis. Performance of a VCTMRR with three asymmetric rings is also reported and compared with the performance of a VCTMRR with two symmetric rings in the present work. The design provides transmission characteristics where spurious transmission (crosstalk) at the interstitial frequencies that lie between the extended FSR is adequately suppressed. Group delay and dispersion characteristics are also presented.

Digital Control Strategy for Single-phase Voltage-Doubler Boost Rectifiers

In this paper, a digital controller design procedure is presented for single-phase voltage-doubler boost rectifiers (VDBR). The model derivation of the single-phase VDBR is performed in the s-domain. After that the simplified equivalent z-domain models are derived. These z-domain models are utilized to design the input current and the output dc-link voltage controllers. For the controller design in the z-domain, the traditional K-factor method is modified by considering the nature of the digital controller. The frequency pre-warping and anti-windup techniques are adapted for the controller design. By using the proposed method, the phase margin and the control bandwidth are accurately achieved as required by controller designers in a practical frequency range. The proposed method is applied to a 2.5 kVA single-phase VDBR for Uninterruptible Power Supply (UPS) applications. From the simulation and the experimental results, the effectiveness of the proposed design method has been verified.

Modeling and analysis of quadruple optical ring resonator performance as optical filter using Vernier principle

Vernier principle based modeling and analysis of an optical ring resonator structure that includes four asymmetric rings are introduced in this paper to obtain very wide free spectral range (FSR). Delay line signal processing approach in Z-domain modeling is used for analysis of waveguide based novel quadruple optical ring resonator (QORR). Two QORR architectures made of SOI and SiN waveguides have been compared, which produce FSR of 343.4 THz 264.6 THz respectively. Apart from obtaining wider FSR and adequate suppression of spurious interstitial modes close to -30 dB, this work presents group delay and dispersion characteristics for QORR made of materials with different effective refractive indices.

Sampled-Data Modeling of Hysteretic Converters Accounting for Intracycle Waveform Propagation

This paper proposes a small-signal model for variable-switching-frequency hysteretic converters operating in continuous conduction mode (CCM) and discontinuous conduction mode (DCM). The model is capable of predicting flip-bifurcation phenomena when the hysteretic converter operates below the CCM/DCM boundary. By developing a discrete-time state-space model of the converter, the z-domain model is derived using the advanced z-transform. Such a tool is suitable to transform in the z-domain signals varying within a switching cycle. A comparison with exact simulations is provided to validate the proposed model. The propagation delay of the feedback control circuit is included due to its significant influence on the low-frequency open-loop gain. Experimental results run on a test chip including a 10-MHz TSMC 0.18 μm-process hysteretic-mode buck converter are also reported along with the model results.

Low-frequency oscillation in digitally controlled DC-DC Buck converters

The z-domain model of digitally controlled Buck converter is derived by only considering the effect of sampler-and-holder. Based on the z-domain model, the cause of the low-frequency bifurcation is analyzed. The location and type of the bifurcation point when a system loses stability is predicted in terms of the system eigenvalues. Moreover, the frequency and the amplitude of the low-frequency oscillation, i.e., the wave equations, are deduced. These theoretical results are verified by PSpice simulations.

Analytical disturbance-based model for nonlinear loads used in UPS applications

A z-domain model describing the steady-state behaviour of nonlinear loads defined by the IEC62040-3 standard for UPS systems is presented. The proposed model makes it possible to obtain the time-domain response from the frequency-domain description of discrete-time repetitive controllers used in these applications. Good agreement between predicted and experimental results validates the proposed model.

Noise transfer characteristics and design techniques of a frequency synthesizer

This paper presents an exact method for the loop parameters' calculation. The noise transfer functions of PLL based synthesizers are derived in the z-domain analysis. Through the comparison of the s-domain model with the z-domain model, we show that the noise peak from inherent sampling behaviors always exists in the loop, and the loop filter with the wide loop bandwidth doesn't suppress it. Such a noise peak causes instability to the system. A stability limit of the wide loop bandwidth frequency synthesizer is extracted by the behavioral simulation using the z-domain model, which depends on the phase margin and the ratio between the reference frequency and the loop bandwidth.

Jitter transfer characteristics of delay-locked loops - theories and design techniques

This paper presents analyses and experimental results on the jitter transfer of delay-locked loops (DLLs). Through a z-domain model, we show that in a widely used DLL configuration, jitter peaking always exists and high-frequency jitter does not get attenuated as previous analyses suggest. This is true even in a first-order DLL and an overdamped second-order DLL. The amount of jitter peaking is shown to trade off with the tracking bandwidth and, therefore, the acquisition time. Techniques to reduce jitter amplification by loop filtering and phase filtering are discussed. Measurements from a prototype chip incorporating the discussed techniques confirm the prediction of the analytical model. In environments where the reference clock is noisy or where multiple timing circuits are cascaded, this jitter amplification effect should be carefully evaluated.

High-performance conversions between continuous- and discrete-time systems

In this paper, a new algorithm for converting an S-domain model to a Z-domain model is proposed. The resultant Z-domain model is much closer to the original S-domain model than that obtained from conventional conversion schemes such as Tustin approximation with or without frequency pre-warping, zero-pole mapping equivalent, and Triangle hold equivalent. The proposed algorithm adopts the standard recursive least squares approach, and it has the following advantages. First, the computation is trivial and can be easily implemented online. Second, it can handle both parametric and non-parametric models, while conventional conversion methods can only handle parametric models. Third, it is very flexible and applicable to Z- to S-domain model conversion, sampling rate selection, re-sampling, time delay system conversion, and model order selection. The superior performance of the method is demonstrated with several simulation examples in this paper.