Switching Power Supplies Get Energy Storage from Output Capacitors
On the voltage-charge relationship graph, the capacitance is shown as a diagonal line, and the energy stored in the capacitance is the area contained under the line. Although the output capacitance of the power MOSFET is nonlinear and varies depending on the drain voltage, the energy stored in the output capacitance is still the region contained under the nonlinear capacitance line. Therefore, if we can find a straight line that gives the same area as the area contained in the varying output capacitance curve shown in FIG. 1, the slope of the line is exactly the equivalent output capacitance that produces the same amount of stored energy.
For some older planar technology MOSFETs, the designer may be able to find the equivalent output capacitance using a curve fit based on the output capacitance values in the data sheet at the commonly specified drain-source voltage of 25V.
(3) The energy storage can then be obtained from a simple integral equation.
(4) Finally, the effective output capacitance is given as
(5)The measured value of the output capacitance and the fitted curve derived from Eq. (3) are shown. It works well with respect to the old technology MOSFETs. However, for MOSFETs using newer technologies such as superjunction technology, where the output capacitance has more nonlinear characteristics, a simple exponential curve fit is sometimes not good enough. Figure 2(b) shows the measured output capacitance of a *new technology MOSFET and the fitted curve using equation (3). For the equivalent output capacitance value, the gap between the two in the high voltage region leads to a huge difference, since the voltage is multiplied for the capacitance in the integral equation. Estimating the equivalent capacitance will result in a much larger capacitance, which can mislead the initial design of the converter.
Output capacitance valuation, (a) old MOSFET, (b) new MOSFET
If the output capacitance value varies based on the drain-source voltage, the energy stored in the output capacitance can be found using Equation (4). Although the capacitance curves are shown in the data sheet, it is not easy to read out the capacitance value. Therefore, based on the drain-source voltage, the stored energy in the output capacitance is given by the graph in the latest power MOSFET data sheet. Using the curve shown in Figure 3, the equivalent output capacitance at the desired direct current (DC) bus voltage can be obtained using Equation (5).
