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Efficiency of Buck Converter

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Efficiency of Buck Converter Application Note Switching Regulator IC Series Efficiency of Buck Converter Switching regulators are known as being highly efficient power sources. To further improve their efficiency, it is helpful to understand the basic mechanism of power loss. This application note explains power loss factors and methods for calculating them. It also explains how the relative importance of power loss factors depends on the specifications of the switching power source. Synchronous rectification type High-side MOSFET Figure 1 shows the circuit diagram of a synchronous 2 푉푂푈푇 rectification type DC/DC converter. Figure 2 shows the 푃푂푁−퐻 = 퐼푂푈푇 × 푅푂푁−퐻 × [푊] (1) 푉퐼푁 waveforms of the voltage of a switch node and the current waveform of the inductor. The striped patterns represent the Low-side MOSFET areas where the loss occurs. 2 푉푂푈푇 The following nine factors are the main causes of power loss: 푃푂푁−퐿 = 퐼푂푈푇 × 푅푂푁−퐿 × (1 − ) [푊] (2) 푉퐼푁 1. Conduction loss caused by the on-resistance of the MOSFET 푃푂푁−퐻, 푃푂푁−퐿 퐼푂푈푇: Output current [퐴] 2. Switching-loss in the MOSFET 푃푆푊−퐻, 푃푆푊−퐿 푅푂푁−퐻: High-side MOSFET on-resistance [훺] 3. Reverse recovery loss in the body diode 푃퐷퐼푂퐷퐸 푅푂푁−퐿: Low-side MOSFET on-resistance [훺] 4. Output capacitance loss in the MOSFET 푃퐶푂푆푆 푉퐼푁: Input voltage [푉] 5. Dead time loss 푃퐷 푉푂푈푇: Output voltage [푉] 6. Gate charge loss in the MOSFET 푃퐺 7. Operation loss caused by the IC control circuit 푃퐼퐶 In the equations (1) and (2), the output current is used as the 8. Conduction loss in the inductor 푃퐿(퐷퐶푅) current value. This is the average current of the inductor. As 9. Loss in the capacitor 푃퐶퐼푁, 푃퐶푂푈푇 shown in the lower part of Figure 2, greater losses are generated in the actual ramp waveforms. If the current Conduction loss in the MOSFET waveform is sharper (peak current is higher), the effective current is obtained by integrating the square of the differential The conduction loss in the MOSFET is calculated in the A and between the peak and bottom values of the current. The loss B sections of the waveform in Figure 2. As the high-side can then be calculated in more detail. MOSFET is ON and the low-side MOSFET is OFF in the A The conduction losses 푃푂푁−퐻 and 푃푂푁−퐿 are calculated with section, the conduction loss of the high-side MOSFET can be the following equations. estimated from the output current, on-resistance, and on-duty cycle. As the high-side MOSFET is OFF and the low-side High-side MOSFET MOSFET is ON in the B section, the conduction loss of the 2 2 (퐼푃 − 퐼푉) 푉푂푈푇 low-side MOSFET can be estimated from the output current, 푃푂푁−퐻 = [퐼푂푈푇 + ] × 푅푂푁−퐻 × [푊] (3) 12 푉퐼푁 on-resistance, and off-duty cycle. The conduction losses 푃푂푁−퐻 and 푃푂푁−퐿 are calculated with the following equations. © 2016, 2021 ROHM Co., Ltd. No. 64AN035E Rev.002 1/15 APRIL 2021 Efficiency of Buck Converter Application Note When the low-side MOSFET is turned ON by the gate voltage Low-side MOSFET while the body diode is energized and then the FET is turned 2 OFF by the gate voltage, the load current continues to flow in 2 (퐼푃 − 퐼푉) 푉푂푈푇 푃푂푁−퐿 = [퐼푂푈푇 + ] × 푅푂푁−퐿 × (1 − ) [푊] (4) 12 푉퐼푁 the same direction through the body diode. Therefore, the drain voltage becomes equal to the forward direction voltage (푉퐼푁 − 푉푂푈푇) 푉푂푈푇 and remains low. Then, the resulting switching-loss 푃푆푊퐿 is 훥퐼퐿 = × [퐴] 푓푆푊 × 퐿 푉퐼푁 very small, as described in the following equation. Low-side MOSFET Δ퐼퐿 퐼푃 = 퐼푂푈푇 + [퐴] 2 1 푃 = × 푉 × 퐼 × (푡 + 푡 ) × 푓 [푊] (6) 푆푊−퐿 2 퐷 푂푈푇 푟−퐿 푓−퐿 푆푊 퐼푃 = 퐼푂푈푇 푉퐷: Forward direction voltage of low-side MOSFET body diode [푉] 퐼푂푈푇: Output current [퐴] 퐼푂푈푇: Output current [퐴] 퐼푃: Inductor current peak [퐴] 푡푟−퐿: Low-side MOSFET rise time [푠푒푐] 퐼푉: Inductor current bottom [퐴] 푡푓−퐿: Low-side MOSFET rise time [푠푒푐] 푅푂푁−퐻: High-side MOSFET on-resistance [훺] 푓푆푊: Switching frequency [퐻푧] 푅푂푁−퐿: Low-side MOSFET on-resistance [훺] 푉 : Input voltage [푉] 퐼푁 Reverse recovery loss in the body diode 푉푂푈푇: Output voltage [푉] 훥퐼퐿: Ripple current of inductor [퐴] When the high-side MOSFET is turned ON, the transition of 푓푆푊: Switching frequency [퐻푧] the body diode of the low-side MOSFET from the forward 퐿: Inductance value [퐻] direction to the reverse bias state causes a diode recovery, which in turn generates a reverse recovery loss in the body Switching-loss in the MOSFET diode. This loss is determined by the reverse recovery time of the diode 푡푅푅 . From the reverse recovery properties of the The switching-losses are calculated in the C and D sections or diode, the loss is calculated with the following equation. in the E and F sections of the waveform in Figure 2. When the high-side and low-side MOSFETs are turned ON and OFF 1 푃 = × 푉 × 퐼 × 푡 × 푓 [푊] (7) alternately, a loss is generated during the transition of the on- 퐷퐼푂퐷퐸 2 퐼푁 푅푅 푅푅 푆푊 switching. Since the equation for calculating the area of the 푉퐼푁: Input voltage [푉] two triangles is similar to the equation for calculating the power 퐼푅푅: Peak value of losses during the rising and falling transitions, this calculation body diode reverse recovery current [퐴] can be approximated using a simple geometric equation. 푡푅푅: Body diode reverse recovery time The switching-loss 푃푆푊−퐻 is calculated with the following 푓푆푊: Switching frequency [퐻푧] equation. High-side MOSFET Output capacitance loss in the MOSFET 1 In each switching cycle, the loss is generated because the 푃 = × 푉 × 퐼 × (푡 + 푡 ) × 푓 [푊] (5) 푆푊−퐻 2 퐼푁 푂푈푇 푟−퐻 푓−퐻 푆푊 output capacitances of the high-side and low-side MOSFETs 퐶푂푆푆 are charged. This loss is calculated with the following 푉퐼푁: Input voltage [푉] equation. 퐼푂푈푇: Output current [퐴] 푡푟−퐻: High-side MOSFET rise time [푠푒푐] 푡푓−퐻: High-side MOSFET rise time [푠푒푐] 푓푆푊: Switching frequency [퐻푧] © 2016, 2021 ROHM Co., Ltd. No. 64AN035E Rev.002 2/15 APRIL 2021 Efficiency of Buck Converter Application Note or 1 2 (8) 푃퐶푂푆푆 = × (퐶푂푆푆−퐿 + 퐶푂푆푆−퐻) × 푉퐼푁 × 푓푆푊 [푊] 2 2 푃퐺 = (퐶퐺푆−퐻 + 퐶퐺푆−퐿) × 푉푔푠 × 푓푆푊 [푊] (11) 퐶푂푆푆−퐿 = 퐶퐷푆−퐿 + 퐶퐺퐷−퐿 [퐹] 푄푔−퐻: Gate charge of high-side MOSFET [퐶] 퐶푂푆푆−퐻 = 퐶퐷푆−퐻 + 퐶퐺퐷−퐻 [퐹] 푄푔−퐿: Gate charge of low-side MOSFET [퐶] 퐶푂푆푆−퐿: Low-side MOSFET output capacitance [퐹] 퐶퐺푆−퐻: Gate capacitance of high-side MOSFET [퐹] 퐶퐷푆−퐿: Low-side MOSFET drain-source capacitance [퐹] 퐶퐺푆−퐿: Gate capacitance of low-side MOSFET [퐹] 퐶퐺퐷−퐿: Low-side MOSFET gate-drain capacitance [퐹] 푉푔푠: Gate drive voltage [푉] 퐶푂푆푆−퐻: High-side MOSFET output capacitance [퐹] 푓푆푊: Switching frequency [퐻푧] 퐶퐷푆−퐻: High-side MOSFET drain-source capacitance [퐹] Operation loss caused by the IC 퐶퐺퐷−퐻: High-side MOSFET gate-drain capacitance [퐹] The consumption power used by the IC control circuit 푃퐼퐶 is 푉퐼푁: Input voltage [푉] calculated with the following equation. 푓푆푊: Switching frequency [퐻푧] 푃 = 푉 × 퐼 [푊] (12) Dead time loss 퐼퐶 퐼푁 퐶퐶 When the high-side and low-side MOSFETs are turned ON 푉퐼푁: Input voltage [푉] simultaneously, a short circuit occurs between the VIN and 퐼퐶퐶: IC current consumption [퐴] ground, generating a very large current spike. A period of dead time is provided for turning OFF both of the MOSFETs to Conduction loss in the inductor prevent such current spikes from occurring, while the inductor There are two types of the power loss in the inductor: the current continues to flow. During the dead time, this inductor conduction loss caused by the resistance and the core loss current flows to the body diode of the low-side MOSFET. The determined by the magnetic properties. Since the calculation dead time loss 푃퐷 is calculated in the G and H sections of the of the core loss is too complex, it is not described in this article. waveform in Figure 2 with the following equation. The conduction loss is generated by the DC resistance (DCR) of the winding that forms the inductor. The DCR increases as 푃퐷 = 푉퐷 × 퐼푂푈푇 × (푡퐷푟 + 푡퐷푓) × 푓푆푊 [푊] (9) the wire length increases; on the other hand, it decreases as the wire cross-section increases. If this trend is applied to the 푉퐷: Forward direction voltage of inductor parts, the DCR increases as the inductance value low-side MOSFET body diode [푉] increases and decreases as the case size increases. 퐼푂푈푇: Output current [퐴] The conduction loss of the inductor can be estimated with the 푡퐷푟: Dead time for rising [푠푒푐] following equation. Since the inductor is always energized, it 푡퐷푓: Dead time for falling [푠푒푐] is not affected by the duty cycle. Since the power loss is 푓푆푊: Switching frequency [퐻푧] proportional to the square of the current, a higher output current results in a greater loss. For this reason, it is important Gate charge loss to select the appropriate inductors. The Gate charge loss is the power loss caused by charging 2 the gate of the MOSFET. The gate charge loss depends on 푃퐿(퐷퐶푅) = 퐼푂푈푇 × DCR [푊] (13) the gate charges (or gate capacitances) of the high-side and low-side MOSFETs. It is calculated with the following 퐼푂푈푇: Output current [퐴] equations. 퐷퐶푅: Inductor direct current resistance [Ω] 푃퐺 = (푄푔−퐻 + 푄푔−퐿) × 푉푔푠 × 푓푆푊 [푊] (10) Since the output current is used in this equation, the average current of the inductor is used for the calculation.
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