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Bob Mammano

First let us defme a resonant converter as apower conditioning system which utilizes aresonant L-C circuit as a part of the powerconversion process. All resonant convertersoperate in essentially the same way: a squarepulse of voltage or current is generated by thepower switches and this is applied to a resonantcircuit. Energy circulates in the resonant circuitand some or all of it is then tapped off tosupply the output. While basically simple, thisprinciple can be applied in a wide variety ofways, creating a bewildering array of possiblecircuits and operating modes.

Introduction to Resonant Power

ConversionOver the years we have seen power condi-

tioning move from simple but extravagantlinear regulators, through early low frequencypulse-width modulated systems, to high fre-quency square wave converters which pack thesame power handling capabilities of earlierdesigns into a fraction of their size and weight.

Today, a new approach is upon us --theresonant mode converter --and while offeringnew benefits in performance, size, and cost, this

new technology brings with it an added dimen-sion of complexity. The purpose of this paperis to offer a means of categorizing and definingthe various topologies and operating modes ofresonant mode converters with the hope ofenhancing the capability for design, analysis,and evaluation of these new power systems.

LINEARREGULATORS 1960's-SIMPlE and earlier-POOR EFFICIENCY

SWITCHING EGULATORS 1970's-COMPlEX-HIGHEREFFICIENCY-DEMANDC CONTROlS-HIGHNOISE-SlOW RESPONSE

CURRENTMODECONTROl 1980's-IMPROVED EGULATION-BETTER ROTECTION-HIGHERBANDWIDTH

Fig. 3 -Basic Resonant Convelter

Resonant Converter AdvantagesBefore getting into these, however, let's

pause to review why we are even interested inresonant mode power conversion.

With the earliest switched-mode power con-verters, it became obvious that higher frequen-cies allow smaller L's and C's and this, in turn,should lead to smaller, lighter, and (hopefully)less costly systems. The down side to moving tohigher frequencies, however, are the problems

of greater susceptibility to parasitic capacitanceand leakage inductance, greater stress in theswitching devices, and increased EMI and RFI.A resonant mode system offers the potential ofachieving the benefits while sidestepping manyof the disadvantages of higher frequencies.With a resonant circuit in the power path, theswitches can be configured to operate at eitherzero current or voltage points in the waveform,greatly reducing their stress levels; the resonantsine wave minimizes higher frequency harmon-

Fig. 1 -Power System Development History

Fig. 2 -Power Supply Switching Freqzlencies

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Classifying Resonant ConvertersBefore attempting to classify resonant con-

verter topologies, it might be helpful to intro-duce the concept of Resonant Switches. Aresonant switch consists of a switching device(a transistor with a steering diode, for example)in combination with a two-element resonant

circuit. This resonant switch may be configuredin several different ways, some of which areshown in Figure 7, but they always perform thesame function as the conventional switch in asquare wave converter. It is a useful concept asmost resonant mode circuit topologies can bevisualized as a conventional PWM circuit withthe power switch replaced with a resonantswitch. We will discuss the operation of thevarious switch configurations in greater detailas we get into the circuit topologies but first,let's take an overview of some of the circuitODtiOns.

Fig. 4 -Resonant Converter Advantages

Fig. 5 -PWM vs. Resonant Switching

Fig. 7 -Resonant Switches

Fig. 6- Switchillg Stress and Switching Loss

ics reducing noise levels; and since the circuitnow requires inductance and capacitance, para-sitic elements may enhance rather than detractfrom circuit performance. With these benefits,power systems operating in the range of 500kHz to 2.0 MHz are now practical and -in fact-are already being produced by a few leadingedge manufacturers.

To bring some order and ease in understandingthe broad range of circuit choices which arepossible as we move to resonant mode opera-tion, it helps to establish a system to classifyresonant topologies by defIDing the followingoperating characteristics:

1. Is the load in series or in parallel with theresonant circuit elements?2. Is the control system a fIXed or variable

frequency type?3. Does current ( or voltage) in the resonant

circuit flow continuously or is it equal tozero for some portion of the switching cycle?

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Fixed or Variable FrequencyResonant converters may be configured for

either constant or variable frequency operation,but these choices infer significant differences intheir operation. Fixed frequency control sys-tems use conventional pulse width modulationto change the output in response to a control

input, as shown in Figure 10. This forces aflXed-frequency system to have at least onenon-zero switching transition and possibly two,thereby voiding one of the more significantreasons for choosing to use a resonant modetopology. This would usually preclude its useunless system considerations required a syn-chronized freQuency operation.

Fig. 10 -Fixed Frequency Resonance

Variable frequency operation, however,needs to be subdivided by the third classifica-tion: whether the resonant circuit current iscontinuous or discontinuous. A circuit operatingin the continuous resonant mode uses the slopeof the resonant circuit impedance curve to

Fig. 8 -Classifying Resonant Converters

For discontinuous operation, it is also im-portant to know:

4. Is the switching designed for zero current orzero voltage activation, and

5. Does the energy in the resonant circuit flowin only one direction or is there a full cyclebefore it returns to stop at zero?

The general properties of any resonant con-verter are completely dependent on theseoptions, so they are a good basis to use as astarting point in understanding the principlesinvolved.

Series or Parallel LoadingSince reson~t converters operate by putting

energy into a resonant circuit and then trans-ferring some or all of it into the load, we needto know that there are two ways this may beaccomplished as shown in Figure 9. If the loadis in series with the resonant circuit elements,as in Fig. 9A, we call it a series loaded conver-ter and the operating characteristics tend

toward a current source with a high impedanceoutput.

Parallel loading is the opposite, with a lowimpedance voltage source output as shown inFig. 9B. Both modes have application to powersystems with high voltage outputs usually usingseries loaded current source drive and lowvoltage supplies using parallel loading.

L--I'Y'm-

A. SERIES LDADING(current output)

RLJf

Fig. 9 -Resonant Mode Loading

Fig. 11- Variable Frequency ContinuousResonance

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but even within this class there are still manyvariations in circuit operation.

As indicated in Figure 12, quasi-resonantcircuit waveforms are not sinusoidal, but havetwo essentially linear portions interspersed withtwo sinusoidal portions.

A quasi-resonant converter control loop isusually conJigured as shown in Figure 13 witha pulse generator driving the resonant circuitat a repetition rate defmed by the controlcircuit. The pulse generator may be set forconstant pulse width -defmed by the resonantcircuit -or set to sense zero crossing of eithercurrent or voltage. With maximum loading andlow line voltage, a quasi-resonant converter canapproach continuous resonance as a lintit whenthe individual oulses run together .

control the output. As shown in Figure 11, thecircuit can operate either above or belowesonance but the principle is the same: thathe control circuit changes the frequency to

move either toward or away from resonance,and thereby controls the amount of energywhich is transferred into the resonant circuit -and therefore to the load.

While many practical systems have usedontinuous conduction, variable frequency oper-

ation, there are several disadvantages:

1. The non-zero switching adds stress to thetransistors.

. As the frequency approaches resonance,peak currents or voltages can get very high,adding stress to the resonant components.

. The control transfer function is very non-linear following the resonant impedancecurve.

The major advantage of the continuousmode of operation is that the frequency varies

ver a much smaller range than with the dis-ontinuous mode.

Discontinuous ResonanceThe discontinuous operating mode works by

upplying constant packets of energy to theoad with the rate, i.e. frequency, determinedy load power demand.

Perhaps the most popular and importantlass of resonant converters with variablerequency and discontinuous current is oftenalled Quasi-Resonance. Most of the remainingortion of this discussion will be orientedoward this Quasi- Resonant converter category

Fig. 13 -Quasi-Resonant Control

Within the variable frequency, discontinuousmode of operation there are two remainingdecisions a designer must make which will havesignificant effect on the characteristics of his

power supply:

Zero-Current or Zero-Voltage

SwitchingSince reducing the stress on the switching

components is a major incentive for resonantoperation, we need to understand ways inwhich that might be accomplished. The mostcommon approach, and the one to which mostof this paper will address, is to switch at zerocurrent so that the dynamic load line stays very

close to the V-I axes. With a sine wave currentshape, it should be clear that the peak currentwill be close to twice the value of an equivalentsquare wave system, and although this adds tothe I2R losses, most semiconductor devices aremuch more comfortable with this than the highpeak power levels reached with square waveswitching.

Of course, low switching stress may also beachieved by switching at zero voltage and oneFig. 12 -Quasi-Resonance Definition

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ZEROOLTAGE

-r::~

ZEROURRENT

-c::=r

-I:::l--~--- FULL ~~~~..-J CYCLE ~~

that zero voltage switching, with its sine voltagewaveform, would force high peak voltages onthe switch and, although t loses control at lightloads, is unaffected by a short circuit.

Half or Full Cycle ConductionIn a quasi-resonant circuit, energy

transmission begins and ends at zero followed

by a wait defmed by the needs of the load. Fullor half cycle conduction elates o whether eachpulse will allow current to flow only fromsource to load, or ring in the resonant circuitallowing surplus energy o return to the source.The waveforms shown n Figure 16 describe heoperation which is controlled by the placementof diodes either in series or antiparallel withthe switch. Effective power supplies can beimplemented with either approach but, as onewould expect, there are significant differences

in their characteristics.

~=~ HALF ~~~ CYCLE ~J

L- DUALITY-1

Fig. 14- Switch Activation

should realize that this approach is merely adual of zero current as shown in Figure 14.The choice of which approach is best is usuallydetermined by whether the parasitic inductance

of the load or the capacitance of the switch isthe bigger problem. Zero voltage switching isprimarily appropriate with very high frequencyoperation where rapid charging and dischargingof the semiconductor switch capacitance couldrepresent substantial power loss. Note from theduality of characteristics shown in Figure 15

Fig. 16 -Half and Full Cycle Wavefonnswith Unloaded Resonant Switch

While half cycle operation may be easier toimplement, the pulse repetition rate is a directfunction of the loading and, when coupled withinput voltage variations, can result in hugeswings in switching frequency. A full cycle

configuration usually requires a diode in serieswith the switch as well as the antiparallel diodein order to prevent any reverse conductionthrough the slow switch body diode. Addition-ally, with current flowing in both directions,conduction losses tend to be greater. The ad-vantage is that by returning surplus energy tothe source, switching frequency is independentof load.

Fig. 15 -Switching TeclmiqlleS Co,?zpared

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Fig. 17 -Quasi-Resonant Switching Operation

Resonant Converter Basic OperationAfter having defmed the various classifica-

tions of resonant mode topologies, we will nowdescribe the detailed operation of one such cir-cuit. This material, derived from work done byDr. Fred Lee and the Power Electronics Groupat V .P 1. is illustrated here in Figure 17. Thecircuit is a single-ended, buck-derived, paiallel-loaded, half-cycle, zero-current switching, quasi-resonant converter. We will later extrapolatethis operation to other circuit topologies.

A resonant converter, like all switching regu-lators, requires an output fllter to smooth the

power delivered to the load. This output flltermust have a break frequency less than one fIfththe /owest switching frequency. Therefore weassume the current through Lo and the voltageacross Co are both essentially constant at theswitching frequency. The waveforms on theright of Figure 17 defme the current and

voltages during the four time increments,To to T4, which make up the total switch-ing period. The portions of the circuit

I which are active during each time incre-ment are shown on the left.

At time To, the output current is allflowing through D2 and with the activationof the switch, inductor current, ILr, startsto ramp up linearly with constant Vi'across Lr.At time TI, the output current transfers

to Lr and the inductor current continuesto rise in a sine wave to a peak defmed byVi and the resonant tank impedance. Atthe same time, Cr starts to charge with acosine function to a value of 2Vi. Whenthe inductor current falls below 10, Cr

begins to contribute to 10 and its voltage startsto fall.

At time T2, the current through Lr reacheszero and 10 can come only from Cr. With aconstant 10, the voltage on Cr falls linearly andwhen it reaches Vi, diode Dl lets the voltagetransfer to the open switch. Note that theswitch can open at any time between this pointand T2.

At time T3, the resonant tank is dry and 10flows completely from D2 until the next switchactivation.

The same process can be used to analyzeother circuit topologies remembering that asquare wave circuit can be converted to a reso-nant circuit by merely adding a resonant switch.Figure 18 shows four such configurations.

Transfonner CouplingThe introduction of a transformer into the

-power path does not change anythingfrom a topology standpoint but it addssome interesting and useful features.Figure 19 shows some possible extensionsof the simple buck regulator discussedabove. In Fig. 19A, the resonant circuit isin the primary and the transformer pro-vides merely an impedance match to aparallel load. This approach has the ad-vantage that the transformer passes onlyload current and therefore current sensingis easily done in the primary side. Fig.19B moves the resonating capacitor to the

Fig. 18- Parallel-Loaded Resonant Convelter Versions secondary with two benefits: the leakageof Square-Wave PoK'er Conversion Topologies inductance of the transformer is no longer

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In all cases, Vo is assumed constant and theprimary diodes defming full-cycle or half-cycleoperation are not shown.

Fig. 19 -Transfonner Coupling

The Series Resonant Converter

Figure 20A; Variable-frequency, Hal/-cycle,Discontinuous Mode: In this mode, current is

allowed to flow in only one direction througheach switch as can be seen from the Ir wave-form. This power stage has a constant poweroutput characteristic where the output power isgiven by 1/2 Cr V .2 F.. An increase in eitherthe input. voltage or the switching frequencywill proportionately increase the power deliv-ered to the load, irrespective of the load im-pedance. In the ideal case, the output voltagecan rise almost infInitely and some methodmust be used to limit it under no load condi-

tions. The slope of the output curve changeswith the load impedance which affects thesmall signal gain of the power stage and makesit more difficult to include inside a feedbackloop. The switching frequency is also dependenton both the input voltage and the load currentand so may have a very wide switching fre-quency range. This circuit and its derivativesare among the most simple and least costly toproduce converter circuits available but theresultant dynamic performance has been tradedfor this low cost.

Figure 2OB; Variable-frequency, Full-cycle,Discontinuous Mode: As the Ir waveformshows, in this mode the switches carry currentin both directions which gives the circuit a con-stant current output characteristic. The low fre-quency model is simply a voltage controlledcurrent source feeding the output capacitor .The switching frequency variation in this con-verter mode is directly related to the outputcurrent. If a wide output current range isneeded, the switching frequency range will alsobe wide. This will restrict the control loopbandwidth when used for a constant voltageoutput. This circuit is most commonly used forhigh voltage outputs because peak voltage onthe secondary is simply equal to the outputvoltage. An interesting aspect of this converteris the way the resonant current waveformchanges slope abruptly on each half cycle as thecurrent crosses through zero. The output

a parasitic but adds directly to the resonatinginductance, and with sine wave current flow,secondary diode switching is soft with less ten-dency for transient ringing.

The Vinciarelli Circuit of Fig. 19C moves the

capacitor further to the other side of the recti-fying diode and while transformer reset mustnow be accomplished by some other means, thelack of reverse current frees the primary side ofthe need for high-voltage, high-speed blockingdiodes. In addition, the transformer now seesonly the square voltage waveform from theprimary switch and thus has to support less volt-seconds. The practical implementation of thiscircuit also builds enough leakage inductanceinto the transformer such that it becomes the

total resonating inductance, eliminating a sep-arate component.

Alternate Resonant Operating ModesWithout going into the same depth that was

used above in the description of the single-ended, buck-derived circuit, we will now exam-ine and compare the whole range of operatingmodes for both series and parallel resonantconverters. For this comparison, we will use aclassic half-bridge topology as shown in Figures20 and 21. These circuits have been normalized

with all waveforms drawn to the same scaleand the following defInitions apply:

V.: The switched input voltage into the reso-nant circuit

Ir: The resonant current in the inductorV r: The voltage on the resonating capacitorVd: The voltage at the transformer secondaryId:The current through each leg of the output

diodes

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Fig. 20 -Series-Loaded, Ha/f-Bridge Converter

voltage is reflected into the resonant circuithrough the diode bridge and when the currenteverses, the reflected output voltage changes

sign. This lowers the effective voltage acrosshe resonant circuit and hence the resonant

current is lower. Note that although the currenthrough the switches and diodes is sinusoidal,he voltage waveforms are square. This behav-or is characteristic of all series resonant con-

verters.

Figure 20C,. Variable-frequency, Continuous,Below Resonance: Notice that in this mode theresonant voltage and current are both partialsine waves. Because the current in the inductoris continuous, each switch transition must forcecommutate the antiparallel diode of the oppo-site switch. Also, as noted before, the diodevoltage is still square although the current issinusoidal. Phase shift is occurring between theswitch voltage and the resonant current. Thetransfer function of the power stage is nonlin-


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circuit is similar to an amplitude modulationsystem. The square wave coming from theswitches has a fundamental frequency andmany harmonics. A change to the pulse widthproduces a similar change in the amplitude ofthe fundamental frequency component. Theaction of the resonant circuit eliminates theharmonics and passes a sinusoidal current atthe fundamental frequency to the outp~t whereit is rectified and fIltered.

ear since its gain is dependent on theimpedance slope of the resonant circuit. Thismakes this circuit somewhat difficult to stabilizebut reasonably wide control bandwidths can bemaintained as long as the output load is able tokeep the circuit in continuous resonance. If theload goes open the switching frequency will goto zero. The small signal analysis of this modeis given in Ref. [3] for both above and belowresonance.

Figure 20D; Variable-frequency, Continuous,Above Resonance: As was noted in thepreceding paragraph, below resonance eachswitch must force the opposite antiparalleldiode off and carry the current which wasflowing through it. Above resonance the switchturns on naturally at zero current because itsantiparallel diode conducts fIrst, but the switchmust turn off with current through it. The anti-parallel diode of the opposite switch will con-duct immediately and is then naturally commu-tated by the resonant circuit in its turn. Aboveresonance, the resonant current resembles asawtooth wave more than a sinusoid eventhough it is made up of sinusoidal sections. Thecapacitor voltage is the integral of the currentand it more closely resembles a sine wave. Thefrequency range of this mode of operation isgenerally low and it operates on the slope ofthe resonant circuit impedance curve the same

way it does below resonance. A required limiton minimum switching frequency allows thecontrol loop bandwidth to be wide although thetransfer function of the circuit in this mode isstill very nonlinear .Also note that with a largeload current variation, the switching frequencyrange will be wide and if the load goes to anopen circuit the switching frequency will go toinfmity .

Figure 20E; Fixed-frequency, Continuous, AtResonance: The waveforms in this mode aresimilar to the ones of variable frequency con-tinuous resonance mode above resonance. Theswitch voltage is different because the resonantcircuit begins to ring after the current goes tozero. This shows up as the funny looking blipin V. which is the start of ringing. Obviously,the switching frequency does not vary with loador input voltage but the pulse width may varyover the whole range. The operation of the

The Parallel Resonant Converter

Figure 21A; Variable-frequency, Hal/-cycle,Discontinuous: This mode again blocks reversecurrent flow through the switches which isreadily seen in the It waveform. Like the seriesresonant converter in this mode, the parallelresonant converter also has a constant poweroutput characteristic which is given by the sameequation: p 0 = 1/2 Ct V .2 F.. An increase inthe switching frequency will produce a similarchange in the power delivered to the loadirrespective of the load impedance. In the idealcase the output current can become quite highunder a short circuit and some means must beused to provide a maximum current limit. Theconstant power output characteristic makes thesmall signal gain of the stage dependent onboth the output load and the input voltage, soit is more difficult to stabilize a feedback looparound a converter operating in this mode. Theswitching frequency dependency on both theinput voltage and the load current results in avery wide switching frequency range if there isa large variation in the load current. A circuitwith a 1 MHz resonant tank might beoperating near 50 kHz at high line and lightload. As was the case with series resonance,this circuit and its derivatives trade perform-ance for simplicity and low cost.

Figure 21B; Variable-frequency, Full-cycle,Discontinuous: Full-cycle conduction providesfor current flow in both directions through theswitches. The resonant current in the inductorhas a DC component on each half of theswitching cycle which is equal to the output in-ductor current. This is also responsible for thesmall time delay on the leading edge of theresonant voltage waveform, V I. This voltage isclamped at zero as long as the output diodes


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Fig. 21 -Parallel-Loaded Hal/-Bridge Convelter

are all conducting. This is the case at the be-ginning of a cycle and it continues until theesonant inductor current, II, is equal to the

output inductor current. The resonatingnductor current does not have to reverse ashown here but if not, the switches must beorce commutated off and the switch dissipation

and EMI output go up considerably. If II is ashown in the figure, the switches will

commutate naturally. Both switch transitionsoccur at zero current and it is thus true zerocurrent switching. This mode of operation hasan extremely linear transfer function and a lowoutput impedance which makes it an excellentvoltage source. Its dynamic characteristics arevery similar to those of a standard PWM buck

converter. It is easy to close a voltage looparound this circuit and achieve excellent dy-namic performance and wide loop bandwidth.The switching frequency is not dependent onthe load current so the switching frequencyrange is reasonably small. This circuit is wellsuited to a wide variety of applications.

Figure 21C; Variab/e-frequency, Continuous,Be/ow Resonance: In this mode, when eachswitch turns on it must force commutate thecurrent flowing in the opposite antiparalleldiode and thus has some switching lossalthough the switches are commutated off nat-urally. The output diodes see a square wave ofcurrent but a sinusoidal voltage, as expectedfrom a single tuned converter. The transfer


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in which case the switching frequency will go toinfinity. The known minimum switching fre-quency allows a wide control loop bandwidthto be achieved, however, the nonlinear transferfunction makes it more difficult to stabilize afeedback loop.

Figure 21E,. Fixed-frequency, Continuous, At

Resonance: These waveforms are very similarto the continuous resonance mode above reso-nance. One of the switch transitions againrequires that the switch be force commutated.The sawtooth section in V. is caused by thestart of ringing when the switch current goes tozero. The switching frequency of the circuit isobviously fIXed but the pulse width may coverthe entire range. The operating principle of thiscircuit is similar to amplitude modulation. Thevoltage waveform from the switches contains afundamental and many harmonics. The reso-nant circuit eliminates the harmonics andallows only the fundamental to reach the out-put circuit. As the pulse width of the switches

function for this mode of operation is nonlinearbecause it is operating on the slope of the reso-nant circuit impedance curve and its small sig-nal properties are similar to those of the seriesresonant converter. The overall switching fre-quency change is reasonably small as long asthe circuit is operating in continuous resonanceso the bandwidths may be reasonable and thecircuit will have good dynamic performance. Ifthe load current goes to zero, the current inthe output inductor will become discontinuousand this will force the switching frequencytoward zero.

Figure 21D; Variable-frequency, Continuous,Above Resonance: Above resonance theswitches are force commutated off but turn onnaturally at zero current because their anti-parallel diodes conduct first. Note that thiscircuit has a phase change from that observedwhen operating below resonance. In this modealso, the switching frequency variation will besmall unless the load becomes an open circuit,

Fig. 22 -Hal/-Bridge Off-Line Quasi-Resonant Converter


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changes, the amplitude of the fundamentalcomponent of the voltage will change corres-pondingly. This varies the amplitude of thefundamental voltage across the resonating capa-citor and thus the output. The rectified sinewaves are then averaged by the output filter .

References

[1] R.P. Severns and G. E. Bloom, ModernDC-to-DC Switchmode Power ConverterCircuits, Van Nostrand Reinhold Co., NewYork, 1985.

[2] P. C. Todd and R. W. Lutz, PracticalResonant Power Converters -Theory andApplication, Poweltechnics Magazine;April, May and June, 1986.

A Practical Resonant Converter

ExampleTo show a more complete power supply

architecture, the schematic of Figure 22 com-bines a ha1f-bridge resonant power stage witha new IC control chip designed by Unitrode foruse in resonant mode power converters ofmany different topologies. This applicationfeatures the parallel-Ioaded, ha1f-bridge top-ology in a variable frequency mode. It includesfull current limiting, minimum frequencylimiting, and over voltage control for zeroloaded conditions, as well as many other pro-tection and programming functions needed forpractical power supply operation. With theintroduction of control circuits like theUC3860, the use of resonant mode powerconversion techniques can be expected torapidly advance and become the technique ofchoice in the next few years.

[3] V. Vorperian and S. Cuk, Small SignalAnalysis of Resonant Converters,Proceedings of the IEEE Power ElectronicsSpecialists Conference, 1983.

[4] Liu, Oruganti, and Lee, ResonantSwitches -Topologies and Characteristics ,Proceedings of the IEEE Power ElectronicsSpecialists Conference, 1985.

[5] W. F. Santelmann, Jr., Designing Ultra-Efficient High Voltage Supplies U sing aHigh Frequency Resonant FlybackTechnique, Proceedings of Powercon 9,Paper G-2, 1982.

[6] F. Lhermite and D. Catala, Control of aSingle Ended Off-Line Quasi-Resonant

Power Supply, Proceedings f PCI; 1987.


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