Determine MOSFET Junction Temperature And Switching Losses For Various Package Types

For example, if a MOSFET in an SO8 package (θ_JD = 15°C/W) dissipates a P_j of 1 W and must maintain a junction temperature below 125°C, then the measured drain temperature must not exceed 110°C according to Equation 1:

T_D = 125°C – (1 W × 15°C/W) = 110°C          (2)

Using Equation 1 implies that P_j can be determined under any operational condition and that the total power generated inside the package is dissipated to ambient through the drain leads. In reality, the accuracy of the P_j calculation is relatively low because switching losses in the MOSFET cannot be calculated accurately enough. Also, since a portion of P_j is dissipated to ambient through the MOSFET package, the actual heat flow through the drain leads is smaller than P_j, which presents another source of error.

The more accurate technique starts by considering the MOSFET thermal model in the figure, which is a modification of the model used in “Estimating TJ of SO-8 Power MOSFETs”.

According to this model, the total heat generated in the package, represented by current source P_j, flows to ambient through two parallel branches. The first is the junction-drain (leads)-to-PCB-to-ambient route (the “drain” or “lead” branch, labeled P_jD) with junction-to-drain thermal resistance θ_jD, drain-to-PCB thermal resistance θ_DB, and PCB-to-ambient thermal resistance θ_BA. The second is junction-to-case (package)-to-ambient (the “case” or “package” branch, labeled P_jC) with junction-to-case thermal resistance θ_jC and case-to-ambient thermal resistance θ_CA. The model represents the case temperature as TC and the ambient temperature T_A by a voltage source.

Applying conventional electrical circuit analysis and Ohm’s law to the model, we obtain the following equations for the heat (P_jD and P_jC) flowing through the respective drain and case branches:

P_jD = P_j/(1 + θ_D/θ_C)     (3)

P_jC = P_j/(1 + θ_C/θ_D)     (4)

where θ_D = θ_JD + θ_DB + θ_BA (total drain-branch thermal resistance) and θ_C = θ_jC + θ_CA (total case branch thermal resistance). So, total heat flow P_j is:

P_j = P_jD + P_jC     (5)

Applying Ohm’s law to the combinations of thermal resistances in each branch of the diagram in the figure, we get two equations for junction temperature:

T_j = T_D + [(T_D – T_A) × θ_jD]/(θ_DB + θ_BA) = T_D + [(T_D – T_A) × θ_jD/θ_DA]      (6)

T_j = TC + [(TC – T_A) × θ_jC)]/θ_CA      (7)

Neither of these equations contain the troublesome heat power term, P_j, and either one can be used to calculate the junction temperature, T_j, as long as the case, drain, and ambient temperatures and the thermal resistances of the package are known.

Consider a typical SO8 power MOSFET with thermal resistances θ_CA = 380°C/W, θ_JC = 18°C/W, θ_JD = 15°C/W, and θ_DA = 20°C/W (given in “Estimating TJ of SO-8 Power MOSFETs,” again). Substituting these values into Equations 3 and 4, we obtain:

P_jD/P_j = 1/[1 + (15 + 20)/(18 + 380)] = 0.92      (8)

P_jC/P_j = 0.08     (9)

In other words, 92% of the total power generated in the silicon is dissipated to ambient through the drain, and the remaining 8% is dissipated through the case.

Another important observation is that θ_CA is much greater than any other thermal resistance in the system, which makes the second term in Equation 7 relatively small. Assuming TC = 125°C and T_A = 85°C for the set of parameters given above, Equation 7 gives a junction temperature of:

T_j = 125 + [(125 – 85) × 18]/380 = 126.9°C     (10)

This is only 1.9°C greater than the case temperature. Using Equation 6, the drain temperature is:

T_D = {T_j + [(T_A ×θ_jD)/θ_DA)]}/(1+ θ_JD/θ_DA) = {126.9 + [(85 × 15)/20)]}/(1 + 15/20) = 108.9°C     (11)

So, the drain temperature is 16.1°C lower than the case temperature. This implies that for an SO8 power MOSFET with a θ_jD on the same order as θ_DA and with a θ_CA much greater than θ_JC, the drain temperature tends to be lower than the case temperature. Also, the plastic case temperature is an accurate representation of the junction temperature.

According to the measured results in “Estimating TJ of SO-8 Power MOSFETs,” the difference between T_j and TC for SO8 packages is typically 1°C to 3°C. If we use the same equations for other MOSFET packages, like PPAKSO8, D2PAK, DPAK, and LFPAK with low junction-to-drain thermal resistances (see the table, again), both the drain and case temperatures are close to the junction temperature. For DirectFET type MOSFETs with metal cases, θ_JD is even lower and, according to Equation 6, the drain temperature is an accurate representation of the junction temperature.

For a more accurate T_j calculation based on Equation 6, θ_DA, which is not available from MOSFET datasheets, can be determined. According to the model, junction-to-ambient thermal resistance, θ_jA, which is provided in datasheets, is a parallel combination of θD and θC resistances and θ_DA = θD – θ_jD. Applying this to the model, we can get:

θ_DA = θ_jA/(1 – θ_jA/θC) – θ_jD     (12)

Taking into account that θC is approximately an order of magnitude greater than θ_jA, Equation 12 can be simplified as:

θ_DA ≈ (1.1 × θ_jA) – θ_jD     (13)

Substituting Equation 13 into Equation 6, we get:

T_j ≈ T_D + [(T_D – T_A) × θ_jD]/[(1.1 × θ_jA) – θ_jD]      (14)

where all the thermal resistance values are available from the datasheets.

We calculated the junction temperature based on parameters specified on a MOSFET’s datasheet and temperature measurements taken from the component under test conditions. A conventional measurement technique for the drain (lead) and case (package) temperature uses thermocouples placed on the package and on the lead areas.

This technique results in measured temperatures that are lower than actual temperatures for two reasons. First, the thermocouple itself works as a heatsink, cooling the device down. Second, its physical placement is critical when trying to determine the device’s hottest temperature. A more accurate temperature measurement method uses an infrared camera to determine the hottest temperature in the areas of interest (case and lead) without interfering with the heat flow.

Once the junction temperature is determined, the total power generated in the silicon, P_j, can be calculated:

P_j = (T_j – T_A)/θ_jA     (15)

where θ_jA is the junction-to-ambient thermal resistance available from the MOSFET’s datasheet. P_j also can be calculated based on Equation 3 and the junction-to-drain thermal resistance, which is also available from the datasheets:

P_j = [(1 + θD/θC) × (T_j – T_D)]/θ_jD     (16)

Although θD and θC are not available from the datasheets, θC is approximately one order greater than θD, so Equation 16 can be simplified as:

P_j ≈ [1.1 × (T_j – T_D)]/θ_jD     (17)

After P_j is determined, switching losses, PSW can be calculated in the conventional way:

PSW = P_j – Pdc – Pg = P_j – [Irms2 × R_DS(on)] – [Q × Vg × F_SW]     (18)

where Pdc = conduction (dc) losses, Pg = gate drive losses, Irms = the rms value of the drain current, RDS(on) = the MOSFET on resistance, Q = total gate charge, Vg = peak gate voltage, and FSW = switching frequency. For a square-wave drain current with peak current of Ipk and duty cycle D, Irms2 = I_pk² × D.

This analysis of the modified thermal model of the MOSFET demonstrates that the hottest spot on the lead and package areas of a power MOSFET is typically a couple of degrees Celsius less than the junction temperature. This hot-spot temperature can be accurately measured by an infrared camera without affecting the device’s heat flow, and the result can be used with the thermal resistance values found in the datasheet to calculate the MOSFET’s junction temperature. Finally, the total power generated inside the silicon and the switching losses can be calculated.