Power supply ringing

[trobbins]

kward, I can recommend the transformer secondary snubbing topic as worthy of appreciating, and using any sources of info but in particular the discussions and reported results and documentation at diyaudio on the Quasimodo threads. Not all power supplies practically benefit from such a snubber, such as for valve diode B+ supplies with highish effective source resistance and lowish load current. Such a snubber is also not a panacea for rectifier related noise, but more an additional technique to apply along with careful selection of diode, and careful layout and cabling and choice of subsequent filter.

I would suggest that the topic of LC filter ringing is ever present, as that is what LC circuits do, and also worthy of appreciating their performance in an application. LC theory is as old as valve technology. With PSUD2, the topic is typically handled during design or restoration by picking an existing design, or a particular part, and checking all the power supply performance levels, including filter resonance frequency (as it is not good to align with a mains harmonic, or within an audio span) and whether dampening performance from practical part selection makes it benign. That dampening is mainly due to choke resistance, and the load acting as a resistance across the filter output capacitance, and the insertion of spurts of energy input from the rectifier that likely happen multiple times during a filter resonance cycle. There are many rules of thumb that have been applied by many people for part value selection.

 

[kward]

Again good information Mike and Tim. The ring frequency I found for the CLC section is easily down under 20 Hz (according to simulation), so I'm probably making too much fuss over it.

Also found PSUD to be a good tool for investigating rise time on the various caps in the supply. But that is another topic...

 

[Retrovert]

A few issues which I don't think have been addressed.

Much of this is pulled from my notes and summarized, as I had many of the same questions.

Pi Filter

The Pi filter in the power supply places a capacitor on either side of an inductor. That configuration creates a parallel resonant circuit which is then stimulated by AC currents and oscillates. The Q of the inductor matters here, because high Q inductors are more prone to LF ringing.

The ringing is driven by the AC currents originating from:

(a) AC ripple, which is not readily removed by the filter capacitors.

(b) Variable load arising from the varying audio signal, which causes the current draw to cycle up and down creating a ripple-like current effect. Unless one listens to square waves (very popular with the kids) with constant duty cycles, this is inherent in the application domain.​

While ripple may be addressed by better filtering, the issue of (b) must be addressed. That's every bit as important as ripple from the AC to DC conversion, because LF waves in the input signal can cause ringing in the power supply.

How Power Supply Q Causes Ringing

The higher the Q of the resonant circuit, the higher the ringing voltage will be and the longer it will continue.

To summarize Q, this (more or less, somewhat simplifying) is an expression of the ratio of the power out versus the power that is consumed or maintained in the system itself.

So the power supply usually has high Q, which means it is underdamped. That high Q means it is consuming/storing relatively little of the power passing through it. A high Q supply thus rings for a long period of time with the damping being very slow, mostly the resistive losses from the inductor's DCR and the capacitors' ESR, plus any resistors that may be present in the power supply line.

The snubber damps the circuit beyond the aformentionend losses, and thereby ends the ringing by converting the energy to resistive losses aka heat.

Now consider why proper specification of the inductors matters.

The inductors used in power supplies tended to have high DCR and the older capacitors (electrolytic paper) had high ESR. That helped to damp out the ringing. Modern capacitors have significantly lower ESR, but modern inductors tend to have roughly the same DCR as the older ones or lower for higher gauge. So the Q of the power supply has been raised by better components.

Printed circuit boards and wiring also cause ringing, but this tends to be a problem at much higher frequencies than audio. Designers of cell phones and switching power supplies generally worry about these things.

Damping Factor (ζ)

Having slogged through a number of application notes on snubbers, I can say that some uncertainty exists about the optimal selection of values for damping factor, called ζ.

Cornell-Dubilier suggests 0.5< ζ < 0.9, but this is best for switched-mode supplies, while a ζ of 0.5 appears to be better for traditional linear power supplies, with ζ = 1/sqrt(2) = 0.707 being nearly optimal and nicely between the two endpoints. That larger value for ζ reduces the size of the snubber resistor to dissipate the ringing, because it's not as heavily damped.

Barbie says, "Analog Design is Hard!".

I worked out some of the math, but I can't get the equations from my notes on snubber equations to paste in here. These are not much different from the C-D equations, or what you'll find elsewhere, just with greater derivation of the intermediate steps to explain what is happening.

Ringing Frequency

The ringing can be at a variety of frequencies, but the goal is to keep it very low. It can be calculated by:

f0 = 1 /(2 × Pi × sqrt(L × C))​

Remember that C is C1||C2, so C = C1 + C2.

Keeping f0 below the lowest frequency the amplifier reproduces moves the ringing out of the audible and stability area, even with higher harmonics.

In general, ringing at a few Hz isn't going to do much to the amplifier. But 20 Hz? That is going to affect the amplifier's performance and be audible.

So the issue becomes what is the Q of that Pi filter, and what is the damping factor of the power supply? These are unknown, as they depend upon the particular components selected.

 

[Retrovert]

Such a snubber is also not a panacea for rectifier related noise, but more an additional technique to apply along with careful selection of diode, and careful layout and cabling and choice of subsequent filter.

That system issue is a good point.

The diode Qrr is also a source of noise, and because it is HF it acts as a carrier for LF noise. That broadcast noise can be received by long component leads or wires and then rectified into noise elsewhere in the amplifier.

That dampening is mainly due to choke resistance, and the load acting as a resistance across the filter output capacitance, and the insertion of spurts of energy input from the rectifier that likely happen multiple times during a filter resonance cycle. There are many rules of thumb that have been applied by many people for part value selection.

Back in the The Olden Days, when copper was less expensive, large chokes with high DCR were used to perform filtering and the damping was quite good. This was, I believe, Stan White's big issue. He promoted monster chokes over capacitors, which he felt were inadequate to remove ripple and deal with amplifier fluctuations. It was the 1950s, of course, and copper was far less costly.

The world, however, moved to smaller chokes and bigger capacitors of better quality, which increased Q and reduced inherent damping.

 

[thorpej]

Ringing Frequency

The ringing can be at a variety of frequencies, but the goal is to keep it very low. It can be calculated by:
f0 = 1 /(2 × Pi × sqrt(L × C))Remember that C is C1||C2, so C = C1 + C2.

Keeping f0 below the lowest frequency the amplifier reproduces moves the ringing out of the audible and stability area, even with higher harmonics.

In general, ringing at a few Hz isn't going to do much to the amplifier. But 20 Hz? That is going to affect the amplifier's performance and be audible.

Yah, whenever I'm drawing up a power supply that uses a filter choke, I keep this formula handy and shoot for a resonance frequency of < 10Hz. In the 60W UL 6L6 amp I built last year, the CLC filter's resonance frequency is < 4Hz (500uF -> 3H -> 100uF), and in the 40W EL84M amp I'm planning now, < 8Hz (60uF -> 2.5H -> 100uF).

 

[BinaryMike]

I think power supplies ought to be entirely non-resonant in high-fidelity amplifiers, especially those using triodes. Subsonic resonance can be excited by bass rhythm in music signals and modulate tube operating points. Single-ended class A triode amps without feedback are susceptible to this problem even though class A is nominally constant-current. They cause changes in power supply current for the same reason they produce so much second harmonic distortion -- lopsided gain at high output.

 

[thorpej]

I think power supplies ought to be entirely non-resonant in high-fidelity amplifiers, especially those using triodes. Subsonic resonance can be excited by bass rhythm in music signals and modulate tube operating points. Single-ended class A triode amps without feedback are susceptible to this problem even though class A is nominally constant-current. They cause changes in power supply current for the same reason they produce so much second harmonic distortion -- lopsided gain at high output.

I totally agree that it's a bit of a Faustian bargain (the devil in this case being the appeal of the filtering capability of a CLC filter with a relatively low DC resistance). But when using vacuum rectifiers (I don't normally, but the above mentioned 40W amp is an exception), it's hard not to take that deal because you're limited in how much capacity you can throw at the rectifier. Sometimes you're just forced to make trade-offs. Strictly using CRC filtering has it's own disadvantage that can also fiddle with the tube operating points (in non-class A circuits, anyway).

I guess my argument is that CLC filtering should't be dismissed outright simply because they can resonate. The pros and cons need to be weighed in context with the rest of the design.

 

[trobbins]

I think power supplies ought to be entirely non-resonant in high-fidelity amplifiers, especially those using triodes. Subsonic resonance can be excited by bass rhythm in music signals and modulate tube operating points. Single-ended class A triode amps without feedback are susceptible to this problem even though class A is nominally constant-current. They cause changes in power supply current for the same reason they produce so much second harmonic distortion -- lopsided gain at high output.

Post #16 has a CLC filter. PSUD2 shows no resonant behaviour for a 2:1 step load - it only shows sag or rebound due to the step. So it would pass the 'entirely non-resonant' rule of thumb.

 

[Retrovert]

Post #16 has a CLC filter. PSUD2 shows no resonant behaviour for a 2:1 step load - it only shows sag or rebound due to the step. So it would pass the 'entirely non-resonant' rule of thumb.

I'm not certain the power supply is entirely non-resonant.

The transformer can be self-resonant and be self-stimulated as well as stimulated by the varying load.

The secondary winding’s leakage inductance forms a resonant LC circuit with the secondary’s internal capacitance plus the capacitance of the rectifier diodes. All small, true, but it's another resonant circuit.

 

[kward]

Edit: The article appears in Linear Audio Volume 5 and is titled Rectifier Snubbing -- Background and Best Practices.

This volume of the magazine is not freely accessible on line (shucks), but a letter to the editor about the article is online. https://linearaudio.net/sites/linearaudio.net/files/MvdG to MJ V5.pdf

 

[Retrovert]

But when using vacuum rectifiers (I don't normally, but the above mentioned 40W amp is an exception), it's hard not to take that deal because you're limited in how much capacity you can throw at the rectifier. Sometimes you're just forced to make trade-offs.

Which is exactly the tradeoff existing up until the 1960s, as rectifiers had limited drive and capacitors were small and expensive, and even the good ones had high ESR and DF. The early amplifiers from the 1920s all used choke Pi filters with small capacitors and large inductors for this very reason. (Except the designers called capacitors "condensers" and were upset by the upstarts who used the name "capacitor", as well as "resistor" instead of "resistance". That's how old long ago this was.) The bigger the choke the better the filtering.

Reading a number of papers about power supply design from the 1940s and 1950s, turns up virtually nothing about choke resonance, even though large chokes were generally considered to be a sign of a quality supply. Authors do discuss damping factor, which is related, but I think the lack of widespread oscilloscopes masked this problem. I don't otherwise know why it would have been relatively neglected as an issue for audio. Yes, these were essentially hobbyist engineers, but they still had a good grasp of the engineering.

Hams knew about resonance in inductors and trasnformers because transmitters suffered from it. I somewhere read a writeup of how the goal was to remove even tiny tenth of a Hz resonance in certain transmitter circuits. But this did not seem to propagate into audio.

As I noted above, Stan White pushed small C huge L filters. But he was one of the few to push the idea of the speaker as a current device instead of a voltage device. Briefly, the voice coil is an electromagnet and the voltage is only necessary to push current through a thinner, i.e. lighter, but higher-resistance wire. When that cone returns the generated back EMF must be damped. And the CLC supply is better able to do that.

I guess my argument is that CLC filtering should't be dismissed outright simply because they can resonate. The pros and cons need to be weighed in context with the rest of the design.

Going back to kward's question, what can snubbers do to reduce the resonance of the inductors and the transformer to a minimal level, and solve this problem in such a fashion that CLC resonance largely vanishes as an issue. If the Faustian bargain requires a simple RC addition, that's hardly much of a detriment.

 

[Retrovert]

This volume of the magazine is not freely accessible on line (shucks), but a letter to the editor about the article is online. https://linearaudio.net/sites/linearaudio.net/files/MvdG to MJ V5.pdf

Interesting. Thanks for posting that.

The MJ observation, "If we can reduce this circuit’s Q to < 0.7, we can prevent ringing – making it unnecessary to worry about amplitude and large-signal effects." matches what I discovered and above described as, "with ζ = 1/sqrt(2) = 0.707 being nearly optimal and nicely between the two endpoints."

However, MJ went on to note that he didn't consider Qrr as the AM broadcast, "I had not considered the transformer/rectifier as a mixer, with rectifier switching causing double sideband suppressed carrier modulation to a capacitively coupled carrier from mains wiring acting as an aerial."

That Qrr is one of the big issues with diodes, and why the lower Qrr diodes produce significantly less noise. I tried to convert my equations about this into something human readable for posting, but failed. Yet another reason why I ceased using the Microsoft Word equation editor.

 

[thorpej]

I've been studying this topic in more detail over the past week. I now see that ringing could occur whenever you have an LC circuit. In the diagram below of a typical power supply used for a tube amp, I believe there are two opportunities for ringing, labeled 1 and 2.

Considering case (2) first: stepping the current load of I1 in PSUD, or just watching the initial rise of the voltage on C2, I was able to see the ring in simulation caused by this CLC circuit.

I just put this into PSUD and ran the simulation, and while I see the initial "startup chime" (sorry, couldn't resist -- I'm a Mac guy), it actually appears fairly well damped already, and I don't see any ring at the load step. This example actually behaves a lot better than my 60W amp's power supply in this regard (where I do get a "startup chime" that lasts for 2 cycles, and a small thunk when the load steps from 212mA [idle] to 400mA [full power]).

https://www.dropbox.com/s/od5u7720unlv037/ST-60-Mk-I.psu?dl=0

 

[Brice]

Yes I see it. If you increase C2 you can decrease it pretty nicely.

It's for a stereo amp or a monobloc? 212mA at idle is most likely for 4 power tubes right? Unless you're using KT120/150.

 

[kward]

I actually tweaked that simulation quite a bit before posting to get the ring out (other than that "chime" you reference on initial startup). It's for a new amp I'm building. A 6L6 Push-Pull, stereo.chassis build. Quiescent current draw from the output stage will be about 160 mA (4x tubes).

 

[thorpej]

Yes I see it. If you increase C2 you can decrease it pretty nicely.

It's for a stereo amp or a monobloc? 212mA at idle is most likely for 4 power tubes right? Unless you're using KT120/150.

Stereo, 2x push-pull 6L6GC (well, I did the design using 6L6GC specifications, but installed 6П3С-Es) per channel, connected ultra-linear. 53mA idle per tube, as measured at a 10 ohm cathode current-sensing resistor.

Yah, I could parallel another cap under the hood to increase the post-choke capacity to tamp that down. I may do that at some point, but the amp performs quite well as it is, so I'm not in any hurry.

 

[thorpej]

I actually tweaked that simulation quite a bit before posting to get the ring out (other than that "chime" you reference on initial startup). It's for a new amp I'm building. A 6L6 Push-Pull, stereo.chassis build. Quiescent current draw from the output stage will be about 160 mA (4x tubes).

Cool, looking forward to reading more about it!

 

[Retrovert]

Another issue is that the lifespan of an electrolytic capacitor depends upon its operating temperature, with suitable de-rating being required. ESR increases over the capacitor's lifespan, and ripple current causes additional heating, shortening the lifespan.

One of the papers I read about this is:

ieeexplore.ieee.org/document/5625486
Lifetime analysis of aluminum electrolytic capacitor subject to voltage fluctuations
by Kun Zhao, Philip Ciufo, Sarath Perera
IEEE 14th International Conference on Harmonics and Quality of Power (ICHQP) (2010)​

Due to their relatively large capacity and low cost, aluminium electrolytic capacitors are widely used in many power electronic circuits. Although the aluminium electrolytic capacitor is the primary choice for industrial applications, it is not a perfect device. The main drawback is their reliability, especially their lifetime [10] [12] [17]. Operating temperature is the main factor causing degradation of the capacitor parameters, especially the equivalent series resistance (ESR). The ripple current and ambient temperature are the main contributors to the temperature rise of the capacitor. The significant degradation mechanisms accelerated by heating are chemical changes in the oxide layer and the electrolyte vapour leakage through the capacitor and seal. Both factors lead to an increase in ESR over the operating life of a capacitor.
...
The ripple-current heating losses in the capacitor are estimated based on this model. Since aluminium electrolytic capacitors have a relatively high ESR, a large ripple current can result in high total capacitor power loss, especially under fluctuating power conditions. The increase of capacitor power loss causes a higher operating temperature inside the capacitor.
...
Therefore, for electrolytic capacitor applications, higher capacitor ripple current will lead to an increased internal heating that in turn accelerates the evaporation of electrolyte and degrades the lifetime.​

NB: I removed all the math since it won't cut-and-paste here.​

I don't know it is more or less authoritative on the subject than other papers, I just happen to have it. The other papers I read on the subject said, more or less, the same sort of thing. This is in keeping with the consensus about electrolytic capacitor lifespan, particularly from manufacturers like C-D, so I would believe it to be true.

So the question is: if ripple current shortens lifespan:

(a) what does effect does oscillation from CLC ringing have upon capacitor lifespan
(b) if (a) is significant, how does this degraded filtering impact the power supply performance during the useful life of the capacitor?
​

I'm not saying this matters to a significant extent, particularly when the capacitor is new. It appears to worsen over time. My supposition is that if ripple slowly degrades the capacitor, then so will oscillation, and that as the capacitor degrades its filtering worsens and ripple current increases.

So the Faustian bargain would now include potentially decreased capacitor lifespan over the CRC filter, but the CRC might have greater heating because more capacitance is required to obtain the same ripple-filtering effect as adding even a small amount of inductance via CLC.

 

[trobbins]

If kward's sim circuit was used with a 500V rated electrolytic, then the ripple current in the first 47uF cap would get close to max rated for a Nichicon UCY. For that particular filter configuration (low first C, and moderate load current), there is good benefit in using series caps - for cost, ripple current, and voltage margin.

 

[kward]

You know...I hadn't looked closely at ripple current (yet). That is something I will investigate though.

Cool, looking forward to reading more about it

Pretty standard stuff on this amp--your regular "Mullard 5-20" style topology (what can I say?--I like that frontend) with a fixed bias output stage. My brother (who requested this amp) wanted something that uses those "cool guitar tubes" but also wants to be able to find replacements 30 years down the line. So that is why I'm using the ordinary workhorse 6L6-GC and not something more exotic on this one (like sweep tubes). Plus I just think this will be a kick-butt good sounding amp. (We all think that before we build our latest creation!)

But I digress off topic...