**1. Introduction**

The transistor LCC resonant DC/DC converters of electrical energy, working at frequencies higher than the resonant one, have found application in building powerful energy supplying equipment for various electrical technologies (Cheron et al., 1985; Malesani et al., 1995; Jyothi & Jaison, 2009). To a great extent, this is due to their remarkable power and mass-dimension parameters, as well as, to their high operating reliability. Besides, in a very wide-working field, the LCC resonant converters behave like current sources with big internal impedance. These converters are entirely fit for work in the whole range from no-load to short circuit while retaining the conditions for soft commutation of the controllable switches.

There is a multitude of publications, dedicated to the theoretical investigation of the LCC resonant converters working at a frequency higher than their resonant one (Malesani et al., 1995; Ivensky et al. 1999). In their studies most often the first harmonic analysis is used, which is practically precise enough only in the field of high loads of the converter. With the decrease in the load the mistakes related to using the method of the first harmonic could obtain fairly considerable values.

During the analysis, the influence of the auxiliary (snubber) capacitors on the controllable switches is usually neglected, and in case of availability of a matching transformer, only its transformation ratio is taken into account. Thus, a very precise description of the converter operation in a wide range of load changes is achieved. However, when the load resistance has a considerable value, the models created following the method mentioned above are not correct. They cannot be used to explain what the permissible limitations of load change depend on in case of retaining the conditions for soft commutation at zero voltage of the controllable switches – zero voltage switching (ZVS).

The aim of the present work is the study of a transistor LCC resonant DC/DC converter of electrical energy, working at frequencies higher than the resonant one. The possible operation modes of the converter with accounting the influence of the damping capacitors and the parameters of the matching transformer are of interest as well. Building the output characteristics based on the results from a state plane analysis and suggesting a methodology for designing, the converter is to be done. Drawing the boundary curves between the different operating modes of the converter in the plane of the output characteristics, as well as outlining the area of natural commutation of the controllable switches are also among the aims of this work. Last but not least, the work aims at designing and experimental investigating a laboratory prototype of the LCC resonant converter under consideration.

Study of LCC Resonant Transistor DC / DC Converter with Capacitive Output Filter 113

than 100 kHz they can be neglected, and the capacitor *С*0 should be placed additionally (Liu

Because of the availability of the capacitor *CS* , the commutations in the output voltage of the inverter (*ua*) are not instantaneous. They start with switching off the transistors *Q*1/*Q*3 or *Q*2/*Q*4 and end up when the equivalent snubber capacitor is recharged from *+Ud* to *–Ud* or backwards and the freewheeling diodes *D*2/*D*4 or *D*1/*D*3 start conducting. In practice the capacitors *С*2 and *С*4 discharge from *+Ud* to 0, while *С*1 and *С*3 recharge from 0 to*+Ud* or backwards. During these commutations, any of the transistors and freewheeling diodes of the inverter does not conduct and the current flowed through the resonant circuit is closed

Because of the availability of the capacitor *C*0, the commutations in the input voltage of the rectifier (*ub*) are not instantaneous either. They start when the diode pairs (*D*5/*D*7 or *D*6/*D*8) stop conducting at the moments of setting the current to zero through the resonant circuit and end up with the other diode pair (*D*6/*D*<sup>8</sup> или *D*5/*D*7) start conducting, when the capacitor *С*0 recharges from *+kU*0 to *–kU*0 or backwards. During these commutations, any of the diodes of the rectifier does not conduct and the current flowed through the resonant

The condition for natural switching on of the controllable switches at zero voltage (ZVS) is fulfilled if the equivalent snubber capacitor *СS* always manages to recharge from *+Ud* to *–Ud* or backwards. At modes, close to no-load, the recharging of *СS* is possible due to the availability of the capacitor *C*0. It ensures the flow of current through the resonant circuit,

When the load and the operating frequency are deeply changed, three different operation

It is characteristic for the first mode that the commutations in the rectifier occur entirely in the intervals for conducting of the transistors in the inverter. This mode *is the main operation mode* of the converter. It is observed at comparatively small values of the load resistor *R*0. At the second mode the commutation in the rectifier ends during the commutation in the inverter, i.e., the rectifier diodes start conducting when both the transistors and the freewheeling diodes of the inverter are closed. This is *the medial operation mode* and it is only observed in a narrow zone, defined by the change of the load resistor value which is

At modes, which are very close to no-load the third case is observed. The commutations in the rectifier now complete after the ones in the inverter, i.e. the rectifier diodes start conducting after the conduction beginning of the corresponding inverter's freewheeling

In order to obtain general results, it is necessary to normalize all quantities characterizing

diodes. This mode is *the boundary operation mode* with respect to no-load.

the converter's state. The following quantities are included into relative units:

et al., 2009).

through the capacitor *СS*.

circuit is closed through the capacitor *С*0.

modes of the converter can be observed.

however not immediate to no-load.

**3. Analysis of the converter** 

*Ud U*<sup>0</sup> = *kU*<sup>0</sup> ′ - Output voltage;

*d* 0

*C Cd xU uU* = = ′ - Voltage of the capacitor *С*;

*<sup>i</sup> y I U Z* = =′ - Current in the resonant circuit;

even when the diodes of the rectifier do not conduct.
