Power Supply Resevoir Size

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I'm just playing with the xfmr-rectifier-cap setup. Toms model, one transformer driving a MBR20100 full bridge into a 5R load with N * 1.2mF 26mOhm caps in parallel.

and I didnt see quite what I expected to see - above about 10mF the conduction angle is constant. thats odd. so I started looking a bit harder. it looks like its the combined effect of ESR (xfmr + diodes + cap bank) & leakage inductance that prevents the conduction angle from narrowing further - IOW it limits the peak current.

The transformer winidng resistances are interesting. Its a forward-mode transformer so the RMS primary and secondary currents are closely related - Ip = Is/N + Imag (this aint necessarily so in a coupled inductor).

generally one designs Imag = small (this is why the huge ratio of Lmag to Lleak - Lmag must be >> Lbase and Lleak << Lbase) so Ip = Is/N. One normally assigns equal volume to equal power windings - so the primary winding area Aw_p should be roughly equal to the secondary winding area Aw_s. Filling this up with Cu then results in Rp = Rs*Np^2. and the resistive losses in each winding are therefore equal (casually ignoring skin & prox effect)

yet in this case Rp/N^2 = 157mOhm but Rs = 290mOhm - the secondary resistance is 1.85x what I would expect it to be. so ignoring magnetising current the secondary accounts for 1.85/2.85 = 65% of the total copper losses.

I might expect to see that in, say, a microwave oven transformer where the poor thing runs hard into saturation (some MOTs draw less current under load because the voltage droop across the primary leakage pulls the core out of saturation. it makes it hard to spot a dead transformer if you dont know this). But nobody in their right mind would do that to a transformer running continuously. and beside with Lmag = 52H the mag current is < 10mA.

It might be to do with the thermal behaviour - if the secondary is on the outside of a toroid it will cool better. I dont know, I havent designed any LF toroidal transformers, but it still seems like a poor idea - especially as it hurts regulation.

the high Lmag seems odd too - 6mA magnetising current is stupidly low* at 120VA thats 0.6% of load.

One would normally pick a number, say 10% full load and design Imag = that much. this reduces the number of turns, and the leakage goes down (and regulation improves). Maybe the manufacturer was trying to get stupidly low Bmax for some reason? who knows, but its certainly odd.

*I used to have a 100kW three-phase 400V:208V transformer with Imag = 200mA (about 0.1%), but that was designed to be switched on and off hundreds of times per day, so was not allowed to "boing" so it had a peak flux density of about 400mT IIRC.

that might be whats happening here - if this transformer were designed for minimum inrush (which is utterly pointless if it then drives a thumping great rectifier-capacitor load) it explains the low Imag and the high leakage.

this transformer might turn out to be a TERRIBLE choice for modelling power supply interactions :)

Terry,

Can you look at the transformer model and come up with some "reasonable" parameters to change it into a 30-Volt transformer with average characteristics, good-enough for 100 Watts RMS into 8 Ohms, which is what Nico originally specified? (If my brain is working correctly right now, which is never guaranteed, we would need Vrms squared / 8 = 100, or Vrms = sqrt(800) = 28.28 Vrms so Vpeak = 40 Volts and a 30V transformer should let us get roughly that. Should we go to 36 Volts for the transformer, so we can more-easily get a real, more-robust 100-Watt output spec?)

It would be nice if we could also use it with 4-Ohm loads but Nico originally specified 8 Ohms, I believe.

If coming up with the model parameters is not possible (or not easy-enough), I might be able to find a differenrt model in the LT-Spice users group's library, at yahoogroups.com . (OR, maybe someone here has a variac and a multimeter and a 30V transformer that they could measure?)

By the way, I am sorry that I have been MIA for a while. I started taking a class every Tuesday and Thursday from 3pm-6:40pm, which is a "mathematics refresher" for post-graduate electrical engineering studies. It's been about three-and-a-half decades since I was really good at that stuff and rust never sleeps. Anyway, although work paid for the course, and it's being given at our facility, for some reason they will not pay for my time to take it and on top of that I have to make up the hours I miss by taking it. So it has cramped my schedule a bit, along with some other unrelated stuff that's also going on here.

Cheers,

Tom
 
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Magic,
are those scope pics showing different starting conditions?
And is anything being shown?

Yeah they are the different starting conditions; basically the ideal way to start up would be to magentize the core either direction at its nominal peak value and apply power at the peak of the corrseponding opposite polarity; that would start the circuit as if it had been going already.

The yellow captions are the different initial states of cores and applying power. The first sets are of a block xformer, those on page 2 I think it was that of a 225VA toroid.
 
Magic,
thanks, thats interesting. I cant read dutch, but the plots and your #563 make it clear. and you are right re. applying -ve Bsat and starting at +Vpeak (or vice-versa). nice scope pics, now I'm jealous, I dont have a colour* LeCroy. but I'm pretty happy with the 9384 I got on Ebay for $800 - half the price of my 9374. (*any colour I want as long as its yellow)

that would be tricky to achieve in practice though - but a more workable compromise might be to reset the remanent flux to zero then start on a peak, any peak. a peak detetor is of course do-able, although not necessarily trivial.

resetting the core to zero could be as simple as a shunt resistor controlled by a DPDT on/off switch.

the caps still need soft-starting though. we used to use half-controlled three-phase bridges on the big stuff (> 10kW. 158mF @ 650Vdc is a BIG bank of caps) and resistor/relay combos on the small stuff.

I suppose you could use a triac in the secondary (oh the losses!) and zero-crossing detector to soft charge the caps once the transformer is running.

or as a compromise: resistor + SPDT relay on the primary, and DPDT on/off switch. resistor shunts primary when off, resetting the core. at turn-on resistor in series with primary, then shunted by relay (or triac, but oh! the losses)

the BH curves are really interesting, and they show once again just how far xfmr designers push these things into saturation. If only they would stop doing that*. its a bit squiffy at 200V, and by 220V its pretty much fully saturated at the peak. this of course explains the unpleasant peaky current waveform, which would look really nasty at 240V.

*Frank, Rod has a nice discussion on xfmr wall-warts and efficiency regs. IIRC he mentions that the new regs rule out iron cores. no they dont, they just mean xfmrs must be designed to NOT saturate. manufacturers do this to save themselves a small amount of Fe & Cu - minimising the cost of manufacture, but maximising the cost of ownership. Aaaargh
 
In the meantime I have found that Frank was absolutely right about using the "real hardware" for simulations, instead of the equation-driven behavioral current sources, at least when it comes to testing the reservoir capacitors. (But it seems like equation-driven resistors would work great. I might still play around with that...)

But, as it turned out, that's OK: With a sinusoidal signal, the error plot (calculated output minus actual output) is good-enough that it still makes it "quite obvious" when something causes a charging pulse to dip into the signal.

The commonly-used approximate formula for the minimum required reservoir capacitance, which is based on average or DC load current (and the assumption that the ripple amplitude is small), is apparently insufficient for catching the cases I've found, during simulations, where low frequency sinusoid signals at certain relative phase angles do cause an occasional unusual/excessive charging-pulse excursion that whacks the signal, distorting it.

I think that the "true" absolute-minimum required reservoir capacitance might be good to be able to calculate, but it turns out that the closed-form mathematical solution for even just the steady-state portion of the full-wave rectifier and capacitor bank behavior, including a load that would allow current and voltage as simple sinusoidal functions of time, is much more complex than some might think it would be. I'm delving into that, on the side, to see if I can end up with a simple "worst-case" rule that would give the minimum reservoir capacitance that would prevent even an occasional incursion of a charging pulse into the signal, given something like the lowest desired undistorted signal frequency and the max input and output power specs.

However, there might be an easier way, in some cases at least, since it looks like the capacitor currents usually get too large, compared to real capacitors' ripple-current specs, before the capacitance gets too low to cause that type of signal distortion. So maybe the capacitors' ripple-current specs will provide a natural "lower bound" for the reservoir capacitance, which would also be much easier to apply.

Interestingly, maybe, other than that (high cap currents), the really-low-reservoir-capacitance cases I looked at seem to perform surprisingly well, except for the occasional signal whack by a charging pulse at low bass frequencies, whenever the total capacitance truly is just not quite enough. (But I haven't yet gotten around to having LT-Spice calculate the THD of the output signal for each run).

By the way, Frank, I set the PSU input voltage to 195.68 in the sine voltage source, for my latest runs. That gives 42-something volts nominal, for the average DC out. Also, I added transformer models in parallel until things stopped changing too much each time I added more in parallel, for some reasonable-looking reservoir capacitance. Then I added some more. Right now I have six in parallel on each side, to try to make sure the model won't color the results.

So a more-reasonable transformer model would be nice to have. But I'm wondering what would be best to use, if we are trying to come up with some "rule" that would be generally applicable. It will depend on the transformer, too. So, to avoid that, should we assume, for example, that the transformer will be "at least good-enough", so that it doesn't need to be taken into account?
 
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Tom, I specified 100 watt 8 ohm since it is probably the most common choice around DIYAudio.

Of course it would be interesting to later test for 4 ohms using the 8 ohm specified system and also take note of how differently it performs and whether it is good to just say 100 watt/8 ohms and 150 watt/4 ohms, again there may exist no such assumption that a 4 ohm load is acceptable in an 8 ohm designed system.

I think we may assume many things and state even more things in audio that just simply is not even close to being factual.

EDIT: Tom there is no reason for not selecting a suitable transformer, however I always just assumed practically one would choose 150% VA to required rms output power, again just a rule of thumb - who's rule? I have no idea.
 
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If only they would stop doing that

Additional info on the 225VA was that it's a 20 year old, 220Vac type.
For EU harmonisation purposes, nominal mains has gone up to 230Vac in the meantime, just think what the +10% peak value of 253Vac image would look like for that transformer.
Fortunately, mains still rarely reaches 230 in most places here.

(if it makes you feel better, Freddy is the head coordinator of a group that developes low tech/cost aids for developing nations, at a university, likely used the job LeCroy)
 
Gootee, or anyone else,
can you simulate a simple resistor as a load for the transformer model.
Adjust the resistor value and determine the output voltage for that new load.
This will allow a plot of regulation vs load current.
From that we can estimate what size of real transformer roughly matches the model performance.
 
EDIT: Tom there is no reason for not selecting a suitable transformer, however I always just assumed practically one would choose 150% VA to required rms output power, again just a rule of thumb - who's rule? I have no idea.

The rule comes from that an audio power amplifier does not have 100% efficiency. That's why it has heatsinks. Depending on type/design it will be around 50%. Have a look here:
Amplifier - Wikipedia, the free encyclopedia
and Amplifier Efficiency
 
You may just have a good opportunity here Harrison.
Give each of these gentlemen one completed amplifier with exact same components then allow each of these gurus to paste on his KICK-*** power supply.

Now rotate to the left and each person gets his colleagues amp to listen and measure, then one final rotation - thereafter let them report their findings both objective and subjective..

The resultant is the best of the best rules of thumb compared objectively and will conclude this thread

Dont be left behind. Experience something new. Your contribution counts. Your opinion matters. Join us now. http://www.diyaudio.com/forums/solid-state/217539-32-pcbs-available-part-2-a.html#post3125241
 
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Gootee, or anyone else,
can you simulate a simple resistor as a load for the transformer model.
Adjust the resistor value and determine the output voltage for that new load.
This will allow a plot of regulation vs load current.
From that we can estimate what size of real transformer roughly matches the model performance.
Andrew, will something like this do the job?

TfmrReg.gif

This matches the model I've been using so far; unrealistically high primary, and hence secondary, voltages but it's just a tool to explore what's going on in this PS/amp interaction ...

Frank
 
Gents, this thread seems to have gone very quiet. My apologies for not throwing in a few responses over the last day or so, I do have a problem with mental stamina, something I've already mentioned to Tom. Too many things happen at once, as was the case over the last day or so, in other areas of life, and my brain closes down; the only way to get back on track again is to chill out for a bit.

So, don't take my low level of input as a sign of lack of interest, rather that I have to take it slow for a tick. Both Tom and Terry (or is that Jerry, :p:D) are submitting great material, so I hope the energy in this conversation can continue ..

Cheers,
Frank
 
Gents, this thread seems to have gone very quiet. My apologies for not throwing in a few responses over the last day or so, I do have a problem with mental stamina, something I've already mentioned to Tom. Too many things happen at once, as was the case over the last day or so, in other areas of life, and my brain closes down; the only way to get back on track again is to chill out for a bit.

So, don't take my low level of input as a sign of lack of interest, rather that I have to take it slow for a tick. Both Tom and Terry (or is that Jerry, :p:D) are submitting great material, so I hope the energy in this conversation can continue ..

Cheers,
Frank

No problem, Frank.

I have been running some fairly-massive (i.e. time-consuming) double-nested stepped-parameter simulations to explore what the real minimum required reservoir capacitance is, with a sinusoidal load, for low frequencies.

It looks like the absolute minimum required reservoir capacitance (to just barely completely prevent clipping at max output power with one sine frequency) might have to be significantly more than the standard ripple-voltage equations imply. Those equations are only approximate, and only apply when the ripple is a very small percentage of the nominal PSU voltage. And they assume a constant output current.

However, the minimum capacitance is also not as low as one might think if one simulated only with basic sine signals and various capacitances. The phase angle of the signal must also be varied, to position the output peaks at different times, relative to the charging pulses and the dips in the rail voltage.

I'll probably only do it for 15 Hz and 25 Hz, and 4 and 8 Ohms at 100 Watts RMS (with appropriate standard-size transformers' rail voltages), to start with.

Initial result: For 15 Hz, with one cap per rail, it looks like a 42.3-Volt rail and a 28.28 Vpk (100 Watt RMS) sine-wave output signal at 15 Hz only requires 4000 uF per rail, if ESR is {0.02/(cap_value*Vrating)}, which was used with Vrating = 100 Volts (i.e. ESR = 0.05 Ohm). I'll probably eventually also try verifying the minimum capacaitance value with one or more of the Cornell Dubilier capacitor models that automatically varies the ESR with frequency, more realistically.

Anyway, that only means that 4000 uF might be the absolute-minimum required capacitance (for the stated scenario) in order to not have gross pre-clipping distortion with a 15 Hz signal at maximum output power.

EDIT: The 4000 uF is probably not enough, for 15 Hz. It's too low for 25 Hz, in the runs I just did. So maybe I didn't vary the phase angle of the input signal in small-enough increments for the 15 Hz case. Will have to re-do it and report back. Sorry to have jumped the gun.

Once I can make sense of all of the results, I will post everything here and you and Terry and everyone can check to see if have made any serious mental blunders (unless you see some already).
 
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No problem, Frank.

I have been running some fairly-massive (i.e. time-consuming) double-nested stepped-parameter simulations to explore what the real minimum required reservoir capacitance is, with a sinusoidal load, for low frequencies.

...

Once I can make sense of all of the results, I will post everything here and you and Terry and everyone can check to see if have made any serious mental blunders (unless you see some already).
Looking very interesting, Tom. One concern I have is that you have, reading an earlier post of yours again, multiple transformers in parallel, 6 I believe, running this simulation. Those many transformers mean that the effective VA rating is very high, 6 times assuming perfectly matching devices, I think, and this is something that no conventional amp would use; the expense would be ferocious for the benefit gained. Unless that's the way you want to go to solve the "problem" ...;)

So in one sense I still come back to using parts therein that match what a typical DIY unit would use, where there is a good balance of where the moneys go for the various bits ...

Anyway, what you're doing is excellent research on the cap side of things, so it will good to see what you've got ...

Frank
 
Tom, very nice work. A couple of thoughts off the top of my head -
1) I expect there is a tradeoff between the amount the rail voltage exceeds the maximum output voltage swing, and the amount of capacitance - higher Vrail means you can get away with less capacitance, up to a point anyway. It would be interesting to quantify this. Probably easy to do for sine wave test signals, real world signals will no doubt require some estimation of "average" power.

2) why did you decide to use 15 and 25Hz test inputs? instead of doing a stepped simulation and changing the phase angle, you could use say 61Hz (assuming 60Hz AC input) and just run for 1 second.
 
Looking very interesting, Tom. One concern I have is that you have, reading an earlier post of yours again, multiple transformers in parallel, 6 I believe, running this simulation. Those many transformers mean that the effective VA rating is very high, 6 times assuming perfectly matching devices, I think, and this is something that no conventional amp would use; the expense would be ferocious for the benefit gained. Unless that's the way you want to go to solve the "problem" ...;)

So in one sense I still come back to using parts therein that match what a typical DIY unit would use, where there is a good balance of where the moneys go for the various bits ...

Anyway, what you're doing is excellent research on the cap side of things, so it will good to see what you've got ...

Frank

Frank,

Yeah, I'm also trying it with fewer VA of transformers, too.

But with 25 Hz and 100 W RMS into a 4-Ohm load, the voltage source driving the transformers says it's supplying 184 Watts, with six transformers per side and 4300 uF per rail. With just two transformers per side and 5300 uF, but nothing else changed, the rail averages about 5 Volts lower and the total power supplied averages about 168 Watts. (Those uF are the approx values where no clipping-type distortion occurs, with a 25 Hz signal, for those configurations.)

It sure would be nice to have a range of transformer model VA ratings.

I haven't looked, recently. But I wonder if one of the transformer manufacturers has posted downloadable spice models for their whole line of transformers, by now.

Tom
 
Frank @573 - no worries. Im a bit busy ATM, but will eventually get around to testing my low-leakage EE-core isolation transformers - they are 2kVA, and should be indicative of what can reasonably be achieved. Its a really, really interesting thread

Jom @ 574 (;D) - now you point this out, in hindsight it is blindingly obvous. As is so often the case. So if we are to design for minimum ripple (a worthy approach because its easy to do) then we probably ought to do it at the lowest audio frequency, not the mains frequency.

and that segues into a second obvious-in-hindsight observation: for a sinusoidal load,
P(t) = 2*Pavg*sin(2wt)

sine waves are also pretty flat near the peaks.

for audio frequencies lower than the AC line eg 10Hz, this will look (to the rectifier) like a steady-state load of 2*Pavg. Dont forget the rectifier conduction time is typically 1-2ms, which is very short compared to the time the audio signal spends near 2*Pavg.

But we currently simulate a DC load, Pdc = Paverage.

So in otherwords we can probably just do the standard 50/60Hz ripple design, but use 2*Pout instead of Pout.
 
mightydub @ 576: nice idea. dont forget the sim has to reach steady-state though, but thats easy - just use smaller x for (60+x)Hz. I like it.

Tom @ 577: if you express the transformer parameters in Per-Unit (of rated load) then for a given manufacturers range they should be roughly constant - and in fact ought be constant for a given core type.

this might not be true crossing from toroids to EE/EI cores, but it might. we dont even need spice models - just measured resistance, Lmag & Lleakage.....
 
Andrew, will something like this do the job?

View attachment 296007

This matches the model I've been using so far; unrealistically high primary, and hence secondary, voltages but it's just a tool to explore what's going on in this PS/amp interaction ...

Frank
Am I reading the plots correctly?
At infinite load resistance: Vout = 73.7Vpk
At 10r load resistance: Vout = 71.2Vpk
At 10r load resistance: Iout = 7.12Apk
VA @ 10r loading = 253
regulation @ 253VA = 3.5%

This would seem to indicate that the transformer model is probably equivalent to a toroid that is quite a bit larger than 253VA, 25.1+25.1Vac
This actual toroid would normally have a 5% to 7% regulation.
 
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