EEVblog Electronics Community Forum
Electronics => Beginners => Topic started by: Brad808 on March 28, 2021, 01:01:20 pm
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I seem to be finding some completely contradicting answers so hopefully someone can clear up the misunderstanding for me. Pretty much every thing I can find on the internet says "Equivalent series resistance of aluminum electrolytic
capacitor (Re) is frequency dependence. Higher the
frequency, lower the ESR." That is a direct quote from a Nichicon paper on aluminum electrolytics.
Almost every ESR meter seems to specify test frequency, Capacitor spec sheets seem to specify frequency, etc
However I'm reading through the sencore lc102 manual and sencore tech tips (specifically 104) and it says
"A number of customers have been told that
ESR must be tested at a particular
frequency. This is not the case, because
true ESR does not depend on frequency.
ESR represents pure resistive losses, and
resistance has the same impedance at any
frequency. The Z METER only measures
resistance.
The confusion appears to come from
formulas which attempt to convert the "D"
(dissipation factor) reading from an AC
impedance bridge to an ESR value. ESR,
however, is only one of the many capacitor
imperfections that causes poor D readings.
D also includes the effects of leakage
resistance, equivalent series inductance,
dielectric absorption, dielectric stress, and
losses (such as water molecule resonance)
in the dielectric. Most of these other losses
are frequency selective, so any attempt to
calculate ESR from D will make it seem that
ESR varies with frequency."
It repeats the same thing in various wording throughout other sencore documents as well.
Something isn't quite clicking in my head so hopefully someone can explain like I'm 5 ;D
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ESR in electrolytics is *NOT* due to a pure resistance. i.e. the voltage difference between any two points in the electrolyte is not strictly dependent on the instantaneous current between them. The charge carriers in the electrolyte aren't electrons, they are ions, so their concentration and relative mobility is another factor that must be considered, and at lower frequencies during a half-cycle, its possible to deplete the ions of a particular polarity in a pore of the aluminum oxide dielectric, replacing them with ions of opposite polarity, of different size and mobility.
http://www.kemet.com/Lists/TechnicalArticles/Attachments/191/Why%2047%20uF%20capacitor%20drops%20to%2037%20uF-%2030%20uF-%20or%20lower.pdf (http://www.kemet.com/Lists/TechnicalArticles/Attachments/191/Why%2047%20uF%20capacitor%20drops%20to%2037%20uF-%2030%20uF-%20or%20lower.pdf) should give you some idea of the complexities involved.
Edit: to clarify that I was only and specifically discussing ESR in electrolytics.
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Weasel words.
"Pure resistance" is meaningless. You could as well say fancy resistance of brown resistance.
I would accept it, but they are claiming to know better than others, so I would expect rigorous language and claims that are true.
By "pure" resistive losses, I'm assuming they mean the resistance is constant over frequency. But this is wrong. Capacitor parasitic resistance is not constant.
Even the most simple types consisting of metal foil and imaginary perfect dielectric do not exhibit constant resistance per frequency, because the resistance of all known metals vary per frequency due to phenomena called skin and proximity effect.
Electrolytic capacitors do have part of their resistance contributed by the metal foil resistance, but much bigger part of their resistance comes from the electrolyte chemistry and this is highly dependent on conditions, including temperature and frequency. With electrolytic capacitors, ESR indeed first goes down per increasing frequency, then up again due to skin effect.
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Sencore shows that there is an affect ESR has at different frequencies, but that ESR is not frequency dependent. See attached (or read through Tech tips 104 for the full thing)
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Really good capacitors, such as polypropylene film/foil units, to first order, have a constant Q rather than constant equivalent series resistance (ESR). That Q is the reciprocal of the dissipation factor of the dielectric itself. Of course, there is always parasitic resistance in the foils and leads. If Q were truly independent of frequency then the ESR would be proportional to capacitive reactance which is inversely proportional to frequency.
Electrolytic capacitors are often dominated by their parasitic resistance, so the ESR is less dependent of frequency.
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As always, our standard passive components aren't ideal. Please see https://en.wikipedia.org/wiki/Capacitor#Non-ideal_behavior (https://en.wikipedia.org/wiki/Capacitor#Non-ideal_behavior) for some hints (Wikipedia shows only a very basic equivalent circuit). Or read http://www.ti.com/lit/pdf/sloa027, (http://www.ti.com/lit/pdf/sloa027,) for example.
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It seems to me that the inclusion of the word 'equivalent' in the term 'Equivalent Series Resistance' implies that it includes all of the dissipative components of the measured impedance. I'd like to read Sencore's Tech Tips 104 (anyone have a link) before disagreeing with them, but I don't see how sorting out the actual ohmic series resistance actually helps. They sort of have a point about deriving ESR from D, but I think the better point to me made is that D is the actual value we should be concerned with and ESR is sort of a simplified way to understand dissipative losses in capacitors.
Really good capacitors, such as polypropylene film/foil units, to first order, have a constant Q rather than constant equivalent series resistance (ESR). That Q is the reciprocal of the dissipation factor of the dielectric itself. Of course, there is always parasitic resistance in the foils and leads.
Those type of capacitors also have very, very low measured ESR, so low I'm not sure it means anything.
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At low frequency, where the reactance is high, the ESR is measurable. For example, a 10 nF capacitor with Q = 1000 will have ESR = 160 \$\Omega\$ at 100 Hz. I have used this measurement to identify unknown capacitors (polyester or polypropylene). The tabulated value of D = 1/Q = 1/3000 is constant from 1 kHz to 1 GHz for polypropylene as a material.
The usual spec for these units is Q > 1000, since it takes too much time to measure higher values.
I was answering the original question: ESR for non-electrolytic capacitors is far from constant with frequency.
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From the point of view of the Keysight Measurement Handbook:
https://www.keysight.com/us/en/assets/7018-06840/application-notes/5950-3000.pdf (https://www.keysight.com/us/en/assets/7018-06840/application-notes/5950-3000.pdf)
Notice the circuit models that are used for the definition of ESR, which in their model is labeled RS.
In this case, it is the residual resistance measurable at the self-resonant frequency (SRF).
Therefore, the implication is that a single-frequency measurement can't determine ESR using that definition. If one loosens the definition to be the parasitic impedance that is also caused by the series parasitic inductance, then one could claim a frequency-dependent "ESR".
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Pure resistance is a perfectly reasonable idea at DC- unfortunately it just doesn't occur in the real world components.
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Found some very interesting reading material on the sources of the wikipedia page for ESR: http://www.ieca-inc.com/images/Equivalent_Series_Resistnace_ESR.pdf (http://www.ieca-inc.com/images/Equivalent_Series_Resistnace_ESR.pdf)
This snip basically sums up that it is a lot more complex than I was originally thinking. It's interesting reading through the paper though. I'm slowly starting to grasp it (I think |O).
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The important thing in that three-component model is that the resistance (in a practical part) is not constant vs. frequency. If it were constant, then the real part of the impedance would be constant as the imaginary part (total reactance) of the unit went from negative at low frequency through zero at resonance to positive (inductive) above the resonant frequency.
A side point: ignoring the inductance for simplicity, an individual capacitor can be modeled (at a given frequency) either as a series capacitance and a series resistance, or a parallel capacitance and a parallel resistance. At that frequency , you cannot tell the difference between those hypotheses. However, if the series resistance were independent of frequency, then the parallel resistance cannot be. See the usual textbooks for the calculations relating the series and parallel models.
Many capacitors intended for rectifier filters are rated for ESR either at 120 Hz for mains rectification, or at 10 kHz for switching power supplies; this is important for design.
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true ESR does not depend on frequency.
ESR represents pure resistive losses, and
resistance has the same impedance at any
frequency.
ESR is very dependent on the frequency. And pure resistive losses are also very frequency dependent.
The active resistance of any piece of wire, or any kind of conductor, depends on the frequency.
Just look for a skin effect (https://en.wikipedia.org/wiki/Skin_effect) to get more details why it happens ;) In short - frequency change equals to change a conductor cross section and as result to a conductor resistance change.
And capacitor ESR depends not only on conductor resistance, but also on insulator dielectric losses. Which is also frequency dependent, unless you're using vacuum capacitor :)
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ESR in electrolytics is *NOT* due to a pure resistance. i.e. the voltage difference between any two points in the electrolyte is not strictly dependent on the instantaneous current between them. The charge carriers in the electrolyte aren't electrons, they are ions, so their concentration and relative mobility is another factor that must be considered, and at lower frequencies during a half-cycle, its possible to deplete the ions of a particular polarity in a pore of the aluminum oxide dielectric, replacing them with ions of opposite polarity, of different size and mobility.
That is my understanding about what is going on also. The resistive component of ESR is constant with frequency however dissipation varies with frequency for the reason you give, which is why solid tantalum capacitors perform better than aluminum electrolytic capacitors at high frequencies.
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Cornell Dubilier has an IEEE paper Improved Spice Models of Aluminum Electrolytic Capacitors for Inverter Applications (https://www.cde.com/resources/technical-papers/impedance.pdf) which include ESR vs frequency and temperature, with detailed discussion on the mechanisms.
Also an Impedance Applet (https://www.cde.com/spice/ImpedanceAppletIntro.html) they have.
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I seem to be finding some completely contradicting answers so hopefully someone can clear up the misunderstanding for me. Pretty much every thing I can find on the internet says "Equivalent series resistance of aluminum electrolytic
capacitor (Re) is frequency dependence. Higher the
frequency, lower the ESR." That is a direct quote from a Nichicon paper on aluminum electrolytics.
Almost every ESR meter seems to specify test frequency, Capacitor spec sheets seem to specify frequency, etc
However I'm reading through the sencore lc102 manual and sencore tech tips (specifically 104) and it says
"A number of customers have been told that
ESR must be tested at a particular
frequency. This is not the case, because
true ESR does not depend on frequency.
ESR represents pure resistive losses, and
resistance has the same impedance at any
frequency. The Z METER only measures
resistance.
The confusion appears to come from
formulas which attempt to convert the "D"
(dissipation factor) reading from an AC
impedance bridge to an ESR value. ESR,
however, is only one of the many capacitor
imperfections that causes poor D readings.
D also includes the effects of leakage
resistance, equivalent series inductance,
dielectric absorption, dielectric stress, and
losses (such as water molecule resonance)
in the dielectric. Most of these other losses
are frequency selective, so any attempt to
calculate ESR from D will make it seem that
ESR varies with frequency."
It repeats the same thing in various wording throughout other sencore documents as well.
Something isn't quite clicking in my head so hopefully someone can explain like I'm 5 ;D
Brad808, you will find this thread interesting: https://www.eevblog.com/forum/projects/impedance-lcr-esr-meters/msg459252/#msg459252 (https://www.eevblog.com/forum/projects/impedance-lcr-esr-meters/msg459252/#msg459252)
It's not possible to make universally true statements about variation of ESR with frequency. You'll see numerous examples in the thread linked above.
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This topic has raised a related question in my mind....
How do circuit simulators deal with the real world operational characteristics of components (specifically, capacitors in this context)? Are they capable of handling "real world" components or do they only consider "ideal" ones and the user has to add bodge items to get the simulation accurate?
In asking this, I daresay there are a range of simulators out there which have very different capabilities and, thus, different answers to the above.
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At low frequency, where the reactance is high, the ESR is measurable. For example, a 10 nF capacitor with Q = 1000 will have ESR = 160 \$\Omega\$ at 100 Hz. I have used this measurement to identify unknown capacitors (polyester or polypropylene). The tabulated value of D = 1/Q = 1/3000 is constant from 1 kHz to 1 GHz for polypropylene as a material.
OK, that seems quite clear and obvious now that you've stated it. I should realize that just because a polypropylene cap is indistinguishable from an ideal one in things I use them for (audio, old tube radio restorations, etc) that doesn't mean someone else might not care about that last 0.05%.
I have no way of doing that measurement. I took a cap from my parts bin, an IC 1.0nF 630V polypropylene, and set it up in my fairly good LCR meter and at 1V/100kHz, I got C=981.6pF (this was very consistent), D=0.000, Q=4400 +/- 10% noise and ESR = 0.4 ohms with noise. I didn't measure Z directly, but it calculates to 1.6K, so all those numbers pencil out as correct. However, at 100Hz, I get no discernable readings, just noise. I get your point that ESR would just be a constant fraction of Z if all the losses were in the dielectric (relaxation?) and the actual resistance of the leads and foil were negligible. But unless I'm missing something, the D/ESR on these things is so low that I can ignore it in my applications--the things I can measure and have to worry about-- Z, θ, C and L/ESL--are all much larger.
I think the error in Sencore's thinking is trying to distinguish those dielectric losses from those solely due to ohmic resistance--the whole point of 'equivalent' is to add in all those losses to one easy-to-digest number. That and the step-function measurement they use fails because it includes L in the measurement. Do you agree?
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When I was working with RF circuits, it was a big pain that Spice could deal with series R-C circuits (i.e. constant ESR) but could not use constant Q, which was a better approximation for our purpose.
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To bdunham7: in my experience, reasonable LCR meters have difficulty resolving the “minority component” with Q > 1000 or so. At 100 Hz, your 1 nF reactance is 1.6 megohm, which might be too high for the meter.
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There are two current production bench LCR meters that offer superior performance. They can show 7 digit results; this is more than is justified by the accuracy specification of .05% and .08%, but can be useful for precision matching of components. The two meters can measure Q up to 10000 (D down to .0001) giving a result accurate to a couple of digits where lesser meters showing Q that high will be measuring noise.
These two meters are the Keysight E4980A and the Hioki HM3570: https://www.hioki.com/en/products/detail/?product_key=5539 (https://www.hioki.com/en/products/detail/?product_key=5539)
Here is a measurement at 1 kHz of a current production Panasonic polypropylene 4.7 uF capacitor on the Hioki. One of the features I like about the Hioki is its ability to show 4 parameters at once:
(https://www.eevblog.com/forum/beginners/is-esr-frequency-dependent/?action=dlattach;attach=1206144)
Really good capacitors, such as polypropylene film/foil units, to first order, have a constant Q rather than constant equivalent series resistance (ESR). That Q is the reciprocal of the dissipation factor of the dielectric itself. Of course, there is always parasitic resistance in the foils and leads. If Q were truly independent of frequency then the ESR would be proportional to capacitive reactance which is inversely proportional to frequency.
Electrolytic capacitors are often dominated by their parasitic resistance, so the ESR is less dependent of frequency.
The fact that the loss tangent of bulk polypropylene is nearly constant up to 1 GHz: https://members.tm.net/lapointe/Plastics.htm (https://members.tm.net/lapointe/Plastics.htm)
doesn't mean that polypropylene capacitors have constant Q. Here is a sweep from 100 Hz to 5 MHz of the Panasonic polypropylene capacitor mentioned above. This image shows the Q of the capacitor (green) and the ESR (yellow) on a graph which is logarithmic in both axes. The vertical axis has a different scale for Q and ESR. For Q the bottom of the image is .1 and the top is 100,000; for ESR the bottom of the image is 1 milliohm and the top is 1000 ohms. The instrument only shows Q up to 10000 and we see that at 100 Hz the capacitor's Q is > 10000. Over the whole sweep the Q varies 5 orders of magnitude, and the self resonance of the cap has a major effect:
(https://www.eevblog.com/forum/beginners/is-esr-frequency-dependent/?action=dlattach;attach=1206148)
Here's a sweep of a 30 year old WIMA MKP capacitor:
(https://www.eevblog.com/forum/beginners/is-esr-frequency-dependent/?action=dlattach;attach=1206152)