A new phase-controlled parallel resonant converter

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two inverters controls the amplitude of the output voltage of the new inverter. ... 2) The power MOSFET's are modeled by switches with. ON-resistance rDs. ... not have parasitic resonances. ... Each switching leg and the dc input voltage source 4 ..... a constant-frequency clamped-mode parallel-resonant converter,”.



A New Phase-Controlled Parallel Resonant Converter Marian K. Kazimierczuk, Senior Member, ZEEE, Dariusz Czarkowski, and Nandakumar Thirunarayan Abstract-A new phase-controlled resonant inverter is obtained by paralleling the ac loads of two identical parallel resonant inverters. A phase shift between the drive signals of the two inverters controls the amplitude of the output voltage of the new inverter. A voltage-driven rectifier is used as an ac load of the inverter which results in a phase-controlled parallel resonant dc-dc converter. A frequency-domain analysis is performed for the steady-state operation of the inverter and two types of voltage-driven rectifiers and design equations are derived. The converter can be operated at a constant switching frequency which reduces EM1 problems. It is found that for switching frequencies higher than the resonant frequency by a factor of 1.07, the load of each switching leg is inductive which allows for the use of power MOSFETs as switches. The converter is capable of regulating the output voltage in the range of load resistance from full load to no load. An experimental prototype of the phase-controlled parallel resonant converter with a center-taped rectifier was built and extensively tested at an output power of 50 W and a switching frequency of 116 kHz.

because the proposed topology exhibits only slightly different impedances as seen by the switching legs. The procedure of obtaining a phase-controlled Class D parallel resonant inverter (PRI) is explained in Fig. l(a) and (b). Fig. l(a) depicts two conventional Class D voltage-switching inverters: inverter 1 and inverter 2, with ac loads connected in parallel. Each inverter is composed of two switches with their antiparallel diodes, a resonant circuit L - C / 2 , and an ac load resistance 2 R, connected in parallel with the resonant capacitor. Capacitors C , are coupling capacitors. The parallel combination of resonant capacitors C / 2 and load resistances 2 R, results in resonant capacitor C and the load resistance R , yielding the circuit of the phase-controlled Class D PRI as shown in Fig. l(b). The equivalent circuit of the inverter for the fundamental components is depicted in Fig. l(c). If the load resistance R, in the inverter of Fig. l(b) is replaced by one of the Class D voltage-driven rectifiers [15] deI. INTRODUCTION picted in Fig. 2, a phase-controlled parallel resonant conONVENTIONAL resonant dc-dc converters [ 11 are verter (PC PRC) is obtained. Its dc output voltage V, can controlled by varying the operating frequency, us- be regulated against load and line variations by varying ually over a wide range. This causes electromagnetic in- the phase shift between the voltages which drive inverter terference (EMI) and filtering problems and makes it 1 and inverter 2. The operating frequency can be maindifficult to effectively utilize switches and magnetic com- tained constant which is an important advantage of the ponents. To alleviate these problems, a concept of phase- converter. controlled converters was introduced and several topol11. ANALYSIS OF CLASS D PHASE-CONTROLLED INVERTER ogies based on this concept have been proposed and A. Assumptions analyzed [2]-[14]. Some of these converters consist of two The analysis of the phase-controlled Class D parallel switching legs and one resonant circuit. The drawback of such configurations is that while one leg is loaded induc- resonant inverter of Fig. l(b) begins with the following tively, the other is loaded capacitively. Therefore, snub- simplifying assumptions: bers in one switching leg are required, adding to the 1) The loaded quality factors QL of the parallel-resocomplexity of the circuit. nant circuits are high enough so that the currents i, The purpose of this paper is to present a steady-state and i , through the resonant inductors are sinufrequency-domain analysis and experimental results for a soidal. new phase-controlled parallel resonant converter. Con2) The power MOSFET's are modeled by switches with necting in parallel ac loads of two parallel resonant invertON-resistance rDs. ers results in inductive loads for both switching legs at the 3) The reactive components of the parallel-resonant operating frequencies higher than the resonant frequency circuits are passive, linear, time-invariant, and do by a factor of 1.07. Therefore, power MOSFET's without not have parasitic resonances. snubbers can be used as power switches. Also, an imbal4) Both resonant circuits have identical components. ance of currents through resonant inductors is low. This is B. Voltage Transfer Function of Phase-Controlled Class D lnuerter Manuscript received June 6 , 1992; revised October 28, 1992. This Each switching leg and the dc input voltage source 4 works was supported by the National Science Foundation under Grant ECS-8922695. of the inverter shown in Fig. l(b) form a square wave The authors are with the Department of Electrical Engineering, voltage source. Since the input currents i , and i, of the Wright State University, Dayton, OH 45435. resonant circuits are sinusoidal, only the power of the IEEE Log Number 9211944.


0278-0046/93$03.00 0 1993 IEEE



fundamental component of each input voltage source is transferred to the output. Therefore, the square wave voltage sources can be replaced by sinusoidal voltage sources representing the fundamental components as shown in Fig. l(c). The coupling capacitors C , are neglected in the equivalent circuit of Fig. l(c) because they act as short circuits for the ac component. The fundamental components of the square-wave input voltage sources are described by u1 =

vmcos ( w t +


u2 =

vmcos ( w t -


where 2

vm= -6 7T

and C$ is the phase shift between u1 and u 2 . The phasors of the voltages at the input of the resonant circuits are expressed by L

- vm e j ( + / 2 )


1 -


vm e



(5) 2 Using the principle of superposition, one obtains the output voltages caused by the voltages VI and V2 as

v ei(+/z)











where w, = \/z/Lc is the resonant frequency and Q, = 2Ri/(w,L) = 2Ri/Z, is the normalized load resistance (or the loaded quality factor). The factor 2 arises from the configuration of a single inverter (1 or 2) in which the value of the resonant capacitor is C/2 and the load is 2 Ri. From (31, (61, and (71, one obtains the output voltage

L' I


[ (:Iz


Fig. 1. Phase-controlled Class D parallel resonant inverter: (a) W O conventional Class D parallel resonant inverters with ac loads connected in parallel; (b) circuit with an equivalent ac load; and (c) equivalent circuit for the fundamental components.


vmcos V 0 = v , ', ~' 0 V 2 =




+ "0


Fig. 2. Class D voltage-driven rectifiers: (a) transformer center-tapped rectifier; and (b) bridge rectifier.



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