Reducing Power Dissipation in Back-to-Back Transformers

[Rob Strand]

This idea came to me after discussing the problems with back-to-back transformers in another thread:
https://www.diystompboxes.com/smfforum/index.php?topic=121201.0

It's kind of hot off the press and I haven't tested the idea on a real set-up.   Nonetheless it's kind of a nifty idea. The downside is the added capacitor has quite a large value.   It might be possible to shift the cap the output side of TX2 and use a smaller value.    I forgot to mention that loading on TX2 might also stuff things up a bit.

Anyway,  the idea is simple: add a capacitive load between the two transformers to shift the phasing of the load current on TX1 so the power dissipation of TX1 is reduced.

The plots go: no cap, cap less than optimum, optimum cap







This one shows how the output voltage of Tx2 is increased and is closer to the primary voltage of Tx1,

[GibsonGM]

Pretty neat, Rob!  I was going to ask if all of this was due to phasing problems! 

[R.G.]

Neat idea, Rob.

Did you put in the winding resistances in your sims?

You're right that transformer specs rarely tell you everything you need, and that the variations in the unspecified things can be large, and that any critical design work requires measurement for one-offs and probably custom design for any production work.

Transformer specs on magnetizing current don't help, as a lot depends on how hard the designer (or his resident bean counter) is working the iron. The higher the primary voltage, the worse this gets. The number of wire turns needed to get a primary inductance high enough to drive down the magnetizing current increases linearly with input voltage, but the core winding window is fixed for a given core size, so wire resistance becomes a bigger and bigger part of the input impedance for a transformer, even with no load.

The bean-counter's hand is heavy in this calculation. Small transformers are low profit margin items, so the pressure is to make them as cheaply as possible, and that pushes for the minimum iron and copper, but also for the minimum care in lamination stacking. The tightness of lamination stacking has a big effect on the actual value of primary inductance. In constructing some transformers from the raw copper and iron components and measuring things, I've seen a four to one difference in primary inductance dependiing on how carefully the iron was jogged together and pressed into square, level contact.

Magnetizing  current is nonlinear, as the primary inductance is something of a fiction. It exists, but varies a lot as the flux density gets close to saturation, where it increases a lot. The variability of primary inductance with flux density is what gives the classical waveform of magnetizing inductance. Given the bean-counter's need to use less iron, copper, and labor, there is a strong push to simply specify magnetizing current as the value for the worst probable example that ccmes off the assembly line. You're right in that any one example of the production run may be anywhere in the distribution. They also don't tell you the distribution. 

Things that make this worse are the power line voltage and frequency. It's worse in 240Vac/50Hz countries than in 120V/60Hz countries. At least if the designer didn't make one version for both 50 and 60Hz countries, implying that all of them have the skinny wire and many turns that the 50Hz country needed. 

It's unfortunate that the required cap would probably be larger than the transformer, given today's capacitors. Back to back electros and NP electros would have a wandering value as the capacitor ages. Film would be stable, but large.

[PRR]

Interesting thinking.

Note that while there is a pure inductive current, in any minimum-cost transformer there is also a very non-linear current as the peaks approach iron saturation.
http://www.jocet.org/papers/69-A30009.pdf
This paper tests a huge lump of iron, but the same trend is seen in thumb-size transformers. (In practice, KVA iron is not worked this hard due to running cost of lost power, but as R.G. says a few-VA $7 lump is often designed-down to just shy of real trouble within warranty.)

The current is not a sine. The current is not proportional to voltage (Tesla). A pure capacitor can be only a very approximate "compensation".

[R.G.]

Yeah, but some might be enough in the very low iron cases.

I'm struck by how similar to a ferroresonant transformer you could make this by adding some external "leakage" inductors before the capacitor. I'm trying to think up (1 ) whether that  could be made to work at all and (2) how the devil you'd "design" for it. The second transformer would be run in nominal saturation all the time, so the iron losses would get bigger, but the reversed-primary would give you out pseudo-square waves.

Of course, that makes what started as a (as the Brits say) cheap 'n cheerful dodge even more complicated yet, even after the film cap.

Maybe a NP would be good enough. Rob - what's the sensitivity of "goodness" to cap value?

[PRR]

I'll just say it. If the second transformer's load is small relative to the total (usually true for heater and B+ on small bottles), and the first transformer may be economically bought 2X oversize, there will be no smoke. It will sag, but that's not normally critical.

[Rob Strand]

I've actually got stuff to do ATM.   

Here's some add-on results.
It does answer some of the hanging questions and issues.

1)  The big cap problem. 
I mentioned it might be possible to move the cap to output of TX2 this means the cap could be a much smaller value.  It also means it could be a poly-cap instead of a bipolar which will significantly improve the reliability.

HV vs LV Cap
HV Cap has 2 to 3% more dissipation in TX1 than the LV Cap.
Output voltage doesn't rise unless cap is smaller than optimum.







2) How accurate does the cap value need to be.

Given the method reduces the power dissipation in TX1 by a *factor* of 8 or so, there's plenty of scope for C to vary yet still have moderate reductions in TX1's power dissipation.

The table below for the LV cap case (ie. cap between the transformers)  but I don't
expect the results to change much for the HV cap case.

Effect of smaller cap on total dissipation in Tx1

C/Copt    Pdiss_tx1 / Pdiss_tx1_no_cap
0.1          0.83
0.2          0.74
0.33        0.51
0.5          0.34
0.71        0.19
1.0          0.12

C/Copt is the ratio of the actual capacitor value to the optimum capacitor value.   So C/Copt = 0.33 means we are using a cap about  a 3rd of the optimum value.

Pdiss_tx1 / Pdiss_tx1_no_cap   the power dissipation in TX1 compared to that when there is no cap present.  Smaller is better.   

So we can see with with a large deviation from optimum a C/Copt = 0.33 is still reducing the power in TX1 by half.

[Rob Strand]

Did you put in the winding resistances in your sims?

Yes.  I'm using a T model  it covers a lot of real behaviours.
Also allowed for more copper in the primary for a small transformer.

and that the variations in the unspecified things can be large

Some of the specs I have trouble believing.  Like I've seen maximum Imag's quoted which are equivalent to 4 times the rating of the primary.   I can't image a transformer coping  with that!

Transformer specs on magnetizing current don't help, as a lot depends on how hard the designer (or his resident bean counter) is working the iron. The higher the primary voltage, the worse this gets.

One thing that puts a bound on skimping is skimped transformers generate more heat and the transformer still has to comply with winding temperature rise limit.   Also (IIRC) the current standards require testing to pass at 25% overvoltage.   

The tightness of lamination stacking has a big effect on the actual value of primary inductance.

Yes, that's certainly going to spread out the range of inductance values.

Magnetizing  current is nonlinear, as the primary inductance is something of a fiction.

The non-linearity is a real issue in the sense that it can dramatically increase the input current; however it is bounded as mentioned before.    While non-linearity does cause the inductance to vary wildly with drive level when you fix the drive voltage to the mains voltage the span is much reduced.   I'd suspect with the normally gap-less cores the previous point might determine the spread.

It's unfortunate that the required cap would probably be larger than the transformer, given today's capacitors. Back to back electros and NP electros would have a wandering value as the capacitor ages. Film would be stable, but large.

Shifting the cap from between the transformers to the output of TX2 solves this problem.   See my second post.   I thought it might turn out like that.    A concern is an NP cap would reduce in value with age and then the current would rise up to it's old bad value.  Not a good situation.

[Rob Strand]

Note that while there is a pure inductive current, in any minimum-cost transformer there is also a very non-linear current as the peaks approach iron saturation.

Yes.  The way I look a it is the peaks will be there when the transformer is operating normally.   The increased losses due to non-linearity would have to be covered in the transformer design in order for it to work in a normal one-transformer configuration.   For the uncompensated back to back case we would see twice the current primary, as we would see in the case where there was no non-linearity.

What you don't want is the added cap to cause the transformer to be driven even deeper into saturation than  normal.   I have a feeling HV cap case might be better here.

I can simulate non-linear magnetics.  I made a point of not doing it to show the idea works in principle.   The only hassle it takes a lot of work tweaking the model to match a given sample.

[Rob Strand]

Pretty neat, Rob!  I was going to ask if all of this was due to phasing problems!

Well it clearly is!    I've remember noticing the problems with back-to-back transformer back when I was about 10yo.    It wasn't until I wrote that last post out in the other thread I realize it could be fixed!.

[merlinb]

Pretty neat, Rob!  I was going to ask if all of this was due to phasing problems!

Well it clearly is!    I've remember noticing the problems with back-to-back transformer back when I was about 10yo.    It wasn't until I wrote that last post out in the other thread I realize it could be fixed!.

But in most cases one or both transformers will be driving a cap-input rectifier that will at least partially compensate for the inductive current, no?

[R.G.]

But in most cases one or both transformers will be driving a cap-input rectifier that will at least partially compensate for the inductive current, no?

??

'Splain dis to me. I'm confused. 

[anotherjim]

I think Merlin was thinking like me, the B+ smoothing cap current, although after a rectifier, are phase shifted anyway? But is that only true for ripple current, which isn't enough to help?

[R.G.]

What confused me was that in a cap input rectifier, the diode(s) conduct only at the peaks of the input sine wave. So the current is a series of peaks phase aligned with the peak AC voltage. It's peaky, but largely in phase with the voltage waveform.

The introduction of a cap between the trannies would have little effect if grossly too small, and would be a heavy capacitive load reflected to the input/primary of the first transformer in parallel with the primary inductance.  So too big a cap draws a lot of primary current as well, but that affects mainly the wire losses, as the higher current has to be provided by the primary.

Things get interesting around resonance. There's the issue of what inductance counts; there is the reflection of the first transformer's primary inductance, in series with the secondary side leakage, then the cap, then the primary leakage of the second transformer, then the primary inductance of the "secondary-primary" of the second transformer, in parallel with any reflected load.

Ferros are set up to use this (mess of) effects by using a very high leakage and capacitance to resonate, store a bunch of energy bonging around in the resonance, and use that to keep the secondary side iron saturating, which amounts to clipping the secondary side voltage waveform output. In this ferros are nice because they have flat-topped output voltages very conducive to capacitive filtering unless they're specially "harmonic neutralized". They're quite dependent on the resonance to keep the flywheel resonance going, so this naturally made me think of what the resonance was doing to this.

My confusion was genuine, by the way, not rhetorical.   

[R.G.]

I must be doing something wrong. I tinkered with modelling transformers in the simulator and couldn't get the power in the first transformer to minimize significantly. I modeled with wire resistance, leakage inductance, nonlinear core inductance; I put a resistive load on the center connection, simulating the heater of a 12AX7, and full wave rectified, filtered, and loaded the output of the second transformer to get 100+V dc, the idea being that the middle connection would run the heaters and the high voltage output would run the plates of a preamp setup.

I set up multipliers for power into and out of the first transformer and then checked out the difference in the power in and power out. For my setup, I wound up with this difference being about 0.7W in all cases with zero or lower capacitive loading on the center low voltage connection.

Subbing in caps in the middle from 10uF up to 500uF, the power difference in the first transformer didn't change much until I got to about 100uF, and from there on up, the power into the first trannie and the power difference dissipated there went up with increases in capacitive loading. That seems to be in line with the idea that capacitive loading sucks more reactive current, which causes real I2R losses in the first transformer's wiring resistance.

What am I doing wrong?

[Rob Strand]

What confused me was that in a cap input rectifier, the diode(s) conduct only at the peaks of the input sine wave. So the current is a series of peaks phase aligned with the peak AC voltage. It's peaky, but largely in phase with the voltage waveform.

That's how I see it as well.  The fundamental is largely aligned.  The peakyness results in harmonics.

The introduction of a cap between the trannies would have little effect if grossly too small, and would be a heavy capacitive load reflected to the input/primary of the first transformer in parallel with the primary inductance.  So too big a cap draws a lot of primary current as well, but that affects mainly the wire losses, as the higher current has to be provided by the primary.

There's definitely going be cases where the rectifier+filter+load dominates and the added cap is going to have minimal effect.
The original motivation is the transformer Tx1 has enough rating to drive the rectifier+filter+load  but the magnetization current is using up a significant capacity of Tx1, perhaps to the point where Tx1 is now overloaded.  Adding the cap then buys back some of the capacity of Tx1.

I haven't looked at the effect of the rectifier+filter+load.   It needs to be checked for sure.  A real circuit also needs to be checked.  My gut feeling the cap would help but is perhaps  less effective that the simple transformer + transformer case.

[Rob Strand]

I must be doing something wrong.

Maybe not.

The Hard Drive with my OS on it died yesterday after about 10 year of use(!).   So I'm going to be dead in the water trying testing anything out for a few days.

I'd start with a simple linear transformer model with only the winding resistances and the magnetizing inductance.
Then gradually build up the complexity of the circuit.
Start by looking at the power dissipation for the back to back no cap case; using AC analysis.
Then add the cap and recheck the power dissipation; again using AC analysis
For AC analysis, I tend to use the expression abs(I(Rp))*abs(I(Rp)) * Rp to compute the power as currents in spice can take on complex values and some expressions give different results to using magnitudes only.
After that switch to a transient analysis.  You have to make sure you are not analyzing a long start-up transient.
After that start to add the rectifier+filter.  First with a small load, which should not change anything, then ramp up the load.
If your magnetizing current is small to start with then it might only take a small load before the rectifier+filter+load dominates.

[PRR]

> I've seen maximum Imag's quoted which are equivalent to 4 times the rating of the primary.   I can't image a transformer coping  with that!

Show one. I speculate that it is a VERY SMALL iron, with high surface/volume ratio. And the winder is not paying my electric bill. (And I am not charged for reactive current.) If a "stupid" design passes tests and is cheaper, why not??

I am sorry for your loss.

[Rob Strand]

Show one. I speculate that it is a VERY SMALL iron, with high surface/volume ratio.

The 12V 150mA one on this page is close.    Variants of that transformer have been kicking around in this country for about 45 years.  The physical size varied somewhat and DC resistance of the windings varied quite a bit, maybe 2.5:1 from min to max across the variations.  Some were rated a bit higher, say 2.5VA.   Some of the larger core variants looked more like 4VA transformers.

https://download.altronics.com.au/files/docs_273.pdf

Here's another one with a more believable magnetization current, still quite high,
https://www.jaycar.com.au/12-6v-ct-150ma-1-9va-centre-tapped-transformer-type-2851/p/MM2006

I'm pretty sure they measure in at 7.5mA but I can't remember if that was for the small or larger iron variants.

But, yes,  the crazy Imag's were for the smaller transformers.

I am sorry for your loss.

Thanks.  It was going to happen one day.  I did a full back-up of the OS & progs about 1 yr ago.   Restore isn't as smooth as I expected.  I've got strong doubts about getting the old drive back to any working state.

[merlinb]

That's how I see it as well.  The fundamental is largely aligned.  The peakyness results in harmonics.

That was what I was getting at -the harmonics all represent reactive power which I believe must be capacitive in nature, i.e. the harmonic currents lag the voltage. I'm not sure how much this counts towards cancelling magnetising current though, since this thread is concerned with weeny little transformer VA ratings where the numbers get weird compared with 'normal sized' transformers.

But I suspect I'm overthinking it. Seems to me all you're trying to do is put a cap in parallel with the magnetising inductance, selected to resonate at 50/60Hz. This can be a big cap on the low voltage side, or a small cap on the high voltage side -the latter is therefore easier since it will be a more accurate cap.* You can only use a squinty-eyed average figure for magnetising inductance since it is so non-linear, but I dare say you can buy back a couple of VA which is worth doing if you're using a 3 to 12VA transformer for T1.

*Moreover, you can measure the magnetising current more accurately on that side of the transformer, before using it backwards.