cd00003894

AN604
Application note
Calculation of conduction losses in a power rectifier
Introduction
This application note explains how to calculate conduction losses in a power diode by taking
into account the forward voltage dependence on temperature and the current waveform.
The ideal current and voltage waveforms of an ultrafast diode in a power supply system
during a switching cycle are shown in Figure 1.
Figure 1.
Ideal current and voltage waveforms of a diode in a switch mode power
supply
I D(t)
I D(t)
I Max
VD(t)
I Min
0
VD(t)
t
VF
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 conduction losses in a diode appear when the diode is in forward conduction mode due
to the on-state voltage drop (VF). Most of the time the conduction losses are the main
contributor to the total diode power losses and the junction temperature rising. This is the
reason why it is important to accurately estimate them.
August 2011
Doc ID 3607 Rev 3
1/12
www.st.com
Contents
AN604
Contents
1
2
Diode forward characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1
Junction temperature dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2
Diode forward characteristics modeling: VT0(Tj), RD(Tj) . . . . . . . . . . . . . . . 3
Conduction losses: basic equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.1
3
4
2/12
Application parameters: average and rms currents . . . . . . . . . . . . . . . . . . 6
An application example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.1
Average and rms current calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.2
VT0 (Tj) and RD (Tj) calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.3
Conduction losses expression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Revision history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Doc ID 3607 Rev 3
AN604
Diode forward characteristics
1
Diode forward characteristics
1.1
Junction temperature dependence
For two different junction temperatures, the current versus forward voltage curves cross at a
current level point Ic, depending on the diode technology. When the current is lower than Ic,
the temperature coefficient αVF of the forward voltage is negative. When the current is
higher, the temperature coefficient becomes positive. This behavior is shown in Figure 2.
For Schottky and bipolar diodes, Ic is high and the working area corresponds to αVF < 0. For
SiC and GaN technologies, Ic is low and the αVF can be positive or negative. When of αVF <
0, the forward voltage and the conduction losses decrease when the junction temperature
increases.
Figure 2.
Forward (IF,VF) characteristics of a diode
IF
T j1
Tj2 > Tj1
αVF > 0
αVF = 0
Ic
αVF < 0
0
1.2
VF
Diode forward characteristics modeling: VT0(Tj), RD(Tj)
Forward characteristics (IF and VF) can be modeled by a straight line defined by a threshold
voltage VT0, and a dynamic resistance RD. VT0 and RD are calculated for 2 forward current
levels (IF1, IF2) for a given junction temperature as shown in Figure 3. Thus we can write:
Equation 1
VF (IF1 , Tj ) = VT0 (Tj ) + RD (Tj ) ⋅ IF1
Equation 2
VF (IF2 , Tj ) = VT0 (Tj ) + RD (Tj ) ⋅ IF2
Using Equations 1 and 2, we obtain VT0(Tj) and RD(Tj) expressions:
Equation 3
RD (Tj ) =
VF (IF2 , Tj ) − VF (IF1 , Tj )
IF2 − IF1
Equation 4
VT0 (Tj ) =
VF (IF1 , Tj ) ⋅ IF2 − VF (IF2 , Tj ) ⋅ IF1
IF2 − IF1
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Diode forward characteristics
Figure 3.
IF
AN604
VT0(Tj) and RD(Tj) parameters
T jRef2 > TjRef1
V F (I F ,T jRef1 )
V F (I F ,T jRef2 )
I F2
1
1
R D (Tjref2)
R D (Tjref1)
I F1
0
V T0 (TjRef2 )
V T0 (TjRef1 )
V F ( I F1 ,TjRef2 )
V F (I F2 ,TjRef2 )
VF(I F2,TjRef1)
VF
V F (I F1 ,TjRef1 )
VT0 and RD are given in each ST diode datasheet. In most cases they are calculated at
125 °C with maximum VF values for IF1 = IF(AV) and IF2 = 2· IF(AV), where IF(AV) is the
average forward current rating of the diode. For a quick calculation these values can be
used. For more accurate estimation, RD and VT0 must be calculated using the specific
application conditions. See the example in Chapter 3.
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AN604
Diode forward characteristics
For any junction temperature VT0(Tj), RD(Tj) and the forward voltage drop VF(IF,Tj) can be
calculated as follow:
Equation 5
(
VT0 (Tj ) = VT0 (TjRef1) + αVT0 ⋅ Tj − TjRef1
Equation 6
(
)
(
)(
RD (Tj ) = RD (TjRef1) + αRD ⋅ Tj − TjRef1
Equation 7
)
VF (IF , Tj ) = VF (IF , TjRef1) + Tj − TjRef1 ⋅ αVT0 + αRD ⋅ IF
)
Where αVTO and αRD are thermal coefficients calculated from the 2 reference temperatures:
Tjref1 and Tjref2. A common choice of Tjref1 and Tjref2 is 25 °C and 125 °C. These thermal
coefficients are calculated with the following equations:
Equation 8
αVT0 =
(
Note:
( )
Tjref2 − Tjref1
Equation 9
αRD =
)
VT0 Tjref2 − VT0 Tjref1
(
)
( )
RD Tjref2 − RD Tjref1
Tjref2 − Tjref1
αVT0 < 0 and αRD > 0 whatever the diode technology.
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Conduction losses: basic equations
2
AN604
Conduction losses: basic equations
Conduction losses are the average dissipated power in the diode during the forward
conduction phase given in Equation 10:
Equation 10
Tsw
∫ V (I , T )⋅I (t) ⋅ dt
1
PCOND (Tj ) =
Tsw
F F
j
F
0
Equation 10 can also be written as follows:
Equation 11
2
PCOND (Tj ) = VT0 (Tj ) ⋅ IF(av) + RD (Tj ) ⋅ IF(rms)
Where IF(AV) is the forward average current and IF(RMS) is the forward root mean square
current flowing through the diode.
Note:
In case of a square waveform, a short formula can be used to calculate conduction losses:
Equation 12
PCOND (Tj ) = VF (IF , Tj ) ⋅ IF(AV) ⋅ δ
2.1
Application parameters: average and rms currents
The average and rms currents are different for each application condition. They can be
calculated using Equations 12 (average current) and 13 (rms current).
Equation 13
I F ( AV ) =
1
Tsw
Ts w
∫ I (t )⋅ dt
F
0
Equation 14
I F (RMS ) =
1
Tsw
Tsw
∫ I (t ) ⋅ dt
2
F
0
Figure 4 presents simplified expression of average and rms currents of commonly observed
waveforms in a power rectifier. In most cases, these waveforms can be used for a rough
estimation.
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AN604
Conduction losses: basic equations
Figure 4.
Average and rms currents of commonly observed waveforms
Square waveform
Trapezoidal waveform
I D(t)
I Max
I D(t)
I Max
I Min
0
δ•Tsw
t
Tsw
δ•Tsw
0
I F (AV) = I Max · δ
I F (AV) =
I F (RMS)= I Max· δ
I Max + I Min
2
I F (RMS)=
t
Tsw
·δ
I2Max+ I2Min + I Max×I Min
·δ
3
Half period sinusoidal waveform
Triangular waveform
I D(t)
I Max
I D(t)
I Max
0
δ•Tsw
Tsw
t
2I Max
·δ
π
δ
I F (RMS)= I Max·
2
δ·Tsw
0
I F (AV) =
I F (AV) =
I Max
2
Tsw
·δ
I F (RMS) = I Max ·
Doc ID 3607 Rev 3
t
δ
3
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An application example
3
AN604
An application example
Let us consider the example of a 90 W notebook adapter. This is a flyback converter
(Figure 5) working in continuous mode. The output voltage Vout is 19 V and the maximum
output current is 4.7 A. The rectifier diode is an ST power Schottky STPS30M100S. Figure 6
shows the ideal waveforms of the diode: IMin = 4 A, IMax = 11.8 A and δ = 0.6.
Let us calculate the maximum conduction losses in the diode for this application.
Figure 5.
Flyback converter
STPS30M100S I
load
AC Line
Snubber
Vin
Vout
Control
Figure 6.
Ideal current and voltage waveforms of the diode in the flyback converter.
I D(t)
I Max
I Min
0
VD(t)
t
VF
0
t
VR
δ·Tsw
Tsw
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AN604
3.1
An application example
Average and rms current calculation
The first step is the calculation of the average and rms currents.
The forward average current is the output current: IF(AV) = Iload = 4.7 A.
As illustrated in Figure 6, the forward current has a trapezoidal shape. The formula to
calculate the rms current of trapezoidal waveform is given in Figure 4. IF(RMS) is then:
Equation 15
(11.8 )2 + (4)2 + 11.8 ⋅ 4 ⋅ 0.6 = 6.4 A
IF(RMS) =
3.2
3
VT0 (Tj) and RD (Tj) calculation
The second step is the calculation of VT0 (Tj) and RD (Tj) in the application condition range.
Figure 7.
STPS30M100S forward voltage drop versus forward current
IFM
Tj = 125 °C
(Maximum values)
Tj = 125 °C
(Typical values)
I Max = 11.8A
Tj = 25 °C
(Maximum values)
I Min = 4A
0.52V
0.43V
0.63V
0.55V
Tjref1 = 25 °C and Tjref2 = 125 °C. To calculate maximum conduction losses, read maximum
values of VF at IMin and IMax in Figure 7. This figure is available in the STPS30M100S
datasheet. These values are summarized in Table 1.
Table 1.
VF(Max) values at IMin and IMax
IF (A)
VF(Max)(IF, 25 °C) (V)
VF(Max)(IF, 125 °C) (V)
IMin = 4
0.52
0.43
IMax = 11.8
0.63
0.55
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An application example
AN604
From Equations (3), (4), (8) and (9) calculate VT0(Tjref1), VT0(Tjref2), RD(Tjref1), RD(Tjref2),
αVT0 and αRD. Calculated values of these parameters are summarized in Table 2.
Table 2.
VT0, RD, αVT0, and αRD parameters
Tjref (°C)
VT0 (V)
RD (mΩ)
Tjref1 = 25
0.464
14.123
Tjref2 = 125
0.368
15.406
αVT0 (V·°C-1)
αRD (Ω·°C-1)
-951.358×10-6
12.839×10-6
From Equations 5 and 6 we can write VT0(Tj) and RD(Tj) as follow:
Equation 16
VT0 (Tj ) = 0.487 - 951.358 × 10-6 ⋅ Tj
Equation 17
RD (Tj ) = 13.802 × 10-3 + 12.839 × 10-6 ⋅ Tj
3.3
Conduction losses expression
From Equations 7, 15 and 16 the expression for maximum conduction losses is then:
Equation 18
PCOND(Max) (Tj ) = 2.866 + 3.987 × 10-3 ⋅ Tj
Finally, let us plot the value of conduction losses in the diode as a function of the junction
temperature (Figure 8).
Figure 8.
Maximum conduction losses versus junction temperature
3.0W
PCOND(Max) (Tj)
2.8W
2.6W
2.4W
2.2W
Tj
2.0W
25°C 35°C 45°C 55°C 65°C 75°C 85°C 95°C 105°C 115°C 125°C
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4
Revision history
Revision history
Table 3.
Document revision history
Date
Revision
Changes
Aug-1993
1
Initial release
03-May-2004
2
Stylesheet update. No content change
24-Aug-2011
3
Completely revised for currently available products.
Doc ID 3607 Rev 3
11/12
AN604
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