A general unified approach to modelling switching DC-to-DC converters in discontinuous conduction mode

A method for modelling switching converters in the discontinuous conucction mode is developed, whose starting point is the unified state-space representation, and whose end results is a complete linear circuit model which correctly represents all essential features, namly, the input, output, and transfer properties (static dc as well as dynamic ac small signal). While the method is generally applicable to any switching converter operating in the discontinuous conduction mode, it is extensively illustrated for the three common power stages (buck, boost, and buck-boost). The results for these converters are then easily tabulated owing to the fixed equivalent circuit topology of their canonical circuit model. The outlined method lends itself easily to investigation of the discontinuous conduction mode in more complex structures (cascade connection of buck and boost converters, for example), in which more thean one inductor current may become discontinuous. As opposed to other modelling techniques, the new method considers the discontinuous conduction mode as a special case of the continuous conduction mode

Modeling and Analysis of Power Processing Systems (MAPPS), initial phase 2

The overall objective of the program is to provide the engineering tools to reduce the analysis, design, and development effort, and thus the cost, in achieving the required performances for switching regulators and dc-dc converter systems. The program was both tutorial and application oriented. Various analytical methods were described in detail and supplemented with examples, and those with standardization appeals were reduced into computer-based subprograms. Major program efforts included those concerning small and large signal control-dependent performance analysis and simulation, control circuit design, power circuit design and optimization, system configuration study, and system performance simulation. Techniques including discrete time domain, conventional frequency domain, Lagrange multiplier, nonlinear programming, and control design synthesis were employed in these efforts. To enhance interactive conversation between the modeling and analysis subprograms and the user, a working prototype of the Data Management Program was also developed to facilitate expansion as future subprogram capabilities increase

Modelling and analysis of switching DC-to-DC converters in constant-frequency current-programmed mode

An analysis of dc-to-dc switching converters in constant-frequency current-programmed continuous conduction mode is performed, and leads to two significant results. The first is that a ramp function, used to eliminate a potential instability, can be chosen uniquely to assure both stability and the fastest possible transient response of the programmed current. The second is the development of an extension of the state-space averaging technique by means of which both the input and output small-signal properties of any such converter may be accurately represented by a linear small-signal equivalent-circuit model. The model is presented and experimentally verified for the cuk converter and for the conventional buck, boost, and buck-boost converters. All models exhibit basically a one-pole control-to-output transfer function response

General topological properties of switching structures

Investigation of a wide variety of switching converter topologies culminates in the establishment of the most general correlation between the converter topologies--the duality relationships. The recognition of this general law leads to a number of new results: new converter topologies generated by the application of the duality transformation to the existing converter configurations, the discovery of the new mode of converter operation (discontinuous capacitance voltage mode) as well as significantly improved understanding of the existing converters and their equivalent circuit models

Modelling, analyses and design of switching converters

A state-space averaging method for modelling switching dc-to-dc converters for both continuous and discontinuous conduction mode is developed. In each case the starting point is the unified state-space representation, and the end result is a complete linear circuit model, for each conduction mode, which correctly represents all essential features, namely, the input, output, and transfer properties (static dc as well as dynamic ac small-signal). While the method is generally applicable to any switching converter, it is extensively illustrated for the three common power stages (buck, boost, and buck-boost). The results for these converters are then easily tabulated owing to the fixed equivalent circuit topology of their canonical circuit model. The insights that emerge from the general state-space modelling approach lead to the design of new converter topologies through the study of generic properties of the cascade connection of basic buck and boost converters

Topics in multiple-loop regulators and current-mode programming

Some general considerations about multiple-loop feedback are discussed, and it is concluded that incorporation of a current-programmed power stage into a "new" power stage model is both justified and useful. A new circuit-oriented model of the current feedback path is derived which augments the well-known power stage canonical circuit model. The current loop gain, though wide-band, is always stable if the conventional stabilizing ramp is employed but has a relatively small low-frequency value. Consequently, the "new" power stage is more usefully modeled by a y-parameter model in which the current loop is not explicit. Expressions for the y parameters are given that are extensions of those previously derived. Another form of the model resembles the original canonical form for duty ratio programming, and shows that current programming effectively introduces lossless series damping that separates widely the two poles of the power stage LC filter. Therefore, although current programming tends to make the power stage output behave as a current source, the control-to-output voltage transfer function exhibits, in addition to the familiar dominant pole, a second pole at the current loop gain crossover frequency, which may lie anywhere from one-sixth to two-thirds of the switching frequency

Topics in multiple-loop regulators and current-mode programming

Some general considerations about multiple-loop feedback are discussed, and it is concluded that incorporation of a current-programmed power stage into a "new" power stage model is both justified and useful. A new circuit-oriented model of the current feedback path is derived which augments the well-known power stage canonical circuit model. The current loop gain, though wideband, is always stable if the conventional stabilizing ramp is employed, but has a relatively small low-frequency value. Consequently, the "new" power stage is more usefully modelled by a y parameter model in which the current loop is not explicit. Expressions for the y parameters are given that are extensions of those previously derived. Although current-programming tends to make the power stage output behave as a current source, the control to output voltage transfer function exhibits, in addition to the familiar dominant pole, a second pole at the current loop gain crossover frequency, which may lie from one-sixth to two-thirds of the switching frequency

Nonlinear Analysis and Control of Interleaved Boost Converter Using Real-Time Cycle to Cycle Variable Slope Compensation

Switched-mode power converters are inherently nonlinear and piecewise smooth systems that may exhibit a series of undesirable operations that can greatly reduce the converter's efficiency and lifetime. This paper presents a nonlinear analysis technique to investigate the influence of system parameters on the stability of interleaved boost converters. In this approach, Monodromy matrix that contains all the comprehensive information of converter parameters and control loop can be employed to fully reveal and understand the inherent nonlinear dynamics of interleaved boost converters, including the interaction effect of switching operation. Thereby not only the boundary conditions but also the relationship between stability margin and the parameters given can be intuitively studied by the eigenvalues of this matrix. Furthermore, by employing the knowledge gained from this analysis, a real-Time cycle to cycle variable slope compensation method is proposed to guarantee a satisfactory performance of the converter with an extended range of stable operation. Outcomes show that systems can regain stability by applying the proposed method within a few time periods of switching cycles. The numerical and analytical results validate the theoretical analysis, and experimental results verify the effectiveness of the proposed approach