Parallel capacitance

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FastEddy said:
" .. have a wine tasting to visit now, but remind me and I'll get to writing out some equations later ..."

I got it ... I'll google it and get back as well ... Hope you find a nice dry Dry Creek Chard or a mellow Alexander Valley Merlot ... Sonoma County = best vino in the world ... so far. 😎

" ... Rock Grotto Audio Forum ..." for the latest Oppo Mods = got it, thanks. As for the link, I wonder which archived article you mean?? (I guess I could read 'em all ... ) 😕

" ... The low esr types seem to often cause metallic sounding treble. ..." I've noticed that as wel, but assumed that it was me and my tired old ears, not the particular type / spec of a cap .. :bigeyes:

It was Santa Cruz Mountains, actually, and I picked up some Bordeaux blend and Zinfandels. Lovely stuff. Good chards come from Dry Creek, I'll agree.

Oppo mods? Me too, please.


As for low ESR caps causing metallic treble, it might be marginal ultrasonic stability because of series inductance in power traces resonating with the capacitor, or possibly the effect I'll describe a bit more deeply here:

Imagine an electrolytic capacitor bypassed with a film cap. We'll assume the film cap has zero series resistance and zero series inductance because it's a reasonable first order approximation and the equations are simpler to understand. The capacitive impedance part of the electrolytic we'll also assume to be essentially zero, also reasonable since we're looking at the regime where series resistance and inductance predominate, so we'll model the electrolytic as an inductor with a series resistance.

The electrolytic impedance with these assumptions is Zel (inductive part) + Zer (resistive part), and the film cap impedance is Zfc (pure capacitance). Parallel impedance equation is:

[1] 1/Z = 1/(Zel+Zer) + 1/Zfc
[2] 1/Z = (Zel + Zer + Zfc)/(Zfc*(Zel+Zer))
[3] Z = (Zfc*(Zel+Zer))/(Zel + Zer + Zfc)

Now the actual impedances of the various parts is:
[4] Zfc = 1/jwCf
[5] Zel = jwLe
[6] Zer = Re
[7] Fr = 1/((2*pi) * sqrt (Le*Cf))

where w = 2 * pi * frequency, Cf = film capacitor's value, Le = electrolytic equivalent series inductance, Re = electrolytic equivalent series resistance, Fr is the resonance of Le and Cf, j = (square root of -1), and 1/j = -(square root of -1) (note minus sign!)

Look at our previous example of a 8400 uf electrolytic with equivalent 0.01 ohm series R and 50 nH series L, bypassed with a 0.05 uF capacitor. At about 3 MHz, from equation [4] Zfc is around -j*1 ohm, and from [5] Zel is j*1 ohm. Plugging those values into equation [3] gives:

[8] Z = (-j * 1 * (j * 1 + 0.01)) / (j * 1 + 0.01 + -j * 1)
[9] Z = (1 + j * 0.01)/(0.01) = 100 + j * 1

Look at what happened in the denominator: the inductive and capacitive impedances canceled out, leaving only the equivalent series resistance as the divisor! The result ends up roughly being the product of the C and L impedances divided by the R.

Now plug in an equivalent series resistance of 0.1 ohm instead. Z ends up as 10 + j * 1, still not great but a lot better than 100 ohms.

[10] Z = (-j * 1 * (j * 1 + 0.1)) / (j * 1 + 0.1 + -j * 1)
[11] Z = (1 + j * 0.1)/(0.1) = 10 + j * 1

What happens if you use a larger film capacitor? Let's try a 5 uF capacitor. Resonance happens at 300 kHz, from [4] Zfc = -j * 0.1, from [5] Zel = j * 0.1, and plugging these values into [3] gives

[12] Z = (-j * 0.1 * (j * 0.1 + 0.01)) / (j * 0.1 + 0.01 + -j * 0.1)
[13] Z = (0.01 + j * 0.001)/(0.01) = 1 + j * 0.1

The resonant impedance is now about 1 ohm instead of 100. We're getting pretty close. If the equivalent series resistance is 0.1 ohm, Z now ends up as 0.1 + j * 0.1.

[14] Z = (-j * 0.1 * (j * 0.1 + 0.1)) / (j * 0.1 + 0.1 + -j * 0.1)
[15] Z = (0.01 + j * 0.01)/(0.1) = 0.1 + j * 0.1


That's why low-ESR capacitors can get you in trouble with bypassing: the low resistance will exacerbate the resonance caused by the electrolytic inductance in parallel with the film capacitance value, and the effect gets worse with smaller film capacitors.

Note how having a bit of ESR actually damps down the parallel resonance and prevents large impedance increases.

The optimum value for a bypass capacitor, as from the conditions in [15] where the absolute values of Zel = Zfc = Zer, turns out to be:

[16] Re = 1/(j * w * Cf), then Cf = 1/(j * w * Re)
[17] Re = j * w * Le, then j * w = Re / Le

and substituting [17] into [16] we get:

[18] Cf = Le/(Re * Re)

Look familiar? It should, it's our old friend the Zobel equation come back for a visit. Funny how it crops up whenever you need to cancel inductance. Look at what happens when you decrease ESR by 10: the optimum value of bypass cap increases by 100.
 
" ... Oppo mods? Me too, please. ..."

Ask SandyK for his friends' mod docs = seems to be quite simple, a few parts replaced and a parallel plastic cap added, etc. Apparently there is quite a little sub-forum ongoing on the Oppodigital.com stuff = many tricks, many slight improvements, a few that may really make some improvements, IMOP. (I am trying to put together a list of successes and possible worthwhile tweaks and post 'em somewhere. Full, wholesale mods don't seem to be needed, just power supply mods, addons and tweaks plus a few software manipulations ... ) :smash:

" ... The electrolytic impedance with these assumptions is Zel (inductive part) + Zer (resistive part) ..." 😕 😕 🙄 :bigeyes:

I usually let the eggheads take care of the esoteric math ... prefering to add or remove or suppliment parts on a trial and error basis ... I used to be able to wade knee deep into transfer functions and the like, but even if you get a clue from the calculations, you still have to refer to suggestions from the tinkerers, the informal, "check it out" on the 'scope types of pundits (Bob Pease, Don Lancaster, et al). They usually show the way without resorting to a complicated spreadsheet. Don't get me wrong here: all the paperwork definately has its place and does point in the proper direction, but knowing which direction that is, is very often more important than the definative slide rule results ... :smash:

How was the beer? :cheers:
 
FastEddy said:


" ... The electrolytic impedance with these assumptions is Zel (inductive part) + Zer (resistive part) ..." 😕 😕 🙄 :bigeyes:

I usually let the eggheads take care of the esoteric math ... prefering to add or remove or suppliment parts on a trial and error basis ... I used to be able to wade knee deep into transfer functions and the like, but even if you get a clue from the calculations, you still have to refer to suggestions from the tinkerers, the informal, "check it out" on the 'scope types of pundits (Bob Pease, Don Lancaster, et al). They usually show the way without resorting to a complicated spreadsheet. Don't get me wrong here: all the paperwork definately has its place and does point in the proper direction, but knowing which direction that is, is very often more important than the definative slide rule results ... :smash:

How was the beer? :cheers:


Thanks for the Oppo tip. I'm thinking of getting the 981 but I wondered whether they'd taken as much care with the audio section as with the video bits.


I dig playing with equations because sometimes there's a hint of something peeking out from behind a corner and it's fun to track it down, for example like the Zobel equation [18] determining the optimal bypass cap for an electrolytic. You need the ESR and ESL, of course, but it looks like a nice little rule of thumb. 'Sides, I wouldn't have gotten into it if there hadn't been a bit of controversy about bypassing driven by folks who'd tried various things.


By the way, if you're using low-ESR parts try inserting a 10 ohm series resistor just before the bypass cap pair on an opamp. Typical traces are around 10 to 20 nH per inch, so if you have a six inch trace feeding a .1 uF bypass cap (let's ignore the electrolytic for the moment) and the opamp isn't drawing a lot of current, you can get into a resonant situation at about 1.5 MHz since the low current draw makes the opamp supply line look like a high-value resistor, which won't damp the capacitor much. Sticking in a series resistor sorts that right out. It trashes the regulation a bit - can't be helped - but opamps typically have decent PSRR at audio frequencies and there's a larger electrolytic beside the .1 uF bypass to fix that anyway.

That was fun; I learned two new things today. Thanks.

The vino rocked last night. Got together with some friends who roasted, over open coals no less, a whole salmon rubbed with sun-dried tomato spread, and the wine was a 2002 Savannah-Chanelle Pinot Noir. Yeah, baby!
 
The Oppo's analogue out is very ordinary , but could be improved a bit with an OPA2134 or LM4562. A friend fitted the OPA2314 but it still wasn't great, so I didn't bother The switchmode mods, plus some chassis dampening does result in excellent audio out via SPDIF. Feed LPCM into a good upsampling DAC ,then PA direct with the digital volume control and it can sound stunning.

SandyK
 
glen65, john65b

I just read your posts.

I have used 0.047 polystyrene caps in parallel with electrolytics for many years. I sometimes also add 10uf polypropylene caps. I use these in parallel to; power supplies capacitors, in speaker crossovers, in line capacitors and also parallel to capacitors that go from power lines to earth.

I began doing this after listening tests which showed a big improvement in high frequency responce. I guess due to improvements in impedance - but can not be sure of this. I have checked with an oscilloscope etc. and find some change due to the parallel capacitors but not enough to cause me any concern. I have never had any instability problems. However this is not to say that you will never get an instability problem if your amplifier is inclined that way. It may be that I have never had a problem with instability because I normally build amplifiers to a conservative design to avoid such problems as instability.

Don
 
SandyK: " ... A friend fitted the OPA2314 [in the Oppo player] but it still wasn't great ..."

I would have guessed that. Most modern op-amps are pretty good as long as they are implimented properly, which the Oppo engineers seeem to be able to do. (Oppo enginnering is done in the Silicon Valley about a mile from Cirrus HQ ... Mfgering is in Hong Kong, I believe ... )

AMV8: " ... I use these in parallel to; power supplies capacitors, in speaker crossovers, in line capacitors and also parallel to capacitors that go from power lines to earth. ... I began doing this after listening tests which showed a big improvement in high frequency responce. ... "

Yes!! plastic caps are the golden ear types' choice for DC blocking (in line 'tween amp stages, etc.) and in crossovers, usually for high pass tweeters and middies as the values for low pass woofers, etc. require cap sizes that may not be available as plastic. ( Examples: http://aussieamplifiers.com/nx150s.htm [that big bruiser at input, foreground in the pics] ... http://www.soniccraft.com/audiocap_theta.htm ) ... :smash:
 
Which brings up another point @ Bypass caps

I remember reading a while back (on Gainclone PS discussion) that someone had bypassed their dual rail electrolytic smoothing caps with a single polypropylene cap (.1uF) across the positive and negative rails. A single bypass cap instead of two, but of course, the cap had to be rated to the additive volts of the two rails...

Anyway, I have two setups of an Aerovox 28uF Polypropylene (400V) paralleled with a TRW .1uF Polystyrene (630V) bypass cap. I want to bypass a dual Mallory 56,000uF cap for +/-60V rails on a UCD400AD.

Is it better I put a single bypass arrangement across the +/- rails or two identical setups across each two 56,000uF caps both connected to ground?

Other question is the 28uF cap doing anything? Just use the .1uF Polystyrene by itself as a bypass cap?
Thanks for the help.
 
" ... I have two setups of an Aerovox 28uF Polypropylene (400V) paralleled with a TRW .1uF Polystyrene (630V) bypass cap. I want to bypass a dual Mallory 56,000uF cap for +/-60V rails ..."

That should do it!

Although personally, I would prefer dual TRW 0.1 Polys ... Sometimes physical limitations may require a single cap across the + & - rails, but generally one would want that middle leg connection to power / signal ground = bypassing the ground leg and more uF on the rails, too. 😎 ... although the truth be known, the difference is very hard to detect on a 'scope or whatever, once the poly snubbing cap(s) are in place.
 
Power Supply Impedance at High Frequencies

The electrolytic impedance with these assumptions is Zel (inductive part) + Zer (resistive part), and the film cap impedance is Zfc (pure capacitance). Parallel impedance equation is:

[1] 1/Z = 1/(Zel+Zer) + 1/Zfc
[2] 1/Z = (Zel + Zer + Zfc)/(Zfc*(Zel+Zer))
[3] Z = (Zfc*(Zel+Zer))/(Zel + Zer + Zfc)

Now the actual impedances of the various parts is:
[4] Zfc = 1/jwCf
[5] Zel = jwLe
[6] Zer = Re
[7] Fr = 1/((2*pi) * sqrt (Le*Cf))

where w = 2 * pi * frequency, Cf = film capacitor's value, Le = electrolytic equivalent series inductance, Re = electrolytic equivalent series resistance, Fr is the resonance of Le and Cf, j = (square root of -1), and 1/j = -(square root of -1) (note minus sign!)

Look at our previous example of a 8400 uf electrolytic with equivalent 0.01 ohm series R and 50 nH series L, bypassed with a 0.05 uF capacitor. At about 3 MHz, from equation [4] Zfc is around -j*1 ohm, and from [5] Zel is j*1 ohm. Plugging those values into equation [3] gives:

[8] Z = (-j * 1 * (j * 1 + 0.01)) / (j * 1 + 0.01 + -j * 1)
[9] Z = (1 + j * 0.01)/(0.01) = 100 + j * 1

Look at what happened in the denominator: the inductive and capacitive impedances canceled out, leaving only the equivalent series resistance as the divisor! The result ends up roughly being the product of the C and L impedances divided by the R.

Now plug in an equivalent series resistance of 0.1 ohm instead. Z ends up as 10 + j * 1, still not great but a lot better than 100 ohms.

[10] Z = (-j * 1 * (j * 1 + 0.1)) / (j * 1 + 0.1 + -j * 1)
[11] Z = (1 + j * 0.1)/(0.1) = 10 + j * 1

What happens if you use a larger film capacitor? Let's try a 5 uF capacitor. Resonance happens at 300 kHz, from [4] Zfc = -j * 0.1, from [5] Zel = j * 0.1, and plugging these values into [3] gives

[12] Z = (-j * 0.1 * (j * 0.1 + 0.01)) / (j * 0.1 + 0.01 + -j * 0.1)
[13] Z = (0.01 + j * 0.001)/(0.01) = 1 + j * 0.1

The resonant impedance is now about 1 ohm instead of 100. We're getting pretty close. If the equivalent series resistance is 0.1 ohm, Z now ends up as 0.1 + j * 0.1.

[14] Z = (-j * 0.1 * (j * 0.1 + 0.1)) / (j * 0.1 + 0.1 + -j * 0.1)
[15] Z = (0.01 + j * 0.01)/(0.1) = 0.1 + j * 0.1


That's why low-ESR capacitors can get you in trouble with bypassing: the low resistance will exacerbate the resonance caused by the electrolytic inductance in parallel with the film capacitance value, and the effect gets worse with smaller film capacitors.

Note how having a bit of ESR actually damps down the parallel resonance and prevents large impedance increases.

The optimum value for a bypass capacitor, as from the conditions in [15] where the absolute values of Zel = Zfc = Zer, turns out to be:

[16] Re = 1/(j * w * Cf), then Cf = 1/(j * w * Re)
[17] Re = j * w * Le, then j * w = Re / Le

and substituting [17] into [16] we get:

[18] Cf = Le/(Re * Re)

Look familiar? It should, it's our old friend the Zobel equation come back for a visit. Funny how it crops up whenever you need to cancel inductance. Look at what happens when you decrease ESR by 10: the optimum value of bypass cap increases by 100. [/B][/QUOTE]


DSP_Geek,


Another way of viewing this problem is that of the Q factor, where the Q factor defines the amount of energy lost per cycle. A high Q factor is indicative of a high impedance, and typically occurs only at one particular frequency.

The Q factor is defined by the equation:

Q = (1/R) * sqrt(L/C).

As can be inferred from the above expression, paralleling multiple capacitors can actually make the situation worse if the corresponding ESR is also reduced. The problem is made worse because the R term (linear) gets smaller faster than the L or C terms (square root) . It turns out that this phenomenon nearly scuttled the design of a major major CPU manufacturer several years ago.

In order to determine if a given power supply is subject to this problem, it is best to perform a measurement with a VNA over a range of ~10 Hz - ~1.0 MHz. If there is an impedance peak, it can be reduced by placing a small resistance in series with the capacitance. This sounds counterintuitive, but the above equation clearly indicates that adding series resistance will lower the Q factor. Note that the resistance need not be placed in series with all capacitors. It typically should be placed in series only with the capacitor whose combination of L and C is causing the problem. Some experimentation, or better, simulation, is useful in determining the best value and location of added resistance.

Good Luck.

JCM
 
JCM has described the situation very well, and it's the reason I cringe when people talk about arbitrarily putting low esr caps in parallel with everything. Linear Technology published a little switching circuit for testing how well bypass caps and combinations of such, work, in their application notes. Highly recommended. There is also an obscure (National?) application note about 3-terminal regulators and noise peaks that shows the pitfalls of very low esr caps on regulator outputs. The output of a regulator has properties of an inductor. Again, a small resistance in series with the cap can work wonders. Another thing to consider is the inductance of lead length, both for bypasses and between the supply and the load.
 
sandyK
I never use low esr types in analogue circuits. I reserve their use for some digital circuitry. NOT around DACS.The low esr types seem to often cause metallic sounding treble.

I do not understand...
Low ESR is a desired feature of any capacitor. (Ideally zero at all frequencies.)
It can reasonably not itself cause sonic deterioration.
 
Lumba
Many supply bypass electrolytic capacitors in analogue circuits are AFTER the voltage regulators, which usually aren't too far from the I.C.s they supply.I prefer to use a normal electrolytic with a 100nF poly. capacitor in parallel.
The answer Conrad gave , (above) explains the reasons why low ESR types should not be used after VREGs.
I do not know for sure,the reasons why, but I also dislike their effect on the sound when used at the input of the analogue voltage regulators too. For that matter, I also dislike tantalum capacitors across the "adjust" terminal of analogue supply regulators. Very few designers seem to use them here in analogue supply regulators. They definitely do affect the sound quality.

SandyK
 
Lumba Ogir said:
sandyK


I do not understand...
Low ESR is a desired feature of any capacitor. (Ideally zero at all frequencies.)
It can reasonably not itself cause sonic deterioration.

Hi,

The reason you want some ESR in a reg output cap has to do with the reg stability. The output cap modifies the reg gain/phase characteristic and you NEED some cap to roll off the reg gain before 180deg phase shift. The reg is a feedback amp basically. The small ESR damps any residual oscillatory tendencies at high frequency load currents.

This is especially important in low-drop-out regs that use PNP pass transistors (to get the low drop-out). Since PNP's generally (in IC's) have less gain/more phase shift, these regs are more prone to oscillations, and often a minumum REQUIRED ESR is specified.

Same goes for 'normal' regs (no low drop-out) for neg voltages, because they also use PNP pass transistors. Neg regs generally are not as good as pos regs at higher freqs. If you have separate pos and neg secondaries on your transformer I would recommend using two pos regs, and connect the "+" output of the "neg" reg to ground, and it's "ground" to neg voltage to the load circuit.

Jan Didden
 
I don't mind the math at all (tutored Calculus/Differential Equations for years), but what I do not have a grasp of is the idiosyncrasies of power supplies that only experience will give. Thats were you guys come in.

Anyway, to get to the point, is there an optimum method of bypassing the smoothing caps I have on my power supply - across rail to rail or a pair across rail - ground?

I do not believe this is a subjective issue around "preference" - like the type, manufacturer and value of bypass cap - rather than one of those objective idiosyncrasies I am not familiar with...

thanks - I was hoping to put the caps in tonight.
 
As a Monday morning troublemaker, I'll suggest that putting low esr caps everywhere is so popular because it either causes a problem people like, or it causes a problem that compensates for some other problem. Or maybe it's mob psychology. I like tantalums because they have a predictable and useful esr, but they have other characteristics that make them less desirable in audio gear. I always keep some resistance wire around, both for making things like low value emitter resistors, and adding that extra bit of esr to caps. Note, however, that real caps tend to have a constant dissipation factor with changing frequency. That means that a single resistor value in series does *not* achieve the same thing. Because programs like LT Spice use a single resistor esr model, it makes simulating cap effects with frequency, difficult.

john65b- I'm sure smarter people can work it all out on paper, but I find physical tests are best. The switching circuit from LT can probably be AC coupled, or you can drive a power supply with an AC coupled with a small cap and properly terminated signal generator. If you "ping" the supply (at the circuitry) with a square wave, you can check for ringing on the scope. I'm far more in favor of proper bypassing at the circuitry where it can do some good, then across the filter caps. Be sure rectifiers are bypassed, or RF will further complicate the situation.
 
Just to add, some caution is necessary when testing high current power supplies for response, ringing, and impedance. For newbies, if you often blow your meter fuse because you left the leads in the current receptacles, or if ohms law and how AC coupling works aren't second nature to you, this stuff should wait a while. There is significant risk of shorting things out, destroying test equipment, and who knows what else. In the meantime, get hold of LT's application notes and read what Jim Williams has to say about bypass caps, probes and probing, and stability.
 
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