Thermal Resistance

The following figure shows a conceptual diagram of thermal resistance, R_θJC. The specified position of temperature depends on the package and product.

Where:
T_J is junction temperature,
T_C is case temperature, and
R_θJC is thermal resistance between junction and case.

Calculation from Case Temperature

Junction temperature, T_J is estimated from the measured values of loss and case temperature, T_C during the power MOSFET/IGBT operation and the thermal resistance, R_θJC described in the electrical characteristics of the data sheet. T_J is calculated by the following equations.

Where:
P is the loss of the power MOSFET/IGBT (W),
R_θJC is thermal resistance between junction and case (°C/W), and
T_C is case temperature (°C).

As an example, when P = 0.6 W, R_θJC = 20 °C/W, and T_C = 80 °C, T_J is calculated by the following equation.

Calculation from Transient Thermal Resistance Characteristics

T_J when power is applied instantaneously is estimated from the transient thermal resistance data. T_J is calculated by the following equation.

Where:
P is the loss of the power MOSFET/IGBT (W),
r_θJC is transient thermal resistance between junction and case temperature (°C/W), and
T_C is case temperature (°C).

The following figure shows the transient thermal resistance characteristics example. For example, when a single square pulse of 100 ms is applied, r_θJC is 2 °C/W.

For example, when P = 0.6 W, r_θJC = 2 °C/W, and T_C = 100 °C, T_J is calculated by the following equation.

Calculation Using Superposition Theorem

This section shows the calculation of the junction temperature, T_J, when a regular square wave power loss occurs in the power MOSFET/IGBT and the junction temperature, T_J, when an irregular square wave power loss occurs in the power MOSFET/IGBT. For such power loss waveforms, it is easy and effective to read the thermal resistance in each period from the transient thermal resistance characteristic graph in the data sheet and use the superposition theorem.

Continuous Pulse

(A) shows the calculation of the junction temperature, T_J, when a regular square wave power loss occurs in the power MOSFET/IGBT. To easily calculate T_J, assume that power losses for two cycles occur in the average power loss over the entire period.
As shown in (B) and (C), T_J is calculated by approximating the power loss and using the superposition theorem.

Next, the junction temperature is calculated for each block in (C).

Thus, T_J when using the superposition theorem is calculated by the following equation.

Where:
T_C is case temperature (°C),
P_M is average power loss (W),
t1 is period (s),
t_P is pulse width (s),
R_θJC is the steady-state thermal resistance between junction and case temperature (°C/W),
r_θJC(t1+tP) is the thermal resistance between junction and case temperature in the period, t₁+t_P (°C/W),
r_θJC(t1) is the thermal resistance between junction and case temperature in the period, t₁ (°C/W), and
r_θJC(tP) is the thermal resistance between junction and case temperature in the period, t_P (°C/W).

Irregular Pulse

(A) shows the calculation of the junction temperature, T_J, when an irregular square wave power loss occurs in the power MOSFET/IGBT. As shown in (B), T_J for each block is calculated by using the superposition theorem.

Thus, T_J when using the superposition theorem is calculated by the following equation.

Where:
T_C is case temperature (°C),
P₁ to P₃ is power loss for each pulse (W),
r_{θJC(t6−t1)} is the thermal resistance between junction and case temperature in the period, t₆−t₁ (°C/W),
r_{θJC(t6−t2)} is the thermal resistance between junction and case temperature in the period, t₆−t₂ (°C/W),
r_{θJC(t6−t3)} is the thermal resistance between junction and case temperature in the period, t₆−t₃ (°C/W),
r_{θJC(t6−t4)} is the thermal resistance between junction and case temperature in the period, t₆−t₄ (°C/W), and
r_{θJC(t6−t5)} is the thermal resistance between junction and case temperature in the period, t₆−t₅ (°C/W).