Guideline for determining switching losses associated with switching resistive, capacitive and inductive loads.

Application Note, V 1.1, May 2001
ANPS061E
Guideline for determining
switching losses associated
with switching resistive,
capacitive and inductive
loads.
by Christian Arndt and Michael Mueller-Heiss
Automotive Power
Never stop
-1-
thinking.
ANPS061E
Guideline for determining switching losses
1. Abstract
3. General
This Application Note is intended to provide help
in all cases where FET switching losses due to
repetitive (such as during PWM mode) or slow
switching processes must be taken into account.
It focuses on thermal considerations for
semiconductor switches in switched DC
applications.
A general idea about how switching losses
occur and an outline about what amount of
power can be dissipated during switching is
given. The effect of these power losses for the
temperature of the semiconductor switch is
covered as well.
The Application Note covers single and/or
repetitive switching for ohmic, capacitive and
inductive loads.
If a load is switched in a DC application, the
switching device passes through various
operating states during the switching operation.
During the switch-on
(referred to the load):
process,
these
are
1) No-load:
A
VDS=Vbb
IDS=0
IDS
2. Introduction
2) Matching
If a semiconductor device is used in a DC
application as a switch for a load, losses always
occur in that device.
Basically these losses can be subdivided into
• steady-state losses (losses during the ON
state) and
• dynamic losses (losses during switching).
VDS=Vbb/2
IDS≠0
UDS
V
UDS
V
UDS
V
A
Calculating the steady-state losses is relatively
easy. They generally result from componentspecific and load-typical parameters. In the case
of semiconductor devices based on a field-effect
transistor principle, these parameters are the
on-resistance RDS(on) and the load current ILoad.
However, calculating the dynamic losses
occurring during switching processes is more
difficult.
IDS
3) Rated operation.
VDS≈0
IDS=ILoad
A
IDS
During the switch-off process, each switching
device passes through these operating states in
reverse sequence.
In the case of inductive loads, commutation
processes may additionally come into play.
These will be discussed in further detail later.
Let us just say for now that during commutation
processes the energies stored in the load
inductance are discharged via the switching
device at voltages greater than the operating
voltage Vbb.
Application Note
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ANPS061E
Guideline for determining switching losses
It can be seen that the maximum losses occur at
half the nominal voltage and half the nominal
current. This corresponds to the matching case.
4. Switching resistive loads
The following section deals first with switching
losses associated with purely resistive loads.
However, the statements made here are also
relevant to the subsequent sections.
In the 3 diagrams (no-load, matching and rated
operation) it may be observed that all the
operating states of the switching device lie on a
dotted gray line. This is the load line. This
means that the switching losses of each
switching operation are influenced by the load.
The losses occurring at this point are:
P̂Switching_max = PMatching =
4.1.2.
Vbb I Load
Vbb 2
•
=
2
2
4 • R Load
Calculation
p Switching =
p Switching =
(1)
p Switching =
To calculate the switching losses, it is now
important to know how the current and voltage
vary over time. A distinction may basically be
drawn between 2 cases.
Linear voltage and current
characteristic
Assumption
4.1.1.
Assuming that the current and voltage vary
linearly over time, the switching losses occurring
at each instant of the switching process are as
follows:
p Switching
PMatching
=
TSwitching
1
T Switching
0
æ u
i ö
ç
dt
çV • I
nom
è bb
11
x(1 − x )dx
10
1
0
4.1.
(2)
If the averaged losses for linear current and
voltage responses are now normalised to the
reference value, these losses will be as follows:
To examine this further, it is useful to introduce
a reference variable which is exclusively a
function of the load. A good reference variable
is the power dissipation in the device during
matching.
This is given by formula (1) as:
PMatching =
Vbb 2
4 • R Load
(x − x )dx = x2
2
2
−
x3
3
1
=
0
1
6
(3)
1 4 2
• = = 67%
6 1 3
The averaged switching losses for a resistive
load and linear current and voltage
characteristics are therefore approx. 70% of the
losses occurring in the matching case,
irrespective of the switching time.
In reality, the 67% calculated may still increase
slightly as a result of the Ron losses additionally
produced close to rated operation, so that 70%
is a wholly realistic figure.
4.1.3.
Validity and typical applications
Switch-on process
1
0.9
VDS/Vbb
0.8
0.7
IDS/ILoad
0.6
V DS / V bb
I DS / I Last
0.5
Pv
0.4
0.3
0.2
PV
0.1
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Figure 1 – Normalized switching losses for linear
current and voltage characteristics
Application Note
This applies to switch-on and switch-off
processes, provided no parasitic inductances
must be taken into account.
Linear current and voltage characteristics may
be observed during slow switching processes.
This may occur, for example, if a slowly rising
input signal is applied to the device by an
external triangular wave generator. This is
®
possible e.g. with discrete FETs, TEMPFET
®
and HITFET devices.
As will be shown later, the linear current and
voltage response constitutes the less favourable
case in thermal terms, since the highest losses
occur here. If the true current and voltage
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Guideline for determining switching losses
response is not known, this response should be
taken as the basis for safety reasons.
4.1.4.
Example
By way of example, let us now consider the
turn-on process of a BTS149. The BTS149 has
been turned on by an external triangular signal.
With a supply voltage of Vbb=10 volts, it drives a
load of 2.18 ohms.
For current (Ch2: 1A/div), voltage (Ch3) and
losses (Math1), the following waveforms were
observed:
voltage across the device has fallen to approx.
20% of the nominal voltage at switch-on, and
the current has increased to approx. 80% of the
nominal current, the switching losses at each
moment of the switching process are as follows:
Switch-on process
1
0.9
VDS/Vbb
0.8
IDS/ILoad
0.7
0.6
V ds
I ds
Pv
0.5
0.4
PV
0.3
0.2
0.1
PV
VDS
0
0
IDS
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Figure 3 – Normalized switching losses for piecewise
linear current and voltage characteristics
4.2.2.
Calculation
The switching losses are now:
p Switching =
Figure 2 – Slow switch-on process of a BTS149
For a switching time of approx. 3.5 ms, this
produces average switching losses of:
1
p Switching
PMatching
p Switching
PMatching
p Switching
PMatching
=
T Switching
=
p Switching =
Vbb • I nom /4
p Switching
p Schalt
= 59%
(4)
p Schalt
4.2.1.
Piecewise linear current and voltage
characteristic
Assumption
If the current and voltage are assumed to exhibit
a piecewise linear response, whereby after
approx. 30% of the total switching time the
Application Note
0
æ u
i ö
ç
÷dt
çV • I
÷
nom
è bb
0,3 æ
2 ö
2 ö
0,7 æ
ç 8x − 64x ÷dx + ç 4 − 6x − 4x dx
ç 3
ç
9 ÷
35 49
0 è 25
è
(5)
4x 2 64x 3
=
−
3
27
0,3
0
4x 3x 2 4x 3
+
−
−
25 35 147
0,7
0
3
8
14
147
7
49
=
−
+
−
−
=
≈ 0,116
25 125 125 3500 750 420
PAnpassung
4.2.
T Switching
0
236µ36µ
1
•
*W
3500µ5 0.01VVs
=
11.5W
TSwitching
0,7 æ 1 2x
1 é0,3 æ
8x
8x ö
4 2x ö ù
ê ò ç (1 − ) • ( )÷dx + ò ç ( −
)•( +
)÷dx
1ê 0 è
3
3 ø
5 7 ø
0 è 5 7
ë
u • i • dt
Tswitching
1
=
49 4
• = 46, 6 %
420 1
In the case of a piecewise linear current and
voltage response, the averaged switching
losses for a resistive load irrespective of the
switching time are approx. 50% of the losses
which can occur in the matching case.
In reality, the 47% calculated may increase
slightly as a result of the Ron losses additionally
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Guideline for determining switching losses
produced close to rated operation, so that 50%
is a wholly realistic figure.
4.2.3.
PMatching
Validity and typical applications
To a first approximation, a piecewise linear
current and voltage characteristic may be
observed
primarily
with
fast
switching
processes. It is attributable mainly to the twostage gate charging process. This is due to the
change in the input capacitance during the
switching operation. With highside switches
®
such as the PROFET devices, the effect of the
charge pump is additionally present.
This applies to switch-on and switch-off
processes provided no stray inductances must
be taken into account.
Fast switching processes exist if the device is
driven via a low impedance directly by the
driver. This is possible in the case of discrete
®
®
®
FETs, TEMPFET , HITFET and PROFET
devices.
4.2.4.
p Switching
1.83µ.83
1
•
*W
34µ4 0.005VVs
=
= 43%
25W
5. Switching capacitive loads
The following section deals with the switching
losses associated with capacitive loads. These
include for example RC networks or lamps
whose time constants are much greater than the
switching time of the device itself.
With capacitive loads, the losses produced in
the device during each switching operation are
again influenced exclusively by the load.
However, in the case of switch-on processes
the power dissipation in the device during
matching under rated conditions is less critical
than the power dissipation during matching
under inrush conditions.
This is given by formula (7) as
Example
By way of example, let us now consider the
turn-on process of a BTS149. The BTS149 has
been driven low impedance by a square wave
signal. With a supply voltage of Vbb=10 volts, it
drives a load of 1 ohm.
For current (Ch2: 2A/div), voltage (Ch3) and
losses (Math1), the following waveforms were
observed:
VIN
PV
P' Matching =
Vbb I inrush
Vbb 2
•
=
2
2
4 • Rinrush
This will be designated “transient matching
power” P’Matching in the following.
Iinrush is the maximum inrush current flowing and
Rinrush the respective total resistance at the
moment of switch-on.
P' Matching = 6..10 • PMatching
Figure 4 - Fast turn-on process of a BTS149
R1
For a switching time of approx. 35 µs, this
results in average switching losses of:
PMatching
=
T Switching
u • i • dt
Tswitching
Vbb • I nom /4
Application Note
(8)
In the case of RC networks, Rinrush results to a
first approximation from all the resistances not
“short circuited” by parallel capacitances. The
following simple example illustrates this. From
the resistances shown in Figure 5,
VDS
p Switching
(7)
In the case of lamps, Iinrush may well be 6 to 10
times Inom. Consequently, for lamps the formula
is usually:
IDS
1
(6)
R2
C1
Figure 5 – Simple RC circuit
R1 results as the effective inrush resistance
Rinrush.
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Guideline for determining switching losses
5.1.
Linear current and voltage
characteristic
Linear current and voltage characteristics may
be observed during slow switching processes
where the switching time is, however, still well
below the smallest time constant of the load.
This may occur if a slowly rising input signal is
applied to the device by an external triangular
wave generator. This is possible, for example, in
®
®
the case of FETs, TEMPFET and HITFET
devices.
Analogously to Figure 1 and formula 3, the
averaged switching losses are given by:
p Switching
P' Matching
p Switching
P' Matching
=
1 4 2
• = = 67%
6 1 3
≈ 6..10 •
6. Switching inductive loads
p Switching
PMatching
(9)
load − dependent
For slow switch-on processes the averaged
power dissipations are therefore approx.70% of
the “transient matching power”.
For slow switch-off processes a distinction must
be drawn between how quickly the device is
turned off again after switch-on.
If switch-off takes place immediately after
switch-on, the averaged switching losses
according to formula 9 are approx. 70% of the
“transient matching power”.
If switch-off occurs after rated operation has
been attained, the averaged switching losses
according to formula 3 are approx. 70% of the
matching power.
5.2.
For fast switch-on processes the effective power
dissipations are therefore approx. 50% of the
“transient matching power”.
For fast switch-off processes a distinction must
be drawn between how quickly the device is
turned off again after switch-on.
If switch-off takes place immediately after
switch-on, the effective switching losses
according to formula 9 are approx. 50% of the
“transient matching power”.
If switch-off occurs after rated operation has
been attained, the effective switching losses
according to formula 3 are approx. 50% of the
matching power.
The following section deals with the switching
losses associated with inductive loads. These
include such loads as coils and valves which
have no additional active freewheel circuitry
(such as a freewheeling diode).
In the case of inductive loads, the losses
produced in the device during each switching
operation are influenced by the load and by the
active Zener or avalanche voltage of the device.
If the switch-on time is much shorter than the
time constant of the load, no switch-on losses
must be taken into account. This is mostly the
case. However, if the device switches off the
inductive load from rated operation, the energy
stored in the load inductance will be dissipated
via the switching device. This process is known
as commutation.
Piecewise linear current and voltage
characteristic
Piecewise
linear
current
and
voltage
characteristics may be observed with fast
switching processes. This is the case when the
device is driven via a low impedance directly by
a driver. This is possible with discrete FETs,
®
®
®
TEMPFET , HITFET and PROFET devices.
Analogously to Figure 3 and formula 5, the
averaged switching losses are given by:
p Switching
P' Matching
p Switching
P' Matching
= 0.116 •
≈ 6..10 •
Application Note
4
= 46.6%
1
p Switching
PMatching
Vbb
induct.
Load
IDS
Switch
VAZ
GND
(10)
load − dependent
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Guideline for determining switching losses
To a first approximation the switch-off losses
are given by:
Wtot = W L + WVbb
Wtot =
1
•L•I 2 +
2
t Switching
0
(Vbb • i(t)) • dt
(11)
1
1
• L • I 2 + • Vbb • I • t switching
2
2
di
I
= L•
dt
t Switching
(12)
If a load is switched on or off on single
occasions, a distinction can be drawn between
VAZ
the average switching losses produced
as
shown in the following table:
we get
Wtot =
1
L
1
• L • I 2 + • Vbb • I 2 •
2
2
V AZ − Vbb
Wtot =
æ
ö
Vbb
1
• L • I 2 çç 1 +
2
è V AZ − Vbb
(13)
For each switch-off process the switching losses
are therefore given by
t Switching
ON
(14)
inductive
Wtot
Switching
process
OFF
ON
æ V AZ
ö
1
• L • I 2 çç
2
è V AZ − Vbb
PSwitching =
Load
capacitive
Wtot =
Non-repetitive switching
7.1.
With
V L = V AZ − Vbb = L •
The previous sections explained in greater detail
how to determine the equivalent switching
losses for various loads to a first approximation.
VL
This section will now attempt to clarify precisely
what this means in terms of thermal loading of
the device. In practice there are 2 cases which
will be examined in detail below.
resistive
Wtot =
7. Thermal considerations
OFF
(immediat
ely after
switch-on)
OFF
(during
rated
operation)
OFF
Switching
time
TSwitching <<
tSwitching >>
tSwitching <<
tSwitching >>
tSwitching <<
tSwitching >>
tSwitching <<
TSwitching >>
Formula
tSwitching <<
tSwitching >>
5
3
/
14
5
3
5
3
10
9
10
9
Table 1 – Overview for determining the switching
losses
Further examination of the thermal implications
now requires precise knowledge of the thermal
conditions of the application as a whole.
For short-duration switching operations up to a
few milliseconds, the Zthjc values specified in the
data sheets can be used to a first
approximation.
However, for longer switching operations,
precise knowledge of the overall thermal
conditions is necessary. For some products, the
data sheet may also indicate how the thermal
linkage behaves on a 6cm² copper PCB. If this
coincides with the application, this can be taken
as the basis.
Application Note
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Guideline for determining switching losses
To determine the temperature swing of a
switching operation, the following steps must be
followed:
measure the switching time tswitching
determine the thermal impedance Zth(tswitching)
from the data sheet
calculate the junction temperature of the device
using formula 15:
ϑ j = PSwitching • Z th (t Switching ) + ϑ amb
7.2.
(15)
Repetitive switching (PWM operation)
If a load is repeatedly switched on or off, in most
cases it must be ensured that the junction
temperature is not exceeded during quasisteady-state operation.
However, the on-state losses (PV(on)) and the
switching losses must be taken into account
here.
For a device operated in PWM mode at a
frequency fSwitching, we get:
Pv = PSwitching(application) + PR(ON) (t ON )
7.3.
Typical application
To illustrate the approximating calculation
methods described before, one examples is
given below.
Temperature swing of a BTS142D for a nonrepetitive switch-on process
Given:
A BTS142D mounted on a 6cm² copper PCB is
controlled externally by a triangular wave
generator. The switching time is extended from
the original typical switching time of 60µs to
tSwitching=1ms.
The BTS142D drives a 1 ohm resistance as a
load. The supply voltage Vbb=14 volts.
7.3.1.
Required:
Of interest is the final temperature which the
device attains after the switching process for an
ambient temperature of 50°C.
7.3.2.
Solution:
(16)
Using formula 2 we have
The total switching losses Pswitching (application) are
given by:
(
P̂Switching_max = PMatching =
)
PSchalt(Applikation) = W Schalt(ON) + W Schalt(OFF) • f Schalt
(
)
Vbb 2
(14V)²
=
= 49W
4 • R Load
4 • 1Ω
(20)
= PSchalt(ON) • t (ON) + PSchalt(OFF) • t (OFF) • f Schalt
(17)
Pswitching(ON) being the switching losses for each
switch-on process and Pswitching(OFF) being the
losses for each switch-off process. These may
differ depending on the application and are
therefore detailed separately here.
Assuming a linear current and voltage
characteristic here, the averaged power
dissipation according to formula 3 is given by:
p Switching = 0.67 • PMatching ≈ 33W
(21)
For a single pulse, the BTS142D data sheet
gives an approximate ZthJA(@6cm²)=0.2K/W.
The on-state losses, PR(ON) (tON), are given by:
In accordance with formula 15, the final
temperature is now therefore:
PR(ON) (t ON ) = P(ON) • duty cycle
2
= I load
• RON (150°C) • t ON • f Switching
ϑ j = PSwitching • Z th (t Switching ) + ϑ amb
(18)
The average junction temperature of the device
is therefore expressed by formula 19
ϑ j = 33W • 0.2K/W + 50°C = 56.6°C
ϑ j = PSwitching • (Rthjc + Rthca ) + ϑ amb
The device thus undergoes a temperature swing
of approximately 6.6K and therefore attains a
junction temperature of 56.6°C after the switchon process.
Application Note
(19)
page 7 of 7
(22)
V1.1, 2001-05
ANPS061E
Guideline for determining switching losses
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9. Infineon goes business
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Edition 2000-07-14
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© Infineon Technologies AG 8/d/yy.
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Application Note
page 8 of 7
Published by Infineon Technologies AG
V1.1, 2001-05