# Aluminum Cap Multipliers - why we can't have them and eat them too

With virtually the highest available CV (capacitance time voltage) capability, accompanied by the lowest cost, aluminum capacitors are still not even close to getting canned into history books, as some would think. Some of our younger engineers get rather charged up thinking about ceramic and modern polymer technologies, but they should really be paying closer attention to the viability and finer design aspects of the still undying aluminum electrolytic capacitor (hereafter called an 'elko').

So why not use an elko?? OK, it has a higher ESR. Granted! But let's not forget that 'all-ceramic' solutions can exhibit dangerous input oscillations, and it is now actually being recommended that to damp out these oscillations we should put a high-ESR elko in parallel to the existing input ceramic cap. We may also require a higher ESR just to ensure stability when using voltage-mode control.

To cut to the chase, let us therefore assume that we finally see the need to use an elko in a particular location. Now the main concern with such a component is its life expectancy. Eventually, the electrolyte inside will evaporate causing the capacitance to decrease, and beyond a certain level we would declare the capacitor 'dead' (worn-out). We can clearly understand that a few factors will play key roles in this process:

a) The hermeticity of the end seals of the capacitor. However, no joint is hundred percent perfect, and so some evaporation will take place slowly over time. But we see the need to pick a vendor with a high (and consistent) quality b) The surrounding temperature. The heat could come from nearby components or through internal heat dissipation. If we lower the temperature, the evaporation rate will decrease, and extend the life. We will see a little later, how this leads to the published 'temperature multipliers' c) The core temperature. We expect that there will be hot-spots inside the capacitor since we have less-than-perfect thermal conductivity inside it. As a worst-case, that is the temperature to consider when calculating life. In fact the entire life expectancy calculation is reduced to accurately predicting this core temperature (since we can't measure it) d) The ESR. This would certainly affect the internal heat dissipation, possibly raising the temperature and aiding the evaporation process e) The frequency. Since ESR can be a function of frequency, the frequency will indirectly affect the life of the capacitor. We will see that this leads to the published 'frequency multipliers'

The most important datasheet parameter is the ripple current rating. This is typically stated in Amperes RMS at 120Hz and 105C. Its essentially means that if the ambient temperature is at the maximum rated of 105C, we can pass a (low frequency) current waveform with the stated RMS, and in doing so we will get the stated life. The declared life figure is typically 2000 hours to 10000 hours under these conditions. Yes there are lower grade 85C capacitors available, but they are rarely used, as they can hardly meet typical life requirements at high ambients.

Let us now understand what a frequency multiplier tells us. The ESR of an elko is also usually stated at 120Hz. The vendor may have directly provided a ripple current rating at 100kHz in addition to the 120Hz number. If not, he would certainly have provided 'frequency multipliers'. A typical frequency multiplier is 1.43 at 100kHz. That means that if we are allowed 1A ripple current at 120Hz, then at 100kHz we are allowed 1.43A. This by design, will produce the same heating (core temperature rise over ambient) as 1A causes at 120Hz. Therefore this is also equivalent to saying that the ESR at 100kHz is related to the ESR at 120Hz by the following equation

Thus the high frequency ESR is about half the low frequency ESR. Frequency multipliers should be used always, or we will overestimate the heating and underestimate the life, possibly forcing us to move to a larger cap size.

Temperature multipliers we have to be more careful about. And we have to clearly understand what they really imply.

The datasheet usually provides certain 'temperature multipliers' for the allowable ripple current. For example for the old but well-known LXF series from Chemicon, the numbers provided are

1. At 65C the temperature multiplier is 2.23 2. At 85C the temperature multiplier is 1.73 3. At 105C the temperature multiplier is 1

This means that if for example the rated ripple current is 1A (at a maximum rated ambient of 105ïC), then we can pass 1.73A at an ambient of 85C, and 2.23A at an ambient of 65C. *But in doing so, the core temperature will remain the same. *

So what is the actual story the temperature multipliers are telling us? The amount of heating and the core temperature rise are proportional to IRMS2, so we if we assume that in every case the final core temperature was the same, i.e., TCORE, then comparing the 105ïC ambient case with that at 85ïC

We can thus solve for T_{CORE} to get

T_{core}=115C.

This says that if we pass 1.73A at 85C, or 1A at 105C, the core temperature will be 115C in either case. In fact, for most 105C rated capacitors, we will have roughly 5C differential from ambient to the outer can and then another 5C from the can to the innards (the core), giving us a total of 10C from ambient to core.

Let us check our reasoning by confirming the 65C multiplier

So the multiplier must be 5^{0.5}=2.236, which agrees with the published datasheet value. Therefore we see that from the vendor's published ripple current temperature multipliers, we can easily deduce his designed-in maximum core temperature.

The problem with this is that if the core temperature is at its maximum rated 115C, the life would always just be the declared 2000 hours or so. But that is hardly enough to get us through even one quarter of a year. We usually need at least about 44000 hours (5 years) of life expectancy from all elkos used in a typical commercial power supply. How do we get there? We do that by reducing the core temperature thereby slowing the evaporation rate of the electrolyte. Does this imply we should not be using temperature multipliers to increase the current?

There is actually another complication. It has been determined that not only is the absolute value off the core temperature important, but the differential from can to core is critical too. So if we increase the differential beyond the designed-in 5C, the life can deteriorate severely, even if the can is held at a lower temperature. But the designed-in differential of 5C occurs ONLY when we pass the maximum specified ripple current (*no temperature multipliers* applied), and that is irrespective of the ambient. Which means that as a matter of fact we cannot use any temperature multipliers at all. So, if the cap is rated to pass 1A at 105C, then even at an ambient of say 65C, we are allowed to pass only 1A, NOT 2.23A.

When the differential is decidedly kept equal to or less than the designed-in value, the life of the elko is then determined by the familiar doubling rule --- every 10ïC fall in core temperature (from its maximum rated), the life doubles. That is how we can finally get the required 44 khours. For example if the core is correctly estimated to be at 65C, then the calculated life of a 2000 hour capacitor is actually 2000ï2ï2ï2ï2ï2=64 khours.

But we do see that we can't have our cake and eat it too. We can increase the ripple current (but not the life) by applying the temperature multipliers OR we can increase the life (but not the ripple current) by not applying these multipliers. We just can't have it both ways!

Elkos give us lots of benefits as it is, and we just shouldn't be asking for any more.

Do write me at sanjaya.maniktala@nsc.com or sanjayamaniktala@yahoo.com. Please copy Steve at sohr@cmp.com too, just so he knows I am not babbling.