Power MOSFET Switching Loss Precise Introducti Analysis Eric Chen, Alex Leng Power MOSFET is widely used in the power cverter; DC-DC and AC-DC cverters have a lot of power MOSFETs. Efficiency is the most important characteristic in the DC-DC and AC-DC cverters applicati and is always decided by the power MOSFET characteristics, like drain-source -state resistance, rise time, and fall time. However, in the typical oscilloscope, the power loss calculating functi is not comm, and an extra method is needed to calculate the power csumpti. In this article, a mathematic method is applied to estimate the power csumpti. Power MOSFET Efficiency The power efficiency of power MOSFET can be divided into two parts: cducti loss and switching loss. The total power loss can be calculated by combining the cducti loss and the switching loss as shown in the Eq. (1). P = P + P (1) total cducti _ loss switching _ loss The cducti loss is simply decided by the loading current and the drain-source -state resistance, and the difference between an experiment and a calculati can be very close. Eq. (2) shows the cducti loss formula. 2 PCducti I RDS ( ) = (2) But for switching loss, the calculati becomes very complex because of the parasitic capacitances. FA Report No: F020810M 1
Switching Power Loss by Linear Approximati In this article, the primary side power MOSFET of Flyback cverter is analyzed as shown in the fig.1. NIKOS P7105ATF is used in the AC-DC cverter priority side, and the switching waveform is shown in the fig. 2 and fig. 3. Fig. 2 is the rising edge waveform, and fig. 3 is the falling edge waveform. Fig.1 Flyback Cverter V DS I D Fig.2 Rising Edge Waveform FA Report No: F020810M 2
Assume the drain current and drain-source voltage are linear during rising and falling edge, and the waveform can be approximated as fig. 4. I D V DS V G Fig. 3 Falling Edge Waveform Fig. 4 MOSFET Ideal Waveform FA Report No: F020810M 3
In the linear approximati, the drain current can be decided by the formula (3), and the drain-source voltage can be decided by the formula (4) during the rising edge. t id ( t) = I D (3) T t vds ( t) = VDS (1 ) (4) T Where T is the rising time, I D is the rated current, and V DS is the drain-source voltage. The power csumpti can be decided by multiplying current and voltage as shown in the formula (5). VDS I D t P( t) = id ( t) vds ( t) = t(1 ) T T (5) The energy can be shown in the formula (6). W risin g = T 0 P( t) dt T VDS I D t = t(1 ) dt 0 T T VDS I DT = (6) 6 Similarly, the energy during the falling edge can be decided in the formula (7) where T off is the falling time. VDS I DToff W falling = (7) 6 FA Report No: F020810M 4
The switching loss can be found by formula (8). W = W + W switching risin g falling VDS I D = [ T + Toff ] (8) 6 The power csumpti can be found by multiplying the switching frequency fs. However, in actual, the waveform is not a linear because of capacitors. Another method is needed to analyze correctly. Switching Power Loss by Riemann Sum The linear approximati is not a very precise method to analyze the switching loss of power MOSFET, so Riemann Sum is recommended. In mathematic, a Riemann sum is a method for approximating the total area underneath a curve a graph, otherwise known as an integral. It may also be used to define the integrati operati. In this article, the rising edge is divided into six sectis as shown in the fig. 5. V DS I D Fig. 5 Riemann Sum Six Sectis of Rising Edge FA Report No: F020810M 5
In very secti, the voltage and the current can be decided by the formula (9) and (10). V2 V1 v( t) = ( t t1) + V1 t2 t1 (9) I I i t t t I 2 1 ( ) = ( 1) + 1 t2 t1 (10) Where V 2 and V 1 is the voltage at time t 2 and t 1 and I 2 and I 1 is the current at time t 2 and t 1. The power can be found by multiplying current can voltage, and the energy can be decided by integral power as shown in the formula (11). t2 risin g = ( ) ( ) t1 W v t i t dt (11) The energy of the six segments shows as below: Secti Ⅰ: (V 1, V 2 ) = (108V, 46V), (I 1, I 2 ) = (0, 0.2A), (t 1, t 2 ) = (0, 9.2ns) 9.2n 62 0.2 WΙ = ( t + 108) ( t) dt 0 9.2n 9.2n 8 = 6.133 10 ( J ) (12) Secti Ⅱ: (V 1, V 2 ) = (46V, 16V), (I 1, I 2 ) = (0.2A, 0.4974A), (t 1, t 2 ) = (9.2n, 17.2ns) 17.2n 30 0.2974 WΙΙ = [ ( t 9.2 n) + 46] [ ( t 9.2 n) + 0.2] dt 9.2n 8n 8n 8 = 8.05296 10 ( J ) (13) Secti Ⅲ: (V 1, V 2 ) = (14.37V, 7.88V), (I 1, I 2 ) = (0.4974A, 0.7044A), (t 1, t 2 ) = (17.2n, 39.6ns) 39.6n 6.49 0.207 WΙΙΙ = [ ( t 17.2 n) + 14.37] [ ( t 17.2 n) + 0.4974] dt 17.2n 12.4n 12.4n 7 = 1.22244 10 ( J ) (14) FA Report No: F020810M 6
Secti Ⅳ: (V 1, V 2 ) = (7.88V, 4.67V), (I 1, I 2 ) = (0.7044A, 0A), (t 1, t 2 ) = (39.6n, 75.2ns) 75.2n 3.21 0.7044 WΙV = [ ( t 39.6 n) + 7.88] [ ( t 39.6 n) + 0.7044] dt 39.6n 35.6n 35.6n 8 = 8.5386 10 ( J ) (15) Secti Ⅴ: (V 1, V 2 ) = (4.67V, 2.96V), (I 1, I 2 ) = (0A, -0.087A), (t 1, t 2 ) = (75.2n, 90.8ns) 90.8n 1.71 0.098 WV = [ ( t 75.2 n) + 4.67] ( t 75.2 n) dt 75.2n 15.6n 15.6n 9 = 2.69833 10 ( J ) (16) Secti Ⅵ: (V 1, V 2 ) = (2.96V, 0.153V), (I 1, I 2 ) = (-0.098A, 0A), (t 1, t 2 ) = (90.8n, 116.4ns) 116.4n 2.807 0.098 WV Ι = [ ( t 90.8 n) + 2.96] [ ( t 90.8 n) 0.098] dt 90.8n 25.6n 25.6n = 2.53932 10 9 (17) The energy can be found by adding form (12) to (17), and then multiplying the switching frequency about 60kHz to get the switching power loss as shown in the formula (18). P = ( W + W + W + W + W + W ) 60k 0.02W (18) risin g Ι ΙΙ ΙΙΙ ΙV V VΙ Similarly, the power loss of falling edge can be found. In this article, the falling edge is divided into two parts as shown in the fig. 6. The energy of the three segments shows as below: Secti Ⅰ: (V 1, V 2 ) = (0.16V, 18.98V), (I 1, I 2 ) = (1.127A, 1.127A), (t 1, t 2 ) = (0, 52ns) 52n 18.82 W = Ι ( t 0.16) 1.127dt 0 52n + = 5.6084 10 7 (19) FA Report No: F020810M 7
Secti Ⅱ: (V 1, V 2 ) = (18.98V, 263.8V), (I 1, I 2 ) = (1.127A, 0.52A), (t 1, t 2 ) = (52n, 116ns) 116n 244.82 0.607 WΙΙ = [ ( t 52 n) + 18.98] [ ( t 52 n) + 1.127] dt 52n 64n 64n 6 = 6.65925 10 ( J ) (20) Secti Ⅲ: (V 1, V 2 ) = (263.8V, 263.8V), (I 1, I 2 ) = (0.52A, 0A), (t 1, t 2 ) = (116n, 144.8ns) 144.8n 0.52 WΙΙΙ = 263.8 [ ( t 116 n) + 0.52] dt 116n 28.8n 6 = 1.97533 10 ( J ) (21) The energy can be found by adding form (19) to (21), and then multiplying the switching frequency about 60kHz to get the switching power loss as shown in the formula (18). Pfall in g = ( WΙ + WΙΙ + WΙΙΙ ) 60k 0.55W (18) Ⅰ Ⅱ Ⅲ Fig. 6 Riemann Sum Three Sectis of Falling Edge FA Report No: F020810M 8
Cclusi In this article, the precise mathematic analysis is presented to analyze the switching loss of a power MOSFET. In theorem, if the waveform can be divided into more sectis, the results can be more accurate. FA Report No: F020810M 9