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 Doc ID 3607 Rev 3 3/12 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. 4/12 Doc ID 3607 Rev 3 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. Doc ID 3607 Rev 3 5/12 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. 6/12 Doc ID 3607 Rev 3 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 7/12 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 8/12 Doc ID 3607 Rev 3 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 Doc ID 3607 Rev 3 9/12 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 10/12 Doc ID 3607 Rev 3 AN604 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 Please Read Carefully: Information in this document is provided solely in connection with ST products. STMicroelectronics NV and its subsidiaries (“ST”) reserve the right to make changes, corrections, modifications or improvements, to this document, and the products and services described herein at any time, without notice. All ST products are sold pursuant to ST’s terms and conditions of sale. Purchasers are solely responsible for the choice, selection and use of the ST products and services described herein, and ST assumes no liability whatsoever relating to the choice, selection or use of the ST products and services described herein. No license, express or implied, by estoppel or otherwise, to any intellectual property rights is granted under this document. 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