Mason's Gain Formula Research Articles

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.

Outage probability of multi‐hop networks with amplify‐and‐forward full‐duplex relaying

The authors consider a multi-hop amplify-and-forward full-duplex relay system. They take a signal flow graph approach for finding the input–output relationship using Mason's gain formula, and use this expression to compute the system outage probability for different equalisers. For sufficiently large target rates, full-duplex relaying with equalisers has lower outage probability than half-duplex relaying, despite the higher residual self-interference (RSI) of the full-duplex approach. The full-duplex system with (unequalised) matched filter at the destination is seen to be sensitive to RSI which shows that equalisation at the destination is a feasible approach to combating the RSI for full-duplex multi-hop systems.

Performance study of optical resonator‐based filter architectures

A comparative study on characteristics and performance of optical ring resonator architectures, i.e. circular, racetrack, and triangular-shaped optical resonators, have been carried out here. Constituent material used for designing these resonators is an silicon on insulator wafer consisting of thin silicon (Si) layer on silica (SiO2) layer carried on a thick Si substrate having group index of 2.379. All the resonators are so designed that all provide equal free spectral range (FSR) of 25.2 THz. All these double-ring architectures have been analysed using delay line signal processing technique in z-domain and Mason's gain formula. FSR expansion has been achieved employing the Vernier principle. Various performance defining parameters have been also investigated.

Analyzing a four quadrant dc-dc Luo converter by means of signal flow graph modeling technique

Abstract In this paper, the signal flow graph technique and Mason gain formula are applied for extracting small signal model and transfer functions from control to output and from input to output. In order to investigate a rather complex system, a four quadrant dc-dc Luo converter known as a second generation and high order power electronic converter is chosen for modeling and analyzing purposes. This converter has received the least attention and its dynamic modeling and analysis is not reported in literature. To get rid of complex equations in modeling high order converters, signal flow graph method is applied to manipulate the equations. Hence, the small signal models for two converters in different states are derived in detail and the obtained models are used to achieve the frequency responses and do stability analysis. The whole paper shows that using the proposed method, derivation of small signal models for all states and frequency domain analysis can be easily carried out in detail.

APPLICATION OF FLOW GRAPHS IN THE MICROWAVE MEASUREMENTS SYSTEMS

Flow graphs are the effective tool for description of the complicated microwave measurement systems and usually are used in the process of creating measurement equation. The algorithm which can find this equation is known as the Mason's gain formula (MGF). This operation needs to perform a lot of symbolic computations so performing of this algorithm without proper software is heavy and is vulnerable to appearing some errors. This paper shows which existing scripts for MATLAB can be use to perform this task.

Output-Impedance Shaping of Bidirectional DAB DC–DC Converter Using Double-Proportional-Integral Feedback for Near-Ripple-Free DC Bus Voltage Regulation in Renewable Energy Systems

This paper investigates the design and implementation of virtual-output-impedance shaping on an inverter-loaded, fuel-cell-battery-powered dc–dc converter system for achieving near-ripple-free dc bus voltage regulation. The method is based on the insertion of a second output-voltage feedback loop as can be inferred from the Mason's gain formula. Three basic modes of virtual-output-impedance shaping (proportional, derivative, integral) are discussed and the closed-loop output-impedance characteristics due to each of them are analyzed in detail and with their Thevenin equivalent circuits derived. Despite the suitability of integral feedback for minimizing converter's output impedance, it can give rise to an unwanted resonance peak near the converter's crossover frequency, thus potentially destabilizing the system. The solution to the problem using combination of basic virtual-output-impedance shaping modes and its practical implementation are discussed. When implemented on a fuel-cell-battery-powered dual-active-bridge dc–dc converter, the second-harmonic distortion of dc bus voltage is shown to have been reduced by 85.5% compared to a conventionally PI-compensated system.

Systematic Derivation of a Family of Output-Impedance Shaping Methods for Power Converters—A Case Study Using Fuel Cell-Battery-Powered Single-Phase Inverter System

For power converters used in renewable energy systems, output-impedance design has become an important design consideration for minimizing the impacts of low-frequency harmonic current on the lifetime of ripple-sensitive energy sources such as fuel cells and photovoltaic cells. In the literature, various methods are proposed to tackle this design issue but they are frequently treated in isolation from each other and specific to the systems being discussed. In this paper, a systematic derivation of four basic modes of output-impedance shaping method is presented. These basic modes can be directly inferred from the Mason's gain formula and other methods are in essence derivatives or combinations of these basic modes. By using a fuel-cell-battery-powered single-phase inverter as an implementation example, their characteristics are discussed thoroughly and their performances in shaping converter's output impedance are evaluated experimentally.

Buck-Boost DC-DC Converter Control by Using the Extracted Model from Signal Flow Graph Method

In this paper, the signal flow graph technique and Mason gain formula are applied for extracting the model and transfer functions from control to output and from input to output of a buck-boost converter. In order to investigate a controller necessity for the converter of assumed parameters, the frequency and time domain analysis are done and the open loop system characteristics are verified and the needed closed loop controlled system specifications are determined. Finally designing a controller for the mentioned converter system based on the extracted model is discussed. Then, a modern control design method is employed for regulator design. For this purpose, a full state feedback control for pole placement is applied. The simulation results are used to show the performance of the proposed modeling and regulation method.

Wide free-spectral-range triple ring resonator as optical filter

A waveguide-based wide free-spectral-range (FSR) triple ring resonator (TRR) as an optical filter has been investigated in this article. The transmittance of the TRR is presented in Z-domain. The delay line signal processing approach and Mason's gain formula have been used to develop the transmittance of the TRR. The TRR in the article is capable of providing an FSR up to 605 GHz with lower crosstalk limited within -10 dB. Another efficacious scheme of TRR with much wider FSR of 1029 GHz and with reduced unit delay length is presented in the article. Here also crosstalk, as well as resonance loss, remains within reasonable limits. The FSRs obtained using the present TRR architectures in this work are until now reported as maximum for a corresponding class of optical ring resonators. The issues of group delay and dispersion, two important parameters associated with high frequency optical communication have been addressed in this article.

Compact Form of Mason's Gain Formula for Signal Flow Graphs

Mason's gain formula requires combining all paths and all loops judiciously. New techniques are presented in this paper to do this. All possible non-touching loop combinations can be generated systematically and represented compactly using a tree structure and/or factoring technique. Both numerator and denominator of the formula can be treated identically. The approach is simple enough to be used in teaching students Mason's gain formula as part of courses in control systems, digital signal processing, graph theory and applications, among others.

Small signal modelling of open-loop SEPIC converters

This study presents the application of a signal flow graph and the Mason's gain formula for deriving small signal models of open-loop single ended primary inductance converter (SEPIC) converters. The control to output and the input to output transfer functions are derived. Conventional modelling methods using the averaging and small signal linearisation techniques are powerful for basic converters like buck and boost. However, for high-order converters like SEPIC, solving of high-order symbolic equations becomes complex and difficult. In this study, the application of the signal flow graph and the Mason's gain formula help the manipulation of equations. Thus, derivation of small signal models can be easily carried out in detail. Theoretical and measured results are shown to verify the accuracy of the derived small signal models.

On distributional robustness of systems with complex uncertainty

The main result of this paper addresses the minimum and maximum expected values of a gain measure for the transfer function of a system which depends on a vector Δ of independent random complex gains. In the distributional robustness framework of this paper, the probability density function for Δ is not completely specified. It is assumed only that the distribution of each component Δ i is non-increasing with respect to | Δ i | , radially symmetric and supported on the disc of radius r i centered at zero in the complex plane. Under these conditions, the expected value of the magnitude-squared of the gain function at a fixed frequency ω ⩾ 0 is shown to be maximized when each Δ i is uniformly distributed over the disc of radius r i and minimized when each Δ i has the impulse distribution. This result is extended to show that an H 2 measure of the gain is also maximized and minimized in the same way. These results apply to quotients of multilinear functions of Δ , which includes system transfer functions obtained using Mason's gain formula.

Control theory applications to the production–inventory problem: a review

Mathematical models based on average or steady-state conditions are insufficient when dealing with dynamic situations faced by production–inventory systems in current business environments. Therefore, the use of mathematical tools based on control theory to handle time-varying phenomena has been reinvigorated in order to accommodate these new needs. Given the variety of research approaches in the field over several decades, there is a need to provide a review of this work. This review identifies some major research efforts for applying control theoretic methods to production–inventory systems. It is shown that in general, control theory is applied to reduce inventory variation, reduce demand amplification and optimize ordering rules. Some control theory tools applied are block diagram algebra, Mason's gain formula, Bode plots, Laplace transform, Z transform and optimal control. Basic approaches are classified within stochastic control theory and deterministic control theory. Two important issues are then identified within the deterministic models. First, separate efforts to integrate systems horizontally (i.e. supply chain) or vertically (i.e. hierarchical approach) are identified. Second, none of the reviewed models implemented a systematic way to calculate all the required model parameters. Some authors presented suggestions to optimize some parameters, but no reference was found that tried to obtain these parameter values from a real system.

Modeling of closed-loop voltage-mode controlled interleaved dual boost converter

An extensive small-signal analysis of a voltage-mode controlled interleaved dual boost (IDB) converter operating in continuous current mode based on signal flow graph approach is proposed. Small-signal flow graph is developed, from which open-loop small-signal transfer functions are derived using well known Mason's gain formula. Closed-loop small-signal input-to-output, control-to-output transfer functions are also derived and frequency response characteristics are determined at different duty ratios. Voltage-mode compensator designed using K-factor approach is used for closed-loop operation of IDB converter. Load voltage regulation against supply voltage and load disturbances are demonstrated through experimental results.

Small‐signal analysis of interleaved dual boost converter

AbstractThis paper presents a systematic development of steady‐state, small‐signal models of interleaved dual boost converter operating in a continuous current mode. These models are derived by employing the well‐known signal flow graph method. This signal flow graph approach provides a means to directly translate the switching converter into its equivalent graphic model, from which a complete behaviour of the converter can easily be studied. Steady‐state performance, small‐signal characteristic transfer functions are derived using Mason's gain formula. The bode plots of audiosusceptibility, input impedance, output impedance, and control‐to‐output transfer functions are determined and illustrated using MATLAB for different values of load resistances, duty ratios. Small‐signal frequency responses obtained from the signal flow graph method are validated with PSPICE simulator results. To validate the signal flow graph modelling equations, sample steady‐state experimental results are provided. Copyright © 2001 John Wiley & Sons, Ltd.

Bond graphs II: Causality and singularity

The concepts of causality and singularity for bond graphs are defined, and related through the idea of a singular (or nonsingular) causal assignment, which is one with zero (or nonzero) discriminant. Necessary and sufficient conditions are given for a bond graph to have a causal assignment. It is proved that every acausal bond graph is acausally equivalent to a nonsingular bond graph, and that every nonsingular acausal bond graph has at least one nonsingular causal assignment for each consistent choice of input variables. The strong components of a causal bond graph B are defined, and it is shown that the discriminant of B is the product of the discriminants of its strong components; in particular, a causal assignment is singular if and only if there is at least one singular strong component. The reduced bond graph R( B) of B is defined and, if B is nonsingular, R( B) is proved to be acausally equivalent to B. Mason's determinant rule and the Mason gain formula are proved, and a simpler way of calculating the discriminant is derived.

Realization of separable first- and second-order 2-D all-pass digital filters

The authors give structures realizing first- and second-order, separable, 2-D, all-pass digital filters. The method employs signal flow graph technique and S.J. Mason's gain formula to obtain the transfer function. The realizations obtained are minimal delay and minimal multiplier structures.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

MASON--Frequency-response program for continuous and discrete control systems

MASON is a frequency-response computer program useful in the design and analysis of linear control systems. Complex signal flow graphs involving either Laplace- or z -transform transmittances are reduced via a computational algorithm based on Mason's Gain Formula. Continuous-time systems are evaluated with s = jw , and discrete-time systems use z = \exp(sT) . The transmittances may include polynomial expressions, transport lags, or actual gain/ phase data from experimental testing. The input structure is user-oriented, providing for simple transfer-function representation between nodes. Frequency response, resonant peak, resonant frequency, and gain and phase margins are calculated where appropriate, and form the program output.

General Method for Calculating the Spectrum of a Zero Substitution Coded Signal

This paper describes a general method for calculating the power spectra of zero substitution coded signals and applies this method to calculate the B3ZS signal spectrum of the DS-3. Many digital radio systems transmit a signal which consists of DS-3 level baseband signals. Therefore, knowledge of the B3ZS spectral characteristics is important in DS-3 level interference and systems studies. The method used for calculating spectral densities of substitution coded signals is based on signal-flow graph analysis. While signal-flow graph identities and Mason's gain formula have been used in the past in the calculation of some substitution coded spectra, they become unduly cumbersome when applied towards complex spectra such as that of the B3ZS signal. In place of the graph identities and gain formula, two matrix techniques are introduced that can be used in general to simplify spectral calculations for substitution coded signals. The methodology used in analyzing these communication signals can also be applied to other related fields such as coding of signals for magnetic recordings.

On the steady-state analysis of the inverter-fed induction motor

The analysis of the induction motor based on the signal flow graphs is carried out. It is shown that the state transition matrix can be determined in a systematic and straightforward way using Mason's gain formula. This method is found computationally very much superior to other methods available in the literature. There is a considerable reduction in the CPU time. The presence of an input signal also does not pose any problems, as inherently the transition signal flow graph includes its effect also.