ESR is not "actual series resistance". There's a reason it's called "equivalent" series resistance. It's not a model that can be used to
*calculate* the impedance versus frequency, as with the schematic you've shown below. Your model has resistors that don't vary with frequency; the ESR model used by the cap manufacturers has an "equivalent" series resistance that varies with frequency, and its value at any given frequency is found by measurement at that frequency. It's just the real part of the impedance as measured, and represents all the losses at that frequency as a single "equivalent" series resistance.
See:
formatting link
Indeed it does, but this isn't what is meant by manufacturers when they talk about ESR. If you measure the impedance of a capacitor at some frequency, the real part of the impedance won't be what you have shown as R1 if there are any other losses, which there usually are.
I now see why you said "...you can't calculate ESR from a single-frequency vector impedance measurement."
This would be true if ESR (as used by the manufacturers of capacitors) were R1 in your schematic, but that isn't what they mean by the term.
ESR (with the meaning as used by the capacitor manufacturers) does vary with frequency. See:
formatting link
Of course, capacitors have an ESL as well as an ESR (the E stands for Equivalent, which means a simple model), and the *impedance* of the capacitor is dominated by ESL above the series resonant frequency.
The Kemet folks show the impedance vs. frequency characteristic for their various MLC's in this file:
formatting link
$file/F3102_CerPerChar.pdf
Given the short connect time, 4ns, of your application it looks like you will care about the (typical) capacitor's impedance well above series resonance, which will probably be dominated by ESL. You might want to use a COG dielectric.
Well, it depends on your definition of "equivalent." Certainly you can measure the vector impedance at some frequency and razzle-dazzle some equations and come up with both an "equivalent" series resistance or, if you prefer, an "equivalent" shunt resistance. Somebody here just did that and got 800+ ohms ESR for a ceramic cap.
But that "ESR" is absolutely meaningless for, say, designing a bypass system or compensating a switching regulator, because it's about
10,000 or so times the true series resistance. And the equivalent shunt resistance is even-worse useless if you're doing DC design, because it's maybe a million times off of being predictive of real leakage current.
So, OK, I was wrong: you can certainly do the calculation, or let some fancy instrument do it for you, and display it to 5 digits of precision, and that's fine for people who don't mind being off by 4 to
6 orders of magnitude.
About the only thing a single-frequency ESR measurement does is sort of predict how the cap will work *at that frequency*
Tricky. Assuming a 1 ns risetime, 4 volts available, only 2 nH or so will get you into trouble. A cap and its leads will get you to about 2 nH, then there's all your wirebonds, not to mention the load itself.
We usually parallel several caps, on a lot of copper, to supply a lot of fast peak current, like through a gaasfet to drive an SRD or a laser.
(Gotta get ready for a Board meeting. What a nuisance.)
Me, my wife and my oldest daughter ARE the board... no nuisance ;-)
...Jim Thompson
--
| James E.Thompson, P.E. | mens |
| Analog Innovations, Inc. | et |
| Analog/Mixed-Signal ASIC\'s and Discrete Systems | manus |
| Phoenix, Arizona Voice:(480)460-2350 | |
| E-mail Address at Website Fax:(480)460-2142 | Brass Rat |
| http://www.analog-innovations.com | 1962 |
America: Land of the Free, Because of the Brave
A bit off this topic, I saw a post where you talk about 11801 ("When you start getting powerup timebase errors, which you will, call me.") I have an 11801 that has this problem. Would you be able to help me fix it?
But for switching applications I(ripple)^2* ESR will cause a temperature rise in the device. More ESR in a smaller device can be catastrophic (ask Joerg about green molten glass perls...)
Of course it does. I have been explaining the definition used by the capacitor manufacturers. It's the only (resistance; ESL is another number) number you will find in their specs, and they get it by simple measurement.
That's just what they do, and if a person wants to make sense of their numbers, he should realize how they got them.
I provided that number, and it would accurately tell you the dissipation in that capacitor if it were handling a 20 Hz current.
It's not meaningless at all. The ESR at a given frequency, for example
120 Hz, tells you just how much power is dissipated in the capacitor for a given ripple current (assuming the fundamental is 120 Hz. The harmonics contribute some heat in a typical 120 Hz power supply, but the fundamental dominates). In a switcher, the ripple current is typically trapezoidal and the magnitude of the fundamental ripple frequency is still dominant; the ESR at that frequency gives a good first cut at the dissipation in the capacitor.
Look at the ripple current ratings of these capacitors:
formatting link
Notice how the ripple current rating is less at lower frequencies. That's because the ESR increases at low frequencies. The ESR determines how much heating the ripple current will cause, and it tells it accurately because the ESR includes all the losses in the capacitor.
This is only true at very low audio frequencies. Up around switching regulator frequencies, it's probably quite close to the true series resistance (R1 in your model).
This is why I asked in another post how we would define DC ESR. It doesn't make sense at DC, and it's never given at DC. At low audio frequencies it's defined the same way it's defined at higher frequencies. It's the real part of the impedance measured at a given frequency.
The model you gave is well known, and it's a good tool for design, but it's not what the manufacturers give you. You will have to derive it yourself from a series of measurements, as you said.
And this is quite useful in those situations where the ripple current has a dominant fundamental component, such as in power supply applications. It tells you what the heating in the cap will be with fair accuracy. In fact, the error from neglecting the harmonics is probably less that the error from neglecting the variance in the ESR at a given frequency in a group of capacitors nominally the same.
Of course, there will be applications where the harmonics are important, and then the designer will have to derive the more complicated and more accurate model. But this doesn't detract from the usefulness of the plain old ESR model in many other cases.
While I was waiting for The Board to show up, I cobbled up this:
formatting link
formatting link
It's a 0.1 uF, 0805 cap soldered across a 50 ohm transmission line. It's being driven from (we pause for this commercial message...)
formatting link
which is setup for 5 volts out, 50 ohms, so it's dumping a 100 mA step into the cap with about a 1 ns risetime. The scope bandwidth is 20 GHz.
The first glitch is L di/dt, roughly estimated as 1.5 nH. Extrapolating the slope back to the start gives very roughly 20 milliohms, but it's hard to resolve that small a resistance with this rig. The glitch at about 10 ns is a cable reflection.
This cap is pretty much a dead short in the, say, 3 ns time frame.
My hp4192 Impedance Analyzer, outfitted with an 16034E SMT fixture, used in average mode, says a Panasonic 0.1uF 25V X7R 0805 cap has C = 92nF, plus about 36-milliohms of esr.
John -- since you're not exactly enamored with Howard Johnson, do you have an opinion on Doug Smith there? I met him once and he seems to be considerably more "hands on" than Howard is. (That picture on his web site looks about 10 years old though!)
Go to this link and download SpiCap 3.0 in the software section.
formatting link
Enter in your favorite cap and dielectric, vary the frequency as you watch the ESR change. Most fun I have had with my cloths on in a long time. See that ESL does not change with frequency. That is why we do not use large MLC caps to do AC line filtering, they will let the smoke out. Regards, Harry
If one eyeball extrapolates my slope down to about the midpoint time of the inductive glitch, 40 milliohms isn't an unreasonable guess. At least we aren't disagreeing by 2000:1 or anything like that!
** When cap makers specify the ESR of an electrolytic capacitor - the impedance value in the broad high frequency ( series self resonance) minimum area is what is quoted. Ceramic bypass caps are also quoted as being "low ESR" if their impedance falls to unusually low values at self resonance.
Film caps and others that are likely to be subjected to steep pulses and/or high AC voltage swings at high frequencies are specified by quoting the Dissipation Factor or " Tan Delta".
The cap makers are simply supplying useful info to circuit designers engaged with in particular applications of their products.
Not trying to win a terminology & pedantry contest.
ElectronDepot website is not affiliated with any of the manufacturers or service providers discussed here.
All logos and trade names are the property of their respective owners.