Bypassing a Capacitor

It is important for the engineer just starting out in Power Electronics to understand the truth about bypassing a large capacitor.

The Problem…

is that no real capacitor is ideal. As ripple frequency rises, a capacitor ceases to act like a capacitor! Parasitic resistance (actually lossy!) and then inductance come into play. The response is essentialy the same for all caps, regardless of construction. Minimum impedance occurs at the resonant frequency of the capacitor itself and its effective series inductance (esl.) The Q or peak, if any, depends on the magnitude of the effective series resistance (esr,) as it provides the damping action.

In practice, a typical switcher-grade e’lytic, including the surface mount type, has a resonance at only 2 to 3 KHz! which is far below fs…. Above this resonant frequency, it is just a DC blocked inductance!



In use, it filters out ripple components at fs, 2fs, 3fs, etc. But at those frequencies, its impedance is merely that of a very small inductor (the esl) so its filtering action is just that of a very small inductive impedance to ground [remember that the large ideal capacitor looks like a short to ground at AC.]

Thus, most power supplies in manufacture today are in effect input and output filtered by tiny inductances (esl’s) each DC blocked by a large ideal capacitor! In other words the capacitance of the electrolytic does no filtering at all, since its impedance is swamped by that of the esl at and above the switching frequency.

The Engineer’s Response…

is to bypass the large (usually electrolytic) input or output cap with a smaller, high frequency part. Film caps, tantalums, monolithic and ceramic discaps are favorites; stripline and matched pair traces yield varying amounts of output/ground filtering capacity right on the board.


The Aim…

is to return the capacitance of the agglomerated whole to that of an ideal capacitor with the original electrolytic’s value. Each smaller capacitor is ideal at a higher and higher frequency. By parallelling a series of them, one hopes to keep the impedance capacitive, and thus low at ever higher frequencies, relying on a capacitor’s decreasing impedance with increasing frequency.

Meanwhile, the (rising) impedance of the esl (Xl = 2pifL) of each of them is, in its turn, to be made less important by the succeeding cap, via Xc||Xl = XcXl/(Xc+Xl) = Xc when Xl >> Xc. In other words, each esl’s impedance will be negligibly large! compared to the capacitive impedance of the next smallest ‘beep’ capacitor.

Unfortunately, the technique fails to take into account the fact that a smaller capacitor has a larger actual impedance Xc = 1/2pifC at a given frequency than the larger one it is bypassing! It is not a ‘high frequency substitute’ capacitance.

The Result…

is improved performance, but only to a degree. The bypass cap is small enough to remain purely capacitive at a high frequency, but its small capacitance value does mean that its impedance remains much greater than that of the original electrolytic. In other words, the bypassed component has been improved upon, but has not been made ideal! It does not behave like a pure capacitance with the C value of the original electrolytic.

The situation is diagrammed below for the simplified case of a 1000uF electrolytic ‘beeped’ by a 0.1uF ceramic. The light green line is the resulting impedance of the parallel combination of the two components. Note that the Xc of the ceramic is much greater than the Xc of the electrolytic at any given frequency. For this reason, the resulting high frequency impedance is much greater than it would be if the larger cap were ideal–even though it is much less than the impedance of the electrolytic’s esl.


 

The Good News Is That…

using a sequence of bypass caps will hold the net impedance to a more or less constant minimum value. In fact, the result is essentially that of an ideal capacitor with a small, but finite esr, but no esl. Or at least the esl has been greatly reduced in magnitude by bypassing, so that it does not come into play until a much greater frequency than was originally the case.


 

Assuming that…

one has the good sense to arrange for a complete complement of such “beep” caps (red vs. green line,) the effect is more that of a series RLC than anything else! The difference between it and the original e’lytic’s RLC is mainly that the L (the esl of the smallest bypass cap) is significantly less than that of the origninal!

Meanwhile, the (admittedly slightly zig-zaggy) “R” section is handy in two ways:

1) As an output cap, it will filter out switching ripple if its impedance is much less than that of the load at the corresponding (same) frequency. Further, the fact that the switching frequency and its harmonics land on the “resistive” leg of the frequency response means that the output inductor’s triangular current ripple waveform is not ‘sharpened’ by a rising impedance characterisitc. The result is softer, rounded ripple which is easier on the load!

A similar benefit accrues when the cap is used to filter a switched (square) wave of current, as in the output of a Flyback Converter, or the energy transfer cap of a Cuk Converter. Once again, the non-inductive impedance keeps square waveforms from generating sharp voltage spikes.

2) If it is paired with some inductance, whether discreet or leakage or any other, the response will be similar to that resulting from an actual series resistance! The “tank” will be damped since the inductance’s impedance passes through the resistive part of the series RLC’s response.

Caution: The resonances from the succession of bypass caps must themselves be damped by the various esr’s and wire/trace resistances occurring in the circuit. This is usually the case, since most families of power capacitors are designed to be naturally damped to a moderately low Q by their manufacturers. This ought not to be taken for granted, however, especially if high values of EMI are encounterd at certain discrete frequencies during breadboard test.

Note: The principle mentioned is the same as that employed in shunt damping, where a jog is introduced into a capacitive impedance characteristic by parallelling a cap with a larger capacitor in series with a small resistor. If the impedance of a the associated inductance is driven through the resistive “flat,” no true LC resonance occurs at all, and the characteristic follows first the smaller cap’s 1/sC, then the R’s constant impedance, then finally the rising sL of the inductance!