From low to high frequency capacitors have three behavioral regions---the capacitive region where their impedance falls as 1/f, the resistive region where the 1/f from capacitance and j * w * ESL is less than the ESR, and the inductive region where the impedance rises linearly from frequency due to the ESL. The phase in these three regions is -90, 0, and 90 degrees, respectively, and the width of the resistive region is determined by the ESR. With low ESR caps like MLCCs the resistive region is of negligible width, which is why you see the supply impedance sawtooth in the app note Tom linked---those dips at the "bottom" of the "teeth" are the capacitor's self resonance between their C and ESL. The downward slopes of the sawtooths are where the capacitive region of one of the caps is dominating the supply impedance and the upward slopes are where an inductive region is dominant. The corrolary of this is the supply phase swings from -90 to +90 and back as a function of frequency.
The deal with MLCCs versus tantalum is choosing tantalum usually adds enough ESR to hide the sawtooth, producing a supply with a phase that's more consistently around 0 degrees. But adding ESR to hide the sawtooth means the supply impedance is increased.
If one wants to get a feel for this, a good exercise is to calculate a few caps' individual impedance curves and then put them in parallel to see how different selections affect the supply impedance and phase. You can also grab National Semiconductor, er, TI's, Webench tool and look at what happens with one of their buck regulators as the selection of the output L and C is varied. For low output ripple you want low a ESR cap. But that means moving the ESR to the inductor in order to maintain the regulator's phase margin, decreasing the supply's efficiency. The physics of paralleling bypass caps are essentially the same. Only either you don't have a regulator or are looking at frequencies above the regulator's loop bandwidth.
Hmm, thought the one I was looking at was R || L + R || L + L but didn't zoom in to double check on the rendering. It's of no great importance---and if it is an L it occurs to me it's entirely possible the inductor model includes an ESR term.
A point I haven't seen mentioned is regulator output impedance. Regulators are closed-loop devices, so one wonders how well they might react to low-resistance capacitors on their outputs.
For example, a 7915's Zout rises from 0.01 ohms at low frequencies to 0.1 ohms at 100 kHz, which can be modeled as a 0.01 resistor in series (ESR) with a 160 nH inductor. Electrolytics tend to have ESRs not far from 100 milliohms, so the resonance will be well damped, but the usual 0.1 uF people place in parallel with electrolytics has low ESR (~0.01 ohms), possibly resonating nicely with the regulator ESL. How would this affect phase margins in the regulator control loop?
For example, a 7915's Zout rises from 0.01 ohms at low frequencies to 0.1 ohms at 100 kHz, which can be modeled as a 0.01 resistor in series (ESR) with a 160 nH inductor. Electrolytics tend to have ESRs not far from 100 milliohms, so the resonance will be well damped, but the usual 0.1 uF people place in parallel with electrolytics has low ESR (~0.01 ohms), possibly resonating nicely with the regulator ESL. How would this affect phase margins in the regulator control loop?
Same as any other Miller compenated voltage feedback amplifier; main difference in applying the stuff Tom linked is you don't usually find regulators' GBP in the datasheet. I have the impression it's generally a few MHz. But I've never actually measured it.
ESRs of liquid electrolytic caps tend to be between 20 milliohms and a few ohms. The smaller the cap, the higher it is. Typically I look at datasheets for caps which are speced for ESR, such as Nichicon's HE series, and then estimate the ESR of caps not speced via their ripple current ratings. Polymer electrolytics are usually between 5 and 40 milliohms. Most aren't speced for ESL (and ESL meters with nH resolution are pricey) but one can usually make a resonable guess based on the package and the applications the manufacturer suggests for the parts.
Plug the above into Spice or whatnot, run a parameter sweep, and one should have first order answers for one's design---ESR and ESR are both frequency dependent but that's a second order effect.
ESRs of liquid electrolytic caps tend to be between 20 milliohms and a few ohms. The smaller the cap, the higher it is. Typically I look at datasheets for caps which are speced for ESR, such as Nichicon's HE series, and then estimate the ESR of caps not speced via their ripple current ratings. Polymer electrolytics are usually between 5 and 40 milliohms. Most aren't speced for ESL (and ESL meters with nH resolution are pricey) but one can usually make a resonable guess based on the package and the applications the manufacturer suggests for the parts.
Plug the above into Spice or whatnot, run a parameter sweep, and one should have first order answers for one's design---ESR and ESR are both frequency dependent but that's a second order effect.
Most regulators don't like it: with its output left unbypassed, any 78xx type regulator can be stable without a decent input decoupling.
As soon as you use an output cap, it becomes more demanding on the input cap.
For LDO's, the situation is worse: if the output cap has a too high Q, it will be unstable, no matter what you do. That's the case with most high performance regulators, unless they use exotic compensation schemes.
That is a slippery slope: ESR is just that ESR, that is a synthetic parameter, equivalent to tan δ at some frequency; it is not the same as a physical resistance.
It becomes more or less equal to the physical (ohmic) resistance at the resonance and higher (but not too high) frequencies, but if it is specified at low frequencies, like 100 or 120hz, or even 1KHz, it will be significantly higher, because it is more or less a proportion of the reactance at any frequency.
Such confusions can lead to significant errors when assessing the effect of capacitors in a given configuration.
The confusion is reinforced by the fact that so-called "ESR-meters" measure the module of the impedance at some (generally high) given frequency.
The reality can be quite different.
Most 'lytics I look at are specified at 100kHz. Good enough for first order approximation. Would be interesting to know what lines are specified at lower frequencies.
Post 282's about standard regulators, but most LDOs I end up looking at are stable to 0 ESR---Micrel and National/TI have numerous offerings and Analog Devices has some nice parts as well. Though, granted, it's been a while since I specified output cap type = tantalum on a parameteric search for regulator.
Post 282's about standard regulators, but most LDOs I end up looking at are stable to 0 ESR---Micrel and National/TI have numerous offerings and Analog Devices has some nice parts as well. Though, granted, it's been a while since I specified output cap type = tantalum on a parameteric search for regulator.
The United Chemi-Con EKMH and ESMH aluminum electrolytics have ESR specified at 120 Hz, in the Mouser catalog I'm perusing. And the Cornell Dubilier MLP and MLS flatpack aluminum electrolytics have ESR specified at both 120 Hz and 20 kHz, for 25 degC, while some of their big screw-terminal cans are spec'd at 120 Hz only. It looks like a lot of the larger snap-in and screw-mounted ones are spec'd at 120 Hz, maybe because they are typically used as smoothing caps in linear supplies.
This Cornell Dubilier Electronics Java Applet tells it all, very nicely, at least for their large-ish electrolytics. It also will generate a nice frequency and temperature dependent spice model, for you, automagically! I believe I discussed how to most-conveniently use those models with LTspice, way (way) earlier in this thread. Just click on the little "Impedance Modeler" link at the top, once you get there.
Now I see why some people put their electrolytics where they'll get heated by the heatsink. They have lower ESR and higher capacitance at higher temps.
This Cornell Dubilier Electronics Java Applet tells it all, very nicely, at least for their large-ish electrolytics. It also will generate a nice frequency and temperature dependent spice model, for you, automagically! I believe I discussed how to most-conveniently use those models with LTspice, way (way) earlier in this thread. Just click on the little "Impedance Modeler" link at the top, once you get there.
Now I see why some people put their electrolytics where they'll get heated by the heatsink. They have lower ESR and higher capacitance at higher temps.
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I find the practice of putting a low ESR 0.1uF cap in paralell to a high cap electrolytic cap quite useless. You either get a highisch Q resonanz (if you are careless and dont pay attention to the resulting Q of the circuit) or you add a resistor in series in wich case the cap wont contribute much current anyway. So what is the point of this practice?
Good call.
If you read the earlier part of this thread, I think you'll see that it was agreed that it is a bad idea to indiscriminately parallel a large electrolytic with a small-value low-esr cap, especially if they are not at the point of load.
But sometimes they might both be needed for decoupling close to power pins of chips, for example, because of the power rail inductance (and ESR) and the need to supply transient current demands (without disturbing the rail voltage too much), and, for amplifiers, also to prevent high-frequencies from finding a feedback path through the power rails and causing instability. So there might be a small-value cap right at the power pins while a large-ish electrolytic is technically "in parallel" but is separated from the small cap by power/ground rails' impedance. In that case, the designer needs to perform some type of impedance analysis and choose the values and types of the caps to ensure that no unwanted resonances will be created.
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You're right, either way can have problems. I have a simple answer, you do both. You put a 0.1 uF right at the power pins of a chip or whatever's going to suck up the power, and you also put a series connection of a 0.1uF and a 1 ohm resistor across the rails near the first 0.1 uF cap. This gives a low-impedance resistive path that damps out ringing from wiring inductance resonating with the first cap.
There's the book "High Speed Digital Design" with a subtitle of "black magic." Much or most of it is about PCB design for digital circuits, layout and signal measurement. The title seems a little ironic, as the "digital signals" are treated and analyzed as (among other things) analog transients going through R/C circuits. It's got a chapter or two on power rail bypassing, and talks about adding a cap with a resistor in series IN ADDITION TO the usual 10uF near the power entrance and a 0.1uF right at the power and ground pins of each chip.. There's some formula related to power rail and ground track length/inductance that calculates the "optimum" resistor value, but it tends to be within an order of magnitude of 1 ohm.
Benb
I have also found similar results. The RC acts as a snubber (if you can measure the ringing frequency then you can just add enough capacitance to start decreasing the frequency, or preferably halve it, then a series R of the same resonant impedance value).
To tie this back to the power plane issue you still need a low inductance connection to the pure C and so the power planes again allow these RC's to be located some distance away and still be effective.
Thanks
-Antonio
I have also found similar results. The RC acts as a snubber (if you can measure the ringing frequency then you can just add enough capacitance to start decreasing the frequency, or preferably halve it, then a series R of the same resonant impedance value).
To tie this back to the power plane issue you still need a low inductance connection to the pure C and so the power planes again allow these RC's to be located some distance away and still be effective.
Thanks
-Antonio
Good find; thanks for sharing. It's the other end of the cap spectrum but for MLCCs I usually use TDK's Component Characteristics Viewer; other vendors have similar tools but TDK's UI is lower friction than most.
Just about all my design is with radial or surface mount parts, so that explains it. Pretty much never look at caps that would mount off board.
PRACTICAL SNUBBER AND TERMINATION DESIGN
Below is a pretty slick and practical way to determine parasitic capacitance and/or inductance, and the characteristic impedance and optimal damping or termination resistance (and snubber capacitance) needed when ringing or reflections (as the case may be) are present.This is a very simple method for determining the capacitance and the inductance that are causing a resonance in a circuit or a transmission line or PCB trace, which also gives the characteristic impedance for the resonant circuit, which is everything needed in order to know how to damp it, optimally. (I refer to the C and L as parasitic. But this method and the math may be used when either one, or both, or neither is parasitic, in case an installed inductor and/or capacitor are involved.)
This assumes that there is a ringing condition, already, such as might occur on a digital buss or a transmission line or PCB trace, or in a switch-mode power supply or even an AC-to-DC transformer/rectifier circuit, and in many other types of circuits. (If you don't have ringing and just want to determine some of these parameters, I guess maybe you could try hitting your circuit with a pulse train and decrease the rise and fall times until it rings.)
1. Measure the frequency of the resonance or ringing, using an
oscilloscope (or a circuit simulator, if you've modeled the parasitics well).
2. Add a shunt capacitor and adjust the value of this capacitor until the frequency of the ringing is reduced by a factor of two. I've left out the math but the value of this resulting capacitor will be three times (3X) the value of the parasitic capacitance that is creating the resonance.
3. Because the parasitic capacitance is now known, the parasitic inductance can be determined using the formula:
L = 1 / [(2 · Pi · F)² · C]
where F = (original) resonant frequency and C = parasitic capacitance.
4. Now that both the parasitic capacitance and inductance are known, the
characteristic impedance of the resonant circuit can be determined using the following formula:
Z = √(L/C)
where L = parasitic inductance and C = parasitic capacitance.
5. The resistor value used for the terminator or for the RC snubber circuit should be equal to Z, the value of the characteristic impedance, and the capacitor, if used, should be sized between four and ten times the parasitic capacitance. The use of larger (than 4X) capacitors slightly reduces the voltage overshoot at the expense of greater power dissipation in the resistor.
NOTE: The resistor, alone, is all that is needed to prevent or damp-out the ringing (or reflections, as the case may be). But if power dissipation in the R would then be too high, a C is added in series with the R, so that only the unwanted frequencies cause currents in the resistor. (And that, boys and girls, is the only reason there's a capacitor in a snubber.)
Cheers,
Tom
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This extended ASCII table seems correct:
ASCII Table; ASCII extended character sets; IBM PC
I found some interesting stuff at the Unicode links for some of the characters.
And here is a compacted version (hover over characters for info):
ASCII Table
-----------
Oh my!! The following link seems amazingly complete, regarding "character code" issues! This is The Mother Lode!
http://www.cs.tut.fi/~jkorpela/chars.html
Cheers,
Tom
ASCII Table; ASCII extended character sets; IBM PC
I found some interesting stuff at the Unicode links for some of the characters.
And here is a compacted version (hover over characters for info):
ASCII Table
-----------
Oh my!! The following link seems amazingly complete, regarding "character code" issues! This is The Mother Lode!
http://www.cs.tut.fi/~jkorpela/chars.html
Cheers,
Tom
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How to Easily Use Special Characters with Windows
OK! I FINALLY found "The Easy Way" to post any available character you want, with Windows!
e.g. ∂∆≈
Taj said, "FYI: Windows users can use the built-in "Character Map" software (Start menu> Accessories> System Tools) to select and paste the proper Unicode glyphs into this forum."
On my XP machine, I have to do the following:
Start → All Programs → Accessories → System Tools → Character Map
(Notice the nice arrows...
Then I can simply click on the characters in a table to see them enlarged, click Select to add each one to my list, and click Copy to copy my list to the clipboard.
Ω ≠ ∞
small Pi: π
capital Pi: Π
Not too nice-looking...
But wait! That was the Arial version (i.e. no serifs, since Arial is a "sans serif" font)!
Π π
⅞ ∑ ∏ ∫ ∕ − ≤ ≥ ± ÷ ₪
That's more like it! (But I also had to select and wrap the Pi characters with "Times New Roman" in the Advanced post editor, here.)
And below is the second line without the Times Roman. But it was taken from the "Mathematical Symbols" grouping, after I selected "Unicode Subrange" in the "Group By" selection, to see the table displayed by groupings (and the thing that looks like PI is listed as "n-ary product" in the "Mathematical Operators" sub-grouping):
⅞ ∑ ∏ ∫ ∕ − ≤ ≥ ± ÷ ₪
Larger, in the default font:
⅞ ∑ ∏ ∫ ∕ − ≤ ≥ ± ÷ ₪
Cheers,
Tom
OK! I FINALLY found "The Easy Way" to post any available character you want, with Windows!
e.g. ∂∆≈
Taj said, "FYI: Windows users can use the built-in "Character Map" software (Start menu> Accessories> System Tools) to select and paste the proper Unicode glyphs into this forum."
On my XP machine, I have to do the following:
Start → All Programs → Accessories → System Tools → Character Map
(Notice the nice arrows...
Then I can simply click on the characters in a table to see them enlarged, click Select to add each one to my list, and click Copy to copy my list to the clipboard.
Ω ≠ ∞
small Pi: π
capital Pi: Π
Not too nice-looking...
But wait! That was the Arial version (i.e. no serifs, since Arial is a "sans serif" font)!
Π π
⅞ ∑ ∏ ∫ ∕ − ≤ ≥ ± ÷ ₪
That's more like it! (But I also had to select and wrap the Pi characters with "Times New Roman" in the Advanced post editor, here.)
And below is the second line without the Times Roman. But it was taken from the "Mathematical Symbols" grouping, after I selected "Unicode Subrange" in the "Group By" selection, to see the table displayed by groupings (and the thing that looks like PI is listed as "n-ary product" in the "Mathematical Operators" sub-grouping):
⅞ ∑ ∏ ∫ ∕ − ≤ ≥ ± ÷ ₪
Larger, in the default font:
⅞ ∑ ∏ ∫ ∕ − ≤ ≥ ± ÷ ₪
Cheers,
Tom
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This brings up yet another rant from me, and confusion among a lot of vBulletin posters, especially on the writing board I frequent. People expect, somewhat reasonably, that they can do formatting in Microsoft Word or another text editor/word processor using different fonts and font sizes, and variations such a bold and italic, and that they can copy/paste it into an online message board like this and have it come out right. But the formatting codes are all different and the "clipboard" doesn't know it should convert things when pasting into such a message board editing window, and even if it did there are incompatibilities such as limited number of font sizes that would make the result at best not quite WYSIWIG.
I remember when the IBM PC came out, the (monochrome and CGA) display was "yet another" 8-bit extension to the original 7-bit ASCII character set, after other computers such as the Apple ][, other early microcomputers and innumerable terminals used all different sets for the "upper" 128 display characters. But of course due to the popularity of the PC, the IBM PC's set became the de-facto standard, and eventually part of the "official" ISO character set standard(s). And yes, the "ALT codes" were part of the original IBM PC's BIOS ROM.
There must be some "parallel" to the main discussion here, but offhand I can't think of what it would be.
I remember when the IBM PC came out, the (monochrome and CGA) display was "yet another" 8-bit extension to the original 7-bit ASCII character set, after other computers such as the Apple ][, other early microcomputers and innumerable terminals used all different sets for the "upper" 128 display characters. But of course due to the popularity of the PC, the IBM PC's set became the de-facto standard, and eventually part of the "official" ISO character set standard(s). And yes, the "ALT codes" were part of the original IBM PC's BIOS ROM.
There must be some "parallel" to the main discussion here, but offhand I can't think of what it would be.
(Sorry to get off-topic, for the moment.)
Yeah, tell me about it. I used to write C code for those things, including a bunch of different character-based terminal types under Unix and also made it all portable across Xenix, and Linux, and DOS/Netware, Windows 3.1, etc. I remember that the first source-code function I wrote was something to "put the cursor at screen position x, y", and I built from there. I used the box-drawing characters extensively, to make nice non-scrolling data-entry forms and also to allow drawing general-shaped outlines by entering length & direction pairs (don't ask), and after finally getting that all sorted I also had to figure out how to make it portable across many different printers (remember the Okidata 192?), for printing forms with box-character drawings etc and for PrtScr (which, I remember, was "interesting" on the Wyse 60 terminal, because it involved the code for Ctrl-S, which stopped everything; but I eventually figured it out). When HP's LaserJet II came out, I also wrote a preprocessor for the Unix "nroff" document-formatting utility, so it could use the two fonts I had for my LJ II and actually get all of the font sizing and spacings and margins and tables of contents and page numbering (etc!) and everything done properly. What a pain.
L = 1 ∕ (C(2πf)²)
HOW can I make a line with leading whitespaces, when posting here?
Cheers,
Tom
Yeah, tell me about it. I used to write C code for those things, including a bunch of different character-based terminal types under Unix and also made it all portable across Xenix, and Linux, and DOS/Netware, Windows 3.1, etc. I remember that the first source-code function I wrote was something to "put the cursor at screen position x, y", and I built from there. I used the box-drawing characters extensively, to make nice non-scrolling data-entry forms and also to allow drawing general-shaped outlines by entering length & direction pairs (don't ask), and after finally getting that all sorted I also had to figure out how to make it portable across many different printers (remember the Okidata 192?), for printing forms with box-character drawings etc and for PrtScr (which, I remember, was "interesting" on the Wyse 60 terminal, because it involved the code for Ctrl-S, which stopped everything; but I eventually figured it out). When HP's LaserJet II came out, I also wrote a preprocessor for the Unix "nroff" document-formatting utility, so it could use the two fonts I had for my LJ II and actually get all of the font sizing and spacings and margins and tables of contents and page numbering (etc!) and everything done properly. What a pain.
L = 1 ∕ (C(2πf)²)
HOW can I make a line with leading whitespaces, when posting here?
Cheers,
Tom
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In response to damping the resonance of parallel connected caps. I look at it as pi filter
wich can be damped by either introducing serial resistance or parallel resistance or a combination of it. If parallel resistance is used a serial cap must be used to avoid the otherwise obviously resulting loss in dc power. This serial cap has to be at least 10 times (better 20 times) bigger than the cap at the output of the pi filter. Also it has to be remembered that any small valtage changes at the input of the pi filter will be transformed into much higher amplitude at the output.
wich can be damped by either introducing serial resistance or parallel resistance or a combination of it. If parallel resistance is used a serial cap must be used to avoid the otherwise obviously resulting loss in dc power. This serial cap has to be at least 10 times (better 20 times) bigger than the cap at the output of the pi filter. Also it has to be remembered that any small valtage changes at the input of the pi filter will be transformed into much higher amplitude at the output.
If it is really necessary to use a "parallel" cap it is best to minimize the serial inductance to a point where the losses are sufficient to keep the circuit-Q at or below 0.5 wich most certainly almost always should be possible. Anyway, if I see 0.1uF caps it makes me wonder why it is 0.1uF and not some other value? Has the designer given it much thaught and was he aware of all the the things that should be considered? I find it hard to believe that the rigth value for a parallel cap turns out to be just 0.1uF in each and every case I see those caps applied too.
Here's one that claims to prove that multiple decoupling/bypass values are better than multiple caps of the same value (and that fewer caps can be used if they have higher ESR):
http://www.n4iqt.com/BillRiley/multi/esr-and-bypass-caps.pdf
http://www.n4iqt.com/BillRiley/multi/esr-and-bypass-caps.pdf
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