chap19.pdf

Resonant Conversion

Part V of this text deals with a class of converters whose operation differs significantly from the PWM

converters covered in Parts I to IV. Resonant power converters [1–36] contain resonant L–C networks

whose voltage and current waveforms vary sinusoidally during one or more subintervals of each switch-

ing period. These sinusoidal variations are large in magnitude, and hence the small ripple approximation

introduced in Chapter 2 does not apply.

Dc-to-high-frequency-ac inverters are required in a variety of applications, including electronic

ballasts for gas discharge lamps [3,4], induction heating, and electrosurgical generators. These applica-

tions typically require generation of a sinusoid of tens or hundreds of kHz, having moderate or low total

harmonic distortion. A simple resonant inverter system is illustrated in Fig. 19.1(a). A switch network

produces a square wave voltage As illustrated in Fig. 19.2, the spectrum of contains fundamen-

tal plus odd harmonics. This voltage is applied to the input terminals of a resonant tank network. The

tank network resonant frequency is tuned to the fundamental component of that is, to the switch-

ing frequency and the tank exhibits negligible response at the harmonics of . In consequence, the

tank current as well as the load voltage v ( t ) and load current i ( t ), have essentially sinusoidal wave-

forms of frequency with negligible harmonics. By changing the switching frequency (closer to or

further from the resonant frequency the magnitudes of v ( t ) , and i ( t ) can be controlled. Other

schemes for control of the output voltage, such as phase-shift control of the bridge switch network, are

also possible. A variety of resonant tank networks can be employed; Fig. 19.1(b) to (d) illustrate the well-

known series, parallel, and LCC tank networks. Inverters employing the series resonant tank network are

known as the series resonant, or series loaded, inverter. In the parallel resonant or parallel loaded

inverter, the load voltage is equal to the resonant tank capacitor voltage. The LCC inverter employs tank

capacitors both in series and in parallel with the load.

Figure 19.3 illustrates a high-frequency inverter of an electronic ballast for a gas-discharge

lamp. A half-bridge configuration of the LCC inverter drives the lamp with an approximately sinusoidal

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Resonant Conversion

707

high-frequency ac waveform. The converter is controlled to provide a relatively high voltage to start the

lamp, and a lower voltage thereafter. When the ballast is powered by the ac utility, a low-harmonic recti-

fier typically provides the input dc voltage for the inverter.

A resonant dc–dc converter can be constructed by rectifying and filtering the ac output of a res-

onant inverter. Figure 19.4 illustrates a series-resonant dc-dc converter, in which the approximately sinu-

soidal resonant tank output current is rectified by a diode bridge rectifier, and filtered by a large

capacitor to supply a dc load having current I and voltage V. Again, by variation of the switching fre-

quency (closer to or further from the resonant frequency the magnitude of the tank current

and hence also the dc load current I , can be controlled. Resonant dc–dc converters based on series, paral-

lel, LCC, and other resonant tank networks are well understood. These converters are employed when

specialized application requirements justify their use. For example, they are commonly employed in high

voltage dc power supplies [5,6], because the substantial leakage inductance and winding capacitance of

high-voltage transformers leads unavoidably to a resonant tank network. The same principle can be

employed to construct resonant link inverters or resonant link cycloconverters [7–9]; controllable switch

networks are then employed on both sides of the resonant tank network.

Figure 19.5 illustrates another approach to resonant power conversion, in which resonant ele-

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Resonant Conversion

ments are inserted into the switch network of an otherwise-PWM converter. A resonant switch network,

or quasi-resonant converter, is then obtained. For example, in Fig. 19.5(b), resonant elements and

are combined with the switch network transistor and diode. The resonant frequency of these elements is

somewhat higher than the switching frequency. This causes the switch network waveforms and

to become quasi-sinusoidal pulses. The resonant switch network of Fig. 19.5(b) can replace the PWM

switch network of Fig. 19.5(a) in nearly any PWM converter. For example, insertion of the resonant

switch network of Fig. 19.5(b) into the converter circuit of Fig. 19.5(c) leads to a quasi-resonant buck

converter. Numerous resonant switch networks are known, which lead to a large number of resonant

switch versions of buck, boost, buck–boost, and other converters. Quasi-resonant converters are

described in Chapter 20.

The chief advantage of resonant converters is their reduced switching loss, via mechanisms

known as zero-current switching (ZCS), and zero-voltage switching (ZVS). The turn-on and/or turn-off

transitions of the various converter semiconductor elements can occur at zero crossings of the resonant

converter quasi-sinusoidal waveforms. This eliminates some of the switching loss mechanisms described

in Chapter 4. Hence, switching loss is reduced, and resonant converters can operate at switching frequen-

cies that are higher than in comparable PWM converters. Zero-voltage switching can also eliminate some

of the sources of converter-generated electromagnetic interference.

Resonant converters exhibit several disadvantages. Although the resonant element values can be

chosen such that good performance with high efficiency is obtained at a single operating point, typically

it is difficult to optimize the resonant elements such that good performance is obtained over a wide range

of load currents and input voltages. Significant currents may circulate through the tank elements, even

when the load is removed, leading to poor efficiency at light load. Also, the quasi-sinusoidal waveforms

of resonant converters exhibit greater peak values than those exhibited by the rectangular waveforms of

PWM converters, provided that the PWM current spikes due to diode stored charge are ignored. For

19.1 Sinusoidal Analysis of Resonant Converters

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these reasons, resonant converters exhibit increased conduction losses, which can offset their reduced

switching losses.

In this chapter, the properties of the series, parallel, and other resonant inverters and dc–dc con-

verters are investigated using the sinusoidal approximation [3, 10–12]. Harmonics of the switching fre-

quency are neglected, and the tank waveforms are assumed to be purely sinusoidal. This allows simple

equivalent circuits to be derived for the bridge inverter, tank, rectifier, and output filter portions of the

converter, whose operation can be understood and solved using standard linear ac analysis. This intuitive

approach is quite accurate for operation in the continuous conduction mode with a high- Q response, but

becomes less accurate when the tank is operated with a low Q -factor or for operation of dc–dc resonant

converters in or near the discontinuous conduction mode.

For dc–dc resonant converters, the important result of this approach is that the dc voltage con-

version ratio of a continuous conduction mode resonant converter is given approximately by the ac trans-

fer function of the tank circuit, evaluated at the switching frequency. The tank is loaded by an effective

output resistance, having a value nearly equal to the output voltage divided by the output current. It is

thus quite easy to determine how the tank components and circuit connections affect the converter behav-

ior. The influence of tank component losses, transformer nonidealities, etc., on the output voltage and

converter efficiency can also be found. Several resonant network theorems are presented, which allow the

load dependence of conduction loss and of the zero-voltage- or zero-current-switching properties to be

explained in a simple and intuitive manner.

It is found that the series resonant converter operates with a step-down voltage conversion ratio.

With a 1:1 transformer turns ratio, the dc output voltage is ideally equal to the dc input voltage when the

transistor switching frequency is equal to the tank resonant frequency. The output voltage is reduced as

the switching frequency is increased or decreased away from resonance. On the other hand, the parallel

resonant converter is capable of both step-up and step-down of voltage levels, depending on the switch-

ing frequency and the effective tank Q -factor. The exact steady-state solutions of the ideal series and par-

allel resonant dc–dc converters are stated in Section 19.5.

Zero-voltage switching and zero-current switching mechanisms of the series resonant converter

are described in Section 19.3. In Section 19.4, the dependence of resonant inverter properties on load is

examined. A simple frequency-domain approach explains why some resonant converters, over certain

ranges of operating points, exhibit large circulating tank currents and low efficiency. The boundaries of

zero-voltage switching and zero-current switching are also determined.

It is also possible to modify the PWM converters of the previous chapters, so that zero-current

or zero-voltage switching is obtained. A number of diverse approaches are known that lead to soft switch-

ing in buck, boost, forward, flyback, bridge, and other topologies. Chapter 20 summarizes some of the

well-known schemes, including resonant switches, quasi-square wave switches, the full-bridge zero-volt-

age transition converter, and zero-voltage switching in forward and flyback converters containing active-

clamp snubbers. A detailed description of soft-switching mechanisms of diodes, MOSFETs, and IGBTs

is also given.

19.1

SINUSOIDAL ANALYSIS OF RESONANT CONVERTERS

Consider the class of resonant converters that contain a controlled switch network that drives a linear

resonant tank network In a resonant inverter, the tank network drives a resistive load as in Fig. 19.1.

The reactive component of the load impedance, if any, can be effectively incorporated into the tank net-

work. In the case of a resonant dc–dc converter, the resonant tank network is connected to an uncon-

trolled rectifier network filter network and load R, as illustrated in Fig. 19.4. Many well-known

converters can be represented in this form, including the series, parallel, and LCC topologies.

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