D.C. Hamill

Modeling of chaotic DC-DC converters by iterated nonlinear mappings

In parameter ranges where conventional methods break down, DC-DC converters may be described by iterated mappings, a nonlinear discrete modeling technique. The underlying principles are explained and are applied to the example of a PWM-controlled buck converter. Stable behavior and bifurcations to chaos are predicted by numerical evaluation of the governing mapping and are confirmed by experiment. >

Instability, subharmonics and chaos in power electronic systems

The concept of chaos is applied to a variety of nonlinear power electronic circuits. With the onset of instability, the phenomena of subharmonics, quasi-periodicity, and chaos are predicted and observed. The following examples are dealt with: diodes with charge storage (with application to resonant converters); a ferroresonant circuit; a controlled thyristor rectifier circuit; and a Buck converter controlled by pulse-width modulation (PWM). The examples were chosen to model aspects of real power electronic systems. Analytical and experimental results demonstrate the complex nonlinear phenomena such as subharmonics, quasi-periodicity and chaos can arise in even the simplest systems. >

Subharmonics and chaos in a controlled switched-mode power converter

A difference equation is derived for the output current, at successive switch events, of a simple switching-regulator DC/DC converter using a pulsewidth modulator. Wideband feedback control of the nonlinear circuit leads to a one-dimensional return map of zigzag form from which a stability criterion is found. Operation in the unstable region is described and verified by numerical simulation. The system exhibits a noisy bifurcation, chaos and subharmonics. >

A 'zero' ripple technique applicable to any DC converter

Coupled magnetics filter techniques are important tools in a converter designers arsenal, but are not well understood. Evidence of this is one basic building block of coupled filters, reinvented numerous times during the past 65 years. A detailed analysis of coupled magnetics for DC-DC converters, based on a key building block, is given.

Analysis, simulation and experimental study of chaos in the buck converter

A buck DC-DC power converter, whose input voltage is controlled by naturally sampled, constant-frequency PWM (pulse width modulation), is operated in the continuous conduction mode. Two versions are treated, a first-order and second-order circuit. Their behavior is modeled analytically and numerically. For certain values of the circuit parameters instability occurs. Strange phenomena of multiple pulsing, shipped cycles, subharmonics, and chaos are predicted theoretically and observed experimentally, including a period-doubling route to chaos. There is good agreement between theory and experiment.<<ETX>>

Lumped equivalent circuits of magnetic components: the gyrator-capacitor approach

In place of the conventional reluctance-resistance analogy for forming lumped equivalent circuits of inductive components, a permeance-capacitance analogy is advocated. In this approach, magnetic paths are modeled by capacitive circuits and windings are represented by gyrator two-ports. The technique is applied to the integrated magnetics of a zero-ripple isolated Cuk DC-DC converter allowing its electrical and magnetic circuits to be simultaneously simulated with SPICE. >

Class DE inverters and rectifiers for DC-DC conversion

A new family of Class DE inverters and related rectifiers is presented. Based on the Class D RF inverter, the circuits feature Class E switching transitions (zero voltage, zero dv/dt), giving low switching losses despite device capacitance and stored charge, combined with low voltage stress. Matching between inverter and rectifier is considered, time reversal duality is introduced and a family of inverters and rectifiers is presented. The circuits should find application in megahertz DC-DC converters.

Calculation of the periodic spectral components in a chaotic DC-DC converter

A simple mapping is derived, which describes the behavior of a peak current-mode controlled boost converter operating chaotically. The invariant density of this mapping is calculated iteratively and, from this, the power density spectrum of the input current at the clock frequency and its harmonics are deduced. The calculation is presented, along with experimental verification. The possibility of a novel application of chaos-amelioration of power supply interference-is discussed,.

Gyrator-capacitor modeling: a better way of understanding magnetic components

Engineers new to power electronics often find magnetic components puzzling, especially multi-winding devices and integrated magnetics. Gyrator-capacitor modeling offers an alternative way of understanding such components. This tutorial paper begins with a review of the gyrator-capacitor approach, followed by some examples drawn from the field of DC-DC power conversion: a simple choke; a flyback-converter transformer; a pair of coupled chokes (in which the zero-ripple phenomenon is explained); and a two-output forward-converter transformer. Finally, core saturation is modeled by means of nonlinear capacitance and illustrated by SPICE simulation. Gyrator-capacitor modeling offers a unified, logical way of understanding the magnetic components commonly met with in power electronics.<<ETX>>

Learning about chaotic circuits with SPICE

A study of chaotic circuits is of educational value, both to students and to practicing engineers. Ten circuits that behave chaotically are simulated with SPICE, starting with simple abstract systems and preceding, via familiar circuits such as the monostable and the tuned amplifier, to a controlled DC-DC power converter. The examples show a variety of ways in which chaos can arise in analog electronic circuits. It is shown how SPICE may be used to produce Poincare sections of strange attractors, and bifurcation diagrams. >