Sort OT - Back To Back Transformers

[Paul Marossy]

I am curious about how a back to back transformer configuration affects current capacity. For example, if I have two 120VAC/12.6VAC 300mA transformers back to back, does the amount of current available remain at 300mA or what? And would one expect a voltage drop at the output of the second transformer due to impedance?

The transformers would be connected like this:

120VAC ----> 12.6VAC <-----> 12.6VAC <---- 120VAC -----> Rectifier

[niftydog]

I would expect that the current capapcity would have to be derated, due to the (in)efficiency of the transformers.

It would also depend on which way the transformers were designed to operate. ie; designed as step up transformers or step down transformers.

This would dictate the impedances etc.

It would also depend on the load you place on the output of the 2nd tranny. The "reflected impedance" that the first transformer sees may have a large effect on the overall operation of the whole set up.

curly question, do you have a need to do this or just curious?

[Paul Marossy]

Well, I'm building a "Real McTube II" just for kicks. I had this enclosure lying around that I wanted to use for something...
Anyhow, in the stuff that I have for reference, I can't find anything on transformers being used quite like this.  :shock:

My assumptions before my post is that there would be some sort of reduction in current and voltage due to the inefficiency of the transformers, but how much to expect is something I don't know how to gage...

[R.G.]

I am curious about how a back to back transformer configuration affects current capacity. For example, if I have two 120VAC/12.6VAC 300mA transformers back to back, does the amount of current available remain at 300mA or what? And would one expect a voltage drop at the output of the second transformer due to impedance?

Ah... Mother Nature informs someone else how picky she is!

Transformers can be very closely modelled as an ideal transformer plus some imperfection components added. The ideal transformer is just the voltage:voltage and current:current transformation done by the turns ratios, but with the assumption of zero losses in winding resistance, capacitance, leakage inductance, etc.

Every real transformer has some winding resistance, and the smaller the transformer, the greater effect this has, because physically small transformers have small core areas which require more turns per volt to keep the core from saturating, and small, thin wire to get those turns inside a smaller window.  The winding resistance is modelled as Rp on the primary side and Rs on the secondary side.

The winding resistances cause voltage losses if there is any current flowing, as Georg Ohm told us. This is why the turns/voltage ratios are noticeably off in small transformers. A 120:12Vac @ 100ma transformer is wound with an open circuit secondary voltage of maybe 14V so that when 100ma is flowing, there is 2Vac of sag in the primary and secondary winding resistances.

The differences add up in the low voltage way for back to back setups.

The incoming transformer transforms 120Vac line to 14Vac at the secondary, but we load the secondary with both tube filaments and the input to the second, step up transformer. The incoming transformer resistances cause a sag to 12Vac at the rated 100ma, and we now feed 12Vac to the 14Vac low voltage winding of the second transformer.

That makes the second transformer's output be 12*120/14 = 102.8Vac before there are any resistive losses in the second transformer. When we pull real current in the second transformer, the winding resistances lower the voltages again, and the output from the second transformer gets a lot lower than we though it would be.

Rectification hurts even more. Diode-capacitor rectification pulls all its current in big pulses near the peak of the AC waveform. The pulses are usually ten to a hundred times the average DC current coming out of the capacitor filter. *That* pulse current is what you use to figure the sag due to resistance in the second transformer's windings.

Because of the resistance losses and rectification losses, it is not unusual to lose 25% to 35% of the rated voltage from a set of small transformers back to back. How much you lose depends on the details of the transformers you use.

[Aharon]

here's an excerpt from a thread at Ax84 and you can find the whole thing searching under PT for FireFly.Of course this is not regarding the McTube but the concepts are there.
Aharon

"The 12AX7A and 12AU7 each take 150 mA to heat at 12.6 VAC. That leaves 200 mA at 12 VAC. Step that up through a second transformer to 120 VAC and adjust for the voltage difference. You can draw about 20 mA at 120VAC. Using a doubler to get your DC up to 200 V or so, means your transformer is only going to be able to deliver about 10-15 mA at 200 VDC to your amp circuit without over heating. Each 12AU7 triode at max signal draws about 10 mA and the two 12AX7s each draw about 1.5 mA. That's a total of 23mA. That's not even taking into consideration inefficiencies in the power supply. You will be overheating your transformer if you use 500 mA units. Especially if we're talking RS transformers, which probably aren't generously specified. A couple 1000 mA units should give you plenty of room".
Stph

[Paul Marossy]

Thanks RG, Aharon, that sheds some light on the matter.  
I think what I have will work just right.