1. Modelling the Half-bridge Dc-Dc Converter with Selfheating Taken into Account
Małgorzata Godlewska, Krzysztof Górecki
Department of Marine Electronics, Gdynia Maritime University, Poland

2. Outline Introduction Models of Components of the Converter
Investigations Results
Conclusions

3. Introduction
In the switch-mode power supply systems requiring galvanic isolation between the input and the output half-bridge dc-dc converters are often used.
An important component of such a converter is a pulse transformer with a split secondary winding and semiconductor devices.
In the analysis and design of electronic circuits a computer simulations that require computer models of all components of the analysed system are commonly used.
These models should take into account all relevant phenomena in each of these components, and at the same time should be simple enough to enable obtaining the results of calculations rapidly.
Therefore, many models of electronic components dedicated to different applications and characterised by varying accuracy are presented in the literature.
This paper presents the results of simulations and measurements of the half-bridge dc-dc converter taking into account self-heating phenomena in semiconductor devices and in the transformer.

4. Models of Components of the Converter
The most important element of the converter is a transformer.
In its model, three blocks are distinguished:
Core Model,
Winding Model
Thermal Model.
The model of the core is based on the modified Jiles-Atherton model.
In this model the magnetic force corresponds to the voltage on the terminal H.
The magnetic flux density corresponds to the voltage at the output terminal B.
Power losses in the core are equal to the voltage at terminal Ploss.

5. Models of Components of the Converter (2)
The winding model includes three circuits representing respectively: the primary winding and two secondary windings.
In the model of the primary winding the resistor RS1 represents the series resistance of the winding at the reference temperature, the controlled voltage source ERS1 describes resistance changes with the change of temperature TU.
The controlled voltage source EV models the voltage induced in the primary winding; the controlled current source GL1 represents the magnetising current, the controlled current source GR - energy losses in the core.
Voltage VRMS1 is used to designate peak magnetisation and is calculated by means of the controlled voltage source ERMS1.
The secondary winding model contains only elements used for modelling the voltage winding (EV) and the series resistance of that winding (RS, and ERS)
The thermal model allows the calculation of the core temperature TR and the winding temperature TU taking into account self-heating and mutual thermal coupling between the core and windings.
The MOS transistor and the diode are described with the use of linear hybrid electrothermal models.

6. Investigations results
half-bridge dc-dc converter
The examined converters containing the sequence toroidal :
powder core RTP-26.9x14.5x11 made of the material T106-26,
ferrite core RTF-25x15x10 made of the material F-867
the nanocrystalline core RTN-26x16x10 made of the material M-070.
Each transformer includes three windings of 20 coils made of enamel copper wire of the diameter of 0.8 mm

7. Investigations results (2)
the converter containing the transformer with the RTP core f = 200 kHz, d = 0.3 Vin = 25 V.
Good agreement between the results of measurements and calculations for the authors’ model of the transformer.
For the model of an ideal transformer large discrepancies (even more than 25%) with the results of measurements and calculations.
The measured watt-hour efficiency reaches the maximum 0.72 for R0 = 20 Ω, and then decreases to 0.03 with resistance R0 = 10 kΩ.

8. Investigations results (3)
the converter containing the transformer with the RTF or RTN core.
the measured maximum watt-hour efficiency was 0.83 for R0 =50Ω.
The RTF core is characterised by the lowest value of the saturation flux density and the large surface magnetisation curve.
Hence, the results are largely in line with the measurements - both for simulation of the authors’ transformer model and the model describing the linear transformer.

9. Investigations results (4)
the converter with the transformer containing the core RTP and the RTN at f = 200 kHz, and Vin = 25 V.
The maximum value of the measured Uwy = V is for the powder core at R0 = 10 kΩ and 15.3 V at R0 = 10 kΩ - for the nanocrystalline core.
Big discrepancies between the results of measurements and simulations for small values of R0 (up to 100% for load resistance R0 = 5 Ω).
This reflects the fact that in the analysis of component of power losses in the considered system was neglected, which is important at high output currents.

10. Investigations results (5)
the temperature dependence of the transformer core and windings for each of the three considered cores at:
f = 200 kHz and Vin = 25 V f = 100 kHz and Vin = 60 V.
For f = 200 kHz the highest value of temperaturę was obtained for the powder core. It is equal to 36.4 °C at R0 = 10 kΩ.
For f = 100 kHz the powder core reaches the highest temperature - up to 100°C for load resistance of 200Ω
The results of simulations carried out using the authors’ model are similar to the measurement results.
Of course, it was not possible to perform simulations using the model of ideal transformer.

11. Conclusions
The paper proposes a method of modelling the half-bridge dc-dc converter with thermal phenomena in the semiconductor and magnetic devices taken into account.
The form of the used electrothermal models of the considered components of the converter is presented and their usefulness was verified for the system containing transformers with powder, ferrite and nanocrystalline cores, the power MOS transistors and Schottky diode.
The simulations and experiments results show that the use of the authors’ electrothermal models is more accurate for modelling the considered converter than the classical models of the system components and that also allows determining the internal temperatures of that converter components.

12. Conclusions (2)
A particularly significant advantage of the electrothermal model of the transformer over the linear model of this element are observed for dc-dc converter containing the transformer with powder core.
The presented model of components of the considered converter can be successfully used to simulate other switch-mode power supplies.