Getting double the power out of your power transformer

[nickb]

The math says... more or less...

Well you're not wrong. I have seen those ratios oft quoted, usually by transformer manufacturers. Even then they don't agree amongst themselves. I don't think they are realistic for the tube amp targets.

Let's take a real example, a Hammond 373JX 300-0-300 & 288mA 49 ohms secondary resistance, the primary R is negligible. If we have a full wave bridge rectifier and load it with 189mA and 100uF, the secondary current is 288mA rms. The loaded voltage is 409, unloaded 440, a regulation of 7%. The ratio of Irms/ Idc is 1.52 not 1.2.


For a bridge example, consider a Hammond 290HX intended for JCM800: 356V, 400mA, 52 ohms. This gives Idc=204mA Irms=400mA , regulation= 10%, Irms/Idc=1.92.

This is why I claim a roughly 2x power saving. To get to figures claimed by the manufactures you have to increase the series resistance, in effect a low pass filter, to reduce the distortion. The price you pay, aside from the I^2R loss in the series resistance, are voltage regulations of about 25%.

I do doubt that the exercise is worthwhile if you are just looking to replace a 200VA transformer with, realisticly, a 125VA one as the price differential is not as big as one might expect. On the other hand if it allows you to buy 100 x 250V 150VA transformers instead of ten different types there is an economy of scale and storage.

[darkfenriz]

Would it be inappropriate to suggest a good old humble post-rectifier choke to achieve the similar effect without the hassle of switched mode currents stress?
Just a thought.

[trobbins]

Practical part voltage ratings would suggest a max peak output voltage of something a bit less than a 450VDC rated output capacitor, and given some mains tolerance then the PT secondary would be up to circa 380Vpk (270Vrms) to allow some output ripple Vpp. For 200mA output and 10Vpp mains 2f ripple the output cap would be at least 100uF, which should cope with the mains and switching ripple currents, and audio signal currents.

That would probably need 600V boost diode and FET. I remember getting 600V SiCs many years ago for a similar PFC - they seem like a dime a dozen nowadays and with lower capacitance. That coilcraft part looks an easy way to go - have you asked for free samples?

[Mike Sulzer]

Regarding the full wave/bridge comparison, it is not clear to me how those numbers were derived. First, it seems that the full wave starts with a disadvantage because only half the secondary copper is used at any time, while the bridge uses it all all the time. You could take a transformer with two identical secondaries and use it full wave, or parallel them and use it with a bridge, and get the percentage in each case. But would this be a reasonable comparison? I think you can deliver more power in the second case, and so it is not clear to me that a comparison of rms and average current is the whole story. Furthermore, it would seem that the most efficient use of copper in the two cases could involve different wire sizes in both the secondary and primary, and so you should not make the comparison for the same transformer used two different ways. So I think that this is a really complicated question, but maybe I have it all wrong.

[R.G.]

I should explain more - as if I weren't being long-winded enough.

I used what amounts to techno-mumble about the actual ratios of Irms to Idc because it's variable. I actually ran into some of the math derivations of the numbers when I was reviewing what I thought I knew before submitting that post. I'll see if I can dig a couple of the references out of my browser history or re-create the search.

The ratio of Irms to Idc depends heavily on the amount of filtering and what kind, of course. Inductors force the ratio toward unity by forcing rectified current pulses to get closer to the same current a resistor would pull. In a rectifier-filter arrangement where the first filter element is an inductor, as the inductor gets larger and larger and the current gets larger and larger, there comes a point where the inductor's energy storage and physics let the inductor make up for any voltage issues that would turn off the rectifier diodes. At this level of critical inductance and loading, the inductor can force the voltages seen by the diodes to make the diodes act as synchronous switches. The current out of the transformer never turns off, and the current in the inductor never goes to zero. This work very well, and has GREAT regulation (in the sense that the output voltage doesn't vary much with load) but requires a big, heavy, and expensive inductor, and the guarantee that the load current never drops below a certain critical load. This often requires a ballast resistor. The output voltage is also only a fraction of the input peak voltage. It turns out that it's cheaper to make enough capacitive filtering than inductive filtering, and the industry has gone heavily down the path of capacitive filtering. As a side note, even if the industry had decided to go for inductive filtering, that would now be in the process of being legislated out of existence because of the power waste of minimum loads and ballast resistors.This

For capacitive filtering, the filter element works best at maintaining a reasonably constant output voltage and low ripple when the capacitor is "big" compared to the load. This leads down the design path of huge capacitors. For your trouble in making the caps big, you get predictable output voltages near Vpeak and lighter, less expensive power supplies with no real minimum loading needed. It also forces the current from the AC supply/transformer to flow in very short pulses, and makes the rms value of the current bigger as the cap gets bigger.

That leads down into the "how big is the cap" question. The critical issue the analyses settled on was the value of the capacitor-resistor time constant of the filter cap and the sum of the transformer and diode resistances and the load resistance. For low values of CR, the variation of Irms to Idc is small, because the cap isn't big enough to affect things much - the output voltage runs down into an approximation of a FWR sine wave because the cap can't hold up the load current for a full half-cycle. For HUGE values of CR - effective, great big capacitors, the Irms to Idc doesn't change very much (although more than with very low capacitances) because the cap is so big that the time the rectifiers conduct per half cycle is already tiny, and it's all on that nearly-flat section of the half-sine near the top.

Irms to Idc changes a lot in the range where a capacitor filter is rapidly influencing the ripple voltage. Yes, a little "well, duuuh" thinking gets to that very quickly. It's in this range of capacitor values that the cap's voltage-holding ability is rapidly changing the duty cycle of the diode on-time as a portion of the AC half-cycle.

On the transformers-can't-be-equal comment; of course they can't. I was allowing myself to slip off into design space in my head, where changes to designs can take place as fast as the mind conceives of them, not dealing with the messy business of actually rewinding a core with real wire. However, in design space, a transformer has a fairly fixed power throughput (that is, Vrms*Irms, or VA) that it can sustain that's nearly constant when you pick the amount and form factor of the iron laminations and what amount of the window you will allow to be filled with copper. It really is asymptotically true that a given weight of iron and copper has a power rating when made into a transformer, if you allow that the amount of metal is properly distributed in space and insulated, and there is some temperature maximum the insulation can stand. There is also the need for a skilled human or computer to distribute the iron, copper, and insulation to match the input AC voltage and frequency and load current ratings to get near a design maximum for those parameters. That's a big "if", but if you allow that, the actual output voltage and load arrangement doesn't matter much.

The step between FWB and FWCT does change things, and it's for the reason Mike mentioned: In FWCT, only half of the secondary is active on any half-cycle. That immediately forces the "ideal designer" I hypothesized just a minute ago to do a different optimization for the kind of rectifiers and load. So it's back to design space to redistribute the iron and copper. FWCT is not as efficient a use of the iron and copper, and so we don't see many FWCT designs these days, excepting in anachronisms like tube-rectifier tube amplifier power supplies. The FWCT connection was developed to solve a different issue than we face today. That was the issue that tubes were EXPENSIVE, and transformers (relatively at least) were not, so it made economic sense to adapt the transformer design to the availability of a one-tube rectifier, and not try to minimize transformer expense by using three tubes to rectify. The same derivations of Irms to Idc also talk about the transformer utilization ratio, and FWCT is always lower than FWB. When diodes got effectively free with silicon, we changed over to FWB rectifiers and big caps. A transformer design for FWCT is not the same as a transformer design for FWB, even allowing for the switching of two secondaries into parallel and series because you shift the ratio of winding area and secondary area allowed for copper between primary and secondary as a way to help you out on the issue of half your secondary doing nothing on alternating half cycles.

I'll go see if I can find the derivations of Irms/Idc and transformer utilization that I ran into. But for the purposes of the original topic, FWB setups do offer the most advantage for PFC additions. A FWB setup can have Irms/Idc from about 1.4 to 1.9 or more as you change the capacitor value from "good enough" to "freaking HUGE", with the most improvement is the FH region. A FWCT setup tends to be more limited to Irms/Idc much nearer 1 already. so the improvement available is much smaller, but the transformer utilization is already much smaller because of the rectification method, so you don't have as much "overhead" to improve on.

[Mike Sulzer]

... A FWCT setup tends to be more limited to Irms/Idc much nearer 1 already. so the improvement available is much smaller, but the transformer utilization is already much smaller because of the rectification method, so you don't have as much "overhead" to improve on.

That is exactly where I was trying to get to. Thanks, R.G., really great post.

[Mike Sulzer]

The intent of power factor correction is to make current flow in an approximately sine wave fashion, not the big-pulse-at-the-peak way it naturally does with capacitor input rectifiers. They do this by running from a full-wave rectified DC source, and using switching step-up techniques to boost the voltage from the lower portions of the FWR sine up to the same voltage as the peak that the rectifiers are making from the peaks of the incoming sine waves.

Thinking about this some more, I think the quote above is what the power company wants you to do to lower their losses. But I think what you want to do is minimize the total iron/copper/capacitor expense. Maybe this means using the same type of circuitry to push the current waveform in the "flattop" direction so that it takes less C for a given ripple voltage. Not sure if this can be done with the circuit Nick showed, but I think it should be possible somehow.

[R.G.]

Thinking about this some more, I think the quote above is what the power company wants you to do to lower their losses.

You're right. the power companies are also good at getting governments to do what they want - better than guitar amp makers, anyway - so there are governments that have passed rules and legislation about the topic of how much distortion can be accepted on the AC line. Don't get me started on cross-purposes regulations, but part of the government insists that everything that uses electricity must meet energy efficiency standards, and they are busy boiling us frogs (look up "how to boil a frog") by forcing manufacturers to not make anything available for us to buy that uses more energy than a lit book match. Which is an unfortunate analogy, probably, because consumer safety regulations are themselves making matches less easy to find, have odder and odder compositions, and be harder and harder to strike - but I digress.

This has the interesting result that manufacturers of electrical equipment go to electronically controlled DC motors to run things, partly to get better control, but also partly because they can reduce the total energy used in the motors. As an aside, for those who don't follow energy and power trends, electrical motors make up a slight majority of the electrical power grid's power demands. So to run the total power down, the motors run on modulated DC, not AC.

That then means you have to make the DC in the first place. Yep, you're back to a full wave rectifier and BFC (Big Freaking Capacitor) as the first thing the AC power mains hit, and so an increasing portion of the electrical power grid's AC is being squeezed through rectifiers and filter caps which selectively load down the peaks of the AC cycle, distorting the waveform on the power line. This causes problems on the power lines with equipment that does rely in the AC line being a sine wave, and can cause overheating problems with stuff that still runs OK on distorted sines. So another part of the government obligingly helps the power industry lobbyists by requiring PFC.

The logical thing to do as an overall picture would be to simply require all AC to DC applications be done by PFC'ed switching power supplies. I halfway expect that to happen some time.

But I think what you want to do is minimize the total iron/copper/capacitor expense.

And right again, it's a matter of which stakeholder you happen to be. Or, as it has been more pithily put a long time ago, exactly whose ox was gored. And, increasingly today, what ancestry your particular ox has. Yes, your personal intent might be to minimize the total iron/copper/labor expense (if you make and sell transformers), the transformer/rectifier/capacitor expense if you sell amplifiers, or the parentage and history of the transformers if you're in the "they don't make 'em like they used to" camp, which insists that any transformer made with iron mined after 1963 cannot sound good.I sometimes wonder how the folks at the EPA who play vintage guitar amps feel about this kind of reasoning, given that their personal and professional worlds are at crossed purposes.

Maybe this means using the same type of circuitry to push the current waveform in the "flattop" direction so that it takes less C for a given ripple voltage. Not sure if this can be done with the circuit Nick showed, but I think it should be possible somehow.

Interesting point. There is a transformer technology that takes in sine wave AC from the power line and puts out clipped sine waves that approach flat-topped rectangles for much of the AC cycle. That is the ferroresonant or "constant-voltage" transformer. This beast can not only make flat-tops out of sines, it can dramatically cut the peak pulse demands on the rectifier diodes, make minimal ripple out of smaller caps, and present the incoming AC line with no power-cycle distortion at all.

I recently bought a couple of very small ferros to power my house thermostats. Ferros make their secondary circuits essentially immune to AC mains transients, and I've lost six (!) $150 smart thermostats to lightning transients over the years. This stops here. The ferros will make the 24VAC to power the control circuits. They cost me $30 each on ebay.

Ferros do this by running the secondary in a big, fat resonant tank circuit, and decoupling the secondary from the primary by a huge magnetic leakage. The leakage is not total, but it does allow the primary to pump the resonant circuit up to a high energy level. The secondary sips out of the tank. Primary transients that don't puncture the primary insulation can't move the "heavy" resonant tank very much, and the tank tries to keep its own oscillation going. The unvarnished... er, no, they do varnish them um, plain view of ferros is that they saturate the iron path for the secondary. The iron saturates at a very constant level, and that level limits the peaks of the AC voltage waveform in the secondary, so the AC coming out of the secondary is a clipped sine wave. The ferro regulates by clipping the secondary sine to a relatively fixed level. It's a property of the materials and the windings. Ferros can have 5% no load to full load regulation, which is pretty good for active, feedback regulation, and nearly unheard of for non-feedback mechanisms.

There's lots of harmonics in a clipped sine wave, of course. So many ferros are sold as "constant voltage transformers" and "harmonic neutralized", which means they've tinkered with the windings to put some of the sine-ness back in, and the output is a regulated-size sine wave, not a nearly-square wave. Big Iron IBM mainframes used to run from literally big iron 3-phase ferroresonant transformers. A three phase sine transformer (unregulated, naturally) can be rectified to less than 10% ripple with no filter caps at all. A 3-phase ferro can be rectified to under 5% ripple or less and regulated to under 5% with no filter caps at all. You need some big diodes, though.

So why aren't ferros all that we ever use? How come every transformer isn't a ferro? Well, they're bigger, heavier and more expensive than a non-ferro transformer for the same output power, so they lose economically. They're hot. that saturation in part of the iron causes bigger iron losses in the core, and the resonant circuit keeping that big energy tank running means the copper in the resonant loop is running hot all the time. So they eat a relatively large amount (for a transformer) of energy just keeping the iron running. And they're noisy, acoustically. The high flux density in the saturated iron causes magnetostriction shape changes, so the transformer hums, most notably at 180Hz, the third harmonic of the power line. Electronic regulation is cheaper and lighter, so the power world bypassed the ferro, except for special circumstances. Like my 24VAC control power and the need for lighting immunity.

If you think about it, the proposed PFC circuit actually does make the current into flat-topped pulses. At its heart, a PFC is a flyback boost converter. It is fed a constantly varying input voltage - the full wave rectified sine wave - and no matter what the incoming voltage is, it charges up its boost inductor to full energy, then lets it fly up to the voltage being held by the main first filter cap and dump into that first filter cap. Since the voltage it's working from is half-sine varying, the time it takes to load up the inductor to full is wildly varying through the AC power cycle, but there is always some power being dumped into the first filter cap. The amount of power dumped into the first filter cap is limited as to how much is in the pulse and how far apart the pulses are, but it never gets as bad as turning off at one peak and not turning on again until nearly the next AC peak. So the PFC flyback does help a lot in minimizing the amount of ripple per uF the cap will give you. I'd have to think about it and do some math to think about how much it conserves on the cap, but the energy-bounds argument seems to me to indicate that the minimum cap value for a given ripple will shrink by the same ratio as you've improved Irms/Idc. Just a guess, really, but I would start digging there.

[nickb]

Practical part voltage ratings would suggest a max peak output voltage of something a bit less than a 450VDC rated output capacitor, and given some mains tolerance then the PT secondary would be up to circa 380Vpk (270Vrms) to allow some output ripple Vpp. For 200mA output and 10Vpp mains 2f ripple the output cap would be at least 100uF, which should cope with the mains and switching ripple currents, and audio signal currents.

That would probably need 600V boost diode and FET. I remember getting 600V SiCs many years ago for a similar PFC - they seem like a dime a dozen nowadays and with lower capacitance. That coilcraft part looks an easy way to go - have you asked for free samples?

Coilcraft is one of my favorite manufacturers - I use them whenever I can. I do use the free sample service for commercial products. This is basically a bit of fun and I would not abuse the sample service so.

[nickb]

Regarding the full wave/bridge comparison, it is not clear to me how those numbers were derived. First, it seems that the full wave starts with a disadvantage because only half the secondary copper is used at any time, while the bridge uses it all all the time. You could take a transformer with two identical secondaries and use it full wave, or parallel them and use it with a bridge, and get the percentage in each case. But would this be a reasonable comparison? I think you can deliver more power in the second case, and so it is not clear to me that a comparison of rms and average current is the whole story. Furthermore, it would seem that the most efficient use of copper in the two cases could involve different wire sizes in both the secondary and primary, and so you should not make the comparison for the same transformer used two different ways. So I think that this is a really complicated question, but maybe I have it all wrong.

The numbers I gave were from simulation. Someone about 10 years ago did derive a closed form solution to calculate the Idc/Irms ratio. I can't seem to find it now but I'm sure it was in Power Electronics magazine. Otherwise people use a graphical method as far as I know.

I think your point about the FWB vs FCT on the transformers design is perfectly valid. I was deliberately not going there as it was secondary, but not irrelevant, to the main thrust.

Lots of great points all. Good discussion.

[trobbins]

I would prefer to think of a PFC as a conversion technique that doesn't introduce mains frequency harmonics - everybody then wins. The large generators, distribution transformers, nearby cable, nearby PV generators, all just have a fundamental frequency on them. Efficiency of power transfer is maximised when only fundamental frequency current flows. Any end user equipment also benefits, as less harmonics means easier filtering and lower coupling of harmonics in to sensitive equipment such as audio equipment.

In a house nowadays, it may well be the large DIY hi-fi audio amp that is the worst form of mains harmonic pollution generator.

The 'rectified' output of a PFC then just has a 2x fundamental frequency, and so the output ripple voltage is just a function of the level of regulated boost chosen above the peak voltage of the incoming half-sinewave, and the filter capacitance chosen, and the output power loading - as met by half C V squared.

[Old Tele man]

The Irms-to-Idc ratio is called the 'ripple factor,' ie: RF = Irms/Idc

[Mike Sulzer]

In a house nowadays, it may well be the large DIY hi-fi audio amp that is the worst form of mains harmonic pollution generator.

I would guess that a microwave oven handles the problem by using a power supply that is so badly filtered that it cannot affect the power factor much.

[Mike Sulzer]

...So the PFC flyback does help a lot in minimizing the amount of ripple per uF the cap will give you. I'd have to think about it and do some math to think about how much it conserves on the cap, but the energy-bounds argument seems to me to indicate that the minimum cap value for a given ripple will shrink by the same ratio as you've improved Irms/Idc. Just a guess, really, but I would start digging there.

So I am wondering if large power consuming devices that have a power supply could be designed to sense the electrical environment with sufficient accuracy in order to draw power in such a way as to shift the overall consumption in the direction of fundamental-only current, rather than just attempt self-correction.

[R.G.]

So I am wondering if large power consuming devices that have a power supply could be designed to sense the electrical environment with sufficient accuracy in order to draw power in such a way as to shift the overall consumption in the direction of fundamental-only current, rather than just attempt self-correction.

I'm having trouble parsing the word "could" in there. As in "could it be that large power consuming devices ... already" do this, or "is it possible that in the future large power consuming devices might be designed to do this?"

I think it is possible to design PFC devices in the future in a manner that they would intelligently try to correct the power line towards being a sine, possibly by carrying a "model" of a sine wave in their memories and using that to know which way to try to correct things. In many ways, the intelligent controllers on solar power arrays do this now, attempting to force power back into the grid in a sine-wave format.

This is a tougher job than simply correcting the device's own power use toward being purely resistive. I can see some power-company woes arising from zillions of little power supplies trying to make the world a sine wave.

I don't think they already do this, so that side of "could" is a no in my blind guessing. I think it is possible to do so in the future, but unlikely.

I think that it's unlikely to happen because of the 80-20 effect. Simplistic power conversion with diodes and capacitor-input filters causes a gross power factor issue by putting 100% of the power input in a lump just before the peak of the sine wave. The simple version of PFC, just taking whatever power is there to load an inductor and dump it into the filter cap, causes a dramatic change toward sine form power by moving the power off to both slopes of the sine wave, roughly proportional to the sine value. It's another of those cases where you get a dramatic increase in "goodness" with just the first few steps in the right direction, and may have to work very hard to get a whole lot better. Just my guess, though.

The whole business of the electrical power grid is a little bit of a miracle hidden in plain sight. Power generating plants use actual generators that are rotating-machine sine wave generators that have main shafts that may be several feet in diameter. They're huge. They are commissioned and set rotating, and expected to continue rotating at the exact speed to create power line frequency, and do so for maybe 20 years without ever stopping. They may be taken off line, but it's a big deal if they are. Interconnecting generating plants with one another and doing that so that the monster rotating generators get synched up to shove power into the AC mains instead of pulling it out of the mains is a delicate dance. Remember that the sine wave at a remote generating station is time delayed from other generating stations by the speed of an electrical field in copper, about 1nS per foot. There are a lot of feet there in the power lines, and a lot of generating stations dotted about. Interconnected power grids can get into oscillatory power feeds, with power flows rocking back and forth between sections and popping breakers,or a "normal" protective device trips, sending power into alternate paths, but possibly causing their protection devices to trip, too. Something like this is what caused the power grid for most of the northeastern USA to drop out in 1965 and 2003.

Probably the guys trying to manage power flows in the power grid would be suspicious of a huge distributed load of not-very-intelligent and hackable microcontrollers trying to "fix" their grids' woes.