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One of the often overlooked stresses in power supplies is the input capacitor RMS (root mean square) current. If not properly understood, excessive current can cause the capacitor to overheat and fail prematurely. In the buck converter, RMS current is easily calculated in terms of output current (Io) and duty factor (D) using the following approximate expression:
(Click on equation to enlarge)
provides a plot of this expression; it is a circle with a maximum of 0.5, at 50% duty factor and two zero crossings at zero and 100% duty factor. The curve is symmetric around 50%. Between 20% and 80%, the ratio between the RMS current and the output current is greater than 80%. With duty factors in this range, you can approximate the RMS current as half the maximum output current. Outside this range, you should do the calculation.
Figure 1: : Buck input capacitor RMS current peaks at ˝ of the output current
(Click on image to enlarge)
Over the last few years, significant improvements have been achieved in ceramic capacitors' volumetric efficiency and cost. Ceramic capacitors are now preferred for bypassing power supply power stages. However, their low ESR can generate many nuisances in power supplies such as EMI filter oscillation and unexpected voltage surges (see Power Tip 20).
A paralleled electrolytic capacitor is frequently used to dampen these high Q circuits. You should be mindful of ripple current within the electrolytic in these situations, as much of the power supply ripple current can end up in the electrolytic capacitor.
Figure 2 shows an example 100 kHz switcher with an input capacitance comprised of a 10 µF ceramic capacitor in parallel with an electrolytic capacitor that contains 0.15 O of equivalent series resistance (ESR). The capacitance of the electrolytic capacitor is assumed to be much larger than that of the ceramic capacitor. In this case, almost 70% of the RMS current was in the electrolytic.
Figure 2: Watch the electrolytic capacitor current when using different capacitor types
(Click on image to enlarge)
To reduce this RMS current, you could increase the ceramic capacitance, the operating frequency or the ESR. This curve was generated by taking the Fourier Series of the capacitor current, calculating the electrolytic capacitor current at each harmonic (up to 10) and recombining the harmonics to calculate the electrolytic capacitor's total RMS current.
Note that the current in the ceramic capacitor is in quadrature with the current in the ESR so they must be treated as vectors. If you did not want to invest the time in all these calculations, you can easily simulate this circuit with a current source and three passive components.
To summarize, watch the RMS current in input capacitors, as over-current stress can degrade the capacitor's reliability. Pay particular attention when combining capacitor types, as ceramic capacitors will usually allow high enough ripple voltage to create over-current conditions in paralleled electrolytic capacitors. The cure for this is increasing one or more of the following: operating frequency, amount of ceramic capacitance, the ESR of the electrolytic capacitor or its RMS current rating.
Please join us next month when we will discuss feedback loop basics in a DC/DC converter.
For more information about this and other power solutions, visit www.ti.com/power-ca.
Here is the derivation of RMS current in the input capacitor, assuming infinite inductance, starting with the RMS current in a rectangular pulse (D0.5 * Ipk) and removing the DC component (D * Ipk):
(Click on equations to enlarge)
About the author
Robert Kollman is a Senior Applications Manager and Distinguished Member of Technical Staff at Texas Instruments. He has more than 30 years of experience in the power electronics business and has designed magnetics for power electronics ranging from sub-watt to sub-megawatt with operating frequencies into the megahertz range. Robert earned a BSEE from Texas A&M University, and a MSEE from Southern Methodist University