dm00044087

```AN4021
Application note
Calculation of reverse losses in a power diode
Introduction
This application note explains how to calculate reverse losses in a power diode by taking
into account the impact of the junction temperature (Tj) as well as the reverse voltage VR on
the leakage current.
The ideal current and voltage waveforms of an ultrafast diode in a power supply system
during a switching cycle are illustrated in Figure 1.
Figure 1.
Ideal current and voltage waveforms of a diode in a switch mode power
supply
ID(t)
ID(t)
IMax
VD(t)
IMin
0
VD(t)
VF
t
IR
0
t
Fsw
Tsw
δ
δ·Tsw
IMax
IMin
VF
VR
Switching frequency
Switching period
Duty cycle
Duration of diode conduction
Maximum forward current
Minimum forward current
Forward voltage
Reverse voltage
VR
δ·TSW
TSW
The reverse losses in a diode are the result of a reverse bias applied on the diode. They are
due to the leakage current (IR). This parameter (IR) increases exponentially with the junction
temperature. Most of time, the reverse losses are negligible for bipolar and silicon carbide
diodes. For silicon Schottky structured diodes, these losses should be accurately estimated
as they are the main origin of the thermal runaway risk phenomenon (See AN1542).
April 2012
Doc ID 022588 Rev 1
1/10
www.st.com
AN4021
Contents
1
Diode reverse characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1
Junction temperature and reverse voltage dependence . . . . . . . . . . . . . . . 3
1.2
Diode reverse characteristics modeling: IR(VR,Tj), “c” thermal coefficient . 4
2
Reverse losses: Basic equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
3
An application example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
4
Revision history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
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Diode reverse characteristics
1
Diode reverse characteristics
1.1
Junction temperature and reverse voltage dependence
The leakage current is an intrinsic parameter of the diode. In each ST Schottky and SiC
diode datasheet, a curve of the leakage current (typical value) versus the reverse voltage
and the junction temperature is provided (Figure 2).
Most of the time, the reverse losses are calculated using maximum values in order to
consider the worst operating conditions for the diode in the application. The ratio between
typical and maximum values can be obtained using the values given in the section “Static
electrical characteristic” of the datasheet. (Figure 3)
Figure 2.
1.E+02
Reverse leakage current versus reverse voltage applied for the
STPS20M100S (typical values)
IR(mA)
Tj=150°C
1.E+01
Tj=125°C
Tj=100°C
1.E+00
Tj=75°C
1.E-01
Tj=50°C
1.E-02
Tj=25°C
VR(V)
1.E-03
0
Figure 3.
Symbol
IR
10
20
30
40
50
60
70
80
90
100
Typical and maximum leakage current at the voltage rating of the diode
(VRRM) from the datasheet for the STPS20M100S
Parameter
Test conditions
Reverse leakage current
Tj = 25 °C
Tj = 125 °C
Tj = 25 °C
Tj = 125 °C
Doc ID 022588 Rev 1
VR = 70 V
VR = 100 V
Min.
Typ.
Max. Unit
µA
5
5
10
10
mA
40
40
µA
mA
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Diode reverse characteristics
1.2
AN4021
Diode reverse characteristics modeling: IR(VR,Tj), “c”
thermal coefficient
The parameter (IR) increases by an exponential law with the junction temperature. Knowing
a reference point IR(VR,TjRef) and the value of the thermal coefficient “c”, one can easily
calculate the leakage current at a given temperature Tj using the following formula:
Equation 1
c( Tj -Tj Ref )
IR (VR,Tj ) = IR (VR,Tj Ref )· e
Where VR is the reverse “plateau” voltage applied across the diode.
The “c” thermal coefficient represents the leakage current dependence with the junction
temperature. Each diode has its own coefficient that can be calculated using two points as
follows:
Equation 2
c=
⎛I R (VR ,TjRef 2 )⎞
1
⎟
· ln ⎜
Tj Re f 2 - TjRef1
⎜I (V ,T
⎟
)
⎝ R R j Ref1 ⎠
In each ST Datasheet, TjRef1 & TjRef2 are respectively 25°C and 125°C.
The “c” coefficient is independent of the reverse voltage VR applied across the diode.
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2
Reverse losses: Basic equations
Reverse losses: Basic equations
Reverse losses expression is the average dissipated power in the diode during the reverse
biasing phase:
Equation 3
PREV(Tj ) =
1
Tsw
Tsw
VR (t )·IR (VR,Tj ) · dt
∫
0
In case of a typical square waveform as illustrated on Figure 1, the reverse losses are equal
to:
Equation 4
PREV(Tj ) = (1- d)·VR · IR ( VR ,Tj )
Substitution of Equation 1 into Equation 4 yields
Equation 5
PREV( Tj ) =(1- d ) ·VR· I R(VR ,TjRe f ) · e
c( Tj -Tj Ref)
In some literature, it is possible to find the following expression:
Equation 6
c ·(Tj -T j Ref)
PREV( Tj )=Pref · e
With:
Equation 7
Pref = (1- d) ·VR · I R ( VR ,Tj Ref )
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An application example
3
AN4021
An application example
Let us consider the example of a 45 W notebook adapter, using a flyback converter
(Figure 4) working in continuous mode. The input voltage Vin is 375 V and the output voltage
Vout is 14.5 V. The rectifier diode is a ST power Schottky STPS20M100S (20 A, 100 V).
Figure 5 shows the ideal waveforms of the diode. The duty-cycle of the transistor is: δ = 0.2
and the transformer ratio is: m = 0.148.
Let us calculate the maximum reverse losses in the diode for this application.
Figure 4.
Flyback converter
STPS20M100S I
load
Vin
AC Line
Snubber
m
Vout
Control
Figure 5.
Ideal current and voltage waveforms of the diode in the flyback converter
ID (t)
ID (t)
VD (t)
0
IR
VD (t)
VF
0
t
- VR
Spike
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t
- (m · Vin + Vout)
δ·TSW
TSW
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AN4021
An application example
Step 1: Reverse voltage applied across the diode
When the transistor on the primary side of the transformer is on, the rectification diode is
blocked with a reverse voltage equal to:
Equation 8
VR = m ·Vin+Vout = 0.148 · 375+14. 5 = 70V
Step 2: IR(VR,TjRef) and thermal coefficient “c”:
The second step is to read the reference point value using the Figure 2 given in each
datasheet for the corresponding VR. The reference temperature (TjRef) considered is at a
junction temperature of 125 °C.
In this example:
IR(typ)(VR = 70 V, TjRef = 125 °C) = 5 mA (typical value)
In order to consider the worst case for the power losses, we use the maximum values for the
leakage current using the ratio given by the Figure 3.
Equation 9
Ratio =
IR (max)( 100V,125 °C)
=
40
=4
I R (typ) ( 100V ,125 °C ) 10
I R(max)(VR = 70 V, TjRef = 125 °C) = 5 x 4 = 20 mA
Using Equation 2 and Figure 2, the coefficient “c” can be calculated:
Equation 10
c=
1
· ln(
TjRe f 2- T j Ref 1
-3
I R (V R , Tj Re f 2 )
1
5 ·10
-1
=
·ln(
)=
- 6 ) 0 . 069°C
I R (VR ,Tj Re f1 ) 125 - 25
5· 10
Step 3: Reverse losses expression:
From Equation 5, the maximum reverse losses expression is then:
Equation 11
PREV(max) (Tj)=(1- d ) · VR · IR ( VR ,Tj Ref ) · e
-3
PREV (max)( Tj ) = ( 1 - 0. 2) ·70· 20 ·10 ·E
c(T j - Tj Re f )
0.069(T j - 125)
with TjRef = 125 °C
0.069(T j - 125)
PREV(max) ( Tj ) = 1.12 · e
Finally, one can plot the evolution of reverse losses in the diode versus the junction
temperature (Figure 6).
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An application example
Figure 6.
AN4021
Maximum reverse losses versus the junction temperature
PREV(max)(W)
6,4
6,0
5,6
5,2
4,8
4,4
4,0
3,6
3,2
2,8
2,4
2,0
1,6
1,2
0,8
Tj(°C)
0,4
0,0
25
35
45
55
65
75
85
95
105
115
125
135
145
155
As shown on Figure 6, the reverse losses increase exponentially with the temperature.
For ST Bipolar diodes, the doping being platinum, the leakage current is very low resulting in
negligible reverse losses.
For Schottky diode, there is a trade-off between the forward voltage drop and the reverse
leakage current. In order to improve the efficiency of a Switch Mode Power Supply, a
Schottky diode with a low forward voltage to the detriment of higher leakage current would
be preferred.
In this case, the heat sink size will be larger in order to keep the junction temperature of the
diode low enough and avoid a thermal runaway phenomenon. (Refer to the AN1542).
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4
Revision history
Revision history
Table 1.
Document revision history
Date
Revision
26-Apr-2012
1
Changes
Initial release.
Doc ID 022588 Rev 1
9/10
AN4021
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