Dilbert's mom told him, "When paralleling capacitors, just add the values." As she left the room he couldn't quite hear her mutter under her breath, "Unless you grow up to be an audiophile."
It turns out this simple rule has exceptions. The usual formulas don't take losses into account. If losses are low, it doesn't matter. If losses are high, the results might not be what you expect. It's almost never an issue with film caps, but electrolytics operating at audio frequencies often have high losses. Not necessarily high absolute impedance, a myth, but high losses in terms of resistance vs reactance.
The standard measurement frequency for electrolytics is usually 120 Hz, sometimes 1 kHz for small ones, and these days 100 kHz to get ESR with switching supply filter caps, but rarely do they give you any numbers between 120 Hz and 20 kHz. It's not surprising because those measurements can be difficult to make due to the very low impedances involved, and don't show the parts in their best light.
As you combine capacitors, particularly when you bypass an electrolytic with a smaller film, there are some surprises. The first is that gaining any improvement in high frequency performance is a lot harder than you might think. If you can make measurements for the parts, the linked spreadsheet will give you the answers.
The second surprise is that paralleling a big high loss electrolytic and a low loss film cap can result in a lower capacitance than the electrolytic alone! That's completely contrary to what you might think, but it's real and verified by bench measurements. You add more capacitance and the total goes down. Since nobody has noted it before, I'm naming it The Hoffman Effect! It's not the result of inductance or resonance per se, just high loss, and is really a trick of the math for the series capacitor model. Still, it's rather unexpected. It occurs when the dissipation factor of the high loss part exceeds 1, common with large electrolytics at higher audio frequencies, and the dissipation factor of the paralleled cap is low. Skeptical at first, I had the result checked by two different EE friends of impeccable pedigree, and they confirmed the phenomena to be quite real.
Cap Combo Spreadsheet (Excel)
It turns out this simple rule has exceptions. The usual formulas don't take losses into account. If losses are low, it doesn't matter. If losses are high, the results might not be what you expect. It's almost never an issue with film caps, but electrolytics operating at audio frequencies often have high losses. Not necessarily high absolute impedance, a myth, but high losses in terms of resistance vs reactance.
The standard measurement frequency for electrolytics is usually 120 Hz, sometimes 1 kHz for small ones, and these days 100 kHz to get ESR with switching supply filter caps, but rarely do they give you any numbers between 120 Hz and 20 kHz. It's not surprising because those measurements can be difficult to make due to the very low impedances involved, and don't show the parts in their best light.
As you combine capacitors, particularly when you bypass an electrolytic with a smaller film, there are some surprises. The first is that gaining any improvement in high frequency performance is a lot harder than you might think. If you can make measurements for the parts, the linked spreadsheet will give you the answers.
The second surprise is that paralleling a big high loss electrolytic and a low loss film cap can result in a lower capacitance than the electrolytic alone! That's completely contrary to what you might think, but it's real and verified by bench measurements. You add more capacitance and the total goes down. Since nobody has noted it before, I'm naming it The Hoffman Effect! It's not the result of inductance or resonance per se, just high loss, and is really a trick of the math for the series capacitor model. Still, it's rather unexpected. It occurs when the dissipation factor of the high loss part exceeds 1, common with large electrolytics at higher audio frequencies, and the dissipation factor of the paralleled cap is low. Skeptical at first, I had the result checked by two different EE friends of impeccable pedigree, and they confirmed the phenomena to be quite real.
Cap Combo Spreadsheet (Excel)
You are perfectly entitled to it.
I had already noticed a similar effect, but working in the opposite direction, ie if a small lossy cap is paralleled with a larger lossless one, the total capacitance appears to decrease for a range of frequencies.
I think this kind of effect is also related to "passive amplification": a clever combination of RC circuits (no inductors, transformers and no actives obviously) can "amplify" (modestly and voltage-wise) a signal for some frequencies.
Combined with a unity gain buffer, this can result in an oscillator (a relatively poor one though).
20yrs or so ago, an article about such circuits appeared in Electronics World
Dilbert's mom told him, "When paralleling capacitors, just add the values." As she left the room he couldn't quite hear her mutter under her breath, "Unless you grow up to be an audiophile."
It turns out this simple rule has exceptions. The usual formulas don't take losses into account. If losses are low, it doesn't matter. If losses are high, the results might not be what you expect. It's almost never an issue with film caps, but electrolytics operating at audio frequencies often have high losses. Not necessarily high absolute impedance, a myth, but high losses in terms of resistance vs reactance.
The standard measurement frequency for electrolytics is usually 120 Hz, sometimes 1 kHz for small ones, and these days 100 kHz to get ESR with switching supply filter caps, but rarely do they give you any numbers between 120 Hz and 20 kHz. It's not surprising because those measurements can be difficult to make due to the very low impedances involved, and don't show the parts in their best light.
As you combine capacitors, particularly when you bypass an electrolytic with a smaller film, there are some surprises. The first is that gaining any improvement in high frequency performance is a lot harder than you might think. If you can make measurements for the parts, the linked spreadsheet will give you the answers.
The second surprise is that paralleling a big high loss electrolytic and a low loss film cap can result in a lower capacitance than the electrolytic alone! That's completely contrary to what you might think, but it's real and verified by bench measurements. You add more capacitance and the total goes down. Since nobody has noted it before, I'm naming it The Hoffman Effect! It's not the result of inductance or resonance per se, just high loss, and is really a trick of the math for the series capacitor model. Still, it's rather unexpected. It occurs when the dissipation factor of the high loss part exceeds 1, common with large electrolytics at higher audio frequencies, and the dissipation factor of the paralleled cap is low. Skeptical at first, I had the result checked by two different EE friends of impeccable pedigree, and they confirmed the phenomena to be quite real.
Cap Combo Spreadsheet (Excel)
What spreadsheet? I opened it twice, just some words.
I like to see how you test it, your test setup with pictures.
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That's why I like to see the set up, how the experiment was conducted. One has to be very careful with the setup, what impedance you are measuring. If you are running big capacitance in very low impedance circuit, current is either very high OR the voltage is very small, you have to start worrying lead length, lead inductance, current loop that form a magnetic loop that create and receives magnetic fields. And if the signal is very small, how do you measure the signal? how long is the ground lead of the scope probe?
No point of talking until we see the picture of the setup.
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I checked, the date on the spreadsheet was not April 1. What kind of joke is this?
I would be cautious about attaching my name to something (in this case parallel-series impedance transformations) which has been known for decades (by others). The parallel version of an impedance (which you need to use when combining components in parallel) always has larger numerical values than the series version - in the case where the resistance and reactance are equal the parallel version has twice the values of the series version. As reactance varies inversely with capacitance this means that the parallel capacitance can be half the series capacitance. Note that capacitors are usually marked with the series impedance. Hence the surprise which some may find when paralleling lossy capacitors.
Nothing new here. Nothing particularly relevant to audio either, as this effect is only large enough to confuse people when the capacitor impedance is already very low so fine for all audio purposes.
Nothing new here. Nothing particularly relevant to audio either, as this effect is only large enough to confuse people when the capacitor impedance is already very low so fine for all audio purposes.
The Wheatstone bridge was invented by Christie, but Wheatstone got all the credit! My naming is a bit tongue in cheek, but who knows. I'll probably never invent anything of importance.
As for importance in audio, the decrease in value is a minor effect, though unexpected and quite real, but what's more important, and relevant to audio, is the effectiveness, or lack of it, of bypassing on HF performance, that the spreadsheet makes it easy to explore.
I assume most were able to open the spreadsheet? Possibly filters or something got it on some systems, as I had another report of the same thing, so let me know.
As for the "setup", which is always an important question, I did the initial checks with a standard HP component adapter for their LCR meter, having low impedance and allowing as short a lead length as possible. The meter can operate up in the MHz, so their fixture was quite carefully designed. AFAIK, there are no setup strays that are anywhere near as large as the effect being measured. The fact that the measured results agree with the calculated results also gives some confidence.
DF96- one of your statements seems to have the greater/smaller terms reversed, unless I'm misunderstanding something, which isn't uncommon. Simple parallel capacitance will be smaller than series capacitance as losses increase. Everything else is certainly correct, though I'd still claim that the combined decrease in value under some conditions has been pointed out pretty much nowhere.
As for importance in audio, the decrease in value is a minor effect, though unexpected and quite real, but what's more important, and relevant to audio, is the effectiveness, or lack of it, of bypassing on HF performance, that the spreadsheet makes it easy to explore.
I assume most were able to open the spreadsheet? Possibly filters or something got it on some systems, as I had another report of the same thing, so let me know.
As for the "setup", which is always an important question, I did the initial checks with a standard HP component adapter for their LCR meter, having low impedance and allowing as short a lead length as possible. The meter can operate up in the MHz, so their fixture was quite carefully designed. AFAIK, there are no setup strays that are anywhere near as large as the effect being measured. The fact that the measured results agree with the calculated results also gives some confidence.
DF96- one of your statements seems to have the greater/smaller terms reversed, unless I'm misunderstanding something, which isn't uncommon. Simple parallel capacitance will be smaller than series capacitance as losses increase. Everything else is certainly correct, though I'd still claim that the combined decrease in value under some conditions has been pointed out pretty much nowhere.
Parallel has larger impedance values, so smaller capacitance values.Conrad Hoffman said:
It is not a combined decrease, unless inductance plays a role (which it often will). This effect is well known. The fact is that every real capacitor has two ideal values (the parallel one and the series one). Only for a lossless capacitor are these two values equal. If you use a circuit where the parallel value is relevant, but then measure with a meter which gives you the series value then you can be surprised.
RF people do this sort of series-parallel conversion all the time - or at least the older ones do, while youngsters probably just believe whatever a simulator tells them.
Alan, here's a link to the fixture in question, but you're not taking losses into account, so the combination is always greater. Connecting Fixture (Gain-Phase) The math is in the spreadsheet.
DF, are not the total impedances of equivalent parallel model and series model capacitors equal?
DF, are not the total impedances of equivalent parallel model and series model capacitors equal?
The net impedance is the same, but expressed in two different ways. There is a third way: impedance magnitude plus impedance phase.Conrad Hoffman said:
That already assumes that you are using the parallel version of the component impedances, or assuming ideal lossless components.Alan0354 said:
For the benefit of baffled bystanders, this is what Conrad and I are discussing:
Any real impedance (e.g. a component) can be expressed as either the sum of a resistance and a reactance in series, or as a parallel combination. In the case of an electrolytic capacitor at lowish (i.e. audio) frequencies the best model is a capacitor in series with a small resistor. The resistor is ESR (say, 0.1R). The capacitor is the value marked on the can (say, 100uF).
As frequency increases the capacitive reactance decreases. ESR may increase a little, but we will assume for simplicity that it stays constant. There will come a frequency (15.9kHz) where capacitive reactance equals ESR. At this point the component no longer has the 90 degree phase of a pure capacitor but 45 degrees. It can be expressed in three ways:
0.1R + 100uF in series
0.2R in parallel with 50uF
0.1414R magnitude, 45 degrees phase
If you measure this with a capacitance meter what you will see depends on what frequency the meter uses and how it chooses to interpret the raw data.
Now add a perfect 1uF in parallel. This gives 0.2R with 51uF in parallel. Converting this back to series form gives 0.09798R + 100.02uF. The extra 1uF has almost disappeared! The main effect of the extra 1uF component is a small reduction in ESR. Given the real world with measurement error and some series inductance too it is easy to see why it might be thought that the total capacitance reduces. Note that all this applies at a single frequency only; you have to repeat the calculation for each frequency.
DF, that's an excellent summary in very few words, better than I've done. IMO, the parallel model is best for high loss/low Q situations, but when considering components for audio, where we go from quite low frequencies, to high, it could be confusing to people to change models somewhere in the range. In theory, either model predicts what happens just fine, though the "gut feel" for the model values will be a bit odd when the "wrong" model is used. Thus comes about the oddities when using the series model at high frequencies with highly imperfect components.
One can't emphasize enough that both these models are valid for a single frequency only. At that single frequency, whatever capacitive (-) and inductive (+) reactance add, leaving only a single value, be it one or the other, and are not considered separately. The loss term covers pretty much everything else, even including dielectric absorption, leaving only some non-linearities unaccounted for. With a true bridge, those show up as a non-zero residual when the bridge is balanced.
In your example, take the losses a bit higher. I think you'll find the total Cs does in fact decrease. It's not a measurement artifact. Using a bad example of something like a big electrolytic and a moderate value OSCON with very low losses at high frequencies, it can decrease by quite a lot, though you get the benefit of markedly improved losses- the bypass is actually effective in that case!
One can't emphasize enough that both these models are valid for a single frequency only. At that single frequency, whatever capacitive (-) and inductive (+) reactance add, leaving only a single value, be it one or the other, and are not considered separately. The loss term covers pretty much everything else, even including dielectric absorption, leaving only some non-linearities unaccounted for. With a true bridge, those show up as a non-zero residual when the bridge is balanced.
In your example, take the losses a bit higher. I think you'll find the total Cs does in fact decrease. It's not a measurement artifact. Using a bad example of something like a big electrolytic and a moderate value OSCON with very low losses at high frequencies, it can decrease by quite a lot, though you get the benefit of markedly improved losses- the bypass is actually effective in that case!
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