Design of an LCC current-output resonant converter for use as a constant current source

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1 Deign of an L current-output reonant converter for ue a a contant current ource A. J. Gilbert, D. A. Stone,. M. Bgham*, M. P. Foter SHEFFELD UNVERSTY Department of Electronic & Electrical Engeerg Mapp Street, Sheffield, S1 3JD, U.K. Tel.: +44/ (0) * c.m.bgham@heffield.ac.uk URL: Keyword Reonant converter, D power upply, Soft witchg, ZVS converter Abtract A methodology for the deign of L reonant current-ource converter, i preented. Unlike previou technique, the reultg converter provide near contant teady-tate output current over an extended load range when excited at the reonant frequency, through ue of a elf-ocillatg controller. ntroduction t i well etablihed that reonant converter are advantageou -term of ize and efficiency. Thi paper firt etablihe that an L current-output converter can be made to perform a a contant current-ource at the reonant frequency and then provide a imple deign proce. Many of the underlyg equation ued the propoed methodology have been previouly reported [1-3]. The deign proce utilie the accuracy of Fundamental Mode Approximation (FMA), at the reonant frequency, and the potential for rapid analyi that it provide. The analyi i baed on the L current-output reonant converter hown Figure.1. r L V dc N : 1 v c lf Lf V i vcp p v cf f R L vo (a)

2 (b) (c) Fig. 1: L current-output reonant converter (a) chematic (b) prototype converter (c) elf-ocillatg phae lock controller Deign Methodology n [3] it i hown that the tank component are related to the tank ga at reonance G tr, the tranformer turn ratio N, the reonant witchg frequency f r, the parallel to erie capacitor ratio (A p / ) and load reitance R L a follow: 4 Gtr π p 3 π N RL 16 f r (1) N RL L 3 4π f G 4 ( A + 1) G π 16) r tr G tr tr 4 π 16 () where A p /, G tr i the tank ga at reonance i.e V o V G tr /N at reonance, f r i the reonant frequency and R L i the load reitance. t i now hown that a the load reitance i creaed, the converter output current tend to a contant value. Solvg both (1) and () for f r equatg the reult and further olvg for G tr give: (3) 4 4 Gtr 64L + N RL pπ ( A + 1) + X 4π L where 4 4 ( ) ( ) + 18L N R A 1 + N R 1 L pπ L p π X 4096 L A + Now, for a given output current, the tank ga at reonance can be calculated a follow: o VGtr R N L (4) ubtitutg (3) to (4) give an expreion for the output current a load i varied and the converter witched at reonance.

3 The output current ideally tend to a contant mimum value a the load reitance i creaed and the converter witched at reonance. Thi can be hown by takg the limit of (4) a R L (opencircuit) after G tr i elimated through the ue of (3) givg: VN p A+ 1 (5) L Thi i the mimum output current the converter will produce when excited about the reonant frequency. When the load reitance i lowered, the output current will be larger. Given that the maximum current (at mimum load reitance) i K time larger than the mimum current ( o_max K. o_m ) allow the required value of A to be calculated. Solvg (5) for p /L then yield: p 4 (6) L N ( A + 1) V Dividg (1) by (), elimatg G tr through the ue of (4), replacg o with K. o_m and R L with R L_m, equatg the reult with (6) and fally olvg for A give: 4 N RL _ m π K ( K 1) + 16V (1 K ) (7) A 4 K N R π K 1 16V ( ( ) ) L _ m t i now poible to generate a contrat on the mimum and maximum allowed value of N for a given deign pecification. To generate the mimum, the value of A mut never be -ve, hence, olvg for N (7) at A0 give: 4V R < L _ m Kπ N (8) To generate the maximum value, olvg (7) for the limit of N a A give the followg contrat: N < π R L _ m 4V K 1 (9) Hence, for a given pecification, the range of N mut firt be calculated, the tranformer turn ratio N pecified, the capacitor ratio A calculated from (7), the G tr calculated at the mimum load by aumg o K. o_m and olvg (4), and fally computg the required component from (1) and (). The mimum reonant frequency correpond to f r. The peak reonant frequency will correpond to the reonant frequency of the converter with the rectifier diconnected. The methodology i now applied to the deign of a contant current converter. The pecification for the upply are provided Table 1. Table 1 D-D onverter Specification D nput urrent ource Output voltage Range Voltage Range 18V 0 1A 10 0V The theoretical open circuit output current, at reonance, i elected to be 10% larger than the required peak current, thereby enurg that paraitic effect (uch a diode voltage drop) will not reduce the

4 current o a to make the deign effective and will enure above-reonance operation at the peak required output current,. Therefore o_m 1.1A. Now, electg K 1.1 enure that at the mimum pecified load reitance, the output current at reonance will not exceed 1.1A. Equation (8) and (9) provide a contrat on the range of N. At 1A output, the mimum load reitance i 10Ω, hence 0.60<N<1.45. Selectg an N of 1 for implicity and reduction converter cot, give a G tr 0.67 and from (7) the value of A i therefore found to be Aumg a mimum witchg reonant frequency of 133kHz, the required tank component from (1) and () are p 18nF 0nF and L 13.6uH. For the component value elected above, Fig. provide the teady-tate output current when witched at reonance, a the load i varied. The data i obtaed from a prototype converter, ideal imulation, and deign proce (ee equation (3) & (4)) Experimental Simulated Deign proce Output current, A Load reitance, Ohm (a) Normalied output current Normalied Experimental Normalied Simulation Normalied Deign Procedure Load reitance, Ohm (b) Fig. : (a) Output current (b) normalied output current w.r.t ideal converter imulation a load i varied from 5Ω to 10Ω when witched at reonance

5 From Fig. (a) it can be een that the prototype teady-tate output current varie little a the load i changed and the converter witched at reonance. Sce a erie-ductor reitance of 0.15Ω i preent the converter, it i expected that the experimental output-current data will be lightly lower than that of the ideal imulated converter. Note that from an ideal perpective the preence of a forward voltage drop hould not reduce the output current below the theoretical open-circuit current ce the diode effectively make the load reitance appear larger, thu forcg the converter to naturally compenate by creag the reonant tank current. Figure (b) provide a meaure of error the propoed analyi. n the preented data, the larget error between the analyi and imulated ideal converter i approximately 4%. The maximum error between experimental output-current and the analyi occur at the highet output power, and i approximately 10%. Thi make the deign proce ideal for prototype component election epecially when one conider the implicity of the equation. A benefit of the propoed deign procedure, when a contant load current i deired, i the ability to operate near reonance acro the full load range. Thi maximie the converter efficiency ce le reactive power i preent the reonant tank. Figure 3, provide the efficiency of the prototype converter for the load range pecified Table 1, when witched at reonance. onverter efficiency, % Load reitance, Ohm Fig. 3: Prototype efficiency when operated at reonance over the pecified load range oncluion An L reonant converter current-ource deign methodology, baed on the FMA analyi technique, ha been preented. The teady-tate output current ha been hown to rema near contant over an extended load range when witched at the reonant frequency. f upplied by a contant voltage, the converter i capable of virtually contant output-current regulation open-loop via a elfocillatg at reonance witchg mechanim. Reult from a prototype converter have validated the propoed methodology.

6 Reference [1] R. L. Steigerwald, A comparion of Half-Bridge Reonant onverter Topologie, EEE Tran. Power Electronic, vol.3, no., April 1988, pp [] Marian K. Kazimierczuk, Dariuz zarkowki, Reonant Power onverter, John Wiley on, c 1995, SBN , hapter 8 & 17. [3] A. J. Gilbert, D. A. Stone,. M. Bgham, Rapid deign of L current-output reonant converter with reduced electrical tree, Power Electronic and Application, 005 European conference on Sept 005.

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