State-plane Diagram Research Articles

The Multiresonant Converter Steady-State Analysis Based on Dominant Resonant Process

The steady-state analysis of the multiresonant converter is presented. The multiresonant converter utilizes multielement resonant network that consists of resonant inductor and switch capacitances. The resonant process between resonant inductor and capacitances across rectifiers has been found as dominant resonant process. All key circuit parameters are normalized in terms of the characteristic impedance and resonant frequency given by resonant inductor and capacitances across rectifiers. The effects of the transformer magnetizing and leakage inductances have been analyzed. It is shown that dc output values and resonant current rms value strongly depend on load and switching frequency to resonant frequency ratio. It is shown that the resonant process of the resonant inductor and MOSFET output capacitances have no significant influence on overall dc conversion ratio at heavy loads. The simplified analysis is presented and resonant tank order is reduced. The circuit utilizes four different modes of operation. In each mode of operation, the 2-D state-plane diagram is derived. The dc conversion ratio, normalized rms MOSFET, and rectifier capacitance currents have been calculated. A 2.5-kW prototype has been built and tested.

A generalized program for extracting the control characteristics of resonant converters via the state-plane diagram

This paper presents a generalized computer program that can be used to derive the control characteristics of resonant power converters from their state-plane trajectories. It has been shown that the geometrical properties of the state-plane trajectory can be used to derive the control characteristics of a given resonant power converter topology. These characteristics are essential in determining the design parameters such as the power converter gain, component stresses and the required feedback controller. The main program consists of several subroutines each of which is associated with a segment of the state-plane trajectory. Such a program will make it faster and easier for a design engineer to obtain the design parameters of any given resonant topology. >

Small signal analysis of the LCC-type parallel resonant converter

In this paper, the small signal analysis of the LCC-type parallel resonant converter (LCC-PRC) operating in the continuous conduction mode is given. This analysis is based on both the state-plane diagram, which has been successfully used to obtain the steady state response for resonant converters, and the Taylor series expansion. Applying perturbation directly to the steady state trajectory, a discrete small signal model for the converter can be derived in terns of the input voltage, switching frequency, and the converter state variables. Based on this analysis, closed-loop form solutions for the input-to-output and control-to-output transfer functions are derived. It is shown that the theoretical and computer simulation results are in full agreement.

State-plane approach for the analysis of half-bridge parallel resonant converters

Generalised state-plane analysis for a half-bridge parallel resonant converter (PRC) operating in continuous conduction mode is presented. It is shown that a PRC circuit of any order can be analysed in terms of simple two-dimensional state-plane diagrams, without having to use any sinusoidal approximation. The approach presented makes use of the state-variable transformation technique previously used for the analysis of second- and third-order resonant converters. This method is applied to a specific example of a sixth-order parallel resonant converter operated in the continuous conduction mode.

Analysis and implementation of a full-bridge constant-frequency LCC-type parallel resonant converter

A comprehensive analysis of the full-bridge constant-frequency LCC-type parallel resonant converter (LCC-PRC) is presented. Owing to operation under constant frequency, the filter designs are simplified and utilisation of magnetic components are improved. The LCC-PRC takes on the desirable characteristics of the pure series and the pure parallel converter, thus removing the main disadvantages. A useful analytic technique, based on classical AC complex analysis, is introduced for designing the LCC-PRC. By using a proper transformation on the state variable, the converter is analysed by means of a two-dimensional state-plane diagram, which shows that the converter possesses three operation modes (I, II, III). It is shown that operating the converter in mode II provides the desirable higher efficiency for a wide load range. A CPU (8031) is used to control the phase-shift time. Its control characteristic is very accurate and the cost is low. Finally, a constant-frequency controlled full-bridge LCC-type parallel resonant converter (LCC-PRC) using the CPU (8031) control is implemented.

Generalized approach to the small signal modelling of DC-to-DC resonant converters

A generalized small-signal analysis approach that is based on both the Taylor's series expansion and the state-plane diagram is presented. A generalized discrete small-signal model for a double-ended DC-to-DC resonant converter operating in the continuous conduction mode is also given. Based on the model derived, the frequency responses for two transfer functions, namely, the line-to-output and the control-to-output transfer functions, are obtained. The technique is verified by applying it to the conventional series resonant converter whose small-signal analysis is known. >

Frequency response for the conventional parallel resonant converter based on the state-plane diagram

The small-signal analysis of the conventional parallel resonant converter (PRC) operating in the continuous conduction mode is given. This analysis is based on the state-plane approach that has been successfully used to obtain the steady-state response for resonant converters. Applying perturbation directly to the steady-state trajectory, a discrete small-signal model for the converter can be derived in terms of the input voltage, switching frequency, and the converter state variables. Furthermore, this method can be applied to resonant converters in general, regardless of the order of their resonant tanks. Based on the derived closed-form solution, the frequency responses of input-to-output and control-to-output transfer functions are obtained. Computer simulation and experimental results are reported.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Series resonant converter with third-order commutation network

To compensate for the poor output voltage regulation of the series resonant converter (SCR), a converter is derived by adding an inductor in parallel with the resonant capacitor of the conventional SCR. The resulting converter is called the LLC-SRC. This converter is analyzed via a two-dimensional state-plane diagram through a proper transformation of its state variables. Based on the analysis results, a set of characteristic curves is derived showing that the control characteristics and component stresses of the new converter are improved compared with those of a conventional SRC. Based on these curves, the design procedure for the LLC-SRC is formulated. The experimental results from the breadboard model were used to verify the theoretical work. >

Steady-state analysis of the parallel resonant converter with LLCC-type commutation network

A novel converter topology known as LLCC-type parallel resonant converter (PRC-LLCC), in which the tank circuit consists of two inductors and two capacitors, is introduced. Using the state-plane approach, the steady-state analysis of the PRC-LLCC operating in the continuous conduction model is carried out. It is shown that by using the state variable transformation technique the steady-state response of the converter can be represented by two state-plane diagrams. Using these diagrams and the circuit equations, a set of control characteristic curves which are useful for converter design is derived. Based on these curves, a design procedure along with a specific design example is given. The correctness of the analysis results is verified via computer simulations.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

State plane approach to frequency response of resonant convertors

The steady state response of a resonant convertor can be represented graphically by the state plane diagram. On using the perturbation method on the steady state trajectory, a discrete small signal model for the convertor can be derived from the input voltage, controlled switching frequency and state variable perturbations. The conventional series resonant convertor is used as an example to demonstrate an analytical approach. However, this method of analysis can be applied to resonant convertors in general. From the small signal model derived, the frequency response of the convertor can be calculated.

High-frequency link parallel resonant convertor with fourth-order commutation network

A technique of steady-state analysis for the fourth-order parallel resonant convertor circuit is proposed. The method makes use of the two-dimensional state-plane diagram that has been used successfully to analyse resonant convertors of lower order. Our theoretical results are verified by computer simulations.

Nonresonant and resonant coupled zero voltage switching converters

Two zero-voltage switching power converters with nonresonant and resonant coupling are presented. These are high-order multiple resonant converters in which the circuit modes associated with the converter operation may have different resonant frequencies. The steady-state responses of these converters are derived in terms of state-plane diagrams by using proper state variable transformations. It is shown that the converters have all the desirable features for high-frequency applications and overcome the drawback of load-range limitation of zero-voltage switching associated with the conventional class-E converter.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

High-frequency high-order parallel resonant converter

A novel approach to the analysis of design of a high-order high-frequency LCC-type capacitive coupled parallel resonant converter (PRC-LCC) operated in the continuous-conduction mode is presented. The presence of an additional capacitor in series with the inductance of the conventional PRC results in a converter with more desirable control characteristics. It is shown that, at switching frequencies lower than the resonant frequency, the gain of the LCC-type converter is lower than the grain of the conventional PRC. This facilitates the converter design with a lower turn-ratio transformer and therefore allows for a higher operating frequency. The complete state-plane diagram of the LCC-type converter, from which a set of steady-state characteristic curves is plotted, is given. Various design curves for component value selections and device ratings are given. A design example with computer simulation results is presented. >

Parallel resonant converter with LLC-type commutation

It is shown that by using a proper transformation of state variables, the third-order system of the parallel resonant converter (PRC) with LLC-type commutation can be analyzed by means of a two-dimensional state-plane diagram. A set of characteristic curves which can be used for the converter design is derived from the analysis. It is shown from these curves that the converter possesses more desirable features than the conventional PRC. >

Design of parallel resonant convertor with LCC-type commutation

Using a set of characteristic curves derived from the stateplane diagram, a novel approach to the design of the LCCtype capacitive coupled parallel resonant convertor (LCC-type PRQ, operating in the continuous conduction mode, is presented. The steady-state response of the convertor can also be obtained from the characteristic curves, from which the convenor's component stress can be easily assessed.

Comparison of performance characteristics between LLC-type and conventional parallel resonant convertors

By using a proper transformation of state variables, the third-order system of the parallel resonant convertor with LLC-type commutation (PRC-LLC) can be analysed by means of a two-dimensional state-plane diagram. A set of characteristic curves is derived from the analysis, based on which a comparison between the present convertor and the conventional PRC is given. It is concluded from our results that the convertor possesses more desirable features than the conventional PRC.

Analysis and Design of Series Resonant Converter by State-Plane Diagram

Analysis based on the state-plane diagram is given for series resonant converters operating in the frequency range 0.5 ? fs/fo ? 1.0. When the voltages and currents in the converter are normalized, design parameters take on special geometric meanings in the normalized state diagram. Examples of converter design using graphical methods are given for the cases of ? and ? control. Control characteristics of the converter operating in the continuous conduction mode are derived. The concept of the energy reflection coefficient is introduced as a measure of power transfer efficiency in the converter design.

Design of series-resonant convertor with normalised state-plane diagram

Using the normalised state-plane diagram, a novel approach to series-resonant convertor design is described. The design procedure as well as steady-state responses are given for convertors operated in the frequency range 0.5≤fs/fO≤1.