IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 14, NO. 5, SEPTEMBER 1999 803 Self-Sustained Oscillating Resonant Converters Operating Above the Resonant Frequency Humberto Pinheiro, Member, IEEE, Praveen K. Jain, Senior Member, IEEE, and G´ eza Jo´ os, Senior Member, IEEE Abstract—This paper presents a new control technique for res- onant converters. Unlike conventional variable frequency control which externally imposes the switching frequency, the proposed scheme is based on controlling the displacement angle between one of the resonant circuit variables, typically the current through the resonant inductor, and the voltage at the output of the inverter. As a result, zero-voltage switching (ZVS) can be ensured over a wide operating range. The proposed control technique can be applied for series, parallel, and series-parallel resonant converters. As an example, the static characteristics and dynamic model of a series-parallel resonant converter with the proposed controller are derived and the system behavior is investigated in detail. Experimental results are given to demonstrate the operation of resonant converters with the proposed controller and to validate the analysis. Index Terms—DC–DC power conversion, describing functions, frequency control, frequency response, resonant power conver- sion, switched mode power supplies. I. INTRODUCTION T HE SWITCHING losses in voltage-fed load resonant converters can be eliminated by ensuring that the inverter output current lags the inverter output voltage. In this way, the inverter output current has the required polarity to charge and discharge the snubber capacitors, ensuring that the turn-on and turn-off of the switches take place under zero voltage, therefore eliminating the switching losses. A common approach of achieving zero-voltage switching (ZVS) in resonant converters is to operate them above the resonant frequency [1], [2]. However, the resonant frequency of these converters depends on the power circuit parameters and can vary significantly with the load, as in the case of series-parallel resonant converters [3]. In the conventional variable frequency control, in order to guarantee ZVS under all load conditions, the switching frequency has to be limited at a value much higher than the nominal resonant frequency, resulting in derating of the converter. Although there are a number of control techniques for resonant converters, they have at least one of the following limitations: 1) they are based on nonlinear control laws which make their practical implementation complex [4]–[6]; 2) the control law is derived for a particular resonant circuit con- figuration [7], [8]; and 3) the operation above the resonance Manuscript received July 24, 1998; revised February 12, 1999. Recom- mended by Associate Editor, L. Xu. H. Pinheiro is with the Department of Electronics and Computer Engineer- ing, Federal University of Santa Maria, Santa Maria, Brazil. P. K. Jain and G. Jo´ os are with the Department of Electrical and Computer Engineering, Concordia University, Montr´ eal, P.Q., Canada. Publisher Item Identifier S 0885-8993(99)07298-1. frequency is largely dependent on the power circuit parameters [9]. In order to overcome the above-mentioned limitations, this paper introduces a new control scheme for resonant converters. The main goal of this control scheme is to ensure ZVS condi- tion for all operating points of the converter independently of the power circuit parameters. This is accomplished by making the converter operate in self-sustained oscillation mode where the phase angle between the inverter output voltage and one of the resonant circuit variables is directly controlled. The remainder of this paper is organized as follows. In Section II, the operation of the proposed controller with dif- ferent resonant converters is explained. In Section III, the implementation of the proposed controller is addressed. In Section IV, the impact of the proposed self-sustained con- troller on the static characteristics and dynamic behavior of a series-parallel resonant converter is investigated in detail. In Section V, a comparison between the conventional variable frequency control and the proposed controller is carried out. In Section VI, experimental results that validate the analysis carried out and demonstrate the feasibility of the proposed scheme are presented. II. RESONANT CONVERTERS IN SELF-SUSTAINED OSCILLATION MODE In this section, the operating principle of the proposed controller is described. The operation of a number of resonant converters with this controller is examined and the range of the control variable for proper operation with ZVS is identified. A. Proposed Controller Operating Principle A necessary condition to achieve ZVS in voltage-fed load- resonant converters is to have current lagging the voltage at the inverter output terminals, as indicated in Fig 1. The phase angle between the current and the voltage at the inverter output terminals can be controlled by generating the inverter output voltage from the current . Fig. 2(a) shows the case where the voltage is generated by shifting the current by an angle . According to this figure, the current lags the voltage if 90 180 . It is worth noting that the switching frequency is no longer externally imposed as in the conventional variable frequency control approach since the voltage is generated from the current . As a result, the converter is said to operate in self-sustained oscillation mode. The question that arises at this point is associated with 0885–8993/99$10.00  1999 IEEE