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The 33rd Annual Conference of the IEEE Industrial Electronics Society (IECON) Nov. 5-8, 2007, Taipei, Taiwan Modelling and Regulation of Dual-Output LCLC Resonant Converters Y. Ang, C. M. Bingham, M. P. Foster, D. A. Stone Department of EEE, The University of Sheffield, Sheffield, UK. E-mail c.binghamgsheffield.ac.uk Abstract-The analysis,
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  The 33rd Annual Conferenceof the IEEE Industrial ElectronicsSociety (IECON) Nov. 5-8, 2007, Taipei, Taiwan Modellingand Regulation of Dual-Output LCLC Resonant Converters Y. Ang, C. M. Bingham, M. P. Foster, D.A.Stone Department of EEE, The University of Sheffield,Sheffield, UK. E-mail c.binghamgsheffield.ac.uk Abstract-The analysis, design and control of 4th_order LCLC voltage-output series-parallel resonant converters (SPRCs) for the provisionofmultiple regulatedoutputs, is described. Specifically, state-variable conceptsare employedand new analysis techniques are developed to establish operating mode boundaries with which to describethe internal behaviour of a dual-output resonant converter topology. The designer is guided through the most important criteria for realising a satisfactory converter, and the impact of parameter choices on performance is explored. Predictions from the resulting models are compared with those obtained from SPICE simulations and measurements from a prototype power supply under closed loop control. I. INTRODUCTION With the increased power capability, improved control and reduced cost of power semiconductor devices, designers of electronic equipment, computers and electronic instrumentation are increasingly demanding higher energy and more efficient power supplies. Moreover, thetrend towards miniaturisation of electronicsystems,particularly for communicationand entertainmentproducts, and the emergenceof improved power switchtechnologies, is leading to the use of switching frequencies in the 100s kHz to several MHz range. To improve the overall power density of resonant power supplies, research is now being directed towards converter topologies that can providemultiple regulated outputsparticular growth areas being the telecommunications, computer and microprocessor industries, with mobile phones, PDAs and handheld products typically requiring3.3V, 5V, ±12V and ±15V supplies for various interfaces. However, cross-regulation errors that accompany output load variations, which manifests itself by the regulation of one output voltage impacting on the performance of others, can be a significant limitation for voltage sensitive electronicsystems. II. MULTI-OUTPUT CONVERTERS To-date, several approaches havebeen explored to addresscross-regulation, complexity and overall circuit performance issues of multi-output converters, the solutions being divided into three distinct categories. The first regulates a single primary output using closed-loopfeedback, with theauxiliary outputs being semi-regulated and, therefore, subject tocross- regulation error. The second category achieves precise post- regulation ofeach output by using eitherlinear regulators or hard-switched dc-dc converters. However, although relatively straightforward to design, such circuits are rarely used in practice due tocost constraints. The third category is specific to applications which require only two regulated outputs, as is commonly found in signal processing and microprocessor based systems. They avoid the need for post-regulation by utilising two closed-loop feedback configurations. A 3rd-order LLC converter with two independently controlled outputs was reported in [1]. However, optimum performance characteristics have yet to be forthcoming, primarily due to the significant complexity associated with the highly non-linear behaviour between the various outputs as a function of load. Nevertheless, it is a solution that broadly falls within this third category that is thesubject of this paper. Specifically,dual-output resonant LCLC converters, are considered, with control ofeach output being achieved by switching the power devices asymmetrically over each half switching cycle using a combination of PWM and frequency control. III. DUAL O/P LCLC-SPRC MODELA half-bridge LCLC-SPRC with two outputs is shown in Fig. 1(a). To demonstrate the ability of the converter to deliver asymmetrical output voltages under balanced load conditions, the transformer is constrained to have unity turns-ratios for both outputs and the high- and low-side parallel resonant capacitors are constrained to have identicalvalues. Since current flows through the primary side of thetransformer to the top and bottom sides of the rectifier during different half- cycles of tank excitation, see Fig. 1 (b), each output is replenished with energy alternately.IV. PRINCIPLE OF OPERATION To achieve zero-voltage switching, the converter is assumed to operate on the negative gradient of the input-output frequency characteristic, above the primary resonant peak. When operating in this region, the resulting waveforms can be sub- divided into two distinct time intervals, viz. intervals 1 and 2, as depicted in Fig. 1(b): Interval 1: Clamping of the parallel capacitor voltage. Here, the combined series inductor Ls+Llp and capacitor Cs provide resonant behaviour whilstthe voltage across the effective parallel tank inductor and capacitor (Lp (Lm) and Cp) is clamped by the output voltage. As the current through the series inductor, LS, decays to zero, Cp begins to contribute to resonant behaviour, and operation enters the second interval. 1-4244-0783-4/07/ 20.00 C 2007 IEEE 2130  Luo take on a sinusoidal characteristic. Since the outputs are effectively disconnected from thetank, both Cp1 and Cp2 DI contribute to resonant behaviour. Both rectifier currents are zero, and the converter outputs are in an  idle state with Rf1 lS energy being supplied solely by the charge on the filter capacitors. By initially neglecting the rectifier on-state - | voltage, and noting that the effective parallel resonant X 2i R 2 capacitance CL is the sum of the shunt network capacitances W C~p and C,2, vcp1 during the capacitor charging period is described by: ST SBAv_; .1+_ (a) t2 cp(t= cpi  t, ) +  i n sin(2)7,t) dt p tl where lin =iLS-ILp Evaluating (1) with initial conditions VR (tl) = VCp1 (tl) = -Vjut2 yields: (1) (2) 1i t2 (b)Fig.1 Dual-load 4th_order resonantconverter (a) schematic (b) typical operating waveforms Interval 2: Decoupling of the rectifier and output filter. Here, all the t nk components contribute to resonant behaviour, with the rectifier effectively becoming reverse biased. Current into both the high- and low-sidediodes remains zero, and the parallel capacitors are charged until their voltage is clamped at either +V± ,, or -V,,12, thereby providing the boundary at the end of this time interval. During each half-cycle of operation, three Modes, Ml, M2, and M3 can be identified, as shown in Fig. 1(b). Circuit Mode Ml (to < t < tl). At the start of Ml, SW2 is turned off at to and SWI turned on. The series inductor current, iLs, is negative and flows through the internal diode of SWI, thereby facilitating ZVS of SWI. Also during this period, iLs allows D2 to conduct and transfer energy to support VOW2, whilstthe voltage on Cp2 is clamped to VoW2. Allthe rectifier current, therefore, flows to the load. At the end of Ml, the rectifier current iR2 has decayed to zero, and both the high side andlow side diodes, and the output filter, are effectively decoupled from the resonant tank.Circuit Mode M2 (t < t <t2). Here, the series resonant inductorcurrent iLs becomes positive. Since SWI is turned on during Ml, current flow is now through SWI. Initial conditions for this mode are that iLs=O and Vcp2= vout2- The inductorcurrent iLs and parallel resonant capacitor voltages The boundary for the end of thecapacitor chargingperiod is VCpl(t2) = +Voutl, which yieldsthe rectifier non-conduction angle, Oc, associated with a positive polarity of current, iR, through the high side rectifier: t2 = 2 f xcos K (0,C)cv cos (3) where vtot = vout, + Vout2 Circuit Mode M3 ( t2 < t < TI /2). At t t2, D1 becomes forward biased whilst D2 reverse biased. The rectifier diode current iR2 remains zero throughout theduration of M3, and DI clamps the capacitor voltage vcp, to +Vout± until iLs decays to zero, at which time the second half cycle of operation commences. For 50 0 duty-cycle excitation, the2nd half-cycle of operation is the mirror image of the first. However, for asymmetrical excitation,the output rectifier diode (D2) non-conduction angle, associated with the series resonant inductor current being of negative polarity, is given by: Sb2 co -K1 2zf Cpvtoj (4) where ii (is- iLp). The voltage, v across theparallel resonant capacitor can, therefore, be expressed as a function of the angle 0 see Fig. 1(b): for K 2 + 2f x  I -cos(9)) + Vout2 voltl - 2.in6 x  I cos(o)) Vo,t2 = ...° for 0=9  i.. for 0= .+2 for   f + 0c2 2i (5) 2131 Llp*L-  P44 r,; ,;T+C,921 I cos(2zf - tl )) vcp I (t2 )   V,,t 2 + ii, x , (t2 2zf,Cp IR  Under steady-state conditions,the mean output current ioutl, flowing through DI towards the output filter and load, can be determined from the mean current flowing through the rectifier when it is of positive polarity. Since this occurs during the interval Oc1 < 0 < iz, iout is given by: iol=-X ix n sin(O)dO (6) 2 f Substituting (3) into (6) and evaluating theintegral provides thesolution for ioutl ioUtl 2- x (1 + COs( 1 )) = p tot (7) 2yz yz Simple mathematical manipulation of (3) and (7) then gives the corresponding rectifier non-conduction angle c15c: terms are, therefore, obtained by equating voltages at either side of the rectifier for each respective half-cycle: vC., = sgn(iL)(VOtj + vdiode) sgn(iL)(vCf 1 + Vdiode) (13) vCq2 sgn(iL )(Vout2 + Vdiode ) sgn(iL )(Vcf 2 + Vdiode) Assuming a constant rectifier voltage, (12) can be manipulated to: dvc,.1 dvcf I dC dvcf 2 dt sgn(iL) dt dt sgn(iL) dt (14) Considering the rectifier current, iR2, to be zero during thepositive half-cycle of the parallel capacitor voltage, the rectifier current iRj, is given from: 'L -RI 1Cp2  R2 = sgn(iL   RI Vcf 1 CpI Cf Cf IRLI (8) VO,tl is determined by assuming the output filter capacitance Cf is sufficiently large to impart negligible output voltage ripple. In this case: vout 2 = ioutIRLI = +(I+COS(f =CV (9) Equations (6) to (9) can be further manipulated to provide the complementary D2 non-conduction angle, 5c2, and the output current, iout2, and output voltage Vo0t2, as follows: iout2   2in X  1 + COS(0)2  , VoW2 = L2 X 'n sC1)outl (1 0) 2z Z I~~i 1+RLfICP V. STATE-VARIABLE ANALYSIS A state-variable model describing the behaviour of the dual-output converter can be obtained by considering the electrical network shown in Fig. 1 and separating the dynamics into 'fast' and  slow sub-systems, with their interactionrelated by a set of coupling equations. The fast sub-system is considered to describethe dynamics of the resonant tank andpower switches: dvcs iLs diL sKf Vcs VLpdiLp VLp dt Cs dt Ls dt Lp dvCpl 'Ls 1Lp -RI tCp2 1R2 dvCp2 'Ls 1Lp 1R2 tCpl -RI dt Cpl dt Cp2 (11) The output filter dynamics are described by: dvcf I - 'RI Vcf 1 dvcf 2 1R2 Vcf 2 (12) dt Cf1 CfIRLI dt Cf 2 Cf 2RL2 As discussed, during interval t1 -4 t2 (seeFig. 1(b)) vcpl is clamped to vcf, during the positivehalf-cycle, and conversely, to -vcf2 during the negative half-cycle, due to the action of the diodes. By noting that there will be negligible current flowing through Cp during these periods, the rectifier input voltage is dependent on the direction of thecurrent leaving the resonant tank inductances, i.e. iL = iLs -iLp . The relevant coupling . i C=plCf I iL -iCp2 -iR2 Sgn(iL )Vf I RI sgn(iL)Cpl   Cfl CpK C+fl)Vl2 This leads to the following coupling equations which describethe rectifier currents within each half of a switching cycle: CpCl 1L 1Cp2 (R2 +   f I for vQpl Vout, + vdode 1.RI= Sgn(iL)CPl±Cf1 Cfr C IRL I 0 for vcpl<Vout + vdiode   p2Cf2 riL iR2 | sgn(ZL  Cp2   Cf2 +sgn QL qfr 2 C C+'(L2 for vCp2 = Vout2 + Vdode cp2 Cf2RL2 0 for VCp2 < Vout2 + Vdiode (16) Notably, the voltage across Lp, can be considered a reflection of the voltages across Cp1 and Cp2, and the state vector for the parallel inductor current in the fast sub-system (see (11)) simplifies to VLP = VCp I The state-variable equations for the parallel resonant capacitor voltage (11) can be simplified to: Cp I B LsLp iR dvCp2 -B Lp iR (17) dt 2Cp1 dt 2Cp2The complete state-variable model of the dualload converter (excluding the effects of output leakageinductances) is, therefore, given by: where Fo3X3 A1 o2x37 x = A2 o2X2o2X2 x   B 02x302X2 A3 X =VCpI VCp2 VC,  Lp 'L, VCf IVCf2 2C1p2C1p Fl0 0 Al II A2 Lp 1 2C2 2( 0 A 0 1 LL j C, B [ iR _iR 01X2 Vin 1 R2 ] L2C PI 2Cp2 L, C fl Cf2 (18) 1   3= C -RL (19) The model can used to investigate the behaviourof dualload converters when subject to asymmetrical input excitation. By way of example, the parameters of a candidate converter are 2132 (15) -I )Ziouti -)7fscp Vtot oc,   Cos Mout, + )7fsc pVtot  given in Table I when supplied from a 30V dc link. A plot of the resultingsteady-stateoutput voltage characteristics of the converter, Vf0t, and VW2, as a function of switching frequency and duty-cycle ratio is given in Fig. 2. It is evident thatfor operation above resonance, the sum of the output voltagesapplied to the loads increases as the operating frequency tends to the effective resonant frequency, for fixed values of duty-cycle ratio. Furthermore, for a 50O duty-cycle, giving symmetric square-wave excitation of the tank, the converter delivers identical voltages to both the high side and low side outputs,for a fixed operatingfrequency, as expected. For a given operatingfrequency, a decrease in the duty-cycle ratio, from 500O, is seen to deliver more energy from the resonant tank to energize output V,,tl, thereby yielding a correspondingly higher output voltage and power, and vice- versa. It is, therefore, clear that for balanced loads, the voltage andpower distribution to each output can be independently influenced by asuitable choice of duty ratio and switching frequency. For completeness, Fig. 3 compares the ratio of the two realisable output voltages, from which it can be seen that the slope of the curve is greater for lower values of switching frequency. This implies that when alarge difference between the output voltages is required,the converter should be operated close to resonance, leading to high efficiencyoperation, and zero voltage switching. However, this also means that the tank components are subjected to higher electrical stresses. For asymmetric excitation of the converter, the duties of SWI and SW2 are denoted, respectively, by D and 1 -D, where D is the ratio of the turn-on period with respect to the switching period. Asymmetric switching therefore provides an asymmetrical voltage source Vin to excite thetank, of amplitude VDC: Jn {VDC i - 0=0...2zD 9 = 2zD ...2ff Assuming that only the fundamental component excites the resonant tank, and applying therelationship tan- (cos(o)/sin(O)) =T/2+0, the fundamentalof the input voltage, Vin 1), and its phase angle, 5vi l) are given by: Vi(= DC1 - cos(2)D) x sin(OX + vi 1)) vi(1) = 2--,I (21) The condition for inductive switching can now be written as A nz(O.5-D), where,3in is the phase lag between the fundamental of the input voltage and current). TABLE I CONVERTERMODEL PARAMETERS ParametersValue Characteristic impedance (Q) 2.5 Resonant frequency,fj (kHz) 130Resonant capacitance ratio, C, 0.03 Resonant inductance ratio, L, 0.01Series loadquality factor, Q0p' 6 le . IS-~ 14 - 12 I- 3 0 140 -qu Frequeny (kHz) 20 [Duty ( ) Fig.2 Variation of output voltage distribution withswitchingfrequency and duty-cycle ratio Duty P Fig.3 Variationof normalised asymmetrical output voltagewith switching frequencyand duty-cycle ratio VI. EXPERIMENTAL RESULTS Measured results havebeen obtained on an experimental converter with a step-down capability, the measuredcomponent values beinggiven in Table II. A ferrite core, 3F3, suitable for highfrequency applications, wasused for both the transformer core and the resonant inductor. Since the transformer leakage inductances are dependent on the winding arrangement, thesecondaries were bifilar wound adjacent to the core, beneath the primary winding, so as to reduce secondary leakage flux. TABLE II PROTOTYPE DUAL OUTPUT CONVERTERCOMPONENT VALUES Parameter Value DC link input voltage, VDC (V) 15 Series resonant inductances, L, (,uH) 0.85 Series resonant capacitances, C, (,F) 1.5 High sideparallel resonant capacitances, CP1 (Ff) 0.116 Low sideparallel resonant capacitances, CP2 (,F) 0.116 Load resistance, RL (Q) 4 Transformer turns ratio 1 Filter capacitance, Cf (,F) 100 Transformer output leakage inductance, LI, (,uH) 0.1  gnetising inductance, Lm (,uH) 109Transformer primary leakage inductance, LIP (,uH) 0.7 2133
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