1. Introduction
For industrial applications, reliability and power density are two important considerations in the design process of power converters. Modern power converters with increased power density require efficient and intelligent thermal design and management [
1,
2] to ensure the reliability of the systems. Accordingly, there is an ongoing need to build thermal models to help thermal analysis and power converter optimization.
The forth-order Foster [
3,
4] and Cauer networks [
5,
6] are being widely used to describe the thermal response of junction-to-case for power components. Based on the Cauer network, the one-dimensional thermal network can be extended to one or two orders of case-to-heatsink as shown in
Figure 1 [
7] for thermal analysis. The network is fast to calculate the junction temperatures (
Tj) of power components. While this kind of model just focuses on the self-resistances, it cannot calculate the thermal coupling.
In a compact IGBT (insulated-gate bipolar transistor) module, multiple IGBT chips and diodes are packaged as shown in
Figure 2a.
Tj of the Si-chips can be affected thermally by the neighboring chips placed on the same substrate. Based on the multi-chip structure of an IGBT module, the networks built in [
8,
9] consider the conduction thermal coupling resistance (
Rcdcp) generated by neighboring Si-chips. The model in
Figure 2b can be used to calculate the
Tj of power devices and the method is more accurate than the ones that do not consider the effect of thermal coupling among the surrounding chips. While this kind of thermal model just focuses on a single module, it ignores the coupling between modules in a system.
FEM simulations [
10] can be used to describe the thermal distribution of components or converter systems and the junction and case temperatures can be extracted by adding virtual thermal probes to active and passive power components. The thermal coupling matrix in [
11] is extracted by FEM simulation with a given power to heat up the chip. In this study
Rcdcp is dependent on the geometric positions of the chips in a LED module. This thermal matrix is used for
Tj estimation. Heat flow in
Figure 3 shows the
Rcdcp that is generated among several structure layers and the model in [
12] compares the temperatures at the same position in the vertical direction of each layer and computes the thermal resistances among them. However, to build more accurate FEM models, familiarity with complex geometric structures, appropriate meshing methods, and boundary conditions are essential [
13]. This model focuses on the coupling between different layers in a single module and it does not consider the coupling between neighboring modules.
Erik et al. built a thermal model which considers the
Rcdcp between the components in a power converter based on the surface or case temperatures (
Tc) mapping in [
14]. The
Rcdcp in the red color in
Figure 4 are generated by connected copper traces in the PCB and these resistances are dependent on the location of the components. Their locations can be optimized based on the temperature’s mapping network and a power converter is optimized in [
15]. The advantage of this model is that it considers the components in the overall system. While this model just focuses on the conduction coupling, it ignores the convection coupling effect.
Higher power and smaller size are required for high-power density converters [
16,
17], which make the process of thermal dissipation more difficult. Moreover, power devices are exposed in power converters and part of the heat that is released in the narrow space by the way of convection and thermal convection is environmentally dependent. Changes of convection coupling will be induced when the thermal environment is changed in the converters. Due to these factors, thermal convection cannot be ignored [
18], and the thermal models should incorporate the convection thermal coupling resistances (
Rcvcp) among the heating components. These thermal models in the literature ignore the effect of convection coupling [
19]. Furthermore, the method is not extensively discussed and analyzed for the purposes of calculating the thermal coupling resistances (
Rcp) which include
Rcdcp and
Rcvcp.
The major contributions of this paper are as follows: thermal analysis of a boost converter system has been given to compare the junction temperatures and the increments under different working conditions; a multi-variable thermal analysis resistances network has been built which includes Rcdcp and Rcvcp; the coupling resistances, MOSFET to the diode () and the diode to MOSFET (), have been respectively calculated based on the proposed model; and the relationships between Rcp and their impact factors (separation distances and working currents) have been discussed.
The paper is organized as follows: First, the thermal analysis of a boost converter is given in
Section 2. Measurement of thermal coupling of power components and losses calculation are presented in
Section 3. A multi-variable thermal resistances model has been established in
Section 4. Calculation and coupling measurements at new separation distances have been built to verify the proposed model in
Section 5. Finally, the main conclusion is drawn in
Section 6.
2. Thermal Models in a Boost Converter System
There are two important considerations in the converter design phase to ensure the reliable operation of the converter: (1) Maximum junction temperature
Tj of the devices, e.g., Si-based devices, cannot exceed 175 °C [
1,
20]; and (2) the ability to share heat among the components with a much greater uniform temperature distribution [
14,
21].
Figure 5 describes three cases of thermal maps, where
Figure 5c shows the best thermal profile for converter design and operation. This means it is desirable to control the temperatures at junctions in order to operate the power devices at good temperature ranges within the safety operation region even in the worst-case scenario. Thermal coupling resistances analysis among the components can help with the thermal distribution.
In a DC-DC boost converter, the MOSFET and the diode are two key heating components which can affect the performance of the overall converter systems [
22]. PLECS has its advantages to simulate the dynamic systems for power converters [
23]. The simulation schematics are shown in
Figure 6. These figures give basic thermal models which are used for thermal descriptions and the
Tj increments’ (
) comparisons.
The thermal model simulates the boost converter at different frequencies (10 kHz, 20 kHz, and 50 kHz) and different loading resistances (5 Ω, 8 Ω, and 10 Ω).
Figure 7 gives the
at different frequencies (load: 5 Ω) for the MOSFET (duty cycle: 0.5) and the diode with a shared heatsink (System 1) and two separate heatsinks (System 2), respectively.
Figure 8 gives the
at different loads (frequency: 20 kHz). The load voltage, load current, and inductor current under different working conditions are also given in
Figure 7 and
Figure 8.
Based on the simulation results, the value of increases while the frequency increases which indicates a greater thermal coupling effect at a higher frequency. The value of decreases with the smaller operating current (by increasing loading resistance). In other words, the greater thermal coupling effect will be induced by a larger current passing through the MOSFET and the diode, and vice versa. Moreover, the Tj of the MOSFET and the diode with a shared heatsink are relatively higher than the ones with separate single heatsinks. The major reason for causing these is the conduction thermal coupling between the two devices, since they share the same heatsink. However, these kinds of models cannot calculate the convection coupling.
6. Conclusions
In this study, comparisons of junction temperatures and the increments in a boost converter system have been given to show the conduction thermal coupling effect under different working conditions. Conduction and convection coupling have been added into the mutual thermal effects and a multi-variable thermal resistances model has been built, which includes the variable thermal resistances, and . In addition, the relationships between the thermal coupling resistances and their impact factors (d and I) have been discussed. Calculation and measurements have been done to verify the concept. The errors between the calculations and measurements are less than 4% for both the MOSFET and the diode, which prove the efficacy of the proposed method. Based on the proposed thermal model, Tj can be estimated. Moreover, heatsinks can be included by adding the thermal resistances of heatsinks to discuss the cooling schemes. Additionally, extension thermal models can be given for the overall converters by adding thermal resistances of other components (e.g., capacitors, inductors) to assist the components layouts and the separation distances between them in order to optimize the power converters.