Modern high speed insulated gate bipolar transistor (IGBT) applications in switchmode power supply (SMPS) circuits provide considerable cost, current density, and onstate voltage advantage. However, accurate IGBT loss analysis in sinusoidal switchmode circuits is a difficult proposition. In power factor correction (PFC) circuits, each switching cycle is at a different current and duty cycle. As shown in Fig. 1, IGBT losses are a nonlinear function of the collector current, collector voltage, and junction temperature. The loss plane represents IGBT turnoff losses at a single clamp voltage (400Vdc).
Let's look at a behavioral modeling technique for determining losses and junction temperature of an IGBT operating in a switchmode power circuit. The 500W continuous mode PFC application of Fig. 2 demonstrates how the behavioral model simplifies the loss analysis. The circuit implementation is in closedloop form such that the junction temperature has an impact on transistor losses. Results obtained from this simulation are the average IGBT losses, junction, case, and heat sink temperatures. Modeling the 500W PFC circuit is best understood by breaking the schematic into its functional sections:
 Input waveform calculations
 Duty cycle calculation
 Ripple current determination
 IGBT behavioral model input voltages and currents
 Loss calculation and thermal modeling.
Input Waveform
The circuit in Fig. 3, on page 20, generates a rectified voltage and current as a function of the dc voltages V_{rms} and V_{powerIn}. The 90Vdc value of V_{rms} is multiplied by a V amplitude 50 Hz sine wave V_{ref} producing a 90V_{rms} ac input. Block X17 then rectifies this result to produce a rectified sinusoidal voltage comparable to V_{acABS} in Fig. 2.
The 500Vdc supplied by voltage source V_{powerIn} sets the PFC input power to 500W. Block X13 divides V_{powerIn} by V_{rms} to produce 5.556Vdc, representing the rms value of the input current for 500W input at 90Vac. Block X18 multiplies V_{ref} by the output of X13. Block X18 output represents the 50 Hz 5.556A PFC circuit input current. Absolute value function block X3 rectifies this current to develop the rectified boost inductor L1 current. The I_{on} output of X3 represents the time varying average boost inductor current IL1 in Fig. 2.
Looking at the summing and divide blocks X11 and X12 in Fig. 4, calculate the IGBT conduction duty cycle. The 390Vdc V_{out} represents the PFC circuit dc output voltage. The V_{inABS} voltage is the absolute voltage output of X17 from Fig. 3.
You can see the resulting time varying duty cycle in the graph in Fig. 4.
Boost Inductor Ripple
Current I_{on} developed in Fig. 3 is the average current in boost inductor L1. The inductor current also contains a ripple component at the switching frequency; its peaktopeak value is:
The circuit in Fig. 5, on page 22, performs the functions of Equation (2). The circuits in Figs. 3 and 4 provide the numerator terms of this equation. The denominator is the product of the switching frequency V_{freq} (1V/Hz) and L1 boost inductance V_{L1} (1V/H). The output of X25 is the peaktopeak L1 ripple current (1V/A).
The IGBT operating loss expressions are within the behavioral model block X2 in Fig. 6. Equation (3), on page 24, is representative of the form of the behavioral model equations. Coefficients c1 to c10 represent devicetype specific constants. The model equations are configured such that the input parameters are represented as voltages. A complete listing is provided in reference^{[2]}.
Developed in Fig. 3, on page 20, and Fig. 5, on page 22, are the IGBT behavioral model input currents. The average current, I_{on}, developed in Fig. 3, is directly entered as the I_{on} input current drawn by the IGBT behavioral model during conduction. The IGBT model in Fig. 6, on page 22, uses this value and the T_{j} temperature input to calculate the conduction voltage V_{sat(Ion,Tj)}.
Block X15 subtracts half the peaktopeak boost inductor current from I_{on} and applies this value to the IGBT model I_{ton} input terminal. This is the value of IGBT current at the instant it's turned on. The IGBT model uses the I_{ton}, T_{j}, and V_{ton} input values to calculate the turnon loss in joules per switching cycle, E_{on} output.
Block X8 adds half the peaktopeak boost inductor current to I_{on} and applies this value to the I_{toff} terminal. This is the value of the current at the instant it's turned off. The model uses the I_{toff}, T_{j}, and V_{toff} input values to calculate the turnoff loss in joules per switching cycle, E_{off} output.
The V_{out} voltage from Fig. 4, on page 20, is used as V_{ton} and V_{toff} IGBT model inputs. The IGBT behavioral model has separate V_{ton} and V_{toff} inputs for applications that clamp at a higher potential during the turnoff period.
Loss Calculation and Thermal Modeling
The IGBT model outputs are combined in Fig. 7, on page 22, to determine the total IGBT losses and close the junction temperature thermal loop.
Block X5 multiplies the IGBT E_{on} output terminal voltage (1V/J) times the IGBT switching frequency V_{freq} (1V/Hz). This provides the turnon switching loss in watts as a function of inputs I_{ton}, V_{ton}, T_{j}, and time.
Similarly, X6 multiplies the IGBT E_{off} output terminal voltage (1V/J) times the switching frequency V_{freq}. This provides the turnoff switching loss in watts as a function of inputs I_{toff}, V_{toff}, T_{j}, and time.
The threeinput multiplier X1 multiplies the IGBT model V_{sat} output terminal voltage times the IGBT conduction DutyCycle(t) developed in Fig. 4 and the IGBT average I_{on}(t) current developed in Fig. 3. This provides time varying average IGBT onstate losses (1V/W) at the X1 output.
The three IGBT losses are combined by threeinput summing block X7 to develop an output voltage proportional to total IGBT losses (1V/W). The output of X7 converts to a current (1V/A) by voltage controlled current source G1.
Current source output G1 (1A/W) is applied to the IGBT model's internal junction to case thermal impedance through the I/O terminals Z_{jc} and T_{case}. The G1 current flows out of the IGBT T_{case} terminal and through the casetosink and sinktoambient thermal impedances into the temperature represented by the voltage source V_{amb} (1 V/°C).
The resulting junction temperature is applied to the IGBT model T_{j} input by the thermal impedance between T_{case} to T_{j}. This closes the thermal loop such that the resulting junction temperature is used by the model loss equations.
The IGBT junctiontoambient thermal model contains thermal capacitances representing thermal time constants in the power loss path^{[4]}. Because of these time constants, simulations must be run over multiple cycles of the ac mains to reach a stable junction temperature. The run time may be reduced by setting the initial junction operating point. The initial condition switch X9 and initial temperature V_{_Initial_Temp} accomplish this. Pulse voltage source V6 opens X9 1 msec after the simulation starts.
The value of the thermal capacitance, C_{sink_amb}, was reduced to shorten the simulation run time for junction temperature convergence. This capacitance value, the product of the heat sink mass and specific heat can be large (50+ Farads). You can reduce the value while ensuring the heat sink ripple temperature is minimal at the ac mains frequency.
If this technique is used for systems requiring a large transient overload analysis, you must use the actual C_{sink_amb}. You may reduce the analysis run time by determining the preoverload steadystate T_{j} with minimal C_{sink_amb}. Then set the V_{_Initial_Temp} at this T_{j} and make the transient overload analysis with the correct C_{sink_amb} value.
Simulation Results
Fig. 8 is a time domain plot of the stabilized IGBT junction temperature and total IGBT losses over one cycle of the ac mains. The junction temperature stabilizes at 108.7°C with a ripple temperature of 8.54°C.
The 23.72W average IGBT loss (Fig. 8) can be broken down to the individual losses (Fig. 9). In this example, reducing the switching frequency has the greatest impact on IGBT losses and junction temperature.
This modeling simulation technique provides an improved method in comparison with previous techniques^{[1]}, where development of application specific expressions is necessary. This approach gives the designer ability to configure circuits using conventional schematic capture programs. It also evaluates IGBT junction temperature under transient overload conditions. This technique was previously correlated using Mathcad^{[1], [2]}. Results obtained with the IGBT behavioral model correlates with measured results with a less than 6% difference.
References

Randall, R. H., Laprade, A., Wood, B. (2000), “Characterizing IGBT Switching Losses for Switched Mode Circuits,” PCIM Europe 2000, pp. 269275, June 2000.

Laprade, A., Randall, R. H., Craig, A. (2000), “Analyzing IGBT Losses by Translating Empirical Data Into SPICE Behavioral Models,” PCIM Europe 2000, pp. 263268, June 2000.

Intersil Corporation, Mountaintop, PA, Data Sheet HGTP12N60A4, File Number 4656.2, 1999.

Worman, J.W., “Transient Thermal Impedance Explored,” PCIM Magazine, February 2000.
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