Paralleled Capacitors Don't Always Add Up!


If you're a mathematically astute RF engineer, comfortable with converting models and working in the complex impedance plane, this page isn't for you. Or at least have a beer or something before reading it. The effect described will be obvious and trivial, with no real practical application. For the rest of us it's an interesting quirk of how the models work, and lesson in choosing the right ones.


When he was small, Dilbert's mother explained that when you parallel capacitors, you just add the values. As she was leaving the room, he didn't quite hear her mutter under her breath, "unless you're one of those crazy audiophiles."

It's a common, though somewhat dubious, practice for audiophiles to parallel small film capacitors with larger electrolytics, hoping to bypass the perceived high inductance of the larger cap. It isn't so widely understood that even at and above self resonance, the total impedance of the larger cap is extremely low and the tiny inductance value is more dependent on physical dimensions than anything else. Thus, it's almost impossible to improve the situation with any reasonable sized low dissipation factor film cap. In fact, adding such a cap may encourage unwanted resonances. It was during an investigation of what happens when you parallel caps that I noticed the unexpected results that occur when you combine high-loss and low-loss parts using the series model of capacitance.

As long as internal losses are small, the usual rule applies- just add the cap values. With film and other capacitors having good high frequency performance, that will usually be the case. However, with aluminum electrolytics operating at audio frequencies, internal losses can be high and the rule breaks down; you need more complete formulas that take the losses into account.

For a good technical explanation of the formulas you can download this application note.

To do the conversions, download my impedance converter to do this for two caps, or this spreadsheet for N caps, plus a few other things. Note that the spreadsheet has several tabs across the bottom for the various examples.

The Hoffman Effect

The fact that a correction for losses is needed isn't too surprising, but what did surprise me is that there's a region of values and losses where adding a parallel capacitor will actually reduce the total series model capacitance, rather than increasing it. Being quite sure I had made some mistake, I had the results checked by two other experienced engineers. One of them was Henry P. Hall, designer of the General Radio Corp. Digibridge, the first "modern" solid state bridge. He was also surprised by the results and suggested I call it The Hoffman Effect. Maybe a bit tongue in cheek, but then Wheatstone did get his name attached to a bridge invented by Samuel Christie!

The reason this effect isn't more widely noted is probably due to five factors:

Admittedly, understanding how losses affect parallel capacitor combinations probably won't have any impact on the world of electronic design, and switching to a parallel model more suited to high loss situations avoids the issue, but it's an interesting bit of trivia to file away, should the situation ever arise.

I'm indebted to my friends, Eric H., who first checked my results and confirmed I wasn't completely crazy, and Henry P. Hall, who, even after working with all forms of impedance over his long and distinguished career, and probably having better things to do during his retirement, found the effect interesting enough to take a closer look and develop the formulas in the app note.

C. Hoffman
last edit August 25, 2015