Thermal Resistance

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

T_J is junction temperature,
T_L is lead temperature,
T_A is ambient temperature,
R_th(J-L) is thermal resistance between junction and lead, and
R_th(J-A) is thermal resistance between junction and ambient.

Calculation from Lead Temperature and Ambient Temperature

Junction temperature, T_J is estimated from the measured values of loss and temperature (lead temperature, T_L, ambient temperature, T_A) during diode operation and the thermal resistance described in the electrical characteristics of the data sheet. T_J is calculated by the following equations.

• Calculation estimating from the lead temperature

TJ = P × Rth(J-L) + TL



• Calculation estimating from the ambient temperature

TJ = P × Rth(J-A) + TA

Where:
P is the loss of the diode (W),
R_th(J-L) is thermal resistance between junction and lead (°C/W),
R_th(J-A) is thermal resistance between junction and ambient temperature (°C/W),
T_L is lead temperature (°C), and
T_A is ambient temperature (°C).

As an example, when P = 0.6 W, R_th(J-A) = 20 ° C/W, and T_A = 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 diode (W),
r_th(J-A) is transient thermal resistance between junction and ambient temperature (°C/W), and
T_A is ambient temperature (°C).

The following figure shows the transient thermal resistance characteristics of SJPZ-N18. For example, when a single square pulse of 100 ms is applied, r_th(J-A) is 9 °C/W.

For example, when P = 0.6 W, r_th(J-A) = 9 °C/W, and T_A = 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 diode and the junction temperature, T_J, when an irregular square wave power loss occurs in the diode. 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 diode. 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).

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

Where:
T_A is ambient temperature (°C),
P_M is average power loss (W),
t1 is period (s),
t_P is pulse width (s),
R_th(J-A) is the thermal resistance between junction and ambient temperature in the entire period (°C/W),
r_{th(J-A)(t1+tP)} is the thermal resistance between junction and ambient temperature in the period, t1+t_P (°C/W),
r_th(J-A)(t1) is the thermal resistance between junction and ambient temperature in the period, t1 (°C/W), and
r_th(J-A)(tP) is the thermal resistance between junction and ambient 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 diode. 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_A is ambient temperature (°C),
P₁ to P₃ is power loss for each pulse (W),
r_{th(J-A)(t6−t1)} is the thermal resistance between junction and ambient temperature in the period, t₆−t₁ (°C/W),
r_{th(J-A)(t6−t2)} is the thermal resistance between junction and ambient temperature in the period, t₆−t₂ (°C/W),
r_{th(J-A)(t6−t3)} is the thermal resistance between junction and ambient temperature in the period, t₆−t₃ (°C/W),
r_{th(J-A)(t6−t4)} is the thermal resistance between junction and ambient temperature in the period, t₆−t₄ (°C/W), and
r_{th(J-A)(t6−t5)} is the thermal resistance between junction and ambient temperature in the period, t₆−t₅ (°C/W).