Capacitor Measurements on an Impedance Analyzer

[The Electrician]

There is always interest in LCR meters, ESR meters, and various DIY measurement techniques for capacitor parameters.

The most comprehensive technique is to use an impedance analyzer, but such instruments are usually only available to working engineers; not so much to hobbyists! 

Since I happen to have access to an impedance analyzer, I thought I would use it to examine some capacitors.

The analyzer I'll be using is the Hioki IM3570 (http://www.hioki.com/newproduct/im3570/im3570_e.html).  This analyzer can measure components over a 4Hz to 5 MHz range.  It can display any two parameters you can think of!  I'm going to sweep from 50 Hz to 5 MHz, mostly displaying impedance (Z) and ESR (Rs).  I'll display other parameters on occasion.

I want to start out by analyzing mostly aluminum electrolytic capacitors.  The display is logarithmic on the frequency axis.  The vertical scale is also logarithmic with 100 ohms at the top and 1 milliohm at the bottom.  The impedance is the green curve and ESR (Rs) is the yellow curve.  Note that ESR is always less than Z, and normally touches the Z curve at the series resonance frequency (SRF) of the capacitor.

The first attached image shows the curves for a modern MKP film capacitor.  I'm showing this to give an idea what a very low loss capacitor looks like.  The ESR is very low, reaching a minimum of 3 milliohms, varying about 1.5 orders of magnitude over the swept range.  Notice how the impedance curve descends to a rather sharp point at the SRF of the capacitor.  We'll see that lossier capacitors, such as electrolytics, have an impedance curve whose minimum is much broader.

The second image shows a typical aluminum electrolytic cap, 2200 uF @ 10 volts.  Notice how the green curve (Z) is rather broad at the bottom and is pretty much touching the ESR curve for about 2 decades of frequency.  At higher frequencies the impedance curve does again rise above the ESR curve.  At very low frequencies the ESR does rise somewhat, and at very high frequencies the ESR does not increase.  This is an average capacitor; it is not a low ESR cap, but it doesn't have a particularly high ESR either; the ESR is 53 milliohms at 100 kHz.

[The Electrician]

Some more capacitor sweeps.

The first image shows a very small aluminum electrolytic, 47 uF, 25 volts.  It's about .15 inches in diameter and height.  The ESR rises at lower frequencies, but the impedance never rises above the ESR after the frequency passes 50 kHz.  This is a quite lossy capacitor, with an ESR at 100 kHz of 1.02 ohms.  It's a new capacitor which was in the Electronic Goldmine electrolytic assortment box.

The second image shows a 10 year old axial leaded moderate sized cap (about 1 in. by 2 in.), probably intended for power supply filter use.  Note that the impedance curve is not nearly so broad at the bottom.  The ESR rises at low frequencies and also at high frequencies, although the total variation over the frequency range isn't much; it's nearly constant with frequency.

[The Electrician]

The first image here shows an Aerovox VPE series capacitor.  This series is a rated for high ripple current.  You can see that the bottom of the impedance curve is not very broad at all, and the ESR is quite low.  This is about as good as it gets for aluminum electrolytics.  Again, we see that the ESR doesn't vary too much with frequency.

The second image shows a General Instrument 500 uF, 25 volt cap, never used, date code 7240.  Note that the impedance curve is not very broad at the bottom.  The ESR is not especially low, but at 115 milliohms at 100 kHz, it's not bad for a 40 year old capacitor.  However, do note the substantial rise in ESR at high frequencies; this much rise is not typical for modern electrolytics in my experience.

The third image shows a dipped tantalum, 33 uF, 25 volts.  The ESR isn't low, and there isn't a pronounced SRF.

[The Electrician]

Here are a couple of really small, old, capacitors.  I think they came out of a 1960s vintage pocket transistor radio.

The first image shows an 8 uF, 3 volt cap.  It has a plastic case with what appears to be an epoxy seal.  The first image shows a sweep of Z and ESR as the previous caps did.  The second image shows a sweep of Cs (capacitance in series mode) and ESR.  Note that the measured capacitance at 50 Hz is about 20 uF even though the value printed on the case is 8 uF.  The ESR at 50 Hz is about 25 ohms; both the capacitance and ESR decrease monotonically with increasing frequency.  This capacitor is no doubt somewhat dried out, but it's interesting how the capacitance behaves with frequency.

The third image shows a 1 uF, 10 volt capacitor from the same source with displayed parameters of Z and Rs.  The fourth image shows the same capacitor but with measured parameters of Cs and ESR.  The measured capacitance at 50 Hz is about 3 uF, compared to the rated value of 1 uF.

Both these capacitors would appear to be defective but the increased capacitance at 50 Hz is a puzzle.

[The Electrician]

One of the things that happens when you get access to an LCR meter is that you start measuring everything in the lab.  Anybody who has been a working EE for some years accumulates samples of various electronic parts that salesmen bring around to the office.  I measured a number of capacitor kits and samples that were lying around and I came across some nice TRW capacitors that were in an envelope of 5 samples.  Of the 5, one was peculiar.  Here are a couple of sweeps of identical, unused film capacitors.  Notice that the impedance curves (green) are nearly identical, but look at the ESR curves.

The 50 Hz ESRs are the same, as are the high frequency ESRs, but one can't help but wonder what could account for the substantial difference around the 10 kHz to 100 kHz range.  These caps are axial extended foil type and all I can think of is that the sprayed metallization on the ends isn't making contact with all the foil ends leading to a high resistance connection, but that at high frequencies, the capacitive coupling between layers of foil at the ends bridges across the missing metallization.

This is the sort of defect that one would only see with an impedance analysis  In the 10 kHz to 100 kHz region,  The ESR is an order of magnitude higher in the "bad" capacitor.  What sort of circuit malfunction would this cause, and in what circuit application?  In some circuits it probably wouldn't cause a problem at all, but in others it might.

[robrenz]

Great stuff, very interesting and please keep posting regardless of apparent interest.

[KD0CAC John]

I am trying to learn as much as I can from the perspective of repair & building of ham radio gear .
I've gone through a number of antenna analyzers , have to at this time an MFJ-269 and the one I am mentioning here because it does a screen readout .
http://www.timewave.com/support/TZ-900/TZ-900.html
Thanks for the thread , I'l have to see what my TZ-900 will show , without as many options of your impedance meter .
There's never enough toys

[StubbornGreek]

Great thread; keep it up, kindly and thanks.

[Conrad Hoffman]

Always interested in this stuff! Try some combinations of larger electrolytic filter caps and smaller film bypasses. Audio people like to do this but IMO it's of no real benefit unless the film bypass is unusually large, like a motor run cap! I'm curious what it would take to create a very low phase shift (DF or esr) cap over a wide range, say 10 Hz to 100 kHz.

[The Electrician]

Always interested in this stuff! Try some combinations of larger electrolytic filter caps and smaller film bypasses. Audio people like to do this but IMO it's of no real benefit unless the film bypass is unusually large, like a motor run cap! I'm curious what it would take to create a very low phase shift (DF or esr) cap over a wide range, say 10 Hz to 100 kHz.

Here are the results of paralleling a 10 uF, 1 uF, 150 nF and 30 nF film capacitor; note: no electrolytics.  They were not on a PC board with well defined power, ground, etc., planes.  I measured their impedance and ESR separately, and then measured the parallel combination.   I soldered them in parallel with as short connections as possible.  On a plane the results may have been somewhat different, but the fact is that each capacitor has a minimum ESL no matter how short the leads are and there will be multiple resonances.  This is the sort of behavior multiple bypasses will give.

I think the best one can do would be to damp the resonances by artificially increasing the ESR of the capacitors.  If electrolytics are used for some of the caps, the relatively high ESR of electrolytics might be advantageous.

[Mechatrommer]

this is the second confirmation after Janne's that paralleling caps can be a bad idea. thank Q for providing us info from higher end gear.

[The Electrician]

Conrad asked about the case where an electrolytic is paralleled with a film cap.  Here's a 10,000 uF, 25 volt electrolytic in parallel with a .22 film cap.  Both capacitors were connected to the fixture with as short leads as possible.

The first image is a sweep of the electrolytic alone, the second with the .22 uF film cap in parallel, and the third is both sweeps superimposed.  This is what you will get with no additional resistive losses added to the combination.

Whether the impedance and ESR of the combination is desirable is a question I leave up to the reader!

I suppose that with some effort, one could add resistive loss at appropriate places and do better.

[The Electrician]

Following Conrad's suggestion further, the first image shows a sweep of a GE 50 uF motor run capacitor.  This cap is not as low loss as a typical polypropylene cap that one might use in a switcher, but it's not bad.  Notice that even though this is not an electrolytic, the ESR doesn't increase at low frequencies.  Since this cap is intended for use at grid frequencies, it's to be expected that the manufacturer would pick a dielectric with low loss at low frequency.

The second image shows the sweep of the 10,000 uF electrolytic from a provious post.

The third image shows the same sweep as the second image plus the effect of paralleling the motor run cap.  At the high frequency end, the lower of the green and the yellow curves are the parallel combination of the 10,000 uF and the 50 uF motor run.

In this case, the relatively high losses of the motor run cap prevent the formation of a high-Q resonance, and the net effect is a reduction in both the impedance and the ESR.

Whether the amount of the reduction is worth it, is a question I leave, once again, to the reader.

[PA4TIM]

First, i like the idea, this gives people a better view but be carefull in reading and interpeting the traces.

On small correction, SRF is self resonant frequency ( see Agilents impedance measure handbook, network analysis from Siebel, RF design from Bowick, RF measurements from Terman, ect) not important in this case, because in this case we see a series resonance, but a coil has a SRF too and that is parallel resonance. I like the use of the right terms. ( to be complete, series and parallel resonance is there in two flavours, there is imaginaire resonance and Phase resonance ( see AC theory by D Knight for the math and more background)

Paralleling caps can serve serveral means, lowering ESR is one, but an electrolytic cap with for instance 100 nF is very normal ( just look at the avarage 78XX regulator) or look at all caps in a powerrail.
But to do this mindless is not good. You can get parallel resonance effects at the wrong frequency.

You see in the pictures if it is the right choise. Remember the working frequency is important, for a switcher you want good impedance at a high frequency but if it is for 100 Hz who cares ( most times) the cap is worthles at 100 KHz.

if your design works at 100 Hz the reactance at that frequency is important. But if there is a switcher near by at 100 KHz, or the emc caused by f.i. switching diodes is at some frequency where you do not want it, a small parallel cap with the right reactance at that frequency will maybe give a ugly ( negative) bump in your nice flat log/log sweep but if it is at the right frequency it is what you need (i use reactance but at the end the  impedance is important too, but be carefull, if the impedance is high because of ESR instead of reactance ( because for instance, skin loss, dielectric loss instead of reactance you dissipate power instead of filtering, also ESL is lowering the capacitive reactance)

There are high speed designs  where capacitors with their ESR and ESL also caused by vias and traces are tuned by vna to resonance to get the lowest possible impedance, or that value that gives you the right phase margin. So you have caps with high ESR, even with build in resistors.

I myself always use for (electrolitic and other) caps the following traces ( i can show 8 traces at on sweep and 6 frequency markers with data from all traces. so that makes it easy) Rs + jX , |Z|, Cs and phase. The phase to be sure I'm looking at real SRF and that makes it also easy to see calibration mistakes. For old caps I clean the legs first because if you are in tens of milliOhm area the resistance of oxide, thermal effects ( seebeck), humidity, dirty fingers, temperature but even a cell phone can influence measurements)

After the SRF the cap behaves inductive, that is also why i use phase and reactance too. Z is a scalar, you do not see the sign. Ok, if Z goes up after the lowest Z value the cap is probably becoming inductive. It is still X Ohm but if it is + jX it will have other effects as being -jX. But Z can go up and this dip is not allways the SRF. For instance the R part can drive the impedance more up as the ESL drives the reactance down. Z looks like SRF but in fact it is not there. You need to sweep Xc and phase to be sure.

Do not forget this are log/log sweeps, they look nice and flat. I rather use linear sweep. That gives me more information. On a log/log a line seems to be more flat but in reallity a straight line then represents a rather exponential behaviour. If you for instance measure the Diode Vf knee on a log/log scale you get a straight line ( see several articles of Bob pease)
However commercial they like to use log/log to give a huge range but for most because it looks better.
The origin was to get a bigger dynamic range. If you make a ( vertical) linear filter sweep you see only a small part of the stopband, lose details in the pass band if you want to fit the whole picture. But here we do not need a very high dynamic range, here log scales just hide details and make them nice and smooth. But making pretty linear sweeps can be challenging.

[Conrad Hoffman]

Very interesting- thanks for doing that! I have to do it point by point, which is why it rarely happens. Though I like good film caps I always caution people to be careful that they don't create a problem due to stray inductance in the circuit. I keep some resistance wire around and sometimes there's an advantage to slipping in an extra ohm or three. The difference is that ESR changes with frequency, whereas an added resistance doesn't. I'll also leave it to the reader/designer what combinations and methods are best in a given application.

[The Electrician]

On small correction, SRF is self resonant frequency ( see Agilents impedance measure handbook, network analysis from Siebel, RF design from Bowick, RF measurements from Terman, ect) not important in this case, because in this case we see a series resonance, but a coil has a SRF too and that is parallel resonance. I like the use of the right terms. ( to be complete, series and parallel resonance is there in two flavours, there is imaginaire resonance and Phase resonance ( see AC theory by D Knight for the math and more background)

SRF is only self resonant frequency if an author chooses to define it that way.

I also like the use of right terms.  I especially don't like authors who use abbreviations without defining them.  But I also subscribe to the notion that an author may define his own terms.  I chose SRF to mean series resonant frequency quite deliberately, and I defined it that way early in the thread.

A coil may have more than one "self resonance frequency" and any particular one may not be a parallel resonance frequency.  See the attached image showing an impedance sweep of a coil with multiple resonances, some series, some parallel.  If an author referred to the "self resonance frequency" of a coil, how would we know if he meant a parallel resonance or a series resonance?  Better to be more particular and refer to the "first parallel resonance", or the "second series resonance", etc.  Even capacitors can exhibit this phenomenon, but usually at higher frequencies.

In these sweeps of capacitors I've posted, only one self resonance appears, and it's a series resonance.  I want my readers to be well aware of this fact.

After the SRF the cap behaves inductive, that is also why i use phase and reactance too. Z is a scalar, you do not see the sign. Ok, if Z goes up after the lowest Z value the cap is probably becoming inductive. It is still X Ohm but if it is + jX it will have other effects as being -jX. But Z can go up and this dip is not allways the SRF. For instance the R part can drive the impedance more up as the ESL drives the reactance down. Z looks like SRF but in fact it is not there. You need to sweep Xc and phase to be sure.

How can ESL drive the reactance down (I assume you mean with increasing frequency)?  If the R part is so large with respect to the reactance that it is a dominant part of Z, then the phase angle isn't going to be much different from zero degrees.  This is the case when the impedance curve has a very broad bottom, and the Z curve is coincident with the ESR curve over a wide frequency range.  The fact that they are coincident means that the phase is very nearly zero and we know that without plotting phase.  The very concept of resonance is rather indeterminate in such a high loss situation, so there would seem to be little need to be sure of the frequency of resonance.  For example, if the definition of resonance chosen is zero phase angle, then a pure resistor is resonant at all frequencies.

Some of the issues you raise are important at high frequencies, but not so much at the frequencies where electrolytic caps are used.

[PA4TIM]

Oops, made a mistake. You are right offcourse, ESL is increasing the reactance with increasing frequency.

You are free to use SRF like you please, indeed you wrote what you mean so it is not a problem. I only mentioned it because in the literature SRF is allways used for self resonance frequeny. But nobody forbits you to use it to your liking like nobody forbits me to use ESR for enlarged serial reactance
if i would like to do this ;-)

You are right about coils, they have more SRF ( self resonant frequencies) and those can be parallel and serial but i only mentioned it as an example, i did not wanted to polute this topic by discussing coils. I did and do a lot of inductor meaurements ( also on microstrip, stripline, cavaties ect) but we save that for other discussions.

I use phase angle (0 to -180 degrees and 0 to 180 degrees) for checking calibration and measurement. And I allways first check after calibration with an open, short and airline sweep. I am talking about the phase a VNA meaures. This is different from what a LCR meter measures ( loss angle or phase angle from 0 to 90 degrees)
On a VNA it is a very good check because only at resonance the phase is zero. The firm of the phase jump alo tells you a lot.

For the readers who lose track. The TS is measuring with a very advanced impedance meter but special made for LCR meaurements. Very accurate and I have no doubt about his measurements. Just some small comments who do not seem to fall right, i do not mind, network analyses is more my thing, but this was related and I do a lot of cap meaurements so that's why I reacted, but i will shut up after this.

This Impedance meters are most times 4 wire IV measurements. They source a voltage and meaure voltage nd current and the phase differece. They can measure a very broad range of impedance.

I measure using Vector Network Analysers, if you read the desciption of both instruments you would think they work the same way but they work on a totally diferent way. A VNA is much more complex to operate and everything depends on the calibration but the possibilitys are allmost endless ( if you know how to operate one) The base is return loss and Phase, from this you can calculate allmost everything. From open to short is 180 degrees, if it is a inductive reactance, so the upper hlf of the smith chart, it is positive, if reactance is capacitive, phase is negative.
But for those interested in VNA's I have a written a series of tutorials, they are in English, some are translated in Frensh and the one about calibration akso in German. They are on my site for download

[The Electrician]

You are free to use SRF like you please, indeed you wrote what you mean so it is not a problem. I only mentioned it because in the literature SRF is allways used for self resonance frequeny.

It is not true that SRF is always used for self resonance frequency.  See for example:

http://www.compexcorp.com/chip.html

http://www.acronymfinder.com/Series-Resonance-Frequency-%28SRF%29.html

http://www.microwaves101.com/encyclopedia/capacitormath.cfm

http://www.kemet.com/kemet/web/homepage/kfbk3.nsf/vaFeedbackFAQ/C084E081B628723885256A8700515CF1?OpenDocument&source=find~~

http://electrical-integrity.com/Paper_download_files/EPEP03_cap_models_poster.pdf

[PA4TIM]

Official literature, not internet sites. It is very easy to find wrong things on the inet. Look for a wrong spelled word and you find lots of that written the same wrong way, it still stays wrong spelled. Some one else can quote you, or me in this discussion as proof, that still does not say a thing.
This is just like return loss and swr, on internet you find the wrong notation many many times more as the right one. That huge number still does not make it right ;-)
( Returmn loss is often wrongly stated as a negative number, for instance RL= -20 dB, it should be RL= 20 dB and VSWR as something like 1.5:1 instead of the right notation VSWR=1.5

But like I said, I do not mind how you use it and you can not convince me, maybe you are right but I stay with the defenition as wrote in Literature like my network analyses books ( Hiebel, Dunsmore, Agilent impedance measurenent handbook ect ), component books, books about AC and RF theory ect. Some of them even warn the reader the term SRF is often wrongly used for series resonance frequency)
Only important thing now is, I know what you mean by SRF in this topic.

[The Electrician]

Official literature, not internet sites.

You have not defined "official literature".  The examples I gave you consisted of "official" manufacturer's literature:

http://www.compexcorp.com/chip.html
http://www.kemet.com/kemet/web/homepage/kfbk3.nsf/vaFeedbackFAQ/C084E081B628723885256A8700515CF1?OpenDocument&source=find~~

and a paper presented at an "official" conference:

http://www.kemet.com/kemet/web/homepage/kfbk3.nsf/vaFeedbackFAQ/C084E081B628723885256A8700515CF1?OpenDocument&source=find~~

And to show that it's very "official", that last paper is published in an IEEE conference proceeding:

http://ieeexplore.ieee.org/xpl/articleDetails.jsp?tp=&arnumber=1250009&contentType=Conference+Publications&matchBoolean%3Dtrue%26searchField%3DSearch_All%26queryText%3D%28%28p_Abstract%3Aseries+resonance+frequency%29+AND+p_Abstract%3Acapacitor%29


Even though "wrong" things may be found on the internet, right things may be found there also.

But like I said, I do not mind how you use it and you can not convince me, maybe you are right but I stay with the defenition as wrote in Literature like my network analyses books ( Hiebel, Dunsmore, Agilent impedance measurenent handbook ect ), component books, books about AC and RF theory ect. Some of them even warn the reader the term SRF is often wrongly used for series resonance frequency)

On what page of Hiebel's book does he use the term SRF for self resonance frequency?  It's not in the index.

Please give the reference that warns that the term is often wrongly used for series resonance frequency.

I'm not denying that SRF may be used as an acronym for "self resonance frequency".  I am allowing for both uses, but you are asserting that  "...in the literature SRF is allways used for self resonance frequeny."   I think you are mistaken, and I gave references to show that..

[The Electrician]

Technically you should always define any acronym at its first use at least that’s the way I was taught.

SRF – Self Resonant Frequency or Series Resonant Frequency

That's what I learned also, and I make it a point to practice that.  If an acronym is found in use to mean more than one thing:

http://www.acronymfinder.com/SRF.html

then I definitely feel that it's ok to use it as one wishes after defining it.

I would only feel that it's "wrong" if an acronym is so very commonly used to mean one thing that it would cause substantial confusion to define it differently.  For example, in electronics the acronym RF seems to universally be understood to mean "radio frequency"; VNA is "vector network analyzer".   I've never seen those used to mean anything else, but I have commonly seen SRF used to mean both "series resonance frequency" and "self resonance frequency".

But I'd like to get back to making some measurements with the analyzer.

[PA4TIM]

Please be careful with the term SRF. It always stands for self-resonant frequency. In a capacitor the SRF and the series-resonant frequency happen to be the same. However, for an inductor the SRF is a parallel resonance. If you always remember that SRF stands for self-resonant frequency you won’t go wrong.

From analog SEEKrets from Lesly Green

Handbook of microwave component meaurements, Dunsmore : list of acronyms last line second page: self resonant frequency.

I'm not at home right now, and Hiebel is not as pdf on my ipad, (Dunsmore, i have here in paper with me)
Do a google on self resonant frequency and you have hours of reading. In 90 % of all documents ( Agilent, vishay, murata, IEEE, EDN, TI, and many more) they talk about self-resonance frequency as they state SRF.  Why self-resonance is simple, because it is the self resonance of a single component. And that can be a series self-resonance frequeny or a parallel self-resonance frequency.

So SRF can be used for series resonant frequency, no law forbids it, no law tells it must be self-resonant frequency, so do not make a big del out of it. You react like I insult you, that is not my intention.  It was just a remark. Like I wrote before, ( and you too) as long as it is defined what they mean by an acronym there is no poblem.

The resonance  effect you see when looking at a single component is it's self-resonance frequency. And that can be series or parallel. So that is why I agree with Green.

Have fun measuring, i like what you write. Sorry for my remak, and I will not bother you again. I noticed your other topic about inductance and skineffect. I have done a lot of test/measurements on that area too ( only a upto higher frequencies) very interesting subject but do not be afraid, will only read, not react ;-)

[The Electrician]

Here's an interesting web site concerning ESR in capacitors:

www.lowesr.com

There are a lot of references, and a lot of curves of ESR versus frequency, temperature and technology.

For the curves, see the performance data page:

http://lowesr.com/esrfreqperfcurves.asp