Estimating junction temperature of Power MOSFETS using RC Thermal Network (Cauer)

         The estimation of junction temperature is useful to predict the reliability of power MOSFET in a circuit. It is known that junction temperature must be kept as low as possible. Also it can be useful to create a quasi-dynamic thermal model of MOSFET, by meaning of changing the voltage threshold and drain source resistance function of temperature. It is known that in reality, temperature affects the transfer curve of MOSFET. For create a model , we need a circuit simulator like LTSPICE, and will show later in this article how to use the thermal RC network offered by manufacturers (like International Rectifier). The RC network is included in the SPICE model, but has to be "activated".

Reference 1

            The figure above represent the mechanism (logic diagram) of creating the quasi-dynamic model. It is shown that two parameters are modified by the junction temperature:

            -voltage threshold is decreasing by increasing the temperature junction, that means will turn on faster

            -resistance drain source is increasing by increasing the temperature junction

            The implementation of this can be done simple by introducing a series voltage source ( for emulate the voltage threshold changes) in series with MOSFET gate, and a variable resistance in series with the drain MOSFET. Don't forget to calculate the dissipation power from MOSFET plus the dissipation from resistance, because it's broken out but it's emulate the changing Rds (resistance drain source). Later in this article we will shown an example from LTSPICE.

           We will take for example the IRF7341 power mosfet, and his SPICE model with included RC network (3 terms RC and is sufficient to represent the entire thermal impedance curve). The spice model of IRF7341 is shown below (courtesy of International Rectifier). This model can be used with LTSPICE.

.SUBCKT irf7341q 1 2 3
* SPICE3 MODEL WITH THERMAL RC NETWORK
**************************************
* Model Generated by MODPEX *
*Copyright(c) Symmetry Design Systems*
* All Rights Reserved *
* UNPUBLISHED LICENSED SOFTWARE *
* Contains Proprietary Information *
* Which is The Property of *
* SYMMETRY OR ITS LICENSORS *
*Commercial Use or Resale Restricted *
* by Symmetry License Agreement *
**************************************
* Model generated on Feb 11, 05
* MODEL FORMAT: SPICE3
* Symmetry POWER MOS Model (Version 1.0)
* External Node Designations
* Node 1 -> Drain
* Node 2 -> Gate
* Node 3 -> Source
M1 9 7 8 8 MM L=100u W=100u
.MODEL MM NMOS LEVEL=1 IS=1e-32
+VTO=2.06826 LAMBDA=0.00115249 KP=20.5203
+CGSO=7.04452e-06 CGDO=3.07926e-07
RS 8 3 0.0149433
D1 3 1 MD
.MODEL MD D IS=5.67066e-11 RS=0.0120989 N=1.22605 BV=55
+IBV=0.00025 EG=1.2 XTI=1 TT=1e-07
+CJO=3.08331e-10 VJ=5 M=0.500521 FC=0.5
RDS 3 1 5e+07
RD 9 1 0.0174969
RG 2 7 2.30282
D2 4 5 MD1
* Default values used in MD1:
* RS=0 EG=1.11 XTI=3.0 TT=0
* BV=infinite IBV=1mA
.MODEL MD1 D IS=1e-32 N=50
+CJO=1.17624e-09 VJ=0.5 M=0.9 FC=1e-08
D3 0 5 MD2
* Default values used in MD2:
* EG=1.11 XTI=3.0 TT=0 CJO=0
* BV=infinite IBV=1mA
.MODEL MD2 D IS=1e-10 N=0.4 RS=3e-06
RL 5 10 1
FI2 7 9 VFI2 -1
VFI2 4 0 0
EV16 10 0 9 7 1
CAP 11 10 1.71653e-09
FI1 7 9 VFI1 -1
VFI1 11 6 0
RCAP 6 10 1
D4 0 6 MD3
* Default values used in MD3:
* EG=1.11 XTI=3.0 TT=0 CJO=0
* RS=0 BV=infinite IBV=1mA
.MODEL MD3 D IS=1e-10 N=0.4
.ENDS irf7341q

*SPICE Thermal Model Subcircuit
.SUBCKT irf7341qt 3 0

R_RTHERM1 3 2 13.21106213
R_RTHERM2 2 1 33.25724181
R_RTHERM3 1 0 16.01857683
C_CTHERM1 3 0 0.003348557
C_CTHERM2 2 0 0.027461688
C_CTHERM3 1 0 2.30357543

.ENDS irf7341qt

 The lasts lines are related to the thermal model subcircuit. It is sufficient three RC terms ? The answer is in the next figure. The continuos lines is the real thermal impedance, and dotted line is the approximation curve (curve fitting).It is shown that three group of RC is exact the thermal impedance. To improve the accuracy of junction temperature prediction (estimation), have to look at material properties like thermal resistance and thermal capacitance if is changing with the temperature. It is shown in literature (reference ) that Silicon is changing properties with the temperature. We will discuss later about this. Many engineers using this network to predict the temperature junction , and is currently widely used. We will try to improve this model.

Reference 2

References
1) Simulation assists thermal management in power semiconductor, David Divins (Senior Staff Field Applications Engineer, International Rectifier,USA)
2) Multidomain Simulation in Power Electronics:Combining Circuit Simulation,Electromagnetic and Heat Transfer, Andreas Musing, Marcelo Lobo Heldwein,ETH Zurich,Gecko Research