Reducing Power Dissipation in Back-to-Back Transformers

[merlinb]

Secondary T2: 182V AC
Rectified high voltage: 245V

That's lower than I expected, 182 *sqrt(2) -2 = 255 or 230 x12/15 *sqrt(2) -2 = 258.

That's normal. The textbooks don't bother to tell you that sqrt(2) only works with no load. Under load you need to use a figure of about 1.35 (or even less for low voltage, high current power supplies).
http://valvewizard.co.uk/psu.html

[PRR]

That's normal. The textbooks don't bother to tell you that sqrt(2) only works with no load. Under load you need to use a figure of about 1.35 (or even less for low voltage, high current power supplies).

Schade said (drew) it best.

http://www.madbeanpedals.com/projects/_folders/Tube/schematics/UberTuber.gif

While the diodes look like tubes, they are "Ideal". (This was drawn before wide use of crystal power rectifiers.)

On this chart, 'Em' is the Peak voltage, so the 1.414 is already in there.

He varies the capacitor and the series resistor.

For almost all audio work, we will be in the right side of the capacitor scale. Note that above some minimum, capacitor value has little effect.

There is always some series resistance. Never real "small" because that would cost a lot (big iron+copper).

Taking a wild-stab: typical small iron regulation of 10% implies Rs around 0.1 of R. Note that this tops out around 0.78 of Em, so Vdc will be near 1.1 times Vrms.

In fact we have to design cap-input supplies for Idc significantly less than Iac. Assuming half current, Rs/R may be 0.05, factor Edc/Em about 0.84, maybe Vdc of 1.2 times Vac.

Even this is disappointing, we often have to use a larger transformer with lower losses.

[Perfboard Patcher]

Is this the transformer?

https://www.amplimo.nl/images/downloads/ds%20standardrange/17012.pdf

(or maybe
https://www.amplimo.nl/images/downloads/ds%20standardrange/18612.pdf
)

No, Rob, they're not the type numbers you mentioned, although they're practically the same transformer:
18012-2x12V-30VA
and also
08013-2x15V-15VA

Maybe measure the DC current on the HV side first to get an idea what load current you are dealing with.  The rms AC current is typically just under two times the DC current.

I wasn't trying to measure the current (peak or stationary) per se I was looking out for too much current. I was more considering the possibility that using a back-to-back transformer could cause a high peak current when switching the preamp on. But it might as well be that the only thing that happens is the loading of the e-caps.

The aim is to reduce the input current and stop Tx1 overheating, not to increase the output voltage.

Was more some wishfull thinking from my side to squeeze the last drops of voltage out of it. Didn't know the current was already that low. See also the next quote.

Secondary T2: 182V AC
Rectified high voltage: 245V

That's lower than I expected, 182 *sqrt(2) -2 = 255 or 230 x12/15 *sqrt(2) -2 = 258.

That's normal. The textbooks don't bother to tell you that sqrt(2) only works with no load. Under load you need to use a figure of about 1.35 (or even less for low voltage, high current power supplies).

There's hardly any load present. But at your service. I've removed the 1M1 resistor and did some new measurements. Voltage across the secondary is 184V AC and rectified voltage is 248V. Calculating with 184V gives 258V. Where's my 10 volts?

[Rob Strand]

No, Rob, they're not the type numbers you mentioned, although they're practically the same transformer

OK thanks.

Was more some wishfull thinking from my side to squeeze the last drops of voltage out of it. Didn't know the current was already that low. See also the next quote.

If you don't need to tune the power, and your transformers don't need it, then you certainly can tweak the cap to get the last drops outs.  Nothing wrong with that idea.

There's hardly any load present. But at your service. I've removed the 1M1 resistor and did some new measurements. Voltage across the secondary is 184V AC and rectified voltage is 248V. Calculating with 184V gives 258V. Where's my 10 volts?

I suspected that was the case but I wasn't sure.    Both AC and DC measurements are under no load, yeah?   I know I've tried to track stuff like that down before.   There's an assumption when you go from AC to DC that the AC is purely sinusoidal (which relates rms to peak) which might not be the case with light loads.   IIRC when you measure the AC and DC you put a tiny resistive load like 1/50th (maybe 1/10th)  the maximum load and things start lining up.     

[Rob Strand]

For kicks I took the Jaycar Imag data and tried to work out what VA transformer survives back to back connection *without* the added cap.  The basis for that is the rated output current referred to the primary (ILp= VA / Vmain)  must be greater than the magnetization current Imag.   In other words,  the ratio ILp / Imag must be greater than 1.   It actually needs to be greater than 1.1 to 1.2 to survive *without any load on the TX2* and if you want to put a load on TX2 then an even larger ratio is required.

Click to Enlarge:


Assuming the Jaycar EI transformer data is correct we need at least an 8VA to 10VA for a back to back connection to work.  The toroids from the Amveco data have high ratios for even small transformers and are clearly in the good zone.   The Altronics Imag data implies we need even higher VAs.

Because of variations in transformer designs it's hard to extrapolate the results to other EI core transformers.  Nonetheless the 6VA on the original McTube is dancing around the bad side of 8VA so we might expect some 6VA transformers to work and some to fail.
-------------------------------
EDIT:

Here is the graph for same series of Jaycar transformer but from the 2008 catalog.
It looks like the transformers were revised to comply with newer editions of local standards around 2008;
the specs might be for the old version?
The point where the ratio exceeds 1 is a bit higher at around 10VA; mainly from the "noisy" data.  Notice the higher Imag part at 18VA. (I could not compare the dimensions of the 2008 transformers as they aren't given.)

[Rob Strand]

I'm not going to add much to this thread until I pull some old transformers out of hibernation and measure some stuff.

[R.G.]

That's normal. The textbooks don't bother to tell you that sqrt(2) only works with no load. Under load you need to use a figure of about 1.35 (or even less for low voltage, high current power supplies).

Maybe. Textbooks are remarkably good at telling you a lot of things, including both ideal-world, unreachable perfection and ever better approximations to the function of the real world. If they didn't do that, people would throw them away and write new textbooks that were better at explaining things. At least engineering textbooks are that way. Don't know about texts in the School or Arts and Flowers. 

One thing that the textbooks do tell you in some detail is that you can do remarkably accurate modelling with the T form of the transformer model. The factor of 1.414... is the peak-to-RMS number for an undistorted sine wave. Distort the sine wave, that no longer applies. This is vastly more relevant in today's world where most people have computers and when circuit modelling can be downloaded for free. It removes most of the need to understand the math from circuit design. You don't even need to understand why the square root of two is important to get the sim to match the reality to a close degree as long as you can follow some simple models. Easy availability of sim software makes the need for rules of thumb much less.

Capacitor input filters distort the sine wave because they only conduct for very limited times near the peak of the sine wave. selective voltage losses in leakage inductance and winding resistance let the effective voltage sag because of the current pulses, and this happens only during the diode conduction interval near the peak. So the combination of pulse current and series impedance with the diodes effectively flattens the peaks of sine waves. In cases where the leakage inductance and wiring resistance of transformers is small compared to the load, there is little distortion of the sine wave fed to the rectifier/capacitor filter, and the non-ideal losses come from the forward resistance of the diode and the reactive charging of the cap.

In tiny transformers run at low frequencies, you just can't wind them so they simultaneiously have negligible resistance, negligible leakage, and are cheap. So the imperfections get to being bigger and bigger parts of the reality.

Back 18BC (Before Computers, the 1970s) I had to design tranformer-rectifier-filter circuits by hand with equations, pencil, and paper. And graphs, and rules of thumb, and the grizzled veterans telling me I'd done it wrong again.     The output voltage from this kind of setup varies a lot - not least with the value of the load resistor and capacitor, ala Schade. I shudder to think of doing that now. Took forever. I can flip in some parts in a simulator, get really, really close to what the real result will be, and the differences are largely how accurately I measured the real-world parts for inclusion in the sim circuit.

Rules of thumb are great, if all you have are fingers and thumbs. 

[PRR]

It is interesting that the Schade charts remained the foundation of design, even re-printed in TI's 1977 regulator handbook; also Motorola 1982.

There are manageable (slide-rule size) approximations which give results hardly better than rules of thumb. Today we can *try* to guesstimate all the parasitics and force SPICE to chomp it in sliced-time. (There is also PSUD which uses unique techniques, often gets real dang close, but I have seen it go off the tracks.)

"1.414" is like you take a $50,000 job. You don't ever get $50k. New suits, new house, taxi fare, after-work drinking, IRS, all take a slice.

[R.G.]

The one I always liked was when the green newbies forgot about diode drops not being 0.7V when you're full wave rectifying 20A for the bulk supply for a 5V logic supply, and the diodes were operated well up into their resistive region. Then I could usually get them again for not remembering that a FWB always has two diode drops subtracted from the raw input voltage.

It's always a death of a thousand cuts. Ripple voltage is always down from the peak, never straddles the DC average output line. Capacitor ESR and ESL subtract disproportionately from the incoming charging pulses than from the outgoing DC average currents.

I just never want to catch my capacitors drinking with their friends.

[R.G.]

Actually, I just had another thought, not about transformer/rectifier/filter circuits, but people.

Back when I was extruded through the calculations for output voltage of a rectifier circuit, it was already so old-hat and boring that the EE student body tried strenuously to find a way not to study it. So did I. But there were few EEs in the populace, and only a small fraction of them remembered transformer/rectifier/filter stuff one second longer than turning in the final.

I find it dramatic that today, circuits and communications interests have grown so much that lay people voluntarily wonder about this, to the point that they ask for explanations. That is in my book, a remarkable success story for the rise of science in the popular mind.

Now I'm just going to sit here and count all my other blessings.   

[PRR]

> EEs ...only a small fraction of them remembered transformer/rectifier/filter stuff one second longer than turning in the final.

As you know, when they went out in the world, 99% of them never designed a rectifier. There was one guy in the division did all that all day long. (Actually he must have had other duties; even Acopian does not do that many from-scratch rectifiers.)

I consider it a fundamental skill for any electronic fiddler. Even though there is never an "exact" answer, you should have a good concept of how much windage to provide.

[Rob Strand]

> EEs ...only a small fraction of them remembered transformer/rectifier/filter stuff one second longer than turning in the final.

At university the ripple is always calculated using half the mains period but in reality it's probably 60% to 70% of that.

I consider it a fundamental skill for any electronic fiddler. Even though there is never an "exact" answer, you should have a good concept of how much windage to provide.

Back in the 1990's I derived some formulas which give somewhat better results.   IIRC they gave results for peak and RMS currents, conduction times, regulation, ripple, allowance for transformer impedances.    Took several pages to derive but the final formulas were relatively short.

I'm with RG I much prefer to plug stuff into spice.  I suppose you could call it virtual fiddling.

[R.G.]

At university the ripple is always calculated using half the mains period but in reality it's probably 60% to 70% of that.

For a full-wave, the run-down part of ripple is just what's left after the caps are charged, and it's asymptotic to the full half-cycle. That's only approached at nearly no load. You can pessimistically approximate ripple as dV = Idt/C where you make dt be the half cycle. The bigger the capacitor compared to the load resistance, the smaller the ripple gets. But the charging pulses can't be infinitely tall and infinitely short. From my own scoping rectifiers in the lab on +9V and +15V supplies (for regulating to 5.000V and 12.000V) I came to the conclusion that I could use 8mS out of the 8.666mS of the 60Hz half cycle, and I do, and it seems to work OK in most cases. However, my "most cases" are mostly not fed by high impedances referred to the secondary side of a chain of two or more transformers, so I don't have good intuition on the two-tiny-transformers-in-series and I always try to sim these when I build one.

The reality can be that the charge pulse time can be as little as 5% of the half cycle under loading with very large capacitances and diodes with small internal resistance. That leaves 95% of the cycle for run-down, and maybe the school thought that using 100% was conservative. Well, I guess it is.

[Rob Strand]

From my own scoping rectifiers in the lab on +9V and +15V supplies (for regulating to 5.000V and 12.000V) I came to the conclusion that I could use 8mS out of the 8.666mS of the 60Hz half cycle, and I do, and it seems to work OK in most cases.

It does come down to specifics.   Like how much ripple and the voltage of the DC rail, transformer resistances.

The bigger the capacitor compared to the load resistance, the smaller the ripple gets. But the charging pulses can't be infinitely tall and infinitely short.

One thing I noticed is the charge pulses don't get as high as you expect because narrowness doesn't get as narrow as you would expect.   When you are near the peak the voltage drop,Vin - Vcap, can't get enough charge into the cap because the current is limited by the transformer resistance I =(Vin - Vcap)/Rt.   So what happens is Vcap sits a bit lower than what you expect.  That does two things: the lower Vcap allows more current to flow, however, the important thing is it increases the T_on time of the rectifier somewhat.   When you are near the peak it doesn't take much lowing of Vcap to take a wider slice off the top of the sine wave and T_on quickly increases.   This also explains why you can have big caps and low ripple yet the power rating of the transformer doesn't need to be much different to the small cap case.   If the current pulses were *really* narrow the RMS current would sky rocket and the transformer would overheat but we don't see that.  This effect showed up in my old calculations.   I did verify the results in pspice.

I remember thinking at the time when you understand the fine details of something the technology is probably obsolete.

[PRR]

> It is interesting that the Schade charts remained the foundation of design,
> There are manageable (slide-rule size) approximations

FWIW, FYI, here is Schade's paper. Not the best scan, and only 10% of a 6MB download.
https://www.americanradiohistory.com/Archive-Bookshelf/Technology/RCA/RCA-Electron-Tubes-II.pdf
(Also in Proc I.R.E. July 1943, if you have IEEE access.)

> high impedances referred to the secondary side of a chain of two or more transformers

You can get guidance from Schade's Fig 4, which covers source resistance to 100% of load resistance. That gives VDC of 35% of peak AC, so awful saggy.

Of mild interest to empty-heads: Fig 8 has V/I curves for vacuum rectifiers. Plain everyday home and broadcast bottles. At first they look "linear", but it is actually a 3/2 power law (10X over makes 31X up). We "know" this from Simplified Theory, but the deviations in apparently-measured data are smaller than the pen-line. There should be a "soft distortion" in here. (Merlin and Fender have done so, but generally below the 1V 1mA origin of this graph.)

[Rob Strand]

FWIW, FYI, here is Schade's paper. Not the best scan, and only 10% of a 6MB download.
https://www.americanradiohistory.com/Archive-Bookshelf/Technology/RCA/RCA-Electron-Tubes-II.pdf
(Also in Proc I.R.E. July 1943, if you have IEEE access.)

You can get a nice copy of the original using google.

You can get guidance from Schade's Fig 4, which covers source resistance to 100% of load resistance. That gives VDC of 35% of peak AC, so awful saggy.

There's a few things about that paper that need to be cleared-up:
- For a bridge rectifier we would use the full-wave Schade's curves.   Rs remains unchanged.
- The ripple in Schade's paper is RMS not peak or the more common peak-to-peak.  (Peak to peak is about 3.2 x Rms.)
- E_ac_max  (~E in the paper ) is the maximum AC value with no load.  Technically we should also subtract the diode drops.

I find that fig 4 doesn't line up with pspice; pspice produces a lower Eav/Eac_max value.
I just check it again and it looks OK; graph is about 1% high.  I must have screw up reading the graph somehow.  I'm pretty sure I checked some points against pspice in the past and they were a bit off.

The ripple from fig 7 seems OK.
(Eg.  24V 1A transformer 10% reg + 5000uF cap + bridge rectifier.)

[merlinb]

(Merlin and Fender have done so, but generally below the 1V 1mA origin of this graph.)

For posterity:

[Rob Strand]

For posterity:

Every time I look at those curves I think diode + resistor.

[R.G.]

And you'd be right: posterity would appreciate knowing that you can generate your own charts by sticking an ideal diode and a resistor into the circuit and mapping the V-I curve and varying the resistor.

The posterity chart makes a great tool for fitting a semiconductor diode and resistor to the tube's action. This is, I suspect, what Weber did to make their copper top rectifier "tubes". You can get remarkably, remarkably close to a tube rectifier by "dirtying up" a semiconductor diode.

[Rob Strand]

I've seen people DIY this type of thing but I hadn't come across that product.
There's a nice pic of the innards a the bottom of this page:
http://www.diytube.com/phpBB2/viewtopic.php?f=14&t=4921

(I don't know if they other using fast diodes to reduce glitches.  I doubt they add any caps across the diodes.)

You can get remarkably, remarkably close to a tube rectifier by "dirtying up" a semiconductor diode.

I agree but I can hear those hard-core tubers chanting in the distance "get rid of that silicon".