*Using a simulation tool*

*Using a simulation tool*

*Predicting the thermal behavior of devices has become an issue of significance for power converter applications that require a tradeoff between efficiency, size and thermal and electrical performance. For such demanding applications, combined electrical-thermal simulation tools can significantly speed up the design process. One such simulation tool, PLECS, has inbuilt thermal domain modeling capabilities that permit the thermal behavior of a circuit to be simulated alongside the electrical circuit.*

*By Dr. John Schönberger, Plexim GmbH*

In this article, the thermal modeling capabilities and simulation approach offered by PLECS will be explained. A case study, in which the temperature rise of a MOSFET in a flyback converter is simulated, will be presented to demonstrate the application of the thermal modeling technique.

**Thermal simulation using PLECS**

PLECS is a circuit simulation toolbox for Simulink that is well suited for simulations of switching electrical systems that comprise both an electrical circuit and control system. The hallmark feature of PLECS is its use of ideal switches and its piecewise linear approach to solving switched electrical systems. Rather than simulating switching transitions using a small simulation time step and non-linear component models, PLECS uses ideal switching events. After each switching occurence, PLECS immediately jumps to the new operating point by forming a new set of circuit equations. This approach permits the use of a larger time step and simpler component models. The end result is that electrical simulations are fast and robust. Although PLECS was originally designed as an electrical circuit simulator, its simulation capabilities have been extended to the thermal domain. One-dimensional modeling of thermal structures and simulation of thermal power flows is possible through the use of PLECS’ thermal library.

A thermal simulation is created in PLECS by adding loss information to electrical component models and by defining the thermal network between the loss-producing components and the environment. The key component in the thermal network is the heatsink.

Unique to PLECS, this component is a uniform temperature surface that is the link between the electrical and thermal domains. Losses from all components mounted on the heatsink are automatically injected into the thermal network.

Switching and conduction losses are defined for components by extending the standard electrical component models. Example conduction and switching losses for a power diode is shown in Figure 1.

Conduction losses are defined using a 2-D lookup table in which the forward voltage drop is characterized as a function of junction temperature and conducting current. During each simulation time step, the conduction loss in Watts is calculated by multiplying the device’s forward voltage drop with the conducting current.

Switching losses are defined by creating a 3-D lookup table in which the losses are defined as a function of junction temperature, blocking voltage and conducting current. The lookup tables are created by the user using an inbuilt visual editor. During a simulation, the switching energy loss in Joules is obtained from the lookup table after each switching instant. This lookup tablebased approach adopted by PLECS is much faster when compared with the alternative method of calculating the losses from the current and voltage waveforms across the device. The alternative approach requires detailed physical device models in conjunction with a small simulation time step, resulting in slow simulations.

During an electrical-thermal simulation, interaction occurs between the electrical and thermal domains. Component losses are computed in the electrical domain and the results are fed to the thermal circuit. With each update of the thermal circuit, the junction temperatures are fed to the electrical circuit in order to account for the temperature dependency of the component losses.

### Case Study

To demonstrate the thermal modeling capabilities of PLECS, the temperature rise of the FCD4N60 MOSFET in a single-switch flyback converter for an LED supply was simulated. The results were compared with experimental measurements. The flyback converter, shown in Figure 2, converts a rectified 230 Vrms mains input into a constant DC current output of 700 mA for supplying a load of three series-connected LEDs. The converter parameters are shown in Table 1.

### Simulation Model

The electrical simulation model is designed to replicate the conditions experienced by the MOSFET in the target circuit. The PLECS circuit schematic is shown in Figure 3 with the FCD4N60 MOSFET mounted on the heatsink in order to collect the conduction and switching losses. Due to the static operating point of the converter, several simplifications were made to the electrical circuit. The input rectifier stage was replaced with a 325 V DC bus and the current control loop was omitted. The simulation model operates in open loop current control mode, regulating the peak voltage across the 1 W current sense resistor to 0.4 V. It should be noted that the switching logic for the current controller is not shown in the circuit schematic because this is modeled in the Simulink worksheet that hosts the PLECS circuit.To complete the simulation model, thermal loss information was added to the MOSFET. Lookup tables were added to the MOSFET model to account for the turn-on and turn-off losses. The loss values used, shown in Table 2, were obtained from experimental measurements taken at 27°C and 100°C. To obtain the measurements, the MOSFET was mounted on a separate heatsink with thermal glue. The thermal resistance of the heatsink structure was approximately 23 K/W therefore the thermal impedance in the simulation model was set to this value. The thermal capacitance, not given in the heatsink datasheet, was assigned to a small value of 0.2 mJ/K in order to allow the heatsink and MOSFET temperatures to converge rapidly to their final values. In practice, the thermal capacitance would be larger but the actual value is unimportant since the purpose of the simulation is to obtain the final temperature differential. The conduction losses were modeled by configuring the drain-source resistance of the MOSFET to an average value of 1 W as recommended by the datasheet. The load, consisting of three Luxeon LXK2 1A LEDs, was modeled by adding a forward voltage drop and on resistance value to an ideal diode model. Each LED was assigned a forward voltage drop of 3.1 V and an on resistance of 0.6 W such that the forward voltage drop at 1 A matches the typical datasheet value of 3.7 V.

### Results

The results, which show the temperature rise of the MOSFET case compared with the ambient temperature, are given in Figure 4. The experimental results show that the case temperature at the beginning of the experiment is 27°C. The case temperature rises to 35°C by the end of the experiment; however, the ambient temperature also rises by 3°C making the final temperature differential 5°C. For the simulation results, the final ambient temperature of 30°C is used as the starting case temperature. At the end of the simulation run, the MOSFET case temperature is 34.3°C, or 4.3°C above the ambient temperature. The simulation results show a good approximation of the experimental measurements. The temperature difference obtained with the simulation model is 4.3°C, or 14% lower than the experimental results. It should be noted that the temperature of the simulation model converged to its final value within 20 ms whereas the experimental system took approximately one minute to converge. The reason for this discrepancy is the thermal capacitance of the heatsink model was deliberately reduced in size to shorten the simulation time. If a more realistic value is needed to replicate the experimental system, it should be noted that PLECS includes a steady state analysis tool that iterates rapidly to the final steady state solution without wasting minutes or hours of simulation time.

**Conclusion**

This article has explained the principles of simulating combined electrical and thermal circuits using PLECS and has demonstrated the validity of the PLECS approach to this problem. PLECS uses a lookup tables to account for switching losses, simplifying the switching transitions and maintaining a fast simulation speed. The unique heatsink concept also permits simple coupling between the electrical and thermal domains. As an example, a thermal model of a single MOSFET switch in a flyback converter was presented and the simulated increase in case temperature showed close correlation with actual experimental measurements. More complicated thermal structures and circuits can be implemented using PLECS, including hierarchical component models and thermal circuits with multiple heat flow paths. One important point holds true regardless of the simulation complexity. The results are only as accurate as the data supplied and the validity of the electrical model.

**Acknowledgements**

The author would like to thank Michael Weirich and Marcus Schmeidl from Fairchild Semiconductor Europe for supplying the MOSFET switching loss data.