Testing capacitor failure

[salvarsan]

Having recently lapsed into delusions of competence, I am repairing some antique guitar amps.

Electrolytic capacitors are a common component failure point and I like to test them in an unpowered condition before a viscous smelly liquid slowly bubbles out of them. Ammonium borate in glycol is not to be trifled with.

You need an LCR meter that can test capacitance, dissipation factor, and equivalent series resistance (Cs, D, and ESR) at 1kHz.

Here's the gotcha -- check both D and ESR because one may be bad without the other.

For any electrolytic you might see in an old guitar amp, ESR should be 3 ohms or less @1kHz and may test so even when the cap has a 50+% dissipation factor.

[R.G.]

Hmmm. It seemed to me that the ESR and DF were related. I no longer have the textbook I used for that (from about 1971), so I went looking for something more recent. From the wikipedia entry on dissipation factor:

Electrical potential energy is dissipated in all dielectric materials, usually in the form of heat. In a capacitor made of a dielectric placed between conductors, the typical lumped element model includes a lossless ideal capacitor in series with a resistor termed the equivalent series resistance (ESR) as shown below.[1] The ESR represents losses in the capacitor. In a good capacitor the ESR is very small, and in a poor capacitor the ESR is large. Note that the ESR is not simply the resistance that would be measured across a capacitor by an ohmmeter. The ESR is a derived quantity with physical origins in both the dielectric's conduction electrons and dipole relaxation phenomena. In a dielectric only one of either the conduction electrons or the dipole relaxation typically dominates loss.[2] For the case of the conduction electrons being the dominant loss, then

ESR = \frac {\sigma} {\varepsilon \omega^2 C} , where

\sigma is the dielectric's bulk conductivity,

\omega is the angular frequency of the AC current i,

\varepsilon is the lossless permittivity of the dielectric, and

C is the lossless capacitance.

A real capacitor has a lumped element model of a lossless ideal capacitor in series with an equivalent series resistance (ESR). The loss tangent is defined by the angle between the capacitor's impedance vector and the negative reactive axis.

If the capacitor is used in an AC circuit, the dissipation factor due to the non-ideal capacitor is expressed as the ratio of the resistive power loss in the ESR to the reactive power oscillating in the capacitor, or

DF = \frac {i^2 ESR} {i^2 |X_{c}|} = \omega C \cdot ESR = \frac {\sigma} {\varepsilon \omega} = 1 / Q .

Which comes out cryptically, it seems that DF = 2*pi*F*C*ESR; that seems to say if you have ESR, you can compute DF at any frequency, although it is frequency related.

For the caps under the most AC stress, the power filter caps, you'd want to compute DF at 120Hz, 180, and 240 to get the four biggest components of ripple. The others may well be small enough to ignore.

So for those not blessed with an LCR meter, measuring ESR and using a calculator will get you there. ESR meters are somewhat easy to hack or fab from a kit. Mine cost $30 and works well.

Probably the biggest issue is the ratio of C and ESR. Big C and big ESR means big DF. The ESR meter I have has suggested maximum ESRs on the top of it. This makes sense: the bigger the cap, the more current will pour through it, and the more the dissipation from the ESR and the current squared.

[Gtr_tech]

If antique means late 60s or older, why even bother testing the lytics? They're old...way old....and its time for fresh ones.

[Mick Bailey]

A problem with testing caps is that a shorted cap will show low ESR (and corresponding high dissipation). Most ESR meters won't highlight a shorted cap, but a multimeter will. Also, many ESR meters don't relate test frequency to cap value, though I wonder how much this would actually matter if the test frequency was high enough to effectively eliminate the reactive component form the reading.

A test frequency of 1khz would be too low - you couldn't get a reading as low as 3 ohms for PSU electrolytics (for example, an 8uf cap has a reactance of almost 20 Ohms at 1Khz). I test at 150khz.

[salvarsan]

Which comes out cryptically, it seems that DF = 2*pi*F*C*ESR; that seems to say if you have ESR, you can compute DF at any frequency, although it is frequency related.

For the caps under the most AC stress, the power filter caps, you'd want to compute DF at 120Hz, 180, and 240 to get the four biggest components of ripple. The others may well be small enough to ignore.

In principle, I agree.

In practice, we are at the mercy of what our instruments report to us and how well we understand what they mean.

So, after an evening of entertainingly ambiguous readings, I offered up my advice for what makes a quick test.
Yup, Wikipedia's Dissipation Factor page is germane.

The loss angle is a good indicator, I think.

Dept. of Shameless Plugs

While I'm crufting up an Arduino for ESR testing, I got impatient for results and torched $160 on yet another LCR meter, the UNI-T UT612, which tests up to 100kHz and reports ESR and loss angle, too. I like it.

A Sprague Atom 16uF/450V power supply cap, fresh from the vendor, measures as follows:

Hz	uF	%DF	ESR(Ω)	loss δ (degrees)
100	17.0	2.9	2.8	-88.2
120	16.9	3.2	2.5	-88.0
1k	16.5	14.5	1.4	-81.6
10k	13.3	87.7	1.0	-48.4
100k	2.16	103.0	0.76	-43.8

The loss angle δ = arctan (ESR/|X_c|) where Xc is the pure capacitive impedance,
= -90° for a perfect capacitor. It tells the story more succinctly than all the other measurements.

Given capacitance and ESR, you can calculate all the rest, or do arctan(DF), but I plead unregenerate laziness.

-drh

[salvarsan]

A test frequency of 1khz would be too low - you couldn't get a reading as low as 3 ohms for PSU electrolytics (for example, an 8uf cap has a reactance of almost 20 Ohms at 1Khz). I test at 150khz.

If all you have in hand is an Extech LCR meter, then you test at 1kHz.

That said, you really need 100+kHz for an unambiguous ESR measurement.

[R.G.]

[FONT=arial]In principle, I agree.

In practice, we are at the mercy of what our instruments report to us and how well we understand what they mean.

As Yogi Berra said, in theory there's no difference between theory and practice. In practice, there is.

We used to stick an acronym on some of our tech writeups, indicating that all the measurements were approximations, and the real value was KOTG.

It took a long time for any of the bosses to ask us what "KOTG" meant. They were told "Known Only To God".

Given capacitance and ESR, you can calculate all the rest, or do arctan(DF), but I plead unregenerate laziness.

Yep. As a practical matter, there are measurements which need only measured to "greater than" or "less than", even on a sliding scale; as well as cutoff conditions.

In tube amps, one cutoff condition is age. If an amp is a working tool, someone feeds their family with it, then any cap older than 10 years ought to be replaced. If it's a favorite because of sound, and a couple of weeks in the shop is not a killer, then caps older than 20 years ought to be replaced as a matter of course. If it's a museum piece, valued for being "original" more than "works reliably", then any age or condition of originality outweighs working.

If caps are failing before cutoff dates (which are, obviously, a number set by the tech doing the work, not may favorite numbers above), then a quick look at ESR tells you if the ESR is bigger than X. X is a matter of experience, but there are guides. A cap with a wildly out-of-whack ESR is about to fail, no matter what it's DF and loss angle say. Probably a wildly out-of-whack LF or DF would do the same thing.

Most techs don't even have the equipment to measure ESR.

Fortunately, ESR is easy to measure. And from the KOTG era, easy to measure beats precise but difficult to measure every time for repairs. As to the frequency range of ESR measurements, the measurements don't have to be at any specific frequency. They just have to be high enough that the cap being measured has an inconsequential impedance compared to the ESR being measured. So a 100uF cap has a lower minimum ESR measurement freuqency than a 1uF. And if the measurement device measures on edge rate, not sustained frequency, the frequency is almost immaterial, as the frequencies in an edge are very, very high. LCR meters with fixed measurement frequencies are actually answering a different question than capacitor quality, I think.

And fortunately again, the range of stuff to measure isn't big. 1uF to 100uF will cover the vast majority of tube amp repairs. Non-electros don't degrade the way that electros do, so as a practical matter, ESR is most useful for electros. I've never measured ESR on non-electros once I got past the new-toy stage with my meter.

[salvarsan]

It took a long time for any of the bosses to ask us what "KOTG" meant. They were told "Known Only To God".

Medical variation: GORK (God Only Really Knows) is applied to the permanently comatose.

If it's a museum piece, valued for being "original" more than "works reliably", then any age or condition of originality outweighs working.

Yes.

(buries face in hands, heaves long sobbing sigh)

If I'm lucky, I get to replace a canister cap with a near equivalent.
Less lucky, I get to disconnect it and wire in some axial caps.

I was once asked to bore out the canister (while preserving the paper label) and hide a functioning cap in it. Because of the HAZMAT nature of the chore, I dissuaded the owner by hinting at a dialysis+chelation treatment price tag.

One client wants me to procure wax paper caps for a retrofit job, not unlike an appendix transplant.

Kill me now.

-drh

[Enzo]

Ask him to provide you the caps, and specify that they be first tested and pass the leakage requirements.

[Steve Conner]

Smells like vintage fish for dinner. :-@

I always thought of ESR as being due to the resistance of the electrodes (and electrolyte) and dissipation factor as due to hysteresis losses in the dielectric, which look more like a shunt resistance than a series one. Similar idea to copper losses and iron losses in a transformer.

But of course you can lump in the dielectric losses when calculating the ESR, and lump in electrode resistance to the DF figure. LCR meters probably do that.

The relative contributions of actual series resistance and dielectric loss to the ESR and DF figures will depend on the test frequency, which (IMO) is why these figures change so drastically with frequency. There are two loss mechanisms but the meter is trying to boil them down to a single figure.

[salvarsan]

Smells like vintage fish for dinner. :-@

My tendency is to venomously rebuke cork sniffage by Les Sniffeurs de Corque ... except when *I* do it.

I was presented with two small combo amps of the same model. One is all original with wax paper caps intact, the other had a partial cap replacement and sounds distinctly inferior.

The speakers are surprisingly close given their age. Turns out, you can extract Thiel-Small parameters by weighting the cone and measuring the resonance point shift.

Added to the mystery is the grid leak biased input stage, a topology which is sensitive to the tube manufacturing tolerances. Swapping input tubes made a partial difference, so the rest of it is in the caps. Yeah, if there was such a thing as an appendix transplant, this is the guitar amp equivalent.

</cork_sniffing>

But of course you can lump in the dielectric losses when calculating the ESR, and lump in electrode resistance to the DF figure. LCR meters probably do that.

The relative contributions of actual series resistance and dielectric loss to the ESR and DF figures will depend on the test frequency, which (IMO) is why these figures change so drastically with frequency. There are two loss mechanisms but the meter is trying to boil them down to a single figure.

Thanks for the insights, Steve. That lowers the "huhn?" coefficient quite a lot and got me off my ass to look at SPICE capacitor models.

LTSpice models a capacitor generally as this:



These wax paper caps have a frequency-dependent DF, 25% @120Hz vs. 8% @1kHz.
I wonder what the various reactive contributions are.

-ciaoder