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AN11156
Using Power MOSFET Zth Curves
Rev. 1 — 28 September 2012

Application note

Document information
InfoContentKeywords

Power MOSFET, Zth curves, Junction temperature, Single shot,
Rectangular pulse, Composite waveform, Pulse burst, Zth(j-mb),
Superimposition, Thermal impedance

Abstract

Most applications which include power semiconductors usually involvesome form of pulse mode operation. This paper gives several worked
examples showing how junction temperatures can be simply calculatedusing the device Zth curves. Examples are given for a variety ofwaveforms.

AN11156

NXP Semiconductors

Using Power MOSFET Zth Curves

Revision history
RevDateDescription

1.0

20120928

initial version

Contact information
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For sales office addresses, please send an email to: salesaddresses@nxp.com
AN11156

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AN11156NXP Semiconductors

Using Power MOSFET Zth Curves

1. Introduction
Most applications which include power semiconductors usually involve some form ofpulse mode operation. This paper gives several worked examples showing how junction
temperatures can be simply calculated using the device Zth curves. Examples are given
for a variety of waveforms:• Single shot rectangular pulse• Composite waveforms• A pulse burst• Non-rectangular pulses
Throughout this document we will use the SOT404 BUK961R6-40E device as anexample.

2. Calculating junction temperatures
From the point of view of reliability it is most important to know what the peak junction
temperature will be when the power waveform is applied. Peak junction temperature willusually occur at the end of an applied pulse and its calculation will involve transient
thermal impedance. The temperature difference caused by the dissipated power isT(j-mb).

2.1 Single shot rectangular pulse
Referring to Figure 1 it can be see that for a single shot pulse, the time period between
pulses is infinite, i.e. the duty cycle  = 0. In this example 1000 W is dissipated for a periodof 20 s. To calculate the peak junction temperature we use the following data:t = 20  106 s
P = 1000 W
=0Zth(j-mb) = 0.011 K/W (value taken from the ‘single shot’ ( = 0) curve shown in Figure 2)
Therefore:T  j – mb  = P  Z th  j – mb  = 1000  0.011 = 11C
This result shows that the peak junction temperature will be 11°C above the initial
mounting base temperature

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SRZHU :












WLPH V 

7M

7M SHDN

7PE






WLPH V 

Fig 1.

AN11156

Application note

Single shot rectangular pulse

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aaa-002855

1
Zth(j-mb)
(K/W)
10-1

δ = 0.5
0.2
0.1

0.05
10-2

P

δ=

0.02

tp

single shot
10-3
10-6

10-5

10-4

10-3

10-2

10-1

tp
Tt
T

tp (s)

1

Transient thermal impedance from junction to mounting base as a function of pulse duration.

Fig 2.

Transient thermal impedance curve for the BUK961R6-40E

2.2 Composite waveforms
In practice, a power MOSFET frequently has to handle composite waveforms, rather thanthe simple rectangular pulse shown so far. This type of signal can be simulated bysuperimposing several rectangular pulses which have both positive and negative
amplitudes.
By way of an example, consider the composite waveform shown in Figure 3. The
waveform consists of three rectangular pulses, P1 (400 W for 10 s), P2 (200 W for
130 s) and P3 (1000 W for 20 s). The peak junction temperature may be calculated at
any point in the cycle, although in this example we will consider only the temperature at
endpoint time t(x). To be able to add the various effects of the pulses at this time, all thepulses, both positive and negative, must end at endpoint time t(x). Positive pulses
increase the junction temperature, while negative pulses decrease it.

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NXP Semiconductors

Using Power MOSFET Zth Curves

W[SRZHU :

333
WLPH VSRZHU :WWWW

3

3




3


3




3

Fig 3.

DDD

Composite waveform

2.2.1 Calculation of Tj at time endpoint time t(x)To calculate the junction temperature at endpoint time t(x) we use the following equation:
T j – mb =  P1  Z th  j – mb t1  +  P2  Z th  j – mb t3  +  P3  Z t  h  j – mb t4  –  P1  Z th  j – mb t2  –  P2  Z th  j – mb t4 (1)The values for P1, P2 and P3 are known:
P1 = 400 W
P2 = 200 W
P3 = 1000 W
The thermal impedance values are taken from Figure 2. Table 1 summarizes the Zth(j-mb)
for this example.
Table 1.

AN11156

Application note

Zth values summarizedt(x)time (s)Zth (K/W)

t1

1800.040t2

1700.038t3

1500.034t4

200.011All information provided in this document is subject to legal disclaimers.

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Substituting these values into Equation 1 for T(j-mb) gives:T  j – mb  =  400  0.04  +  200  0.038  +  1000  0.011 –  400  0.038  –  200  0.011  = 17.2CAssuming Tmb = 75 C:
T j = T mb + T  j – mb  = 75 + 17.2 = 92.2CHence, the peak value of Tj is 92.2 C at t(x).
This technique could be extended to any waveform capable of being broken up into
constituent rectangular parts.

2.3 Burst pulses
Power devices are frequently subjected to a burst of pulses. This type of signal can betreated as a composite waveform and as in the previous example simulated bysuperimposing several rectangular pulses which have a common period, but both positive
and negative amplitudes.
SRZHU :W[








WLPH V







W




W




W




W




W






DDD

Fig 4.

Burst mode waveform

Consider the waveform shown in Figure 4. The burst consists of three rectangular pulsesof 1000 W power and 20 s duration, separated by 30 s. The peak junction temperature
will occur at time t = t(x) = 140 s. To be able to add the various effects of the pulses atthis time, all the pulses, both positive and negative, must end at time t(x). Positive pulses
increase the junction temperature, while negative pulses decrease it.
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T t –mb =  P  Z th  j – mb t1  +  P  Z th  j – mb t3  +  P  Z th  j – mb t5 –  P  Z th  j – mb t2  –  P  Z th  j – mb t4 (2)Where Zth(j-mb)(t) is the transient thermal impedance for pulse time t
The Zth values are taken from Figure 2. Table 2 summarizes the Zth(j-mb) for this example.
Table 2.

Zth values summarizedt(x)time (s)Zth (K/W)

t1

120

0.032

t21000.028

t3

700.022t4

500.020t5

200.011

Substituting these values into Equation 2 for Tth(j-mb) gives:T  j – mb  =  1000  0.032  +  1000  0.022  +  1000  0.011 –  1000  0.028  –  1000  0.02  = 17C
T j  peak  = 75 + 17 = 92CHence, the peak value of Tj is 92 C at t(x).

2.4 Non-rectangular pulses
So far, the worked examples have only covered rectangular waveforms, or waveforms
which could easily be broken down into rectangles. However, triangular, trapezoidal andsinusoidal waveforms are also common. In order to make thermal calculations for
non-rectangular waveforms, the waveform is approximated by a series of rectangles.
Each rectangle represents part of the waveform. The equivalent rectangle must be equalin area to the section of the waveform it represents (i.e. the same energy) and also be of
the same peak power. With reference to Figure 5, a triangular waveform has been
approximated to one rectangle in the first example, and two rectangles in the second.
Obviously, increasing the number of sections the waveform is split into will improve theaccuracy of the thermal calculations.

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power (W)power (W)

500

500

Ptot

400

400

300

300

200

200

100

100

0020

4060

80

1000P2

P1020

power (W)power (W)

1000

1000

900

900

800

800

700

700

600

600

500

500

400

400

300

300

Ptot

200

Fig 5.

406080100time (μs)

time (μs)

P2
t3

200

100

10000100

100200

200

300

300

P1

P1t2

t1
aaa-002858

Non-rectangular waveformIn the first example, there is only one rectangular pulse of duration 50 s, dissipating
Ptot = 500 W. Therefore:T  j – mb  = P tot  Z th  j – mb  = 500  0.02 = 10CT j  peak  = 75 + 10 = 85C
When the waveform is split into two rectangular pulses:
T  j – mb  =  P2  Z th  j – mb t3  +  P1  Z th  j – mb t2  –  P1  Z th  j – mb t1 (3)In Equation 3, the values for P1 and P2 are known:
P1 = 250 W
P2 = 500 W
The Zth values are taken from Figure 2. Table 3 summarizes the Zth(j-mb) for thisexample.

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Table 3.

Zth values summarizedt(x)time (s)Zth (K/W)

t1750.023

t2500.020

t3

37.50.018

Substituting these values into Equation 3 for T(j-mb) gives:T  j – mb  =  500  0.018  +  250  0.020  –  250  0.023  = 8.3CTj(peak) = 75 + 8.3 = 83.3 C
Note the difference in calculated peak temperature when the two different methods ofapproximation are used.

3. Conclusion
A method has been presented to allow the calculation of peak junction temperatures for avariety of pulse types. Several worked examples have shown calculations for various
common waveforms. The method for non-rectangular pulses can be applied to any wave
shape, allowing temperature calculations for waveforms such as exponential andsinusoidal power pulses. For pulses such as these, care must be taken to ensure that thecalculation gives the peak junction temperature, as it may not occur at the end of thepulse. In this instance several calculations must be performed with different endpoints tofind the maximum junction temperature.

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Trademarks

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5. Contents
12
2.1
2.2
2.2.1
2.3
2.4
3
4
4.1
4.2
4.3
5

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Calculating junction temperatures. . . . . . . . . . 3
Single shot rectangular pulse . . . . . . . . . . . . . . 3
Composite waveforms . . . . . . . . . . . . . . . . . . . 5
Calculation of Tj at time endpoint time t(x) . . . . 6
Burst pulses . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Non-rectangular pulses. . . . . . . . . . . . . . . . . . . 8
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Legal information. . . . . . . . . . . . . . . . . . . . . . . 11
Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Disclaimers . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Trademarks. . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Please be aware that important notices concerning this document and the product(s)described herein, have been included in section ‘Legal information’.

© NXP B.V. 2012.

All rights reserved.

For more information, please visit: http://www.nxp.com
For sales office addresses, please send an email to: salesaddresses@nxp.com
Date of release: 28 September 2012
Document identifier: AN11156