Mason's Gain Research Articles

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.

Analysis of the modified MOS Wilson current mirror: a pedagogical exercise in signal flow graphs, Mason's gain rule, and driving-point impedance techniques

A pedagogical analysis of the modified MOS Wilson current mirror using signal flow graphs (SFGs), Mason's gain rule and driving-point impedance (DPI) techniques is presented as an exercise for undergraduate electrical engineering students learning to analyze transistor-level circuits with multiple-feedback loops. While students often prefer the SFG representation for single feedback loops, they often abandon it in favor of the more familiar nodal analysis methods for multiple loops. Yet these methods can be long and cumbersome and contribute little to intuition. In an attempt to preserve the intuitive grasp of tradeoffs, this paper presents an exercise of several well-established analytical techniques for generating and analyzing SFGs. The modified Wilson current mirror is used to compare three analytical approaches: (1) fundamental laws with brute-force algebra; (2) fundamental laws with Mason's gain rule; and (3) DPI technique with Mason's gain rule. The concepts reinforced in this paper include: (1) tradeoffs between gain and other quantities such as output resistance or bandwidth; (2) how Mason's gain rule simplifies the analysis of closed-loop gain; and (3) how DPI techniques simplify the generation of SFGs.

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.

Gain partitioning: a new approach for analyzing the high-frequency performance of compound semiconductor FETs

A novel approach for analyzing the high-frequency performance of compound semiconductor FETs is presented. The approach is based on a circuit description that separates intrinsic and parasitic circuit elements of active devices in a general way. Mason's gain (U) and current gain (A/sub i/) are used to illustrate this approach. Significant results from U are related to a more commonly used nomenclature involving maximum stable gain and maximum available gain and, in particular, to the transition from a potentially unstable device to a potentially stable device. Results show that the requirements for maximizing these cutoff frequencies are different. Minimized parasitic circuit elements maximize f/sub tau /. A maximized f/sub max/, on the contrary, may be obtained if interactions of parasitic and intrinsic circuit elements satisfy certain conditions. >

Reconciliation of methods for estimating f/sub max/ for microwave heterojunction transistors

An attempt is made to reconcile the various approaches that have recently been used to estimate the maximum frequency of oscillation f/sub max/ in high-performance AlGaAs/GaAs HBTs. f/sub max/ is computed numerically from the full expression for Mason's invariant gain using y-parameters derived from the different approaches, i.e., the hybrid- pi equivalent circuit, the T-equivalent circuit, and the drift-diffusion equations. It is shown that the results for f/sub max/ are essentially the same, irrespective of the source of the y-parameters, provided that the phase delays due to transit of carriers across the base and the collector-base depletion region are properly accounted for. It is also shown, for the particular device studied, that the widely used analytical expression for f/sub max/, involving f/sub T/ and effective base resistance and collector capacitance, is remarkably accurate for frequencies below those at which transit-time effects become important. >

Comments on "Unilateral gain of heterojunction bipolar transistors at microwave frequencies

A general expression for Mason's gain U is derived and expressed in the linear two-port h parameters of a network. In a recent paper by S. Prasad et al. (ibid., vol.35, no.12, 1988, p.2288-94) an incorrect expression for U is presented. The commenter shows that the two expressions are equal at only one frequency, f/sub max/, i.e. when U is solved for U=1.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

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.

Signal flow graphs-Computer-aided system analysis and sensitivity calculations

Concepts which promise to extend many fundamental results of network theory to general systems are introduced. The basis for these extensions is the introduction of two matrices, the summing matrix S and the branching matrix B, which completely describe the topology of a signal flow graph. This leads to a formulation of system equations in terms of submatrices of the S- and B-matrices suitable for digital-computer programming. Consequently, many computer-aided circuit analysis and design programs can now be employed for the computer-aided analysis and design of systems representable by signal flow graphs. This formulation also leads to a straightforward algorithm for obtaining the system gain, an alternate to using Mason's gain formula. Furthermore, the power of this formulation, and its strong relation to network theory, is demonstrated by the derivation of a theorem similar to Tellegen's theorem in network theory. The theorem depends only on the topological properties of the summing and branching matrices and not on the functional relationships between the branch

Simple derivation of Chen's multiple-node removal algorithm

A new and simple derivation of Chen's multiple-node removal algorithm is given, starting from signal-flowgraph equations and using only Mason's gain formula.

Formulation of the state equations for active degenerate RLC network by signal flow graph†

Abstract In this paper a method of drawing the signal flow graph of an active degenerate RLC network is given. From this signal flow graph the state equations of the network are obtained using Mason's graph gain formula.

A simple derivation of Mason's gain formula

A simple derivation of Mason's gain formula